varieties of dependence

8/9/2019 Varieties of Dependence

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Ontological Dependence: An OpinionatedSurvey

Kathrin Koslicki

1. Introduction The purpose of this essay is to provide an opinionated survey ofsome recent developments in the literature on ontological depend-ence.1 Ontological dependence is typically taken to be a relation whose relata are entities. The following cases are often cited in theliterature as putative candidates of pairs of entities which exhibit arelation of ontological dependence of some sort:

(i) Smiles ontologically depend on mouths that are smiling.(ii) Sets ontologically depend on their members.

(iii) Events or states of affairs (e.g., lightning or heat) ontologicallydepend on their participants (e.g., electrons or molecules).

(iv) Chemical substances (e.g., water) ontologically depend on theirmolecular/atomic constituents (e.g., H2O-molecules).

(v) Tropes (e.g., the redness of a particular tomato) ontologically

depend on their ‘bearers’ (e.g., the tomato).

(vi) Aristotelian universals (e.g., redness) ontologically depend ontheir ‘bearers’ (e.g., objects that are red).

(vii) Holes (e.g., the holes in a piece of Emmentaler cheese) ontolog-ically depend on their ‘hosts’ (e.g., the piece of Emmentalercheese).

(viii) Boundaries (e.g., the boundary around a football field) ontologi-cally depend on their ‘hosts’ (e.g., the football field).

1 For other useful surveys, see also Correia 2008 and Lowe 2005.



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In all of these cases, if in fact they do constitute examples of pairs ofentities related by an ontological dependence relation of some sort,

the dependence relation in question may plausibly be taken to beasymmetric.

One can define any number of relations which may or may not meritthe title, ‘ontological dependence’. As we will see in what follows,some of the most popular definitions are formulated in modal terms;others in non-modal (e.g., explanatory or essentialist) terms; some(viz., the existential construals of ontological dependence) emphasiserequirements that must be met in order for an entity to exist; others

(viz., the essentialist construals of ontological dependence) focus onrequirements that must be met in order for an entity to be the veryentity that it is at each time at which it exists; some are rigid, in thesense that they involve a relation between particular entities; othersare generic, in the sense that they involve only a relation between anentity and some entities or other, which bear certain characteristics.

With this plethora of defined dependence concepts, one wondershow to evaluate the explanatory usefulness of one such technical no-tion as compared to another. One possible way to measure success inthis area is by considering how well a particular notion does in classi-fying putative cases of ontological dependence, such as those men-tioned above. But this explanatory goal of classifying particular casescorrectly does not yield an uncontroversial measure of success. Fordifferent philosophers, depending on their particular views concern-ing specific cases, will disagree over which putative cases in fact con-stitute good examples of pairs of entities exhibiting a relation of on-

tological dependence of some sort and in which direction the de-pendence relation in question runs. For example, some trope theo-rists (who view particular objects as bundles of tropes) will disagree with other trope theorists (who do not view particular objects asbundles of tropes) over the status of (v): according to some tropetheorists, the ‘bearers’ of tropes in fact depend ontologically on thetropes that compose the bundle in a manner analogous to (ii), viz.,the way in which sets ontologically depend on their members, while

other trope theorists may find that (v) correctly describes a genuinecase of ontological dependence. Moreover, these philosophers mayor may not find it necessary to be committed to Aristotelian univer-



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ontologically depend on their ‘host’. For how could one be in a pos i-tion to judge that holes are in fact ontologically dependent on their

‘hosts’, unless one is already in possession of some conception of what sorts of entities holes are and of what is meant by ‘ontologicaldependence’ in this connection. But such a conception, if we haveone at all, cannot very well be characterised as ‘pre-philosophical’ or‘pre-theoretic’. If, on the other hand, by ‘intuition’, we mean an epis-temic state that is already informed by philosophical theorising, thenit is quite likely that the ‘intuition’ in question is somehow wrappedup with the three explanatory goals I have identified in this section as

potential measures of success against which a particular account ofontological dependence may be evaluated. Or, if in addition to thethree explanatory goals I have identified there are additional ones thatI have missed, then these should be made explicit as well. Once thishas been done, their plausibility can be subjected to scrutiny; but, atthat point, it seems that we have left appeals to ‘intuition’ behind andhave entered into the business of explicit theorising.

2. Existential Dependence

2.1 Ontological Dependence in Aristotle’s Categories 3

Ontological dependence is often construed existentially. For example, when Aristotle famously says in the Categories that all the other entitiesdepend in some way on the primary substances, he is standardly readas putting forward an existential claim. Thus, the following crucialpassage from the Categories is commonly translated as involving anexistential construal of ontological dependence:

Thus all the other things are either said of the primary sub-stances as subjects or in them as subjects. So if the primarysubstances did not exist it would be impossible for any of theother things to exist . ( Categories , chapter 5, 2b3 –6, my italics)4

But where the English translation has ‘exist’, the Greek simply hasthe verb ‘einai ’ (‘to be’), which can sometimes be rendered in an exis-

3 For more discussion on ontological dependence in Aristotle, see alsoCorkum 2013.4 Translation by J. L. Ackrill (cf. Barnes 1984).



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tential sense, but need not be so rendered. Thus, using the more neu-tral terminology of ‘being’ rather than ‘existence’, we may read Aris-

totle as putting forward the following counterfactual dependenceclaim: ‘If the primary substances were not [or: did not have being], it would be impossible for any of the other things to be [or: to havebeing].’

Notice that Aristotle in the passage quoted above speaks of two dif-ferent ways in which entities may depend ontologically on the prima-ry substances: (i) either by being said of the primary substances assubjects or (ii) by being in them as subjects. He understands the tech-

nical relation, ‘being in a subject’, in the following way: what is insomething (a) not as a part and (b) cannot be separately from what itis in ( Categories , chapter 2, 1a24 –25). (Again, the occurrence of ‘to be’[‘einai ’] here is standardly translated as ‘exist’: ‘... and cannot exist sepa-rately from what it is in’; but the same point as above applies here as well.) I interpret Aristotle’s two dependence relations, viz., being saidof a subject and being in a subject, as corresponding to two differentforms of predication: essential predication, as when we say of some-

thing (e.g., Socrates) that it is a member of a certain taxonomic cate-gory, i.e., a species (e.g., human being) or a genus (e.g., animal); andaccidental predication, as when we say of something (e.g., Socrates)that it bears a certain accidental feature (e.g., paleness).

Neither the dependence relation which corresponds to the relation,being in a subject (viz., as indicated by accidental predication), nor thedependence relation which corresponds to the relation, being said ofa subject (viz., as indicated by essential predication), should be read in

an exclusively existential way.5 If the particular instance of palenessthat currently inheres in Socrates is construed as a non-repeatableentity, then it is certainly true that it would be impossible for this in-dividual instance of paleness to exist unless Socrates existed as well. And, given an Aristotelian conception of universals, it would similarlybe impossible for universals in any category to exist unless individuals

5 Aristotle’s dependence claim in the Categories , when read in an exclusively

existential way, gives rise to the following definition: ‘x existentially dependson y ↔df. If y did not exist, then it would be impossible for x to exist’. Anon-existential reading of ontological dependence in Aristotle is also de-fended in Corkum 2008, 2013 and Peramatzis 2008.




in the category of substance existed as well. For in order for the universal, colour, to exist for example, individual instances of colour

must exist; and in order for individual instances of colour to exist,individual substances in which these individual colour-instances caninhere must exist.

At the same time, as has often been observed, if we construe onto-logical dependence in Aristotle’s Categories in a purely existential fash-ion, then the entities he identifies there as primary substances (e.g.,individual organisms, such as human beings or horses) would lack thedistinctive asymmetric ontological independence Aristotle seems to

want to attribute to them. For, in order for a substantial individual,such as Socrates, to exist, some substantial and non-substantial individuals and universals must exist as well which can be predicated ofSocrates either accidentally or essentially. Even though Socrates canexist without the particular colour-instances that are predicated ofhim accidentally at any particular time, some colour-instances or oth-er must be present in him at any time at which he exists. And the ex-istence of some colour-instances or other in turn necessitates the

existence of some more general non-substantial universals as well,such as paleness and colour, to which these individual colour-instances essentially belong. Finally, if the more general substantialcategories of which Socrates is essentially a member (e.g., the species,human being, or the genus, animal) did not exist, it would be impos-sible for Socrates to exist as well.

Therefore, if the notion of ontological dependence at work in Aris-totle’s Categories were interpreted in a purely existential manner, then

individual substances, such as Socrates, would come out as roughlyon a par with respect to their degree of ontological independence with non-substantial universals, such as colour. But Aristotle clearlythinks that individuals in the category of substance are ontologicallyindependent in a way in which other types of entities are not and thatentities of other types are ontologically dependent on the primarysubstances in a way in which they are not also ontologically depend-ent on other types of entities. We should thus conclude that an exclu-

sively existential construal of Aristotle’s dependence thesis in the Cat- egories does not provide the most charitable reading of what Aristotle



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has in mind there when he claims that all the other entities in some way ontologically depend on the primary substances.6, 7

2.2 Modal Existential Dependence

2.2.1 Rigid Existential Necessary Dependence

A straightforward modal/existential notion of ontological depend-ence is for example that defined by E. J. Lowe under the heading,‘Rigid Existential Necessary Dependence’:8

6 Corkum 2008, 2013 for example interprets Aristotle’s conception ofontological dependence in the following way: other entities are ontologicallydependent on the primary substances because they inherit their ontologicalstatus from the primary substances to which they are either accidentally oressentially related, while the primary substances do not in turn inherit theirontological status from other entities. How plausible this proposal is ofcourse depends on how we are to understand the key notion of inheritingone’s ontological status from something; as it stands, this notion is not elab-orated in Corkum 2008 to a sufficient degree to get a good handle on it. Forfurther discussion, see Corkum 2013. Peramatzis 2008 interprets Aristotle’sconception of ontological priority (the flip-side of ontological dependence)as the ontological correlate of definitional priority. The notion on whichPeramatzis focuses is thus perhaps more tailored to the views Aristotle es-pouses in his later work (e.g., the Metaphysics ), where form seems to take onthe status of primary substance, than to those we find in the Categories , where certain kinds of particular objects (e.g., organisms and artifacts) oc-cupy the role of primary substances: for particulars, for Aristotle, cannot be

defined, but only perceived.7 In contrast, Husserl, in the Logical Investigations , really does seem to havein mind existential dependence when he speaks for example of a colour-moment that is part of a particular more inclusive whole as being foundedupon an extension-moment that is part of the same whole, and vice versa. Amoment, he says, is a non-independent object in the sense that it requiressomething in addition to itself to exist (a more inclusive whole of which themoment is a part) in order for it to exist. And a moment is founded uponanother moment, if the first moment cannot exist unless it is part of a more

comprehensive unity which connects it with the second moment. Both Hus-serl’s conception of non-independent object and his conception of founda-tion thus seem to appeal to a notion of existential dependence. For discus-sion, see for example Correia 2004 and the references found therein.




R IGID EXISTENTIAL NECESSARY DEPENDENCE (ND1)x is rigidly existentially necessarily dependent on y ↔df. Necessarily, x

exists only if y exists.In Section 1, the following explanatory goals were identified against which a particular definition of ontological dependence may be eval-uated. (i) Does it achieve a particular desired classification of para-digmatic cases of ontological dependence? (ii) Is it useful from thepoint of view of formulating an independence criterion of sub-stancehood? And (iii) does it allow for substantive non-existentialdisagreements in ontology over questions of fundamentality? When

evaluated against these explanatory goals, a straightforwardly mod-al/existential construal of ontological dependence along the lines of( ND1) turns out not to be satisfactory. Such a construal of ontologi-cal dependence, among other things, gives rise to the following well-known difficulties, in particular with respect to desiderata (i) and (ii).

Suppose that Aristotle’s claim in the Categories is correct and every-thing in some way ontologically depends on the primary substances, while the primary substances do not in the same way ontologicallydepend on the other entities. As pointed out for example in Lowe1994, among the apparent trouble cases which arise for ( ND1) are thefollowing. Suppose that a substance can exist only if certain of itsconstituents exist; then, by ( ND1), such a substance will turn out todepend ontologically on these constituents.9,10 The same will be true

8 See also Simons’ notion of ‘Weak Dependence’ (cf. Simons 1998, 236).For Lowe’s most up-to-date views concerning ontological dependence, seeLowe 2006, 2005 (last revised in 2009), 2008, 2012, 2013. For discussions ofontological dependence in his earlier work, see Lowe 1994, 1998. Also relevant are his views concerning criteria of identity; see for example Lowe1989, 1997, 2009.9 Simons’ notion of ‘Strong Dependence’ or ‘Strong Rigid Dependence’simply rules out this particular group of apparent counterexamples by add-ing a clause which requires y not to be a proper part of x (cf. Simons 1987,303; Simons 1998, 236). This exclusion of proper parts from a definition of

ontological dependence raises difficult issues, especially when the notion ofontological dependence in question is used in the formulation of an inde-pendence criterion of substancehood; I will not address these issues here,but see for example Toner 2010 and Koslicki forthcoming for discussion.



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if, in some cases, a substance can exist only if it originated from acertain entity. For example, a human being might be thought to be

related in this way to the particular sperm and egg or to the particularzygote from which he or she developed. Moreover, suppose there areobjects which exist necessarily (e.g., the number 8); then again, by( ND1), everything will ontologically depend on them. Finally, supposethere are particularised properties which are necessarily had by their‘bearers’ (e.g., Socrates’ humanity) or four-dimensional entities whichare necessarily coexistent with the substances with which they areaffiliated (e.g., Socrates’ life); then again, by ( ND1), substances will

turn out to be ontologically dependent on these entities. Cases suchas these suggest that modal/existential dependence is too coarse-grained to yield an adequate notion of ontological dependence.

2.2.2 Generic Existential Necessary Dependence

Not all cases of existential dependence are cases in which an entitycan be said to be rigidly existentially dependent on another entity. Insome cases, an entity may only require for its existence that some enti-

ties or other , which bear certain characteristics, exist as well. To capture

10 It is difficult to find uncontroversial examples which would illustrate whyit might be plausible to think that an alleged substance candidate can existonly if certain of its constituents exist. I, for one, would argue that organ-isms for example provide us with a case in point. For, according to the mer-eological version of hylomorphism I defend in Koslicki 2008, a particularorganism, such as Socrates, is analysed as a compound of matter and form;

moreover, Socrates’ form and matter, on this view, are regarded as beingliterally and strictly speaking proper parts of Socrates. Given the strong cor-relation between form and essence, such a view quite naturally gives rise tothe consequence that Socrates can exist only if his form exists. But ofcourse nearly all the assumptions used in generating this example are highlycontroversial and can be (and are) rejected by other philosophers who donot subscribe to this particular version of hylomorphism. Perhaps, it is suffi-cient for our purposes to keep in mind that even a philosopher like Simons, who is sympathetic to a modal/existential construal of ontological depend-

ence, feels the need to add an exclusion clause for proper parts in his formu-lation of ‘Strong Dependence’, since he allows for the possibility that allegedsubstance candidates can ontologically depend on their own proper parts inthe sense of ( ND1).




these sorts of cases, Lowe defines the notion of ‘Generic ExistentialNecessary Dependence’:11

GENERIC EXISTENTIAL NECESSARY DEPENDENCE (ND2)x is generically existentially necessarily dependent on F s ↔df. Neces-sarily, x exists only if some F s exist.

To illustrate: those who subscribe to an Aristotelian (as opposed to aPlatonist) conception of universals will presumably take ( ND2), butnot ( ND1), to be appropriate for a characterisation of the relationbetween universals and the particulars that instantiate them. For it is

part of the Aristotelian conception that universals can only exist ifparticulars instantiating them exist as well. But the existential depend-ence in question would have to be generic and not rigid, since the Aristotelian conception certainly does not commit one to thinkingthat a universal, e.g., redness, can exist only if some specific red ob-ject, e.g., a particular tomato, exists as well, only that the existence ofsome red objects or other is required for the existence of the univer-sal, redness.

( ND2), however, is overly coarse-grained for much the same reasonsas ( ND1) is: existentially generalised versions of all of the same coun-terexamples that were seen to arise for ( ND1) can be generated for( ND2) as well. Suppose for instance that a putative substance candi-date such as Socrates turns out to be rigidly existentially necessarilydependent, in the sense of ( ND1), on certain of his constituents, hisorigins, the number 8, certain necessary properties, or necessarily co-existent four-dimensional entities. Then, by ( ND2), Socrates will also

turn out to be generically existentially necessarily dependent on some constituents or other, some entities from which he originated or other,some necessary existents (e.g., numbers) or other, some necessary prop-erties or other, as well as some necessarily coextensive four-dimensional entities or other. And even if we leave aside explanatorygoal (ii) (viz., the formulation of a plausible criterion of substance-hood), ( ND2) also leads to undesirable consequences with respect to(i) (viz., the adequate classification of paradigmatic cases of ontologi-cal dependence). For, according to ( ND2), a universal (e.g., redness)

11 See also Simons’ notion of ‘Generic Dependence’ (cf. Simons 1987,297).



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for example turns out to be generically existentially necessarily de-pendent not only on its instances (viz., the particular red objects), but

also on numbers, triangles, sets and everything else that can plausiblybe taken to exist necessarily. Thus, while the notion of dependencedefined in ( ND2) may achieve some explanatory goals (e.g., it may beof help in characterising the relationship between an Aristotelian universal and the particulars that instantiate it), it certainly cannot single-handedly satisfy all that we expect from a notion of ontological de-pendence.

2.3 Other Forms of Existential Dependence

2.3.1 Necessary vs. Essential Existential Dependence

A persistent problem which besets all modal/existential construals ofontological dependence, as noted above, is that they appear to be toocoarse-grained to yield the correct results in cases involving necessari-ly existing entities. For example, as it stands, all of the mod-al/existential construals of ontological dependence considered so farseem to mis-classify the relationship between a putative substancecandidate, such as Socrates, and the number 8 or numbers in general.For example, according to ( ND1), Socrates would be classified as rig-idly existentially necessarily dependent on the number 8, since neces-sarily Socrates exists only if the number 8 exists, given our assump-tion that the number 8 exists necessarily. Similarly, ( ND2) classifiesSocrates as generically existentially necessarily dependent on numbersin general, since necessarily Socrates exists only if some number orother exists, given our assumption that numbers in general exist nec-

essarily. Moreover, we also noted that, independently of the questionof whether a particular criterion succeeds in classifying the substanc-es correctly, ( ND2) also yields the unattractive result that the universal,redness, for example turns out to be dependent on necessarily exist-ing entities, such as numbers, triangles and sets.12

12 Whether Aristotle’s counterfactual dependence claim in the Categories , when interpreted existentially (‘If the primary substances did not exist, it

would be impossible for the other entities to exist as well’), also mis-classifies these cases depends on how one deals with counterfactuals withimpossible antecedents, such as ‘If the number 8 did not exist, it would beimpossible for Socrates to exist as well’ or ‘If numbers in general did not




One possible solution to these problems (endorsed by both E. J.Lowe and Kit Fine) is to adopt a non- modal conception of essence,

which contrasts with the more mainstream modal conception of es-sence in the following way.13 An essential truth, according to a modalconception of essence, is just a modal truth of a certain kind (viz.,one that is both necessary and de re , i.e., about a certain object); andan essential property is just a feature an object has necessarily, if it isto exist. The essential truths, according to this approach, are thus justa subset of the necessary truths; and the essential properties of ob-jects are just a special kind of necessary property. Quine for example

has such a modal conception of essence in mind, when he argues thatthe view he calls ‘Aristotelian essentialism’ is incoherent, because itrequires quantification into intensional contexts (cf. Quine 1953).

But the view Quine calls ‘Aristotelian essentialism’ is for a variety ofreasons not one Aristotle himself would have found congenial, sincehe does not subscribe to a modal conception of essence. For Aristo-tle, the essential truths are not even included among the de re neces-sary truths; and the essential features of an object are similarly not

included among its de re necessary features. Rather, Aristotle con-ceives of the de re necessary truths as being distinct and derivativefrom the essential truths; and he conceives of the de re necessary fea-tures of objects, traditionally known as the ‘propria’ or ‘necessaryaccidents’, as being distinct and derivative from, the essential featuresof objects. For example, for Aristotle, while it is part of the essence

exist, it would be impossible for Socrates to exist as well’. Certainly, if coun-

terfactuals with impossible antecedents are treated as trivially true, then thiscounterfactual/existential construal of ontological dependence will yield thesame counterintuitive results as ( ND1) and ( ND2) with respect to cases involving necessarily existing entities.13 A non-modal conception of essence was held by Aristotle (cf. Posterior Analytics ) and also constitutes a central component of the neo-Aristotelianapproach to metaphysics defended over the last two decades by Kit Fine (seefor example Fine 1994, 1995a, 1995b, 1995c). (The similarities and differ-ences between Aristotle’s and Fine’s non-modal conception of essence are

discussed in more detail in Koslicki 2012a.) The contrasting modal concep-tion of essence is so widespread among contemporary metaphysicians that itis almost unnecessary to give references; but for some representative exam-ples, see Plantinga 1974, Forbes 1985, Mackie 2006.



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of planets that they are heavenly bodies that are near, it is merely a dere necessary (but non-essential) feature of planets that they do not

twinkle; the latter follows from, but is not strictly speaking part ofthe essence of planets. Thus, the definition, whose job it is to statethe essence or what it is to be a planet, would have to include thatplanets are heavenly bodies that are near; but the definition shouldnot also include that planets do not twinkle, since this would wronglyrepresent a derivative feature of planets (namely their not twinkling)as a basic or non-derivative feature of them (namely their nearness tothe earth).14, 15

Those who are attracted to such a non-modal conception of essencenow have the option of formulating stronger essentialist versions of( ND1) and ( ND2), as illustrated by Lowe’s ( ED1) and ( ED2):

R IGID EXISTENTIAL ESSENTIAL DEPENDENCE (ED1)x is rigidly existentially essentially dependent on y ↔df. It is part ofthe essence of x that x exists only if y exists.

GENERIC EXISTENTIAL ESSENTIAL DEPENDENCE (ED2)

x is generically existentially essentially dependent on F s ↔df. It is partof the essence of x that x exists only if some F s exist.

14 See for example Aristotle, Posterior Analytics , A.13 and B.16. Aristotlethought of the planets and other heavenly bodies as being arranged andmoving in accordance with a series of fixed heavenly spheres, with the earthlying at the center. This arrangement, which in Aristotle’s view is eternal andperfect, does not allow for change with respect to the movement of the

heavenly bodies or their position relative to the earth.15 I realize that this talk of something’s being part of an essence or some-thing’s being included in a definition (a statement of the essence) of som e-thing is obscure and stands in need of elucidation. A proper attempt at elu-cidating what might be meant by these phrases would take us too far afield(but see Koslicki 2012a and 2012b, for some relevant discussion). For Fine,since he conceives of essences as propositions (or collections of proposi-tions) and takes these propositions to have constituents, one can understandthe idea of something’s being part of the essence (or its being included in

the definition) of something in terms of the notion of being a constituentof a proposition. But, if one does not subscribe to this conception, then thequestion of what it would mean for something to be part of the essence (orto be included in the definition) of something still remains to be answered.




Presumably, given an appropriately constrained conception of es-sence, ( ED1) and ( ED2) are not open to the same range of apparent

counterexamples as ( ND1) and ( ND2). To illustrate, even though it is ade re necessary truth about Socrates that he exists only if the number8 or numbers in general exist, it is not similarly plausible to think that what it is to be Socrates has anything to do with numbers. Hence, with a suitably narrow conception of essence in hand, we can resistclassifying the proposition that Socrates exists only if the number 8exists or the proposition that Socrates exists only if numbers in gen-eral exist as an essential truth about Socrates. In what follows, when I

speak of ‘essence’, ‘essential features’, ‘essential truths’, etc., I have inmind such a suitably constrained non-modal conception of essence.

Unfortunately, even if we move from modal to non-modal formula-tions of existential dependence, there are still reasons to be dissatis-fied with purely existential construals of ontological dependencefrom the point of view of meeting the explanatory goals set out inSection 1. Potential trouble-cases for non-modal existential construalsof ontological dependence include the following: Socrates’ humanity

(which may be taken to be, depending on one’s outlook, for examplea trope that essentially belongs to Socrates or a universal that is essen-tially instantiated by Socrates); Socrates’ form (according to a neo- Aristotelian conception of unified wholes as hylomorphic com-pounds); Socrates’ essential proper parts (if he has any); or Socrates’origin (assuming Kripke’s Essentiality of Origins thesis). If in at leastsome of these cases it is plausible to think that it is part of the es-sence of Socrates for example that he exists only if the entity in ques-

tion exists, then putative substance candidates, such as Socrates, willagain be classified as existentially dependent entities even accordingto ( ED1) and ( ED2).

There is of course a lot that could be said by the defender of a non-modal existential conception of ontological dependence about eachof the items on this list of apparent trouble cases. For example, onecould deny that putative substance candidates are hylomorphic com-pounds; or that they are numerically distinct from their forms; or that

they have essential proper parts; or that their origins are essential tothem; and so on. One rather popular strategy which, as I argue inKoslicki forthcoming, is to be avoided is simply to exclude by stipula-



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tion some group of apparent counterexamples (e.g., universals) fromone’s favourite definition of ontological dependence or from one’s

preferred independence criterion of substancehood. Those who en-dorse this strategy violate the third of our three desiderata identifiedin Section 1 (viz., to allow for meaningful non-existential disagree-ments in ontology over questions of fundamentality), since questionsthat should be considered to be extremely substantive (e.g., whetherthe substances are universals or particulars) are then classified as ei-ther trivially answerable (because their answers follow straightforwardly from a definition) or as based on a contradiction (if it is as-

sumed for example that the substances are by definition particulars).2.3.2 Rigid and Permanent Existential Dependence

Fabrice Correia and Benjamin Schnieder have also put forward anexistential construal of ontological dependence which is not purelymodal, since it makes use of the connective, ‘because’, on the right-hand side of the definition. This connective, due to its explanatorynature, is not assumed to be open to an analysis in exclusively modal

terms. The following definition of ‘Rigid Permanent Existential De-pendence’ ( RPED ) comes from Schnieder 2006:17

R IGID AND PERMANENT EXISTENTIAL DEPENDENCE (RPED)x rigidly and permanently existentially depends upon y ↔df. There isan F , such that necessarily for any time, t , at which x exists, x exists att because y is F at t .

Schnieder considers the following to be a paradigmatic case of( RPED ): a particular redness trope, in his view, is rigidly and perma-nently existentially dependent on a particular tomato, say, in which itinheres, since there is an F, viz., redness, such that necessarily for anytime, t, at which the tomato’s redness trope exists, it exists at that timebecause the tomato is red at that time.

17 Schnieder 2006, 412. (My statement of ( RPED ) is slightly different fromSchnieder’s ‘(Dep-7)’, but only in stylistic ways.) Schnieder states that heprefers an ‘innocuous’ interpretation of the quantifier in ‘There is an F...’,

which apparently ranges over properties, along the lines of Rayo and Yablo2001 (Schnieder 2006, 416 n. 26). Correia’s notion of ‘basing’ (Correia 2005,66ff) and his definition of ‘simple dependence’ in terms of ‘basing’ is similarto Schnieder’s ‘(Dep-7)’; see also Correia 2008.




( RPED ) strikes me as problematic for several reasons. To avoid theapparent counterexamples considered above to which mod-

al/existential construals of ontological dependence fall prey, we haveto assume that the explanatory connective, ‘because’, sets some con-straints on how F may be picked relative to the objects, x and y, underconsideration. Consider for example the following blatantly unhelpfulattempt at instantiating ( RPED ): Socrates rigidly and permanently exis-tentially depends on the number 8 just in case there is an F, e.g., actu-ally numbering the planets, such that necessarily for any time, t, at which Socrates exists, Socrates exists at t because the number 8 actu-

ally numbers the planets at that time. Clearly, it should turn out not tobe the case that Socrates depends on the number 8 in this way. And itdoes of course sound extremely odd to say that Socrates exists at anytime, t, because the number 8 actually numbers the planets at thattime: for the fact that the number 8 actually numbers the planets atany particular time strikes us as explanatorily completely irrelevant tothe question of why Socrates exists at that time. But unless more issaid about how to construe explanatory relevance and irrelevance inthis context, the oddness of ‘Socrates exists at t because the number 8actually numbers the planets at t’ does not strike me as in any wayilluminating of the oddness we already recognise in ‘Socrates’ exist-ence at t depends on the number 8 actually numbering the planets at t’.If anything, it seems that the direction of illumination would have togo the other way around: the fact that the number 8 actually numbersthe planets at a time t is explanatorily irrelevant to Socrates’ existenceat t because Socrates’ existence at t does not depend on the number 8actually numbering the planets at t; and not the other way around. In

other words, it is not that two entities, facts, states of affairs, or whathave you, stand in a dependence relation because an explanatory linkobtains between them; rather, a good explanation should reflect anunderlying dependence relation between the relata in question, as forexample the job of a good causal explanation is to capture an under-lying causal dependence relation.18

18 Schnieder does provide some further elucidation concerning the kind ofexplanatory connection that he takes to be relevant to ( RPED ). In his view,the explanatory ‘because’ in statements of ontological dependence is to beconstrued in an objective conceptual way: ‘In general, statements involving



18 KOSLICKI

Suppose, on the other hand, that implicit guidelines are in place forhow F in ( RPED ) is to be chosen relative to the entities, x and y . When

the entities in question are for example the tomato’s redness tropeand the tomato in which it inheres, then we may assume that it issomehow determined that the explanatorily relevant F in questionthat must be exhibited by the tomato at each time at which the toma-to’s redness trope exists is redness (rather than, say, colour), in whichcase the right-hand side of ( RPED ) reads as follows: there is an F,redness, such that necessarily for any time, t, at which the tomato’sredness trope exists, it exists at t because the tomato is red at that

time. But now we ought to wonder whether ( RPED ) has really charac-terised the direction exhibited by the alleged explanatory connectionin question correctly for the following reasons.

Only certain kinds of trope theorists would find this particular in-stance of ( RPED ) congenial. For, as noted in Section 1, some tropetheorists (who take the ‘bearers’ of tropes to be mere bundles oftropes) would presumably think that the ontological dependence be-tween tropes and their ‘bearers’ runs in the opposite direction, i.e.,

that the ‘bearers’ of tropes are ontologically dependent on the tropesthat make up the particular bundle in question, analogously to the way in which non-empty sets are ontologically dependent on theirmembers. So we should ask ourselves whether ( RPED ) in fact correct-ly represents the commitments of those trope theorists who are sym-

complex or elaborated concepts are explained with recourse to more primi-tive concepts (which may or may not enter into an analysis of the complex

concepts)’ (Schnieder 2006, 405). For example, for Schnieder, the conceptdenoted by the phrase, ‘the tomato’s redness’, is a complex or elaboratedconcept which is to be explained with recourse to more primitive concepts,e.g., those at play in the statement ‘The tomato is red’. But it does not seemplausible to think that facts about ontological dependence in general can beexplained by what is or is not classified as primitive or complex relative to aparticular conceptual system. In some cases, nothing important may hang on whether one notion or another is taken as primitive by a particular concep-tual system (e.g., point versus line in some systems of geometry). In other

cases, one concept can be more complex than another, even though whatthe first stands for is ontologically more fundamental than what the secondstands for (e.g., arguably, the concepts, water and H 2 O-molecule , illustrate thispossibility).




pathetic to the idea that tropes ontologically depend on their ‘bear-ers’, and not the other way around.

And it seems to me that ( RPED ) again fails to capture the explanatorylink in question correctly. For one thing, it is questionable whetherfor the kind of trope-theorist we have in mind the existence of thetomato’s redness trope at t is really a distinct fact or state of affairsfrom the tomato’s being red at t. But if we are dealing here with just asing le fact, then the irreflexivity of the explanatory ‘because’ has been violated by this putative instance of ( RPED ), since now a single fact orstate of affairs is said to be explained in a circular fashion in terms of

itself.19 On the other hand, if the existence of the tomato’s rednesstrope at t does, for the trope-theorist at issue, constitute a distinct factfrom the tomato’s being red at t, then it seems that such a philoso-pher would want to explain the tomato’s being red at t in terms ofthe existence of a redness trope that inheres in the tomato at t, andnot the other way around. Otherwise, one wonders what work thetrope theorist’s commitment to the existence of tropes is really doingin the first place and whether we could not get by just as well without

them. Either way, ( RPED ), it seems, does not correctly capture therelevant trope-theorist’s conception of the relation between the to-mato’s redness trope and the tomato in which it inheres.

2.4 Being vs. Existence

In addition to the more detailed objections to various specific exis-tential construals of ontological dependence we have considered inthe foregoing sections, there are also more general reasons for want-

ing to divorce ontological dependence from existential dependence(whether modally analysed or not). Even though the putative cases ofontological dependence listed in Section 1 all seem to involve existen-tial dependence, I agree with Fine (1995a) that existential construalsof ontological dependence do not quite get us to the heart of thisrelation. Fine comments on existential accounts of ontological de-pendence as follows:

19 But see Schnieder 2010 for a response to this kind of worry. Schniederargues there that ‘because’ is sensitive not only to the identity of the factsintroduced by its clauses, but also to the way in which these facts are pre-sented.



20 KOSLICKI

The present examples [viz., impossible objects and identityproperties] highlight a problem that besets any existential ac-

count of dependence, whether it be modal or essentialist inform. For, it does not seem right to identify the ‘being’ of anobject, its being what it is, with its existence. In one respect,existence is too weak; for there is more to what an object isthan its mere existence. In another respect, existence is toostrong; for what an object is, its nature , need not include exist-ence as a part. (Fine 1995a, 274, my italics)20

It is tempting to think that the relationship between smiles and

mouths for example is not exhausted by noting that the existence ofsmiles requires the existence of mouths (pace the Cheshire cat). Ra-ther, as we will explore in the next section, what gets us closer to thecore of this relation is the idea central to essentialist approaches toontological dependence that in saying what it is to be a smile we mustappeal to mouths and what these mouths can do; but in saying whatit is to be a mouth, we need not in turn appeal to smiles and whatsmiles can do. We would not have exhausted the full force of the rela-

tion of ontological dependence if we were to construe the use of the

20 The two examples Fine has in mind here (impossible objects and identi-ty-properties) are as follows. Consider round squares: if it makes sense tosay that round squares have natures, i.e., that there is such a thing as what itis be a round square, then the use of the verb, ‘to be’, here cannot be con-strued in a primarily existential way, since it is impossible for round squaresto exist. Secondly, consider the property of being identical to Socrates. Sup-pose (as Fine does for the purposes of this example) that this property ex-

ists necessarily and suppose further that the property of being identical toSocrates ontologically depends on Socrates (i.e., it is that very property be-cause it is the identity-property associated with Socrates). It would again be wrong to construe the relationship in question as existential dependence,since (by hypothesis) the identity-property exists necessarily while Socratesexists only contingently. Thus, there are worlds in which the identity-property exists while Socrates does not: in order for the identity-property inquestion to exist, it therefore cannot be required that Socrates exists as well;but the identity-property may nevertheless depend on Socrates with respect

to its being what it is, its nature. I am not endorsing the details of either ofFine’s two examples, which are of course quite controversial; my purposehere is only to explain what he has in mind in the passage cited above, with whose general point I wholeheartedly agree.




verb, ‘to be’, in the context of this ‘what it is to be’ construction, inan exclusively existential way. Nevertheless, it does seem plausible to

think (in a wide range of cases at least) that ontological dependenceentails modal/existential dependence, i.e., that when an entity, x , on-tologically depends on an entity, y , it is also true that necessarily x exists only if y exists (see also Lowe 1998).21 The converse, on theother hand, does not always hold, as the trouble cases for the mod-al/existential approach rehearsed above illustrate: it is not true acrossthe board that if necessarily x exists only if y exists, then x ontologi-cally depends on y . I will now turn to the difficult question of what

sort of alternative reading we should substitute in place of an exis-tential construal of ontological dependence. The main goal of thecurrent section was simply to indicate that an exclusively existentialconstrual of ontological dependence, whether modal or non-modal,does not adequately reflect all that is encompassed by this notion.

3. Essential Dependence

3.1 Essential Identity Dependence

Lowe agrees that, among his defined notions, even ( ED1) and ( ED2)do not yet suffice to establish a genuine contrast between those con-crete particular objects which, in his view, deserve the status of sub-stances and all the other types of entities. To this end, he introduces afurther species of essential dependence, viz., ‘Essential Identity De-pendence’:

ESSENTIAL IDENTITY DEPENDENCE (ED3)

x is essentially identity dependent on y ↔df. There is some function φ such that it is part of the essence of x that x = φ( y ).22

21 In order to preserve this entailment from ontological dependence tomodal/existential dependence, Fine’s example involving the property ofbeing identical to Socrates would have to be addressed in some fashion. Forthe entailment from ontological dependence to modal/existential depend-ence seems to fail in this case.22 ( ED3) of course also has a modal counterpart, ( ND3), according to which

x is necessarily identity dependent on y iff there is some function φ such thatnecessarily x = φ( y ). But since ( ND3) is still susceptible to the same sorts ofapparent counterexamples to modal formulations of ontological depend-ence as the relations considered above, I will in what follows leave ( ND3)



22 KOSLICKI

As a paradigmatic instance of ( ED3) Lowe cites for example the rela-tion between a married couple and the individual members of the

married couple, or the relation between a set and its members:23 inthe first of these cases, according to Lowe, there is some function, φ, viz., the ‘marriage function’, such that it is part of the essence of theparticular married couple in question that it is the result of applyingthe ‘marriage function’ to the two individual members of the marriedcouple; and, in the second, there is some function, ψ , viz., the ‘set-formation’ function, such that it is part of the essence of Socrates’singleton set that it is the result of applying the ‘set-formation func-

tion’ to Socrates. Thus, married couples and sets, according to Lowe,are essentially identity dependent on their individual members. Since( ED3) entails ( ED1) and ( ED2), sets and married couples are also rigid-ly existentially essentially dependent on their members and, a fortiori,generically existentially essentially dependent on having some mem-bers or other.

The first thing to note about ( ED3) is that it does in fact take us be-yond a purely existential construal of ontological dependence. ( ED3)

does not set a condition involving an entity, y , which must be met inorder for an entity, x , to exist; rather, ( ED3) sets a condition involvingan entity, y , that is required for x ’s identity, which presumably is not tobe conflated with x ’s existence. The substantive content of ( ED3)concerns whether or not it is part of the essence of an entity that it isthe result of applying a certain function (whose existence we can pre-sumably uncontroversially presuppose) to another entity or entities. With ( ED3), we have therefore moved beyond a purely existential

construal of ontological dependence and thus squarely into the realmof essential dependence.

aside and focus instead on the essentialist version of identity dependence,( ED3).23 Strictly speaking, in order for ( ED3) to apply to these two examples, thedefinition of essential identity dependence would have to be modified in

something like the following way: ‘x is essentially identity dependent on a plurality of entities, y 1 ... y n ↔df. There is a function φ such that it is part ofthe essence of x that x = φ( y 1 ... y n )’. In what follows, I will simply assumethat this modified definition is substituted for ( ED3), wherever appropriate.



24 KOSLICKI

Socrates, is to count as an ontologically independent entity in thesense of ( ED3), then it must be the case that which entity Socrates is is

not fixed by his relationship to any other entities. For Lowe, thismeans that no synchronic criterion of identity or principle of individuation that appeals to numerically distinct entities can be given atall for substance candidates such as Socrates: that they are the veryentities they are at each time at which they exist is simply to be takenas a non-derivative fact about these entities. Thus, if Socrates is infact to qualify as a substance, then it must be the case that he doesnot owe his individuation or synchronic identity, i.e., his being the

very entity that he is at each time at which he exists, to his relation-ship to any other entity numerically distinct from himself.26

Lowe’s conception of the ontological independence of substances ispresumably incompatible with the essentiality of origins, which hefinds in any case implausible. For if it were part of Socrates’ essence

assume, however, that we can apply (CI) to ( ED3) in the following way: sincefor example the identity of sets in general is fixed by appeal to their mem-bers, the identity of every individual set is therefore fixed by appeal to itsparticular members. For more discussion of Lowe’s views concerning therelation between criteria of identity and principles of individuation, seeLowe 2012.26 In Lowe’s view, the unavailability of a criterion of individuation or sy n-chronic identity for substances is compatible with the availability of a dia-chronic criterion of identity for such entities. Thus, for Lowe, compositesubstances persist over time just in case a certain equivalence relation holdsthat is defined over their actual or possible components (cf. Lowe 1989,

168). But why the asymmetry between identity at a time and identity overtime? Why is Socrates’ status as a substance not threatened by the fact thathe persists over time due to a certain relationship that his proper parts atone time bear to his proper parts at another, while his status as a substanceapparently would be jeopardised if something similar were true of his identi-ty at a time? Presumably, the answer to this question, for Lowe, is that dia-chronic identity presupposes synchronic identity. For suppose that it is pos-sible for Socrates (say) to have existed for only one instant: in that case, hisexistence at this instant would nevertheless have required that he is the very

entity that he is at that instant; but his synchronic identity at that instantdoes not require that he persists over time. If, on the other hand, Socratespersists over time, his diachronic identity does require that, at each time at which he exists, he is at that time (i.e., synchronically) identical to himself.




for example to have originated from a particular zygote, then it mightseem that a criterion of individuation or synchronic identity could be

found for a substance-candidate such as Socrates, viz., one whichappeals to Socrates’ origins.27 Moreo ver, Lowe’s conception of theontological independence of substances also conflicts with a certainnatural interpretation of the neo-Aristotelian position according to which unified wholes are compounds of matter and form. For if it were part of the essence of a substance candidate, such as Socrates,to be a compound of some particular matter and some particularform, then it might appear again that Socrates could be individuated

by appeal to his form or matter. Since Lowe is sympathetic to theneo-Aristotelian hylomorphic conception of unified wholes as com-pounds of matter and form, he cannot avoid the conflict just raisedby denying the premises that generate it. Instead, he adopts a differ-ent escape route, which itself carries with it considerable costs: inLowe 1999, he argues that hylomorphic compounds should be identified with their form and therefore are not compounds of matter andform at all. Finally, if a substance candidate, such as Socrates, canhave essential tropes (e.g., Socrates’ particular instance of humanity),then it will have to turn out that even though it is part of the essenceof the tropes in question that they are the result of applying somefunction to their ‘bearer’ (e.g., the ‘abstraction’ function), it is not sim-ilarly part of the essence of the substance which is the ‘bearer’ ofthese essential tropes that it is the result of applying some function(e.g., the ‘construction’ function) to its essential tropes, perhaps be-cause substances are not taken to be bundles of tropes, on Lowe’sconception.28 We will have the opportunity to consider a further po-

27 Though it should be said that it is a controversial question even amongthose who subscribe to a modal conception of essence whether concreteparticular objects can in fact be individuated across worlds by means of theirorigins. See for example Forbes 1985, 1986, 1997, 2002; Mackie 2002, 2006;and the references to be found therein.28 In Section 2.3.1, I brought up the following apparent counterexamples to( ED1) and ( ED2): Socrates’ humanity, conceived of either as (a) an essentialtrope or as (b) a universal that is essentially instantiated by Socrates; (c) Soc-

rates’ form (according to a neo-Aristotelian conception of unified wholes ashylomorphic compounds); (d) Socrates’ essential proper parts (if he hasany); or (e) Socrates’ origin (assuming the essentiality of origins). As notedhere, Lowe has responses to (a), (c), (d) and (e). (b) is not a problem for



26 KOSLICKI

tential trouble-case for essentialist construals of ontological depend-ence below, immediately after the introduction of the account fa-

voured by Kit Fine in the next section.3.2 Constitutive Essential Dependence

Fine 1995a defines the following essentialist notion of ontologicaldependence, which I will call ‘Constitutive Essential Dependence’:

CONSTITUTIVE ESSENTIAL DEPENDENCE (ED4)x is constitutively essentially dependent on y ↔df. y is a constituent ofx ’s essence (narrowly construed).

Smiles for example, on this account, ontologically depend on mouthsin the sense that mouths are constituents of the essences of smiles;but the reverse is not the case, i.e., smiles are not also constituents ofthe essences of mouths.29

Fine’s approach to ontological dependence crucially relies on a dis-tinction between essence, narrowly construed (‘constitutive essence’),and essence, more widely construed (‘consequential essence’). Unless

some such ‘narrow/wide’ distinction for essences can be drawn, Fi-ne’s account of ontological dependence threatens to become vacu-ous, in the sense that everything will turn out to depend ontologicallyon everything else. This result follows because, however exactly wedraw the constitutive/consequential distinction, the consequentialessence of any entity, on Fine’s conception, is closed under logicalconsequence and all the logical truths therefore end up in the conse-quential essence of everything whatsoever. Since for example the

proposition that the number 2 is self-identical is a logical truth, thenumber 2 will turn up as a constituent in the consequential essence

( ED3), since the identity of a particular cannot be parasitic on its being aninstance of a universal, even where the universal in question is essential to it,since other particulars may instantiate the same universal. With respect to(d), Lowe would presumably similarly deny that a potential substance candi-date such as Socrates has any essential proper parts which determine hissynchronic identity, since in his view no numerically distinct entity (including

proper parts) determines that a substance is the very thing that it is at anytime at which it exists.29 Fine’s account assumes that we may think of essences as propositions orcollections of propositions and that these propositions have constituents.




of every object whatsoever. And because the number 2 here waspicked arbitrarily and every object is self-identical, every object by the

same reasoning turns up as a constituent in the consequential essenceof every other object. Thus, if an entity were to count as being onto-logically dependent on all those objects which figure as constituentsin propositions that belong to its consequential essence, then the no-tion of ontological dependence would have been trivialised and everyobject would turn out to be ontologically dependent on every otherobject. It is thus important, at least for the purposes of defining thenotion of ontological dependence in terms of essence, that the no-

tion of essence, as it figures in ( ED4), is understood in the appropri-ately narrow sense of ‘constitutive essence’.30

Fine assumes that, for the purposes at hand, essences can be identi-fied with collections of propositions that are true in virtue of theidentity of the particular object or objects whose essences they are.Such collections of propositions that are true in virtue of the identityof an object or objects, in Fine’s view, can also simultaneously bethought of as real definitions for the object or objects in question.

There is not, then, on this approach, much of a distinction betweenessences and real definitions.

But we may wish to proceed somewhat differently and leave room fora less propositional conception of essences, such as that endorsed by Aristotle for example. For Aristotle, the essence of a kind of thingincludes at least its form. (Whether the essence of a kind of thingalso includes additional components besides the form, e.g., the mat- 30 Given Fine’s non-modal conception of essence, the narrow notion ofconstitutive essence may be taken as primitive and the wider notion of con-sequential essence defined in terms of it through logical closure: the conse-quential essence of an entity is that collection of propositions which con-tains all the logical consequences of those propositions that are included inthe entity’s constitutive essence. Ontological dependence can then be de-fined in terms of the narrow notion of constitutive essence. As I argue inKoslicki 2012b, the other direction (taking the wider notion of consequen-tial essence as primitive and deriving the narrower notion of consequential

essence from it through the so-called ‘generalising out’ procedure) is unsuc-cessful. For a more detailed discussion of Fine’s constitutive/consequentialdistinction for essences, see Gorman 2005, 2006a, 2006b; Koslicki 2012a,2012b.



28 KOSLICKI

ter, is a controversial question which I will not address here.) For ex-ample, the essence of a living being, in Aristotle’s view, encompasses

at least its soul, i.e., the form of the living being. But, given Aristotle’sassociation of the soul with certain kinds of powers or capacities[ dynameis ], e.g., the capacity for growth and nourishment, locomotion,perception and thought, it would be strange to think of the soul of aliving being as a collection of propositions. It is perhaps more naturalto take real definitions, which Aristotle regards as linguistic entities[ logoi ] of some sort, viz., formulae or statements of the essence, ascollections of propositions or perhaps as only a single proposition, if

there is only a single canonical way of stating the essence of a kindof thing. The basic idea underlying Fine’s essentialist approach to ontological dependence can then be reformulated in terms of realdefinitions as follows:

DEFINITIONAL ESSENTIAL DEPENDENCE (ED5)

x is definitionally essentially dependent on y ↔df. y is a constituent ofa real definition of x .31

3.3 Discussion

I will end by mentioning a potential trouble case for the essentialistaccounts of ontological dependence proposed by Lowe and Fine.32

31 The formulation of ( ED5) in the text contains ‘a real definition’, ratherthan ‘the real definition’, since I want to leave open for the time being whether an entity can have more than one real definition. This possibility would obtain if two different propositions (or collections of propositions)could be equally explanatory of the essential nature of the entity in question.For further discussion of the notion of real definition, see Koslicki 2012b.32 Whether Fine’s account runs into trouble with the essentiality of originsand the status of hylomorphic compounds as putative substance candidatesdepends crucially on whether we find the stipulative exclusion of properparts in the formulation of an independence criterion of substancehood to

be admissible. (This strategy would of course also take care of case (d) fromnote 28, viz., essential proper parts, in general.) If the substances are justthose entities which are ontologically independent in the sense of ( ED4) or( ED5) from all other numerically distinct entities except for their proper parts ,




( ED3), ( ED4) and ( ED5) have the following odd consequence. Assum-ing that it is in fact the case, following the Axiom of Extensionality,

that sets are essentially dependent on their members, in the sense of( ED3)-( ED5), then no non-empty set would be classified as an onto-logically independent entity or substance, which is perhaps a welcomeresult.33 But what about the empty set? Its identity cannot in anymeaningful sense be regarded as fixed by the identity of its members,since it has none; nor, for the same reason, can its members appear asconstituents in its constitutive essence or real definition. Rather, itseems that the identity of the empty set must simply be taken for

granted and that its essence must be regarded as simple and non-relational, in the sense that no entities numerically distinct from itselffigure as constituents in its constitutive essence or real definition. Inthat case, however, it seems that, by ( ED3) –( ED5), the empty set qual-ifies as an ontologically independent entity or substance, even thoughno other set does. I take it that this would be an unfortunate conse-quence for an essentialist account of ontological dependence, whenconstrued as yielding an independence criterion of substancehood,since, given a certain taxonomic category of entities, presumably ei-ther all or none of the entities belonging to the category in questionshould count as substances. It strikes me as strange to think that the

then an entity would be able to qualify as a substance even if its proper partsfigure as constituents in its constitutive essence or real definition, so long asno other numerically distinct entities besides its proper parts figure in its

constitutive essence or real definition. If for example the zygote from whicha human being originated at one point was a proper part of it and if theform and matter of which a hylomorphic compound consists are properparts of it (as Fine holds), then (given the exclusion of proper parts) con-crete particular objects could nevertheless qualify as substances even if it ispart of their essence to have originated from whatever entity they actuallyoriginated from and even if it is part of their essence to be a compound ofsome particular matter and form. I investigate these questions further inKoslicki forthcoming. As far as case (b), essential tropes, are concerned, Fine

can avail himself of the same strategy that is open to Lowe as well.33 On the relation between the Axiom of Extensionality and the claim thatsets have their members essentially, see for example van Cleve 1985 andForbes 1985.



30 KOSLICKI

empty set alone deserves substance-status, while none of the othersets do.34

A similar difficulty arises when we consider the relation between thenumber 0 and all the other natural numbers. If we think of the natu-ral numbers as in some sense constructed from the number 0, to-gether with the successor relation, then it seems that which numberthe number 1 is is fixed by its relation to the number 0, viz., by itsbeing the immediate successor of the number 0. The number 1, onthis conception, is therefore naturally taken as having the number 0as a constituent in its constitutive essence or real definition. But we

cannot similarly conceive of the number 0 as being constructed fromother natural numbers, together with the successor relation, since thenumber 0 is not the successor of any other natural number. Rather, inanalogy with the set-theoretic case, the identity of the number 0 mustbe taken as fixed independently of its relationship to the other natu-ral numbers and its constitutive essence again appears to be similarlysimple and non-relational, in the sense that what it is to be that verynumber is not defined in terms of its relation to any other natural

number. But it would be similarly puzzling if a criterion of sub-stancehood classified the number 0 alone, and no other natural num-ber, as a substance. An essentialist account of ontological depend-ence, along the lines of ( ED3) –( ED5), ideally should have somethingto say in response to these considerations.35

34 Perhaps the culprit here is the innocuous sounding sortal uniformity

principle to which I have just appealed, according to which substance statusis to be granted to entities not individually, but by sort. If we substitute‘fundamental’ for ‘substance’, then the result just generated is perhaps lessbewildering: ( ED3) –( ED5), when construed as yielding a criterion for funda-mentality, classify the empty set as fundamental (or as more fundamentalthan the other sets), while they classify the remaining sets as non-fundamental (or less fundamental than the empty set). Still, metaphysicalrealists at least will want to leave some room for a distinction between whatis taken as primitive by a particular theory or conceptual system and what is

ontologically fundamental as a matter of fact. See also my earlier remark inresponse to Schnieder’s account in note 17. 35 These and similar cases are discussed in Lowe 2012; see also Schwartz-kopff 2011.




4. Conclusion

In this essay, I have considered various prominent construals of on-tological dependence in the literature: modal vs. non-modal; existen-tial vs. non-existential; as well as rigid vs. generic construals. And while there is of course nothing wrong in principle with defining whatever technical concept one wishes, the question arises, in the faceof this plethora of relations that go under the name of ‘ontologicaldependence’, what explanatory tasks these notions are designed toaccomplish and how well they in fact meet the desiderata that are setfor them. I have identified three potential measures of success by

means of which particular accounts of ontological dependence maybe evaluated: (i) how well they do in classifying certain paradigmaticcases of ontological dependence in a particular desired way; (ii) whether they allow for the formulation of a plausible independencecriterion of substancehood; and (iii) whether they make room for thepossibility of substantive non-existential disagreements in ontologyover questions of fundamentality.36 Relative to these three goals, wehave seen that modal and existential construals of ontological de-

pendence are open to persuasive counterexamples, while essentialistaccounts seem to perform more promisingly. Still, various questionsremain to be addressed by essentialist accounts as well: in particular,(i) how to handle the essentiality of origins (if it is in fact part of theessence of certain sorts of entities to have originated from whateverthey in fact originated from); (ii) whether and how hylomorphiccompounds can be assigned substance status; and (iii) how a distinc-tion may be drawn between what is taken as primitive by a particular

theory or conceptual system (e.g., the number 0 or the empty set) and what is genuinely ontologically fundamental. Thus, as is to be ex-pected, more work still lies ahead for those who are sympathetic toessentialist accounts of ontological dependence.

36 The first two criteria have played a more prominent role in this discus-

sion than the third, with the exception of my remarks at the end of Section2.3.1. However, the importance of the third criterion should not be underes-timated; I make heavy use of it for example in evaluating competing inde-pendence criteria of substancehood in Koslicki forthcoming.



32 KOSLICKI

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— 1994: ‘Essence and Modality’. Philosophical Perspectives 8 (Logic andLanguage), pp. 1 –16.

— 1995a: ‘Ontological Dependence’. Proceedings of the Aristotelian Socie- ty 95, pp. 269 –90.

— 1995b: ‘Senses of Essence’. In Sinnott-Armstrong, Raffman and Asher 1995, pp. 53 –73.

— 1995c: ‘The Logic of Essence’. Journal of Philosophical Logic 24, pp.241 –73.

— 2001: ‘The Question of Realism’. Philosophers’ Imprint 1. URL:http://quod.lib.umich.edu/p/phimp/3521354.0001.002/1/--question-of-realism?page=root;size=200;view=image.

— 2012: ‘Guide to Ground’. In Correia and Schnieder 2012, pp. 37 –80.




Forbes, G. 1985: The Metaphysics of Modality . Clarendon Library ofLogic and Philosophy Series. Oxford: Oxford University Press.

— 1986: ‘In Defense of Absolute Essentialism’. In French, Uehling,and Wettstein 1986, pp. 3 –31.

— 1997: ‘Essentialism’. In Hale and Wright 1997, pp. 515 –33.

— 2002: ‘Origins and Identities’. In Bottani, Carrara and Giaretta2002, pp. 319 –40.

Frege, G. 1953: The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number , translated by Austin, J. L., 2nd

Edition, Oxford: Blackwell.French, P. A., T. E. Uehling and H. K. Wettstein (eds.) 1986: Midwest

Studies in Philosophy 11 ( Studies in Essentialism ). Minneapolis: Univer-sity of Minnesota Press.

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— 2006a: ‘Substance and Identity -Dependence’. Philosophical Papers

35, pp. 103 –18. — 2006b: ‘Independence and Substance’. International Philosophical Quarterly 46, pp. 147 –59.

Hale, B. and C. Wright 1997: Companion to the Philosophy of Language .Malden: Blackwell.

Husserl, E. 1900 –01: Logische Untersuchungen , 1st Edition. Halle: M.Niemeyer.

Koslicki, K. 2008: The Structure of Objects . Oxford: Oxford UniversityPress.

— 2012a: ‘Essence, Necessity and Explanation’. In Tahko 2012, pp.187 –206.

— 2012b: ‘Varieties of Ontological Dependence’. In Correia andSchnieder 2012, pp. 186 –213.

— forthcoming: ‘Substance, Independence and Unity’. To appear inFeser forthcoming.

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34 KOSLICKI

Lowe, E. J. 1989: ‘What Is a Criterion of Identity?’. The Philosophical Quarterly 39, pp. 1 –21.

— 1994: ‘Ontological Dependency’. Philosophical Papers 23, pp. 31 –48. — 1997: ‘Objects and Criteria of Identity’. In Hale and Wright 1997,

pp. 613 –33.

— 1998: The Possibility of Metaphysics: Substance, Identity, and Time . Ox-ford: Oxford University Press.

— 1999: ‘Form Without Matter’. In Oderberg 1999, pp. 1 –21.

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cyclodedia of Philosophy . URL: http://plato.stanford.edu/ en-tries/dependence-ontological/.

— 2006: The Four-Category Ontology: A Metaphysical Foundation for Natu- ral Science . Oxford: Clarendon Press.

— 2008: ‘Two Notions of Being: Entity and Essence’. In Le Poidevin 2008, pp. 23 –48.

— 2009: More Kinds of Being: A Further Study of Individuation, Identity,

and the Logic of Sortal Terms . Malden and Oxford: Wiley-Blackwell. — 2012: ‘Asymmetrical Dependence in Individuation’. In Correia and

Schnieder 2012, pp. 214 –33.

— 2013: ‘Some Varieties of Metaphysical Dependence’. In this vol-ume.

Mackie, P. 2002: ‘Forbes on Origins and Identities’. In Bottani, Carra-ra and Giaretta 2002, pp. 341 –52.

— 2006: How Things Might Have Been: Individuals, Kinds and EssentialProperties . New York: Clarendon Press.

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Peramatzis, M. 2008: ‘Aristotle’s Notion of Priority in Nature andSubstance’. Oxford Studies in Ancient Philosophy 35, pp. 187 –247.

Plantinga, A. 1974: The Nature of Necessity . Oxford: Clarendon Press.

Quine, W. V. O. 1953: ‘Three Grades of Modal Involvement’. Actes du XIème Congrès International de Philosophie 14. Volume complémen-taire et communications du Colloque de Logique. Amsterdam:

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North-Holland Publishing Company, and Louvain: Éditions E.Nauwelaerts, pp. 65 –81.

Rayo, A. and Yablo, S. 2001: ‘Nominalism through De-nominalization’. Nous 35, pp. 74 –92.

Schnieder, B. 2006: ‘A Certain Kind of Trinity: Dependence, Sub-stance, Explanation’. Philosophical Studies 129, pp. 393 –419.

— 2010: ‘A Puzzle About “Because”’. Logique et Analyse 53, pp. 317 –43.

Schwartzkopff, R. 2011: ‘Numbers as Ontologically Dependent Ob-

jects: Hume’s Principle Revisited’. Grazer Philosophische Studien 82,pp. 353 –73.

Simons, P. 1987: Parts: A Study in Ontology . Oxford: Clarendon Press.

— 1998: ‘Farewell to Substance: A Differentiated Leave- Taking’. Ra- tio (New Series) 11, pp. 235 –52.

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York: Cambridge University Press. Tahko, T. (ed.) 2012: Contemporary Aristotelian Metaphysics . Cambridge:Cambridge University Press

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Van Cleve, J. 1985: ‘Why a Set Contains Its Members Essentially’. Nous 19, pp. 585 –602.



Substance and Independence in Aristotle

Phil Corkum

Individual substances are the ground of Aristotle’s ontology. Taking aliberal approach to existence, Aristotle accepts among existents enti-ties in such categories other than substance as quality, quantity andrelation; and, within each category, individuals and universals. As I will argue, individual substances are ontologically independent fromall these other entities, while all other entities are ontologically de-pendent on individual substances. The association of substance withindependence has a long history and several contemporary metaphy-sicians have pursued the connection.1 In this chapter, I will discussthe intersection of these notions of substance and ontological de-

pendence in Aristotle.Ontological dependence plays a central role in Aristotle’s metaphysicsof properties, as well as in his philosophy of mathematics, philoso-phy of mind and elsewhere. As I will note, he typically uses separa-tion and priority terminology to refer to a notion of ontological de-pendence: one thing is ontologically independent from a second justin case the first is both separate from, and prior to, the second. Togive just a few examples of Aristotle’s use of such terminology: inaddition to the claim that individual substances are ontologically in-dependent from universals and entities in categories other than sub-stance, Aristotle also holds that individual properties are inseparablefrom that in which they are present;2 he asserts that the active intel-lect is separate from the body;3 he describes mathematicians as sepa-

1 See, for example, Hoffman and Rosenkrantz 1991, Lowe 2005, Gorman2006 and Schnieder 2006. For discussion, see Koslicki forthcoming .2 For discussion, see Corkum 2009.3 For discussion, see Corkum 2010.



SUBSTANCE AND INDEPENDENCE IN ARISTOTLE 37

rating mathematical objects in thought,4 and he criticises the Pla-tonists for wrongly separating the Forms.

I will not discuss in this chapter the full variety of applications of thenotion of ontological dependence in Aristotle. Instead, I will be pri-marily concerned with its role as a characteristic mark of individualsubstances. Independence is but one of several such marks. For ex-ample, an individual substance is demonstrable and indefinable, lacksa contrary, does not admit of degree and persists through qualitativechanges. But I will not discuss in detail these other features of sub-stance here. Rather, my main concern will be the narrow intersection

of Aristotle’s notions of substance and ontological dependence. I willcanvass a few contemporary formulations of ontological dependenceand discuss some of the interpretative difficulties in ascribing any ofthese formulations to Aristotle’s characterization of individual sub-stances as ontologically independent. My aim is not to resolve fullythese difficulties but to locate the topics of substance and independ-ence relative to certain other controversies in Aristotle studies. How-ever, I will sketch a position. In particular, elsewhere I have speculat-

ed that Aristotle is both a primitivist and a pluralist with respect toontological dependence,5 and I will develop this line of interpretationa bit further later in the chapter.

1. Individual Substance Primacy

Aristotle’s concern in the Categories is, in part, to provide a linguisticclassification. He distinguishes between two kinds of relations thatmay obtain between a predicate and a subject: cases such as where

‘coloured’ is predicated of a subject and cases such as where ‘human’is predicated of a subject. However, Aristotle also reads off this lin-guistic classification an ontology. Distinctively —compared to, say,Quine’s characterization of ontological commitment as the value ofthe variables in a language indispensable for science —not only doesthe choice of subjects and predicates commit us to correspondingentities but the predicative relations among terms commits us to astructured ontology. He distinguishes among, on the one hand, sub-

stances such as Callias or Socrates and, on the other, entities in vari- 4 For discussion, see Corkum forthcoming a.5 Corkum 2008, 82.



40 CORKUM

substances are. And so any interpretation will be judged in part by thelight shed on these surprising views.

In this section, I will defend the claim that individual substances arethe ground of Aristotle’s ontology. That is to say, I will argue thatindividual substances are ontologically independent from both non-substances and universal substances but that neither non-substancesnor universal substances are ontologically independent from individ-ual substances. I will begin by showing that some of Aristotle ’s sepa-ration terminology refers to some notion of ontological independ-ence. This largely rehearses arguments from Gail Fine (1984). I will

then argue that there is an asymmetry between individual substancesand other kinds of entities with respect to separation: substances areseparate from both non-substances and universal substances but nei-ther non-substances nor universal substances are inseparable fromsubstances. Taken together, these claims show that substances areontologically independent from non-substances but non-substancesare ontologically dependent on substances. I have discussed theseclaims in detail in Corkum 2008 and will be brief here.10

Aristotle does not define separation. But G. Fine persuasively arguesthat he associates separation and the notion of natural priority. Forthere’s evidence that, for Aristotle, the claims that one thing is sepa-rate from another and the second is not separate from the first arejointly sufficient for the claim that the first is naturally prior to thesecond. One passage which G. Fine (1984, 34) offers in support ofthis sufficiency thesis is EE 1.8 (1217b10 –15):

[The Platonists claim that the Idea of the good] is the originalgood, for the destruction of that which is participated in involves also the destruction of that which participates in theIdea, and is named from its participation in it. But this is the

10 The Greek chôris and its cognates in Aristotle can refer to local separa-tion, defined at Phys . 226b21 –3, temporal separation, mentioned for exampleat Meta. 1016b2, and definitional separation, distinguished from simple sepa-ration at Meta. 1042a28 –31. I will assume that unqualified separation termi-

nology in Aristotle refers to the separation which Aristotle ascribes to individual substances. I will use such terms as ‘separate’ and ‘separable’ inter-changeably. For a discussion of the distinction between the state of separa-tion and the capacity of separability, see Corkum 2008, 30 n. 13.




relation of the first to the later, so that the Idea of good is thegood per se; for this is also (they say) separable from what par-

ticipates in it, like all other Ideas.11 The passage is ascribing to the Platonists the following argument: if athing is separate from what participates in it, and what participatescannot be without that in which it participates, then it is prior tothem.12

The relevant notion of priority is substantial or natural priority, whichis characterized at Meta. 5.11 (1019a1 –4): ‘Some things then are called

prior and posterior … in respect of nature and substance, such as( hosa ) those which can be without ( einai endechetai aneu ) other things, while the others cannot be without them.’13 I have flagged the Greekexpressions being translated as ‘such as’ and ‘can be without’ and I will return to the question how we ought to take these expressions.1019a1 –4 is typically taken to be a definition of natural priority, withtwo components:

A is naturally prior to B just in case both of the following condi-

tions hold: (i) A can be without B and (ii) B cannot be without A.

Here and in what follows, I use the letters ‘A’, ‘B’ and so on as vari a-ble ranging over Aristotelian entities: substances, non-substances,individuals and universals. Natural priority, on this reading, is thusdefined as an asymmetric relation involving notions of ontologicaldependence and independence. In the following sections of the chap-ter, will I consider several interpretations of this notion of ontologi-

cal dependence in Aristotle. And I will consider whether 1019a1 –4 is

11 Translations based on Barnes 1984 except as noted.12 Other evidence of the relation holding between separation and priorityinclude Meta . 1028a31 –b2, 1038b29 and 1218a1 –9.13 This notion of natural priority needs to be distinguished from variousother senses of priority, such as temporal priority, local priority, definitional

priority, priority with respect to motion, priority with respect to power, pri-ority in order and so on. Aristotle discusses these at Cat. 12 and Meta. 5. 11.For a discussion of these various senses of priority, see Cleary 1988. I dis-cuss definitional priority further below.



42 CORKUM

best thought of as a definition. First, though, I will argue for a condi-tion of adequacy for any interpretation.

Aristotle holds that substances, alone of the categories, are separate.14 Moreover, Aristotle holds that substances are prior to non-substances. Consider Meta . 12.1 (1069a20): ‘substance is first, and issucceeded by quality, and then by quantity.’ See also Meta . 12.6(1071b5): ‘substances are the first of existing things.’ This, along withthe relation holding between separation and priority, suggests thatnon-substances are inseparable from substances, independently ofthe interpretation of separation terminology as expressing ontologi-

cal independence. But when combined with the evidence canvassedabove for thinking that separation terminology refers to ontologicalindependence, these passages give us good reason to ascribe to Aris-totle that view that non-substances are ontologically dependent onsubstances and that substances are ontologically independent fromnon-substances.

Moreover, Aristotle clearly holds in the Categories that individual sub-stances are prior to, and so separate from, universal substances. Heexplicitly calls individual substances primary with respect to universalsubstances and universal substances secondary with respect to individual substances. See, for example, Cat . 5 (2a11 –19):

A substance that which is called a substance most strictly,primarily, and most of all is that which is neither said of asubject nor in a subject, e.g. the individual man or the individu-al horse. The species in which the things primarily called sub-

stances are, are called secondary substances, as also are thegenera of these species. For example, the individual man be-longs in a species, man, and animal is a genus of the species;so these both man and animal are called secondary sub-stances.15

Finally, Aristotle claims at 2a34 –b7 that the ontological status of allother kinds of entities is somehow dependent on primary substances:

14 See Phys . 185a31 –2, Meta . 1029a27 –8.15 Cf. Cat . 2b4, 3a17, 3b11, 8a15.




All the other things are either said of the primary [i.e., individ-ual] substances as subjects or present in them as subjects....

[C]olor is present in body and therefore also present in an in-dividual body; for were it not present in some individual bodyit would not be present in body at all.... So if the primary sub-stances did not exist it would be impossible for any of the oth-er things to exist ( adunaton tôn allôn ti einai ).

I have followed the Ackrill (1963) translation in taking the Greek einai existentially. I will discuss below whether this is the right interpreta-tion for the relevant ontological dependency relations. Putting these

claims together, Aristotle holdsPRIMACY

Individual substances are ontologically independent from both non-substances and universal substances, and both non-substances anduniversal substances are ontologically dependent on individual sub-stances.16

It is not uncontroversial whether Aristotle consistently endorses

PRIMACY . I will flag some of the reasons for this controversy below.But if we can ascribe the thesis to Aristotle, then PRIMACY provides acondition of adequacy for any interpretation of ontological depend-ence in Aristotle.

2. Boundaries

I will next discuss several interpretations of ontological dependencein Aristotle. Donald Morrison (1985a and 1985b) claims that one

thing is separate from another in Aristotle only if they are numerical-ly distinct. However, Morrison seems to take the notion of separationto be not numerical distinctness but the relation obtaining betweennumerically distinct substances. Morrison takes one thing to be sepa-rate from another if the first is outside the ‘ontological boundaries’ of the second. Thus Morrison advocates what we might label as:

BOUNDARY

A is ontologically independent from B’s just in case A is outside theontological boundaries of the B’s.

16 PRIMACY is what I called the ‘Asymmetry Thesis’ in Corkum 2008.



44 CORKUM

In BOUNDARY , and in the other proposals I will consider below, Itake ‘ A’, ‘B’ and so on as dummy letters for which can be substituted

terms expressing entities such as ‘Callias’, ‘human’, ‘colour’, as well asmeta-ontological expressions as ‘an individual substance’, ‘universal’and ‘non-substance’. Morrison holds that being outside the ontologi-cal boundaries of a thing is equivalent to being numerically distinctfrom it, in his targeted, special sense of being numerically distinct.Morrison gives an example of a man inside the trunk of a hollow oaktree. Although the man is inside the tree, he is not inside the ontolog-ical boundaries of the tree, which excludes the hollow space which

the man inhabits. Morrison (1985a, 140) claims that there are tworeasons why the man and the oak are outside of each other’s ontolog-ical boundaries. He writes that

[t]he reason the man and the oak are ontologically distinct isprimarily, on Aristotle’s view, that they lack unity of motion inplace and time. They lack unity of motion because the oak isstationary whereas the man can leave: he can climb out, walkaround, and so on…. The man and the oak … not only lack

unity of motion. They also lack specific unity, since the man isan organized whole different in kind from the organized wholethat is the oak. The parts of the man are governed by oneprinciple of organization, his soul, and the parts of the oak aregoverned by another principle of organization, its soul. How-ever, their lack of specific unity is not the cause of their onto-logical distinctness. A tiny young oak, potted and set inside thehollow old one, would still be numerically distinct…. What

counts is that the souls are different souls, not that they aredifferent in kind.

So there are two reasons why the man and the oak are outside ofeach other’s ontological boundaries: they lack unity of motion andthey have numerically distinct souls. Morrison elaborates on his no-tion of ontological boundaries by providing a certain metaphysicalpicture. A thing, in Aristotle’s world, is a cluster of non-substancesinhering in an individual substance. Morrison (1985a, 141) writes:

Aristotle’s metaphysics is a conception of the world as orga-nized into clusters, where the principle of clustering is one ofpriority relations, and at the core of each cluster is ousia . My




soul is prior to my body and all of its parts, and your soul isprior to your body and all of its parts. My soul is not prior in

the same ways to any of the parts of your body; therefore theparts of your body are outside of the ‘sphere of influence’ ofmy soul, and hence they are outside the boundaries of my sub-stance, and hence they are separate from me…. [O]ne canthink of priority-relations as the metaphysical glue whoseholding-power gives structure to the universe. To be separatefrom something is to be not attached to it with this sort ofglue; to be ‘in’ something and not separate is precisely to be at-

tached to it in this way. There’s much in Morrison’s cluster picture with which one mightagree. In particular, one might endorse the suggestion that thesethings are grouped together by certain priority relations. The clusterincludes not only body parts of the individual substance but also the various non-substances inhering in the individual substance. Thesenon-substances are thereby posterior to that individual substance; andthe individual substance is thereby prior to the accidents. Of course,

this is just to say that the individual substance is separate from itsinherent attributes and the attributes are inseparable from it.

But regardless, the picture fails to support Morrison’s claims for sev-eral reasons. First, the picture does little to explain the notion of onto-logical boundaries. Second, the picture fails to establish that numeri-cal distinctness is equivalent to some criterion of being within certainboundaries. And finally, were the notion of being within certainboundaries equivalent to numerical distinctness, then the interpreta-

tion would fail to meet PRIMACY . Morrison is committed to the claimthat substances are separate only from other substances. And so he views the separation ascribed to substances as a symmetrical relation.If substances are separate from non-substances, and separation isnumerical distinctness, then non-substances must be separate fromsubstances. So the view is committed to denying either that substanc-es alone of the categories are separate or that it’s not non-substances,from which substances are separate, but only other substances. Mor-

rison takes the second option. As we’ve seen, there’s explicit textualevidence against the first option. The burden on this view is to ex-plain the apparent relation between separation and priority drawn in



46 CORKUM

such passages as 1217b10 –15, discussed above. That is to say, theclaim that separation is numerical distinctness fails to meet our condi-

tion of adequacy on any interpretation of separation in Aristotle,PRIMACY .

3. Existence

Until recently, a standard formulation of ontological dependence wasexpressed in terms of existence conditions. Peter Simons (1987), forexample, holds that something is ‘ontologically dependent on some-thing else when the first cannot exist unless the second exists.’ One way of fleshing out this proposal is as follows:

One entity ontologically depends on a second entity just incase necessarily, if the former exists, then the latter exists.

A standard interpretation of ontological independence in Aristotlefollows the general lead of this formulation. G. Fine (1984), for ex-ample, advocates:

EXISTENTIAL A is ontologically independent from B’s just in case A can exist withoutthe B’s.

Recall that in passages such as 1019a1 –4 Aristotle claims that what isprior can be without ( einai endechetai aneu ) what is posterior. EXISTEN-

TIAL takes the Greek einai in such passages existentially and the endechetai modally. As we will see, this is not the only way to read theGreek but, so read, ontological independence is taken to be a capacity

for realizing a certain condition of existence. The claim that A can exist without Bs is ambiguous between twoclaims. Under one disambiguation, the claim is that, for any givenmember of the class of B things, A can exist without that B. Thisclaim is consistent with holding that A cannot exist without some B or other. Under the other disambiguation, the claim is that, for theclass of B’s, A can exist without any member of that class whatsoev-er.17 Let’s use the following acronyms:

17 For a similar distinction, see Simons 1987 and Correia 2008, 1015.




EXISTENTIAL1

A is ontologically independent from B’s just in case, f or any given B, A can

exist without that B.EXISTENTIAL2 A is ontologically independent from B’s just in case A can exist withoutany B whatsoever.

I will say that EXISTENTIAL1 or EXISTENTIAL2 is exhibited by As withrespect to Bs. Now, do either of EXISTENTIAL1 or EXISTENTIAL2 meetthe demands imposed by our condition of adequacy, PRIMACY ? That

is to say, are either of EXISTENTIAL1 or EXISTENTIAL2 exhibited bysubstances with respect to non-substances and not exhibited by non-substances with respect to substances?

Individual substances exhibit the kind of independence expressed byEXISTENTIAL1 with respect to some non-substances: Callias need notbe generous. So the individual substance Callias can exist without thenon-substance quality generosity. But there are problems for viewingthe relevant notion of ontological independence as EXISTENTIAL1.

First, individual substances do not possess this capacity with respectto all kinds of non-substances. Consider propria , necessary but ines-sential properties. An individual substance cannot exist without its propria . A traditional example not Aristotle’s of a proprium for hu-mans is risibility. If risibility is indeed a proprium for humans, thenCallias cannot exist without risibility. Consider also non-substantialuniversals such as colour. It seems entirely plausible that substancescannot exist apart such general properties: Callias cannot exist colour-

less. There is thus a need to restrict that from which substances areontologically independent, if we are to view ontological independ-ence as EXISTENTIAL1. Under this view, individual substances are notontologically independent from non-substances generally, but onlyfrom accidents. Were ontological independence EXISTENTIAL1, then we would need to weaken PRIMACY to the claim that substances areontologically independent from some non-substances. Moreover, alt-hough individual substances exhibit EXISTENTIAL1 with respect tosome non-substances, non-substances also exhibit EXISTENTIAL1 with respect to some substances. In particular, non-substantial universals also uncontroversially possess this kind of independence fromindividual substances: although Callias can exist without being gener-



48 CORKUM

ous, there can be generosity without Callias. So EXISTENTIAL1 is in-adequate to PRIMACY .18

I turn to EXISTENTIAL2, under which the claim that A can exist without B is the claim that A can exist without any B whatsoever.One might hold that non-substantial universals lack this kind of in-dependence from individual substances. For non-substantial univer-sals cannot exist without any individual substance whatsoever: if noone were generous, generosity (as Aristotle might put it, on this read-ing) would not exist. However, individual substances also lack thiskind of independence from non-substances. An individual substance

such as Callias cannot exist denuded of all attributes whatsoever. Ifthis is what is meant by ontological independence, then it is simplyfalse that substances are ontologically independent. So EXISTENTIAL2 is also inadequate to PRIMACY . This then cannot be the relevant no-tion of ontological independence either. On the assumption that EX-ISTENTIAL1 and EXISTENTIAL2 exhaust the disambiguations of EXIS-

TENTIAL, I conclude that EXISTENTIAL ought not to be ascribed to Aristotle.

4. Essence

Kit Fine has influentially argued for an account of ontological de-pendence in terms of essence, identity and definition. An essence, asdetailed in K. Fine 1994 is not a merely necessary attribute but a col-lection of propositions true in virtue of that entity’s identity. An es-sence is expressed by a real definition. Unlike a nominal definition, which states what a competent speaker of the language understands,

a real definition states what the defined object is. These considera-tions suggest the following formulations:

One entity ontologically depends on a second entity just incase the latter is a constituent in the former’s essence.

One entity ontologically depends on a second entity just incase the latter is a constituent in a proposition that expresses areal definition of the former.

18 For a similar argument against existential formulations of ontologicaldependence, see K. Fine 1995a.




The leading idea of these formulations is that ontological depend-ence is a narrower relation than an incapacity for separate existence.

Attributes do not depend on substances merely since they cannotexist apart from some substance or other. Rather, a specification of what it is to be a certain attribute makes reference to substances. Toillustrate, a specific colour might be defined as a certain reflexiveproperty of the surface of corporeal substances. The definition ofthe colour thereby would make reference to substance. Corporealsubstances are necessarily coloured. But the definition of any sub-stance could be given without any reference to colours.

Recently, Michail Peramatzis has ascribed to Aristotle an essentialistaccount of ontological priority inspired by K. Fine. Recall that Aris-totle takes one entity to be ontologically prior on another if the first‘cannot be ( einai ) without’ the other. G. Fine, we have seen, takes einai existentially. By contrast, Peramatzis takes einai in the ‘can be without’formulation not existentially but essentially. That is, he reads priorityin nature and substance as entailing that just one relata can be what itis without the other. So Peramatzis (2008, 189) offers the following

interpretation of ontological priority: A is ontologically prior to B iff A can be what it is inde-pendently of B being what it is, while the converse is not thecase.

Peramatzis cashes out independence in a thing’s essence by appeal tonon-reciprocal reference in a definition or account of what that thingis. This suggests the following account of ontological independence:

ESSENTIAL A is ontologically independent from the B’s just in case an account of what A is does not make reference to an account of what the B’s are.

Notice, ESSENTIAL is ambiguous in the same way that ESSENTIAL isambiguous. That is to say the claim that A can be what it is inde-pendently of B’s is ambiguous between

ESSENTIAL1

A is ontologically independent from the B’s just in case, for any given B,an account of what A is does not make reference to an account of what that B is.



50 CORKUM

ESSENTIAL2 A is ontologically independent from the B’s just in case an account of

what A is does not make reference to an account of any B whatsoev-er.

For reasons similar to those rehearsed in the above discussion of EX-ISTENTIAL, ESSENTIAL2 is the preferable formulation for the claimthat substances are ontologically independent of non-substances. Although an account of my essence can be formulated without refer-ence to the non-substances which inhere in me, the circumstances in which I can be human are those in which I have, for example, some

colour or other, and where I am risible. So I doubt that non-reciprocal reference, in an account of what the dependent item is,involves a capacity.

ESSENTIAL2 is a promising interpretative suggestion. For Aristotle, anessence is an attribute which belongs to a thing in virtue of that thingitself.19 Like K. Fine, Aristotle holds that an essence is not equivalentto a necessary property: as we have seen, Aristotle holds that thereare necessary but inessential properties. These propria of a thing arefor Aristotle coextensive with an essential property but do not tell us what it is to be that thing: for example, the set of humans and the setof objects capable of learning grammar are, in Aristotle’s opinion,the same, but a capacity for learning grammar is not what it is to behuman. So there are these similarities.

Aristotle’s discussion of multivocality, moreover, also suggests a pic-ture similar to ESSENTIAL2. For example, at Meta . 4.2 (1003a33 –b10)

Aristotle writes: There are many senses in which a thing may be said to ‘be’, butthey are related to one central point, one definite kind ofthing, and are not said to ‘be’ by a mere ambiguity. Everything which is healthy is related to health, one thing in the sense thatit preserves health, another in the sense that it produces it, an-other in the sense that it is a symptom of health, another be-cause it is capable of it.... So, too, there are many senses in

which a thing is said to be, but all refer to one starting-point;some things are said to be because they are substances, others

19 See, for example, Top. 1.5, Meta . 7.4.




because they are affections of substance, others because theyare a process towards substance, or destructions or privations

or qualities of substance, or productive or generative of sub-stance, or of things which are relative to substance, or nega-tions of one of these things or of substance itself.

Here the ontological primacy of substances is described as a system-atic ambiguity in the expression ‘to be’. Again, Aristotle assumes thatour linguistic practices reflect ontology. In his example, a diet orcomplexion is called healthy because of a relation to the health of ananimal: a healthy diet promotes an animal’s health; and a healthy

complexion indicates an animal’s health. So it seems that the relationbetween a dependent entity and the entity on which it depends is atleast in part cashed out in this way: an account of what it is to be thedependent entity makes reference to the entity on which it depends,but not vice versa . ESSENTIAL2, then, arguably expresses the depend-ence in Aristotle of non-substances on substances.

There are reasons to doubt the ascription of any version of ESSEN- TIAL to Aristotle, however. One concern is philological. Peramatzis’ssuggestion that einai at 1019a3 should be read as ‘what it is to be’should be controversial. Aristotle has available to him expressionssuch as ti estin and to tou ên einai to express essence, and it would bepeculiar if, in a definition of ontological priority, Aristotle did notemploy this technical vocabulary, were ESSENTIAL his intention. Forthis reason, I doubt that ESSENTIAL is Aristotle’s general formulationof ontological independence.

A second concern: Aristotle distinguishes ontological priority fromepistemic and definitional priority, characterizing the latter at Meta .5.11 (1018b30 –37). On a natural reading of this distinction, ontologi-cal priorities are disjoint from definitional priorities. So ESSENTIAL arguably conflates ontological and definitional priority. Peramatzis(2011, 268) appears to hold that definitional priorities range overboth real and nominal definitions, where ontological priorities arecoextensive with real definitional priorities. I discuss Peramatzis’s ar-gument in detail in Corkum forthcoming c.

A final worry. Although the formulation may express the dependencein Aristotle of non-substances on substances, it is less clear that the



52 CORKUM

dependence of universal substances on individual substances is cap-tured by ESSENTIAL. In the Categories , Aristotle holds that items in the

category of substance such as a genus are ontologically dependent onthose individual substances which are members of that genus. How-ever, suppose that one entity ontologically depends on a second entityjust in case the latter is a constituent in a proposition that expresses areal definition of the former. Then an individual substance, if defina-ble, depends on the constituents of its definition: its species, genusand differentia. So the ontological primacy of individual substancesmay be violated by a definitional or essentialist construal of ontologi-

cal dependence. As such, ESSENTIAL is inconsistent with PRIORITY .20

Some scholars hold that Aristotle indeed rejects the primacy of theindividual substance, a central thesis of the Categories , and insteadidentifies a universal essence or form with substance in the later work, the Metaphysics . The argument for this position is that Aristotleidentifies essence and form with universals, and substance with es-sence and form. Aristotle occasionally identifies an essence with thecategory of substance. For example, he uses the Greek expressions

translated as ‘essence’ and ‘substance’ interchangeably in Topics 1.9.However, he also identifies an essence with a universal substance, andeither a species or genus. At Topics 1.9, he gives the example that‘man’ or ‘animal’ expresses the essence of an individual man. There isalso a sense of ‘essence’ according to which a term referring to anon-substantial species or genus expresses the essence of a non-substantial individual: also at Topics 1.9, Aristotle gives the examplethat ‘white’ or ‘colour’ expresses the essence of a non-substantial in-

dividual white. This suggests that Aristotle identifies essential and saidof predications. Further support for the identification of an essence with a universal can be found in Aristotle’s epistemological com-ments. He occasionally states that an individual is indefinable andonly a universal can be defined: see, for example, Meta . 7.10 (1036a5 –9). As we have seen, he holds that a definition expresses an essence.Moreover, Aristotle occasionally states that universals alone are theobjects of knowledge: see, for example, Meta . 3.6 (1003a14 –15). He

20 Peramatzis (2011, §11) restricts PRIMACY : non-substances are ontologi-cally dependent on individual substances but universal substances are inde-pendent from individual substances.




GROUNDING2 A is ontologically independent from B’s just in case A admits of its onto-

logical status without reference to any B whatsoever.GROUNDING1 is consistent with the claim that the admission of theontological status of A must refer to some B or other; GROUNDING2 is inconsistent with this claim. Now: are either of GROUNDING1 orGROUNDING2 plausible candidates for an account of ontological in-dependence? Do either meet the demands imposed by our conditionof adequacy, PRIMACY ? I have discussed these issues at length inCorkum 2008 and, again, will be brief here. Individual substances

exhibit GROUNDING1: Callias would have his ontological status as abeing even were he not generous. However, a non-substantial univer-sal does not generally depend on any individual substance for its sta-tus as a being. Generosity would be, for Aristotle, a being no less thanCallias even if he were not generous. Non-substantial universals ex-hibit GROUNDING1 and so the thesis fails to meet the demands im-posed by PRIMACY .

What then of GROUNDING2? Substances do not depend on non-substances for their ontological status as beings. Individual substanc-es are classified as beings independently of standing in any tie to any-thing else independently, that is to say, of being present in or said of any other beings. Universal substances, on the other hand, have theirontological status as beings in virtue of standing in ties to otherthings but only in virtue of being said of individual substances;they do not depend for their ontological status on non-substancesbut they do depend on individual substances. Moreover, a substancedoesn’t depend even on properties from which it cannot exist apart.Consider again propria . Although these properties are necessary, asubstance is not a being in virtue of standing in some tie to its propria .So although, for example, Callias cannot exist without risibility, Calli-as’s claim to having the ontological status of a being does not dependon his being risible. Similar comments could be made for such gen-eral properties as being coloured . So individual substances exhibitGROUNDING2.

What of non-substances and universal substances? Non-substantialuniversals fail to exhibit GROUNDING2; although generosity, for ex-ample, does not depend on Callias, the property would not have the



56 CORKUM

ontological status it enjoys were there no generous people whatsoev-er. Similar comments could be made for universal substances. And

non-substantial individuals also fail to exhibit GROUNDING2. As Imentioned earlier, it is controversial whether these are found in atmost one subject. Let’s call non-substantial individuals recurrent ifthey are found in more than one subject, and non-recurrent otherwise. If they are non-recurrent, then they do depend on the specificindividual substance in which they uniquely inhere. But this, ofcourse, is consistent with a failure to exhibit GROUNDING2. For Calli-as’s generosity, if non-recurrent, admits of its ontological status in

virtue of standing in a tie to some substance or other —namely, Calli-as. And if non-substantial individuals are recurrent, found in morethan one subject, then they admit of their ontological status in virtueof standing in a tie to some substance or other —namely, those sub-jects which share the non-substantial individual. So, to sum up, sub-stances exhibit GROUNDING2 with respect to non-substances andnon-substances fail to exhibit GROUNDING2 with respect to sub-stances. GROUNDING2 conforms to PRIMACY .

I have left unspecified in GROUNDING what constitutes the admis-sion of an ontological status. In response to the similar formulationin Corkum 2008, some scholars have understandably questioned howI intend to develop this notion.22 A plausible requirement is that theadmission ought to be explanatory . The item on which a second de-pends will be a constituent in a proposition specifying that in virtue ofwhich the first has a certain ontological status. I appealed to this ter-minology in my original discussion of ontological dependence in

Corkum 2008, 77, and again in the discussion of GROUNDING above. Much will depend, for the success of this proposal as an in-terpretation of Aristotle, on how we take explanation. Aristotle him-self typically views the explanation of an item as appealing to itemsof higher generality. So the explanation of the species humanity ap-peals to the genus, animal, under which it falls. Such top-down expla-nations are perspicuously represented by demonstrations, the subjectmatter of the Posterior Analytics . This narrower view of explanation isperhaps part of what is driving ESSENTIAL. The interpretative narra-tive here may be that Aristotle comes to reject PRIMACY when he

22 See Peramatzis 2011, 243n11 and Koslicki 2012.



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many take the grounding relation to be irreflexive, asymmetric, transi-tive and hyperintensional.24 I have focused on two of these features

in Aristotle’s discussion of ontological dependence. The upshot ofthe rejection of EXISTENTIAL is that ontological dependence is hy-perintensional —at very least for the Categories ontology. And PRIMA-CY asserts the asymmetry of ontological dependence, again at least when the relata are items from the ontology of the Categories . Indeed,I find this a preferable reading of 1019a1 –4. An assumption com-monly held in the secondary literatures is that Aristotle aims to defineontological priority at 1019a1 –4. Recall, this passage is: ‘some things

then are called prior and posterior … in respect of nature and sub-stance, such as ( hosa ) those which can be without other things, whilethe others cannot be without them.’ There is little reason, however, totake the passage as offering a definiens for natural priority. The Greek( hosa ), translated as ‘such as’, is often used by Aristotle to introducean example or amplification. So the passage gives every appearanceof being a clarification or illustration. If this is correct, then Aristotleis not defining natural priority but simply characterizing it as an asym-metrical relation.

An irreflexive, asymmetric, transitive relation is a strict partial order.So the grounding relation imposes considerable structure on thespace of facts. If ontological dependence in Aristotle is also a strictpartial order, then the notion imposes considerable structure on theontology of the Categories . Notice, however, that these formal charac-teristics fail to uniquely define ontological dependence. As such, not-ing that ontological dependence has certain features underdetermines

any single full account of the relation. And indeed, there may not bea unitary account of ontological dependence beyond these formalcharacteristics shared among several distinct relations. Aristotle may well be a pluralist with respect to ontological dependence. For exam-ple, there may be distinct kinds of ontological dependence corre-sponding to different ontological statuses that, in Aristotle’s view, anitem may have. For Aristotle’s distinction between being said of asubject and being present in a subject gives the appearance of corre-

24 See for example Schaffer 2010, Trogdon 2012 and Audi 2012. Some ofthese characteristics are controversial. For example, Lowe (1998, 145) and Jenkins (forthcoming) question whether grounding is irreflexive.




sponding to different kinds of ontological dependence. The infra-categorical said of tie obtaining between an individual and a universal,

and the cross-categorical present in tie obtaining between a substanceand a non-substance, may both be relations of ontological depend-ence. For one thing, they may both be asymmetric and hyperinten-sional relations. Yet they may nonetheless be distinct and irreduciblerelations of ontological dependence. I sketch one line of fleshing outthis interpretation below.

6. Case Studies

In this section, I will discuss two case studies. One is a case of onto-logical dependence. Recall, it is uncontroversial that, in the Categories , Aristotle holds that universals are ontologically dependent on individuals. The other is a case of ontological independence. It is uncon-troversial that, in the Metaphysics , Aristotle holds that forms are onto-logically independent from matter and from the hylomorphic com-pound of form and matter. A central interpretative controversy in Aristotle studies is how to reconcile these two views.

I raised above the worry that ESSENTIAL does not capture the de-pendence of universal substances on individuals. GROUNDING holdspromise for capturing this dependency. Elsewhere I have canvassedthe suggestion that universals are mereological sums of individuals.25 Let me here briefly rehearse this issue. Aristotle often associates individuals and universals with combinatorial notions. For example, atCat . 5 (3b10 –18), Aristotle characterizes individuals as indivisible ( taatoma ). Moreover, Aristotle uses mereological terminology in certain

technical contexts. For example, he provides a semantics for universalcategorical propositions in the Prior Analytics 1.1 (24b26 –28):

‘One thing is wholly in another’ is the same ( tauton ) as ‘onething is predicated universally of another’.

25 See Corkum forthcoming b. There, however, I do not identify universals with mereological sums of individuals. Rather, I argue for the weaker claimthat the conditions under which a universal predication expresses a true

thought are given in terms of mereological sums of individuals. The associa-tion of universals with sums is a traditional line of interpretation that is cur-rently understudied. The starting point for the interpretation in recent schol-arship is Mignucci 1996.



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The difficulty of interpretation here is partly that Aristotle is employ-ing mereological notions which are foreign to us. Among various

senses of ‘whole’, Aristotle distinguishes at Meta. 5.26 (1023b26 –33)between what became known as quantitative wholes and integral wholes.

We call a whole … that which so contains the things it con-tains that they form a certain unity; and this in two sens-es either as each part being one, or as a unity made up out ofthe parts. For what is universal and what is said wholly, since itis a certain whole, is universal in the sense that it containsmany things by being predicated of each and by being all thoseand each of them one, as for instance man, horse, god are onebecause they are all living things. But the continuous and lim-ited is also a whole, whenever there is a certain unity from themany.

Aristotle draws the contrast between quantitative and integral wholesby appealing to two distinct kinds of constitution relations. A quanti-

tative whole is homoiomerous: the sum of animals, for example, iscomposed of parts each of which is itself an animal. An integral whole, by contrast, is heteromerous. A house, for example, is not aquantitative whole: it’s parts the roof or the door, say are notthemselves houses; and not all of what can be said of a house thatit’s final cause is to provide shelter, say can be said of the parts of ahouse.

If this is the relevant sense of division, then the claim that individuals

are indivisible is the claim that individuals cannot be divided into dis-tinct entities which are homoiomerous parts of that individual, andso that of which the individual is said. Genera, by contrast, are saidof species and species are said of individuals. So Aristotle holds thata genus can be correlated to a collection of the various species fallingunder that genus. A species likewise can be split into subspecies andso on. But individuals provide the limit case, as items which cannotbe further divided into parts of the same kind. Aristotle is not as ex-

plicit on the mereological relation holding between universals andindividuals as we might hope: in his example in 1023b26 –33, above,he only claims that a genus is associated with a whole of which spe-



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weakly supplementary relation is also antisymmetric.) And so the tiesamong individuals and universals impose the kind of structure on the

world which we would expect from a relation of ontological depend-ence. Indeed, the above considerations suggest that the relation ob-taining between universals and individuals is a distinctive relation ofontological dependency: namely, constitution.

Obviously, on this interpretation, Aristotle’s universals are quite dif-ferent from the universals envisaged by contemporary metaphysi-cians. For one thing, such universals are not wholly present in eachinstance. Moreover, as an interpretation of Aristotle, the identifica-

tion of universals with sums of individuals would be highly controversial. But I will leave discussion for another occasion. For my pre-sent purposes, to indicate just one way in which universal substancesmight depend on individuals for their ontological status as universals,the preceding sketch suffices.

I turn to the second of the two case studies which I will sketch here. This case will also allow me to return to the extension question. Re-call, I noted at the beginning of the chapter that Aristotle does notshare all of the intuitions of many contemporary metaphysicians on what the substances are. For example, ordinary objects such as par-ticular men and horses are compounds of form and matter. Perhapssurprisingly to the contemporary reader, Aristotle denies that suchobjects are substances. Rather, he identifies substance with the com-pound’s form and denies that matter or the compound of form andmatter is substance.

Aristotle holds that ordinary mid-sized dry goods are hylomorphic compounds – that is to say, complexes of form and matter. In thePhysics , he requires a material constituent for such things so to explaincertain kinds of changes. The matter of a compound is a substratumpersisting through the substantial changes of such compounds – theircoming into, or passing out of, existence: see for example, Phys . 2.3(194b24). Recall that being the substratum of change is a mark ofsubstance in the Categories . Aristotle arguably retains the view of mat-ter as the substratum of substantial change in the Metaphysics , but hethere denies that the matter is the substance of the compound for itlacks other marks of substance. In particular, matter is neither de-monstrable nor separate: see Meta . 7.3 (1029a28). Since the matter




persists through the destruction of the compound, its inseparabilitycannot be an incapacity to exist apart from either the compound or

its form. Aristotle also denies that the hylomorphic compound per se is a sub-stance, for such a complex is posterior to its constituents: see Meta .7.3 (1029a31). Instead, Aristotle identifies the substance of the thing with its form. As we can see, the independence criterion for sub-stances, expressed in the terminology of separation and priority, does work in the denials that matter or the compound of form and matterare substances: the hylomorphic compound cannot be substance for

it is posterior to its constituents; and matter cannot be substance forit is inseparable. I will next suggest that an interpretation of inde-pendence such as GROUNDING provides a pleasing explanation ofthis role.

First, notice that an account of a composite, as a composite, makesreference to its constituents. It is arguably for this reason that thehylomorphic compound is posterior to form and matter. Lackingindependence in the sense of some such criterion as GROUNDING

precludes the composite from being substance. The criterion alsomakes good sense of the primacy of form over matter. Aristotle dis-tinguishes between actuality and potentiality and, within actuality, be-tween first and second actuality: see De Anima 2.5 (417a21 –b2), forexample. The second actuality of a given substance is a set of activities which are characteristic of things of that kind. The first actuality of asubstance is a state or ability to perform such activities. Aristotleidentifies the form with the first actuality. The matter of the hylo-

morphic compound is a potential for a given first actuality or merecapacity to be in a certain state or possess a certain ability. As such, anaccount of what it is to be matter per se makes reference to the form. This dependency also is manifest in specific accounts of matter: forto be a specific kind of matter makes reference to a specific form. Anaccount of what it is to be flesh or bone, for example, makes refer-ence to what it is to be human. Flesh, as flesh, just is the capacity torealize an ability to engage in human activities. By contrast, although a

human is necessarily flesh and bone, an account of what it is to behuman does not make reference to flesh and bone.



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The question whether it is an essence, as in Meta . 7, or the individualsubstance, as in the Categories , which is ontologically basic, is mistaken.

It is both. The essence, on this interpretation, just is the concrete par-ticular —not considered as a compound of form and matter but inso-far as it is a realized state. I hope that this sketch, despite its brevity,has discharged an obligation I incurred earlier in the chapter: to pre-sent one line of interpretation of individual essences and so to illus-trate how GROUNDING, PRIMACY and the ontological independenceof form might be taken to be consistent.

7. ConclusionI have discussed a characteristic mark of individual substances in Ar-istotle, which I labelled PRIMACY : individual substances are ontologi-cally independent from non-substances and universal substances, while non-substances and universal substances are ontologically de-pendent on individual substances. I have canvassed some of the rea-sons to endorse the ascription of the thesis to Aristotle and somereasons to hesitate. I have also raised difficulties for interpreting PRI-

MACY by appeal to various recent views of ontological dependenceput forward by Simons, K. Fine and others in contemporary meta-physics. I have not aimed to resolve all of these interpretative difficul-ties. My aim, instead, has been to indicate a few of the relationsamong issues in Aristotle studies: for example, the topics of sub-stance and ontological dependence mesh with interpretative ques-tions concerning such other Aristotelian notions as form, essence anduniversality. However, I hope also to have brought out the fruitful

interaction possible between contemporary metaphysics and Aristotlestudies: contemporary metaphysics is an important tool, if appliedjudiciously, for historical research; and the study of Aristotle is a richsource of philosophical inspiration for the contemporary discussionof ontological dependence.26

References

Ackrill, J. L. 1963: Aristotle’s Categories and De Interpretatione: Translated

with Notes and Glossary . Oxford: Clarendon Press.26 Thanks to Alan Code, Miguel Hoeltje, Kathrin Koslicki, Jonathan Schaf-fer, Benjamin Schnieder, Alex Steinberg and an anonymous reader.




Albritton, R. 1957: ‘Forms of Particular Substances in Aristotle’sMetaphysics’. Journal of Philosophy 54, pp. 699 –708.

Audi, P. 2012: ‘A Clarification and Defense of the Notion ofGrounding’. In Correia and Schnieder 2012, pp. 101 –21.

Barnes, J. 1984: The Complete Works of Aristotle: The Revised OxfordTranslation . Princeton: Princeton University Press.

Chalmers, D., D. Manley and R. Wasserman (eds.) 2009: Metametaphys- ics , Oxford: Oxford University Press.

Cleary, J. 1988: Aristotle on the Many Senses of Priority . Carbondale:

Southern Illinois University Press.Corkum, P. 2008: ‘Aristotle on Ontological Dependence’. Phronesis 53,

pp. 65 –92.

— 2009: ‘Aristotle on Nonsubstantial Individuals’. Ancient Philosophy 29, pp. 289 –310.

— 2010: ‘Attention, Perception and Thought in Aristotle’. Dialogue 42,pp. 199 –222.

forthcoming a: ‘Aristotle on Mathematical Truth’. British Journal forthe History of Philosophy .

forthcoming b: ‘Aristotle on Predication’. European Journal of Phi- losophy .

forthcoming c: ‘Critical Notice of Michail Peramatzis, Priority in Aristotle’s Metaphysics, Oxford University Press, 2011’. Canadian Journal of Philosophy .

manuscript: ‘Aristotle on Logical Consequence’.Correia, F. 2008: ‘Ontological Dependence’. Philosophy Compass 3, pp.

1013 –32.

Feser, E. (ed.) forthcoming: Aristotle on Method and Metaphysics . Basing-stoke: Palgrave Macmillan.

Fine, G. 1984: ‘Separation’. Oxford Studies in Ancient Philosophy 2, pp.31 –88.

1985: ‘Separation: A Reply to Morrison’. Oxford Studies in AncientPhilosophy 3, pp. 159 –66.



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Fine, K. 1994: ‘Essence and Modality’. Philosophical Perspectives 8, pp.1 –16.

1995a: ‘Ontological Dependence’. Proceedings of the Aristotelian Socie- ty 95, pp. 269 –90

1995b: ‘Senses of Essence’. In Sinnott-Armstrong, Raffman and Asher 1995, pp. 53 –73.

2001: ‘The Question of Realism’. Philosopher’s Imprint 1, pp. 1 –30.

Frede, M. 1987: ‘Individuals in Aristotle’. In his Essays in Ancient Phi- losophy . Minneapolis: University of Minnesota Press, pp. 49 –71.

Gill, M. 2005: ‘Aristotle’s Metaphysics Reconsidered’. Journal of theHistory of Philosophy 43, pp. 223 –51.

Gorman, M. 2006: ‘Independence and Substance’. International Philo- sophical Quarterly 46, pp. 147 –59.

Hoffman, J. and G. Rosenkrantz 1991: ‘The Independence Criterionof Substance’. Philosophy and Phenomenological Research 51, pp. 835 –53.

Ignacio, A. and C. María (eds.) 1996: Studies on the history of logic . Pro-ceedings of the III. Symposium on the history of logic, Berlin: Walter de Gruyter.

Jenkins, C. forthcoming: ‘Is Metaphysical Dependence Irreflexive?’. Monist .

Lowe, E. J. 1998: The Possibility of Metaphysics . Oxford: ClarendonPress.

2005: ‘Ontological Dependence’. In Zalta, E. N. (ed.): The Stanford Encyclopedia of Philosophy , Summer 2005 ed. URL:http://plato.stanford.edu/archives/sum2005/entries/dependence-ontological/.

Koslicki, K. 2012: ‘Varieties of Ontological Dependence’. In Correiaand Schnieder 2012, pp. 186 –213.

forthcoming : ‘Substance, Independence and Unity’. In Feser

forthcoming.Mignucci, M. 1996 ‘Aristotle’s Theory of Predication’. Ignacio andMaría 1996.




Morrison, D. 1985a: ‘Separation in Aristotle’s Metaphysics’. OxfordStudies in Ancient Philosophy 3, pp. 125 –58.

1985b: ‘Separation: A Reply to Fine’. Oxford Studies in Ancient Phi- losophy 3, pp. 167 –74.

Peramatzis, M. 2008: ‘Aristotle’s Notion of Priority in Nature andSubstance,’ Oxford Studies in Ancient Philosophy 35, pp. 187 –247.

2011: Priority in Aristotle’s Metaphysics . Oxford: Oxford UniversityPress.

Schaffer, J. 2009: ‘On what grounds what’. In Chalmers, Manley and

Wasserman 2009.2010: ‘Monism: The Priority of the Whole’. Philosophical Review 119, pp. 31 –76.


Sellars, W. 1957: ‘Substance and Form in Aristotle’. Journal of Philoso- phy 54, pp. 688 –99.

Simons, P. 1987: Parts: A Study in Ontology . Oxford: Oxford UniversityPress.

Sinnott-Armstrong, W., D. Raffman and N. Asher (eds.) 1995: Modali- ty, Morality, and Belief: Essays in Honor of Ruth Barcan Marcus . New York: Cambridge University Press.

Trogdon, K. 2012: ‘An Introduction to Grounding’. In this volume.



An Introduction to Grounding

Kelly Trogdon

1. Introduction

Consider the fact that there was a global economic recession in 2008. A causal explanation of this fact specifies facts that were causally re-sponsible for the economic meltdown or facts on which the melt-down counterfactually depends, such as the occurrence of predatorylending, deregulation of financial institutions, weak underwritingpractices, and so on. It seems that a metaphysical explanation of thisfact, on the other hand, shows us why the global economic situationin 2008 counted as a recession in the first place. In this case, an ex-

planans is the fact that 2008 was marked by severe declines in con-sumption, investment, government spending, and export activity.

Suppose that you currently have a brain state that is an experience asof motion, and someone asks, ‘Why are you having that experiencerather than one of a different type?’ On the causal/counterfactualreading of the question, an appropriate response might be ‘A ravenjust flew by’. On the metaphysical reading, the questioner wants toknow what it is in virtue of which you’re having an experience as of

motion, and it would seem that the raven fact isn’t a candidate explanans in this case. According to non-reductive physicalism, in the actual world the mental properties are ultimately instantiated in virtue ofcertain physical properties (cf. Levine 2001, chapter 1 and Loewer2001). For the non-reductive physicalist a candidate (partial) explanans is, for example, the fact that there is recurrent activity of a certainsort between your V1 and MT/V5 neural structures.

One diagnosis of the contrast in the two cases above is this: in causal

explanations the explanans and explanandum are connected through acausal mechanism, while in metaphysical explanations they’re con-nected through a constitutive form of determination, that of ground-



INTRODUCTION TO GROUNDING 69

ing (cf. Fine 2012). There is a burgeoning literature on grounding. Theprimary goal of this chapter is to set out and clarify some of the cen-

tral issues and disputes concerning this notion. In the course of thechapter I’ll weigh in on certain positions, treat others as working as-sumptions, and remain neutral on others. In some cases philosopherseither explicitly endorse or reject the positions I discuss, while in oth-er cases the positions have yet to be discussed in any detail.

The plan for the chapter is as follows. I begin by distinguishing twogeneral approaches to grounding – on one our talk of grounding inphilosophy is univocal, and on the other it isn’t – and consider differ-

ent ways in which each view might be further developed (§2). Then Iconsider the logical form of grounding statements as well as thestructural principles that govern grounding (§3 –4). Next, I take upthe matter of how the notions of grounding, modality, and reductioninteract (§5 –6). I close with a brief discussion of the grounds for what grounds what (§7).

2. Is Grounding Talk Univocal?

Many philosophical theses in addition to non-reductive physicalismare naturally cast in terms of grounding vocabulary: maximalismabout truthmaking (for any true proposition, something metaphysicallyexplains why that proposition is true), priority pluralism (the existenceand nature of wholes are posterior to the existence and nature of theirconstituent mereological atoms), non-reductive naturalism aboutmoral properties (in the actual world moral properties are ultimatelyinstantiated in virtue of natural properties), and so on. A natural start-

ing point in thinking about grounding is this: is there a single de-pendence notion corresponding to the various grounding expressionsin theses like those listed above?

One view is that grounding is univocal in that there is but a single de-pendence notion in play here. This is the view recommended by thediagnosis of the contrast I began the chapter with. The contrastingclaim is that grounding is equivocal in that these theses traffic in multi-ple dependence notions marking different phenomena. In this sectionI consider different ways of developing each of these views along thefollowing dimensions of difference: (i) the possibility of analysis, (ii)the relation to ordinary, everyday thinking, (iii) the relation to notions



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we already accept in discussions of dependence in philosophy, and,(iv), assuming that grounding is equivocal in the sense specified

above, how our various grounding notions are related to one another.Let a notion be primitive just in case it can’t be analysed in terms ofother notions, quotidian just in case it figures in ordinary, everydaythinking, and orthodox just in case it already has currency in discus-sions of dependence in philosophy.

We begin with the view that grounding is univocal. Both Witmer et al(2005) and Rosen (2010) claim that grounding is both univocal andprimitive. Given their discussion of grounding claims from both

philosophical and ordinary discourse, Witmer et al think that ground-ing is quotidian, while Rosen is naturally read as claiming that it’snon-quotidian instead. Schaffer (2009) also agrees that grounding isboth univocal and primitive and can be interpreted as claiming thatgrounding is orthodox as well. In his view grounding has played animportant role in the history of philosophy and it traces all the wayback to Plato and Aristotle. Raven (forthcoming) agrees that ground-ing has a venerable historical pedigree and suggests that grounding,

like causation, is such that we have some ordinary understanding ofit. So on Raven’s view grounding is orthodox and (somewhat) quotid-ian.

Bricker (2006), Leuenberger (manuscript), and Skiles (manuscript)claim that grounding is univocal and non-primitive. Bricker recom-mends an analysis of grounding in terms of supervenience and abso-lute fundamentality or perfect naturalness, Leuenberger in terms ofhis notion ceteris absentibus sufficiency, and Skiles in terms of meta-

physical analysis. Absolute fundamentality, ceteris absentibus sufficiency,and metaphysical analysis are non-quotidian and relatively non-orthodox notions.

Now we turn to the view that grounding is equivocal, the thesis thatthere are multiple dependence notions marking different phenomenacorresponding to the various grounding expressions in the sorts oftheses mentioned above. Fine (2012) is sympathetic with this view.He claims that there are various heterogeneous grounding notions,for grounding considered as a generic relation is akin to a disjunctionof special relations. Fine apparently thinks that none of the variousgrounding notions are amenable to analysis, and all are non-quotidian




and non-orthodox. Hofweber (2009) also claims that there are vari-ous heterogeneous grounding notions, but he is naturally read as

claiming that each can be analysed. Hofweber’s view is something likethis: the notion of grounding 1 is analysable partly in terms of con-ceptual priority, grounding 2 in terms of modal entailment, and so on.He claims that, while several heterogeneous grounding notions figurein everyday thinking, there is no ‘special metaphysical sense’ of‘ground’ (Hofweber 2009, 271). Hence, Hofweber is naturally read asclaiming that the various grounding notions are all quotidian and or-thodox. I read Daly (2012) and Wilson (manuscript) as endorsing

similar packages of views.One might claim that, while there are various grounding notions, theyare all unified in an important sense. Consider the primitivist view ofcolour according to which our colour concepts can’t be analysed. Though the primitivist takes the concepts of red and blue, for exam-ple, as primitive, these notions are importantly related, for it’s a priorithat any red thing is coloured, and any blue thing is coloured. Morespecifically, the semantic values of these concepts are determinates

of the determinable property of being coloured. Perhaps the advo-cate of the claim that grounding is equivocal and the various ground-ing notions are primitive but unified would make a correspondingclaim. And perhaps the advocate of the claim that grounding isequivocal who thinks that the various grounding concepts are unifiedand analysable would claim that there is a primitive, general conceptof grounding, and the notions of grounding 1, grounding 2, and so onare species of it. In this case, grounding 1 is analysable as ‘grounding +

differentia1’, grounding 2 as ‘grounding + differentia2’, and so on.Some of those relations Bennett (2011a) calls building relations (e.g.singleton set formation, constitution, and realisation) are natural can-didates for the semantic values of the various grounding concepts inthis case. If, for example, the notion of grounding 1 expresses the rela-tion of constitution, then perhaps differentia1 concerns spatial coin-cidence; and, if grounding 2 expresses the realisation relation, thenpresumably differentia2 concerns role-properties and their corre-sponding role-fillers. If our various grounding concepts expressbuilding relations, presumably these notions are orthodox and rela-tively non-quotidian.




dimensionalism concerning the nature of material objects (cf. Fine2012 and Raven forthcoming).

So how should we proceed with respect to the univocal/equivocaldispute? Later I consider a version of the equivocation view that dis-tinguishes grounding proper and metaphysical explanation. But apartfrom this possibility, for the purposes of this chapter I assume thattalk of grounding in philosophical discourse is otherwise univocal,and by ‘grounding’ I mean full grounding rather than partial ground-ing unless otherwise noted. (The distinction between mere partial andfull grounding doesn’t count as a substantive sense in which our

grounding talk is equivocal.) Though I won’t defend the univocalityassumption here, I think it’s a reasonable starting point. For, just asour default position with respect to our talk of synchronic identity,causation, parthood, and the like is one of univocality, the same istrue of grounding. As for whether grounding is primitive, quotidian,and orthodox, I leave these matters open.

3. What is the Logical Form of Grounding Statements?

In this section I discuss different takes on how best to regiment thenotion of grounding. Consider the following three examples ofgrounding vocabulary: ‘ground’, ‘because’, and ‘in virtue of’. On thesyntactical surface level, the verb ‘ground’ is a relational predicate,‘because’ is a sentential connective, and ‘in virtue of’ is a sentence-forming operator that requires a sentence as its first argument and asingular term as its second. Hence, on the surface level grounding vocabulary comes in different syntactic guises. The debate concerning

the logical form of grounding statements concerns which of theseguises (or still some different one) is the most fundamental. In other words, the debate is about which guise is involved in the ultimate rep-resentation of grounding talk in the best semantic theory.

Some argue that our best semantic theory will treat grounding ex-pressions as predicates introducing a certain relation(s). If the rela-tion view is correct, it makes sense to ask what kinds of thingsgrounds are. Others argue that grounding expressions ultimately be-have like non-truth-functional sentential connectives. On this view it’sultimately misguided to ask what kinds of things grounds are assum-ing that there is no relation expressed by grounding expressions to



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relate any such relata. It’s important to realise that the latter view isn’tthe view that the relata of grounding are sentences; this would be to

treat grounding expressions instead ultimately as predicates introduc-ing a relation that holds between sentences. Such a view is a versionof the view that the best regimentation of grounding is one accord-ing to which the term introduces a relation. (It’s open for the propo-nent of the connective view to add that, non-ultimately speaking, wemay well talk about a relation of grounding, for we can define a rela-tional predicate in terms of the sentential connective.)

Consider, for example, the sentence ‘{Socrates} is grounded in Socra-

tes’. Advocates of the relation and connective views (we will assume)agree that this sentence is true, but they differ on whether it ultimate-ly involves a relation holding between certain entities (e.g. {Socrates}and Socrates, or the fact that {Socrates} exists and the fact that Soc-rates exists), or whether it is best expressed without any relationalterms (e.g. ‘{Socrates} exists because Socrates does’, or some othersentence with a sentential connective).

We find a corresponding debate in the literature on truthmaking. Truthmaking enthusiasts tend to agree that propositions are the bear-ers of truth. And they also tend to agree, for example, that (i) thetruth of the proposition that the rose is red is explained by the red-ness of the rose, and (ii) the proposition that the rose is red is truebecause the rose is red. Rodríguez-Pereyra (2005) and others arguethat (i) with its nominalisations of the adjectives ‘true’ and ‘red’ moreclosely approximates the logical form of truthmaking statements, andthis suggests that talk of truthmaking introduces a relation. As a rela-

tion, truthmaking relates entities – truthmakers (whatever these mightbe) and propositions. By contrast, Hornsby (2005) and others arguethat (ii) more closely approximates the logical form of truthmakingstatements, so truthmaking expressions ultimately behave like non-truth-functional sentential connectives. If this is right, there is noreason to believe that truthmaking requires truthmakers. With thisdisagreement in mind, a gloss of the difference between the relationand connective views with respect to grounding is this: on the former

the ultimate representation of grounding talk requires both ground-ing entities and grounded entities, while on the latter it requires nei-ther.



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what makes possible and “grounds” explanation’ (Rodríguez-Pereyra2005, 28). Here the claim seems to be that the facts about what

grounds what themselves ground the facts about what metaphysicallyexplains what. On this view, grounding proper and metaphysical ex-planation are distinct relations. Recall the view that grounding isequivocal in the sense that there is more than one dependence notionmarking different phenomena corresponding to the various ground-ing expressions in the sorts of grounding claims described earlier inthe chapter. If the notions of grounding proper and metaphysicalexplanation express different relations, it seems that grounding is

equivocal in just this sense. An alternative view – one compatible withour grounding talk being univocal – is that the grounding facts andthe metaphysical explanation facts are the same facts. In this case,grounding proper just is metaphysical explanation. Notice that theidentity view fits well with the view according to which the relata ofgrounding are restricted to facts. For, if for one fact to be groundedin another just is for the latter to metaphysically explain the former,then, assuming that explanation is a relation between facts, the sameis true of grounding. If the grounding relation and the relation ofmetaphysical explanation are distinct, however, then a restriction tofacts in the case of metaphysical explanation seems well motivated, while matters aren’t so clear in the case of grounding.

One might argue against the claim that grounding is categoricallyneutral as follows. Whether or not grounding and metaphysical ex-planation are the same, we can all agree that there are contexts in which citing a ground for a fact (assuming that there are such things

as facts) suffices to metaphysically explain why that fact obtains. Sup-pose that grounding is categorically neutral, and in particular that ob-jects can ground facts. Let’s suppose in particular that the fact thatthus-and-so is grounded in a substance named ‘Kelly’. The problem isthat there is no context in which citing Kelly suffices to metaphysical-ly explain any fact. The reason is that Kelly just doesn’t have the rightkind of structure to be an explanans of anything. Sider (2012, chapter8) makes a similar point when he claims that it’s hard to see how frommerely listing substances we could answer questions such as ‘Arethere helium molecules?’, ‘Are there cities?’, and so on. And Dasgupta(manuscript a) is on to the same point in claiming that it makes nogrammatical sense for a table, for example, to explain anything. He



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case of endless grounding, ‘being would be infinitely deferred, neverachieved’ (Schafer 2010b, 62). Others, however, aren’t so sure. Rosen

finds nothing obviously wrong with the idea that grounding isn’t wellfounded. He claims that, for all we know, ‘the facts about atoms aregrounded in facts about quarks and electrons, which are in turngrounded in facts about ‘hyperquarks’ and ‘hyperelectrons’, and so onad infinitum’ (Rosen 2010, 116). (Notice, however, that Rosen’s re-marks here are compatible with the idea that grounding chains musthave lower bounds.) Bliss (manuscript) argues that one potential mo-tivation for the claim that grounding is well founded – appeals to var-

iations of the principle of sufficient reason – is misguided. Bohn(manuscript), Morganti (2009), and Orilia (2009) each reject the claimthat grounding is well founded; and Cameron (2008) suggests that we’re only warranted in thinking that grounding chains have lowerbounds in the actual world.

Putting the controversy concerning whether grounding is well found-ed to the side, many agree that grounding is non-monotonic (see, e.g., Audi 2012, Rosen 2010, and Raven forthcoming). On the view that

the relata of grounding are restricted to facts, the claim is that, if onefact is grounded in another, it doesn’t follow that, for any third factcompatible with the first two, the first is also grounded in the plurali-ty consisting of the second and third. For example, if [{Socrates}exists] is grounded in [Socrates exists], it doesn’t follow that [{Socra-tes} exists] is also grounded in the plurality consisting of [Socratesexists] and, say, [Hong Kong is a city]. The idea is that the explanato-ry nature of grounding secures its status as a non-monotonic relation.

As Dasgupta (manuscript b) puts the point, given that all parts of anexplanation must be explanatorily relevant, adding irrelevant infor-mation defeats the initial explanation. This route to securing non-monotonicity makes the most sense on the view we discussed abovethat the facts about what grounds what and the facts about whatmetaphysically explains what are the same facts. Matters are less clear,however, on the view that the facts about what grounds what them-selves ground the facts about what metaphysically explains what. This view on the face of it is compatible with metaphysical explanationbeing non-monotonic and grounding monotonic.




Many also agree that grounding is hyperintensional (see, e.g., Jenkins2011 and Schaffer 2009). It is easiest to make sense of this claim on

the connective view of the logical form of grounding statements.Consider the sentences ‘Socrates exists’ and ‘{Socrates} exists’. Eventhough they are intensionally equivalent, substituting one for the oth-er turns the true grounding statement ‘{Socrates} exists because Soc-rates exists’ into ‘Socrates exists because Socrates exists’, which isfalse. This hyperintensionality lends strong support to the claim thatthe grounding locution is not analysable purely in terms of superven-ience, modal entailment, and the like, for the latter are intensional in

nature. The thesis that grounding is non-monotonic has similar im-plications.

5. What are the Modal Consequences of Grounding?

Now we turn to the matter of how grounding and modality interact. Necessitarianism very roughly is the thesis that grounding carries modalentailment; according to contingentism , necessitarianism is false. Leuen-berger (manuscript), an advocate of contingentism, stresses that the

fact that grounding is a determination relation doesn’t by itself giveus reason to think that necessitarianism is correct, for it’s widelyagreed that causation is a contingent determination relation. AndSchaffer (2010a) claims that, since grounding is categorically neutral,grounding and modal entailment can come completely apart; hence,necessitarianism is false. This, however, may be too quick. One way toformulate necessitarianism appeals to the idea that each entity (re-gardless of its ontological category) corresponds to a unique fact: if

one entity is grounded in another, then any metaphysically possible world in which the fact corresponding to latter obtains is a world in which the fact corresponding to former obtains. This view has con-tent only if we specify the relevant sense of correspondence. Hereare some suggestions: for any sentence s , the fact corresponding to sis [ s ]; for any event e , the fact corresponding to e is [ e occurs]; for anyfact f , the fact corresponding to f is f itself; and so on. If we can spec-ify the correspondence relation for entities of each ontological cate-gory, necessitarianism is compatible with the neutral view of ground-ing. We’re assuming, however, the fact view, so for our purposes ne-cessitarianism is the thesis that, if one fact is grounded in another,



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then every metaphysically possible world in which the latter obtains isa world in which the former obtains as well.

Why think that necessitarianism so understood is true? DeRosset(2010) endorses necessitarianism because in his view grounds meta-physically explain what they ground, and the explanans in a successfulmetaphysical explanation modally entails its explanandum . For others(e.g. Audi (2012), Cameron (2010), Correia (2011), Rosen (2010), Witmer et al (2005)), necessitarianism is simply regarded as a plausi-ble assumption supported by reflection on paradigm examples ofgrounding. My sense is that such theorists tend to think that to sepa-

rate grounding and modal entailment completely would be to renderthe former theoretically unconstrained in a way that’s best to avoid.In Trogdon manuscript a I argue that certain epistemic considerationssupport the idea that [ p ] is grounded in ∆ only if there are certainessential truths (in Fine’s (1994) sense) characteristic of [ p ], ∆, theplurality consisting of [ p ] and ∆, or the entities they involve accordingto which, if the members of ∆ obtain, [ p ] obtains as well. Assumingthat essential truths are metaphysically necessary, necessitarianism

follows. There are, however, potential counterexamples to necessitarianism.I’ll consider three. The first is due to Dancy (2004, chapter 3). Sup-pose you reason as follows: (i) I promised to φ, (ii) my promise wasn’tg iven under duress, (iii) I’m able to φ; therefore, (iv) I ought to φ.Suppose further that each of the premises and the conclusion aretrue. Dancy suggests that (i) gives you a reason to commit the action, while (ii) and (iii), though not providing reasons themselves, jointly

enable (i) to do so. A natural way of translating this into talk ofgrounding (what Dancy calls ‘resultance’) is to say that, while [youpromised to φ] grounds [you ought to φ], [your promise wasn’t givenunder duress], [you’re able to φ], and additional relevant facts jointlyenable the promise-fact to ground the obligation-fact. Since the for-mer doesn’t modally entail the latter, we have a putative counterex-ample to necessitarianism. This proposal requires that we take thedistinction between grounding and enabling conditions as a genuine

metaphysical distinction rather than a purely pragmatic one. Chud-noff (manuscript) defends the distinction as a metaphysical one,




though the fact that the corresponding distinction in the case of cau-sation is almost certainly pragmatic seems to count against this idea.

The second potential counterexample to necessitarianism I adaptfrom Schaffer (2010a). Let’s grant for the sake of argument a sub-stance/mode (trope) ontology. Consider, for example, the connectionbetween a rose qua substance and its particular redness qua mode.Modes are dependent modifications of substances, and a natural wayto translate this into grounding talk is to say that [the particular red-ness exists] is grounded in [the rose exists]. If this is right, however,then necessitarianism is false, given that it’s not the case that the lattermodally entails the former. The necessitarian might respond that [theparticular redness exists] is merely partially grounded in [the rose ex-ists], and necessitarianism applies to full grounds. Here the idea isthat [the particular redness exists] is fully grounded in two facts: [therose exists] and [the rose is a particular shade of red]. I think a betterresponse, however, is this: (i) [the rose exists] is explanatorily irrelevant to [the particular redness exists], (ii) if one fact is partiallygrounded in another, the latter is explanatorily relevant to the former;

hence, (iii) [the particular redness exists] isn’t even partially groundedin [the rose exists]. This is Schnieder’s (2006a) view; he argues that, while the existence of the rose is a necessary condition for the exist-ence of the particular redness, [the particular redness exists] is fullygrounded in [the rose is a particular shade of red].

The third potential counterexample I adapt from Schnieder (2006b):[Xanthippe became a widow] is grounded in [Socrates died], yet thelatter doesn’t modally entail the former given that there are possible

worlds in which they were never married. The initial response weconsidered to the second potential counterexample is worth consider-ing here. The proposal in this case would be that [Xanthippe becamea widow] is merely partially grounded in [Socrates died]; the former isfully grounded in two facts: [Socrates died] and [Socrates and Xan-thippe were married].

6. What is the Connection between Grounding and Reduc-

tion?Having taken up the matter of how grounding and modality interact,in this penultimate section we turn to the same question with respect



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to grounding and reduction. Is there a substantive sense in which thegrounded reduce to what grounds them? Audi (2012 ) doesn’t think

so. He states that ‘… grounded facts and ungrounded facts are equal-ly real, and grounded facts are an “addition of being” over and abovethe facts in which they are grounded’, adding that the grounded areno more or less ‘ontologically innocent’ than what grounds them(Audi 2012, 1).

What more can we say about this matter? I’ll consider three ways ofexplicating reduction that have different consequences for the con-nection between grounding and reduction. First, we might character-

ise reduction in terms of identity. Put in terms of facts, the idea isthat [ p ] reduces to [ q ] just in case [ p ] is the same fact as [ q ] (cf. deRos-set 2010 and Sider 2003). On the identity conception, reduction, ofcourse, has the structural features of identity: reflexivity, symmetry,and transitivity. Were grounds to reduce to what grounds them in thissense, every fact would ground itself. As we’ve seen, many claim thatgrounding is irreflexive, which would rule this out. And even those who reject the claim that grounding is irreflexive would presumably

reject the claim that every fact grounds itself. Hence, on the identityconception of reduction it seems that the grounded fail to reduce totheir grounds.

Second, we might characterise reduction in terms of fundamentality.Consider the notion of ontological economy or parsimony, which isanalogous to that of conceptual economy. It would seem that thenumber of theoretical terms a theory countenances is not in general agood guide to its conceptual economy. What is more important is the

number of its primitive notions in terms of which the others arecharacterised; generally speaking, the less primitive notions a theorycountenances, the more conceptual economy it has. In the same way,the number of entities a world contains in general is not a good guideto its ontological economy, or so the idea goes. What is more im-portant is the number of fundamental entities it contains. Generallyspeaking, the less fundamental entities a world contains, the moreontologically parsimonious it is (cf. Schaffer manuscript). (There are,

however, important differences between conceptual and ontologicaleconomy. For example, given an analysis of one term in terms ofanother, the former is dispensable from the statement of the theory




in which it occurs without sacrificing expressive or descriptive power.But the grounding of one fact in another doesn’t underwrite this sort

of dispensability; a theory that mentions the former will generally bedescriptively more powerful than an otherwise similar one thatdoesn’t mention this fact.)

Let’s assume that an entity is fundamental just in case it isn’t ground-ed in anything. A world’s fundamental entities make an ontological impact in the sense of being directly relevant to how ontologically par-simonious that world is. With this conception of ontological impact – what I call direct ontological impact – we can introduce a related no-

tion – indirect ontological impact. Suppose we claim that a derivative(i.e. non-fundamental) entity d exists (obtains, occurs, etc.). In makingthis claim we take on certain fundamentality commitments in the sensethat what we’re saying, if true, puts constraints on the way the worldis, fundamentally speaking (cf. Schaffer 2008). The claim that d exists,in other words, requires there are fundamental entities of some sortthat ultimately ground the fact that d exists. It’s best in this context tostay neutral on just which sorts of entities are fundamental, so it’s

also best to view such commitments as being disjunctive in nature. The truth of our claim might require, for example, that there is a plu-rality of microphysical particles instantiating certain fundamentalproperties (as a particular version of priority pluralism would have it),or that the world as a whole instantiates certain fundamental proper-ties (as a particular version of priority monism would have it) (cf. Schaf-fer 2010b and Trogdon 2009).

Derivative entities, therefore, make an indirect ontological impact in

the sense that claims to the effect that they exist incur fundamentalitycommitments. Notice that we can also speak of the indirect ontologi-cal impact made by fundamental entities. When we claim that someentity f exists, then, if f is fundamental according to our theory, wetake on the fundamentality commitment to f . Henceforth, by ontolog-ical impact I mean indirect ontological impact in particular.

In contrast to the identity conception, the fundamentality conceptionof reduction cast in terms of facts is this: [ p ] reduces to [ q ] just incase both [ p ] and [ q ] obtain and they make the same ontological im-pact. In other words, [ p ] reduces to [ q ] just in case [ p ] and [ q ] obtainand [ p ] incurs a fundamentality commitment C just in case [ q ] incurs

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C . It would seem that a grounded fact makes the same ontologicalimpact as the plurality consisting of all its actual grounds. On the

fundamentality conception, reduction again is reflexive, symmetric,and transitive. A consequence of symmetry is that, not only does afact reduce to the plurality of its actual grounds (which themselvesare pluralities), but the plurality of grounds reduces to the groundedfact as well.

Given the fundamentality conception of reduction, why not claimthat, if one fact is grounded in another, the former reduces to thelatter? The reason is that there are cases in which, though one fact is

grounded in another, the ontological impact of the former is greaterthan that of the latter. Consider, for example, [something is H ]. Sup-pose that this existential fact is grounded in [ a is H ] and it’s alsogrounded in [ b is H ]. It may be that the latter ground incurs funda-mentality commitments that the former doesn’t and vice versa. Sup-posing that this is so, it would be a mistake to say that the fundamen-tality commitments of [something is H ] are the same as those of thefirst ground, for in this case [something is H ] incurs all those funda-

mentality commitments incurred by each ground. Third, we might characterise reduction in terms of essence. This isthe option Rosen (2010) pursues. First, (putting to the side certaincomplications) Rosen argues that (the proposition that p ) reduc-es to <q > just in case <q > is the proposition we get from providingthe ‘real definition’ of the entities involves in roughly Fine’s(1994) sense. For example, we can express the real definition of theproperty of being a square thus: what it is to be a square is to be an

equilateral rectangle. Hence, on this view <something is a square>reduces to <something is an equilateral rectangle>. So for Rosen re-duction is a relation between propositions, and it’s a form of analysis ,in particular a form of metaphysical analysis. Second, Rosen claims thatif is true and <q > is the real definition of , then [ p ] isgrounded in [ q ]. Putting all of this together, we arrive at the following view: if is true and reduces to <q >, then [ p ] is grounded in[ q ].

So while our discussion of the fundamentality conception of reduc-tion resulted in a putative sufficient condition for reduction that ap-peals to grounding facts, Rosen proposes a necessary condition for




reduction that appeals to grounding facts. Another important differ-ence between the two conceptions of reduction is that reduction on

Rosen’s conception is irreflexive and asymmetric, given that meta-physical analysis has these features.

7. What Grounds the Grounding Facts?

In this final section I consider the matter of what if anythinggrounds the facts about what grounds what. This issue is interestingin part because, as deRosset (forthcoming), Sider (2012), and othershave argued, we face a potential problem here. I put the problem in

the form of a dilemma, and it departs in various ways from the dis-cussions of the aforementioned authors.

Suppose that [you’re having an experience as of motion] is partiallygrounded in [there is recurrent activity above a such-and-suchthreshold between your V1 and MT/V5 neural structures]. Is this factitself grounded? Taking the first horn, suppose this fact isn’t ground-ed. Assuming that a fact is fundamental just in case it isn’t grounded,it follows that the fact that the mental fact is partially grounded in thephysical fact is fundamental. And it seems that, if a fact is fundamen-tal, then its constituents are fundamental as well. If this is right, itfollows that the mental and physical facts are both fundamental. Sohere we’re committed to the idea that in describing how the world isfundamentally speaking – in writing the Book of the World to use Sid-er’s (2012) phrase – we must mention the experience as of motion as well as activity between certain neural structures. The problem here isobvious: to describe the way the world is fundamentally speaking, we

needn’t speak of these things. This isn’t to say that it’s clear what would go into such a description; what’s clear is just that these items won’t be among them. (The property dualist who claims that thereare fundamental laws connecting mental and physical properties (cf.Chalmers 1996) might disagree, but we could just as well have used adifferent example. [Hong Kong is a city], for example, is grounded infacts concerning the activities of various people, yet presumably thedualist would agree that the Book of World mentions neither Hong

Kong nor the property of being a city. Moreover, the dualist claimsthat it’s special features of mental properties that secure dualism, not



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general considerations concerning the grounds for what grounds what.)

Taking the second horn, suppose instead that the fact that the mentalfact is partially grounded in the physical fact is grounded. In this caseit’s unclear, however, just what a plausible candidate ground for thisfact might be. What sort of fact could play this role? Moreover, whatever fact we might settle on, we face the question of whether ittoo is grounded, and, if so, how.

As Dasgupta (manuscript a) notes, however, there is a class of

grounding facts whose members intuitively are grounded in certainfacts. Suppose (i) [ p ] is grounded [ q ], (ii) [ q ] is grounded in [ r ], and (iii)[ p ] is grounded in [ r ]. You might claim that, no matter what [ p ], [ q ],and [ r ] come to, (iii) is grounded in the plurality consisting of (i) and(ii) (though see Trogdon manuscript b for a potential counterexampleto this thesis). Suppose this claim is correct. In this case, [ r ] is a ‘me-diate ground’ for [ p ] in the sense that the latter is grounded in theformer only because [ p ] is grounded in [ q ] and [ q ] is grounded in [ r ](cf. Fine 2012 ). Assuming that (i) and (ii) aren’t grounded in a similarfashion – assuming, in other words, that [ q ] is an immediate groundfor [ p ] and [ r ] is an immediate ground for [ q ] – the dilemma set outabove targets such facts. The dilemma, in other words, concerns thefacts about what immediately grounds what.

What are our options here? I’ll consider two. The first proposal is onethat Bennett (2011b) and deRosset (forthcoming) have independentlycome upon. Suppose that [ p ] is (immediately) grounded in [ q ]. Both

claim in this case it follows that [[ p ] is grounded in [ q ]] is grounded in[ q ], [[[ p ] is grounded in [ q ]] is grounded in [ q ]] is grounded in [ q ], andso on. So suppose that [ p q ] is grounded in [ p ]. On this view, [[ pq ] is grounded in [ p ]] is grounded in [ p ], [[[ p q ] is grounded in [ p ]] isgrounded in [ p ]] is grounded in [ p ], and so on.

As deRosset notes, in explaining why [ p q ] is grounded in [ p ], itseems that we should say something about disjunction in addition to[ p ]. Yet on his view [[ p q ] is grounded in [ p ]] is grounded in [ p ], not

[ p ] plus some fact about disjunction. In response to this concern,deRosset distinguishes between facts that ground a given fact, andfacts that would render a metaphysical explanation intelligible to an




audience in certain contexts. With respect to [[ p q ] is grounded in[ p ]], he claims that facts about disjunction play the latter rather than

former role.Dasgupta (manuscript a) objects as follows. He agrees that, when wemetaphysically explain [ p q ] in terms of [ p ], talk of disjunction ismerely an aid to make the explanation intelligible to an audience. Butit doesn’t follow from this that when we metaphysically explain [[ pq ] is grounded in [ p ]] in terms of [ p ] the same is true. In support ofthe claim, he points to a corresponding asymmetry. When we prove p

q from p no reference to disjunction need be made in our premises, while when we prove in the metalanguage that p implies p q ourpremises will include that disjunction introduction is a valid inferencerule.

The second proposal we will consider comes from Dasgupta (manu-script a). He argues that facts about what (immediately) grounds whatare grounded in certain groundless facts concerning the essences ofentities. One version of the proposal he considers is as follows. Recall

from §5 the claim that, if one fact is grounded in another, certainessential truths (in Fine’s (1994) sense) characterise these facts or theentities they involve according to which the latter fact suffices for theformer. Dasgupta agrees and claims that these facts concerning es-sence are groundless. He then claims that these groundless facts con-cerning essence together with certain associated facts ground factsabout what grounds what. Example: suppose that the fact that Os- wald’s killing of President Kennedy was wrong is grounded in the

fact that his action failed to maximise utility. For Dasgupta, this fact isgrounded in (i) the fact that part of what it is to be a wrong action isthat if an action fails to maximise utility then that action is wrong,and (ii) Oswald’s action failed to maximise utility. Dasgupta arguesthat this proposal iterates, so we have, for example, grounds for thefact that certain groundless facts concerning the essences of entitiespartially ground grounding facts.

Returning to the dilemma I opened this section with, recall the idea

that a fact is fundamental just in case it isn’t grounded, and, if a factis fundamental, its constituents are fundamental as well. If this pack-age of views is correct, then Dasgupta is committed to the view that



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the entities characterised by the relevant essential truths are all fun-damental, which is a disastrous result. For Dasgupta, the relevant es-

sential truths are ‘autonomous’: the facts corresponding to thesetruths are groundless not because it just so happens that nothinggrounds them; instead, they aren’t apt for metaphysical explanation inthe first place. I take it that Dasgupta’s view, then, is this: a fact isfundamental just in case it’s ungrounded and not autonomous. ForDasgupta claims that the relevant groundless facts about essencearen’t brute facts occupying the lowest level of the hierarchical struc-ture of the world but part of ‘the scaffolding around which the hier-

archy is built’ (Dasgupta manuscript a, 2).DeRosset (forthcoming) criticises this conception of fundamentalityas follows. The autonomous facts – whatever they are – are, well,facts. Hence, a specification of fundamental reality that leaves out theautonomous facts is one that leaves out some of the facts. This givesus a reason to think that such a specification is incomplete. Assumingthat a specification of fundamental reality doesn’t leave anything out,something has gone wrong here.1

References

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Beebee, H. and J. Dodd (eds.) 2005: Truthmakers: The Contemporary De- bate . Oxford: Oxford University Press.

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Bliss, R. L. manuscript: ‘Metaphysical Foundationalism and the Prin-ciple of Sufficient Reason’.

1 I presented portions of the material from this chapter at the Because IIConference in Berlin (September, 2010) and Hong Kong University (May,2011); I wish to thank my audiences for their objections and suggestions.

Special thanks are due to Paul Audi, Derek Baker, Chris Daly, Max Deutsch,Louis deRosset, Tim Fuller, Miguel Hoeltje, Dan Marshall, Brian Rabern,Raul Saucedo, Jonathan Schaffer, Benjamin Schnieder, Alex Skiles, and AlexSteinberg for helpful discussion and comments on previous drafts.




Bohn, E. manuscript: ‘Against a Particular Notion of OntologicalDependence’.

Bricker, P. 2006: ‘The Relation Between the General and the Particu-lar: Entailment vs. Supervenience’. In Zimmerman 2006, pp. 251 –87.

Cameron, R. 2008: ‘Turtles all the Way Down: Regress, Priority, andFundamentality’. The Philosophical Quarterly 58, pp. 1 –14.

— 2010: ‘From Humean Truthmaker Theory to Priority Monism’. Nous 44, pp. 178 –98.

Chalmers, D. 2010: The Character of Consciousness . Oxford: OxfordUniversity Press.

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Chalmers, D., D. Manley, and R. Wasserman (eds.) 2009: Metametaphys- ics . Oxford: Oxford University Press.

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53, pp. 251 –79. — 2011: ‘From Grounding to Truth-Making: Some Thoughts’. In

A. Reboul (ed.): Philosophical papers dedicated to Kevin Mulligan . URL:http://www.philosophie.ch/kevin/festschrift/.

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Daly, C. 2012: ‘Skepticism about Grounding’. In Correia andSchnieder 2012, pp. 81 –100.

Dancy, J. 2004: Ethics Without Principles . Oxford: Clarendon Press.

Dasgupta, S. manuscript a: ‘The Status of Ground’. — manuscript b: ‘On the Plurality of Grounds’. deRosset, L. 2010: ‘Getting Priority Straight’. Philosophical Studies 149,

pp. 73 –97.

— f orthcoming: ‘Grounding Explanations’. Philosophers’ Imprint .Fine, K. 1994: ‘Essence and Modality’. Philosophical Perspectives 8, pp.

1 –16.



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— 1995: ‘Ontological Dependence’. Proceedings of the Aristotelian Society 95, pp. 269 –90.

— 2001: ‘The Question of Realism’. Philosophers’ Imprint 1, pp. 1 –30. — 2010: ‘Some Puzzles of Ground’. Notre Dame Journal of Formal

Logic 51, pp. 97 –118.


Gillet, C. and B. Loewer (eds.) 2001: Physicalism and its Discontents .Cambridge: Cambridge University Press.

Hale, R. and A. Hoffman (eds.) 2010: Modality: Metaphysics, Logic, and Epistemology . Oxford: Oxford University Press.

Hofweber, T. 2009: ‘Ambitious, Yet Modest, Metaphysics’. InChalmers, Manley and Wasserman 2009, pp. 260 –89.

Horgan, T. 1993: ‘From Supervenience to Superdupervenience: Meet-ing the Demands of a Material World’. Mind 102, pp. 555 –86.

Hornsby, J. 2005: ‘Truth without Truthmaking Entities’. In Beebee

and Dodd 2005, pp. 33 –47. Jenkins, C. 2011: ‘Is Metaphysical Dependence Irreflexive?’ The Monist

94, pp. 267 –76.

Kim, J. 1994: ‘Explanatory Knowledge and Metaphysical Depend-ence’. Philosophical Topics 4, pp. 51 –69.

Lepore, E. and B. Loewer 1989: ‘More on Making Mind Matter’. Phil- osophical Topics 17, pp. 175 –92.

Leuenberger, S. manuscript: ‘Grounding and Necessity’. Levine, J. 2001: Purple Haze . Oxford: Oxford University Press.

Litland, J. manuscript: ‘On Some Alleged Counterexamples to the Transitivity of Grounding’.

Loewer, B. 2001: ‘From Physics to Physicalism’. In Gillet and Loewer2001, pp. 37 –56.

Loux, M. and D. Zimmerman (eds.) 2003: The Oxford Handbook of

Metaphysics. Oxford: Oxford University PressLowe, E. J. 1998: The Possibility of Metaphysics . Oxford: Oxford Univer-

sity Press.




Morganti, M. 2009: ‘Ontological Priority, Fundamentality, and Mon-ism’. Dialectica 63, pp. 271 –88.

Orilia, F. 2009: ‘Bradley’s Regress and Ungrounded DependenceChains: A Reply to Cameron’. Dialectica 63, pp. 333 –41.

Paseau, A. 2010: ‘Defining Ultimate Ontological Basis and the Fun-damental Layer’. The Philosophical Quarterly 60, pp. 169 –75.

Raven, M. forthcoming: ‘In Defense of Ground’. Australasian Journalof Philosophy .

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Dodd 2005, pp. 17 –31.Rosen, G. 2010: ‘Metaphysical Dependence: Grounding and Reduc-

tion’. In Hale and Hoffman 2010, pp. 109 –136.

Ruben, D. 1990: Explaining Explanation . New York: Routledge.

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— 2009: ‘On What Grounds What’. In Chalmers, Manley and Was-

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er’. Philosophical Quarterly 60, pp. 307 –24.

— 2010b: ‘Monism: The Priority of the Whole’. Philosophical Review 119, pp. 31 –76.

— 2012: ‘Grounding, Transiti vity, and Contrastivity’. In Correia andSchnieder 2012, pp. 122 –38.

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stance, and Explanation’. Philosophical Studies 129, pp. 393 –419.

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merman 2003, pp. 180 –208. — 2012: Writing the Book of the World . Oxford: Oxford UniversityPress.



Supervenience: A Survey

Alex Steinberg

The world we live in is structured. Some aspects of reality depend onfurther aspects, and some facts completely determine others. In afamous metaphor due to Kripke (1980, 153f.): when God created the world he had to decide on many things. But he did not have to decideon everything explicitly: decisions on some questions already deter-mined answers to others. To take an uncontroversial example: oncethe truth-functionally atomic facts were settled, all the truth-functionally complex facts were settled as well. God did not need tospecify that (grass is green and snow is white), on top of specifyingthat grass is green and specifying that snow is white. Or consider the

specific shades of colour. Once God had decided on their distribu-tion, he did not have to further specify the distribution of red, greenand blue.

Many philosophers think that an important sort of dependence thatrelates conjunctive facts to atomic facts and the primary colours tothe specific shades can be captured by supervenience claims. A dif-ference in conjunctive facts requires a difference in atomic facts, and ifthere is a difference in the primary colours, this difference will beconsequential on a difference in the specific shades. Traditionally, slightlymore controversial theses were discussed. When R. M. Hare intro-duced the term ‘supervene’ into the current philosophical debate (inhis 1952, 80f.) he was concerned with what he called value-words suchas ‘good picture’. According to Hare, there cannot be two things thatare otherwise completely alike, while one is a good picture and theother is not. G. E. Moore (1922, 261) is often cited as an early cham-pion of the supervenience of moral on nonmoral properties. And

Donald Davidson (1970, 88) endorsed the perhaps most widely dis-cussed supervenience thesis of the mental on the physical.



SUPERVENIENCE: A SURVEY 97

or for pluralities of them. Thus, such claims as the claim that mentalproperties supervene on physical properties and the claim that the

property of being red supervenes on the particular shades of red are what concerns us here.2 In discussions of supervenience a concep-tion of properties as lightweight and abundant is typically assumed. The properties at issue do not have to be fundamental explainers or whatever else natural, sparse, properties may be good for.3 Rather,talk of properties in supervenience theses is a device for generalisa-tion and classification. When we ask whether mental properties su-pervene on physical properties, such questions as the following are

pertinent:(1) Can there be two things which are physically exactly alike, while

one is in pain and the other is not?

(2) If someone believes that snow is white and someone else doesnot, do they have to be physically dissimilar as well?

Questions of the naturalness of sub-and supervenience candidates,on the other hand, are simply not relevant here.4

For present purposes we do not need to decide between various con-ceptions of properties according to which there are enough of them.5 For properties to be able to fulfil their role in the pertinent generali-sations, it is sufficient that the following inferences turn out to be valid, paradoxes aside:6

2 For convenience I assume that colours as well as specific shades of col-ours are properties. Those who doubt the view should replace (shades of)colour talk with talk about the property of having this-or-that (shade of)colour in the examples to follow.3 For a range of potential other uses see Lewis 1983.4 In fact, it is a plausible but non-trivial view that all other properties supervene on the natural properties. It would be trivial if the natural properties were the only properties there are.5 For specific suggestions see e.g. Lewis 1983; Schiffer 2003; Künne 2006.6 The instances of (H) and (¬H) in which ‘F ’ is replaced by ‘self -exemplifying’ cannot be valid. Otherwise, the property of being self -exemplifying would be self-exemplifying just in case it is not, which is im-possible.




w be such a world. Then, given the supervenience of the primary col-ours on the specific shades, in w no two objects will differ in BEN-

properties without differing in SHADE-properties, but there may wellbe a bicycle and a car sporting the very same shade of blue in w .

This difference, however, will typically not show up. In the interestingcases, the supervenience candidates are usually specified in terms oftheir necessary properties : being a mental property, being a physicalproperty, being a primary colour and so forth. While there is a worldat which being red is not thought about by Ben on 21st September2012, there is no world at which it is not a primary colour. Likewise

for being blue and being green. Thus, in every world each COLOUR -property will also be a (primary) colour property and vice versa. Insuch a case set talk and the more colloquial formulation will be inline.8

Like our discussion up to this point, the supervenience literaturemakes frequent use of possible worlds. Since supervenience is charac-terised in modal terms —there can be no difference in respect of so-and-so without a difference in respect of such-and-such —this ishardly surprising. As in the case of properties, no substantial accountof possible worlds needs to be presupposed. There just have to beenough of them for the following inferences to be valid:

It does not matter, for instance, whether possible worlds are taken tobe maximal sums of spatio-temporally related individuals (Lewis1986), maximal possible states of affairs (Plantinga 1974) or mostspecific properties the universe might have had (Stalnaker 2003). Anystraightforward account of possible worlds will aim to validate (◊)and ( □ ). The reader is free to take her pick. It is an interesting ques-tion whether the supervenience debate could in principle do without

8 More generally, this is because the following is a theorem of modal settheory:( □

x ( Fx ↔ □Fx ) x ( x

A ↔ Fx ) □ x ( x = A )) → □ x ( Fx ↔ x

A ).

It is necessary that p At all possible worlds, p

( □ )It is possible that p There is a possible world at which p

(◊ )



STEINBERG104

1.3 Alternative Formulations

Jaegwon Kim (1984, 163) argues that when the supervenience base Bis closed under Boolean operations the notion defined by (Weak)above is equivalent to the one characterised as follows which we willcall weak supervenience K (‘□’ is the box of modal logic, to be read as ‘it isnecessary that’):

Weak K A-properties weakly superveneK on B-properties ↔df.

□ x,P (( P

A x has P ) → P ′′( P ′

B x has P ′ y ( yhas P ′

→ y has P ))).

Let us say that a property P ′ is materially sufficient for a property Pjust in case everything with P ′ also has P . Then (Weak K ) can be put in words thus: A-properties weakly superveneK on B-properties just incase, necessarily, everything with an A-property also has some B-property that is materially sufficient for the A-property.

Kim (1987, 317f.) also showed that there is a similar characterisationof strong supervenienceK :

StrongK A-properties strongly superveneK on B-properties ↔df.

□ x,P (( P

A x has P ) → P ′ ′( P ′

B x has P ′ □ y( y has P ′ → y has P ))).

Let us say that P ′ is strictly sufficient for P just in case it is necessarythat everything with P ′ also has P . Then (Strong K ) says that A-properties strongly superveneK on B-properties just in case, necessari-ly, everything with an A-property also has a B-property which is

strictly sufficient for the A-property. The initial characterisation of strong supervenience differs from thatof weak supervenience in containing an additional world quantifier.In this way, not only intra -world but also inter -world indiscernibility with respect to A-and B-properties is relevant for strong superveni-ence. In a similar fashion, the difference between Kim’s alternativecharacterisation of weak and strong supervenience is merely one inthe strength of the connection between A-and B-properties. While

weak supervenience requires that for every A-property there is a materially sufficient B-property in every world, strong supervenience re-




quires that for every A-property there is a strictly sufficient such B-property.

As an illustration of how the alternative characterisations work re-consider COUNTRY - and PLACE-properties. It is plausible that, neces-sarily, for every COUNTRY -property P there is some PLACE-propertyP ′ such that everything with P ′ also has P . As it happens, there aremany such PLACE-properties for each COUNTRY -property. Everyplace in Berlin is such that being born there is materially sufficient forbeing born in Germany, for instance. In general: necessarily, for eachcountry C and geo-coordinates G, being born at G is materially suffi-

cient for being born in C , provided that G belongs to C. But eventhough many PLACE-properties are materially sufficient for eachCOUNTRY -property, none of them is strictl y sufficient. For instance,no place in Berlin is such that the property of being born there isstrictly sufficient for the property of being born in Germany, sincearea now covered by Berlin could have belonged to Poland instead ofGermany, for instance. In general: no place in any country is suchthat being born at the former is strictly sufficient for being born in

the latter —places do not essentially belong to countries. Thus, COUNTRY -properties weakly but not strongly supervene onPLACE-properties according to both characterisations. Let us nowconfirm that they always give the same verdict as long as the base setis closed under Boolean operations.

A set of properties A is said to be closed under Boolean operationsjust in case whenever P is in A and B is a subset of A,13 some Q and

Q′ that satisfy the following conditions are in A as well:Neg □ x □( x has Q ↔ ¬x has P )

Con □ x □( x has Q′ ↔ P ( P B → x has P ′ )).

13 If B is a subset of A ( B A ), every element of B is also an element of A. If every element of A is an element of B we say that B is a super set of A

( B A ). And the principle of extensionality ensures us that if B is both asubset and a superset of A, then B = A.



STEINBERG106

If P and Q satisfy (Neg), we may call Q a negation of P . If {P 1 , … P n }and Q′ satisfy (Con), we may say that Q′ is a conjunction of P 1 and …

and P n .14 This indicates why talk of Boolean closure is appropriate. Whether there is a unique negation of a given property, and whetherthere is a unique conjunction of a given set of properties depends onquestions of property individuation. On some accounts, propertiesare individuated intensionally. That is, according to these accounts,there are no two properties that are necessarily co-exemplified: if P isstrictly sufficient for P ′ and P ′ is strictly sufficient for P , then P = P ′ .On such a conception, any property will have at most one negation,

and for any P and P ′ there will be at most one conjunction. For defi-niteness, consider a Lewisian conception of properties as sets of pos-sible individuals. Any such property will have exactly one negation, itscomplement with respect to the set of all possible individuals, and allsets of properties B will have exactly one conjunction, their intersec-tion. For simplicity but inessentially, I assume in what follows thatnegation and conjunction are unique.

The following is a proof to the effect that if B is closed under Boole-an operations, A-properties strongly supervene on B-properties justin case the former strongly superveneK on the latter.15 To avoid dupli-cation I focus on strong supervenience in the remainder of this sec-tion. (The proof of the same result for weak supervenience and weaksupervenienceK is a straightforward variant.)

R IGHT TO LEFT: Suppose that A-properties do not strongly supervene on B-properties. Then there are some worlds w and w ′ and indi-

viduals x and y such that x in w is A-discernible but B-indiscerniblefrom y in w ′ . Consequently, there is some A-property P which is suchthat either (i) x has P at w and y does not have P at w or (ii) x does nothave P at w and y has P at w ′. If (i) is the case, at w , x has an A-property, P , but no B-property that is strictly sufficient for P , since atw ′ , y has the B-properties x has at w but not P . If (ii) is the case, y hasP but no B-property strictly sufficient for P . Either way, it is possiblethat there is an individual with an A-property but without any B-

14 Since B may be infinite if A is, satisfaction of (Con) may require ‘inf i-nite’ conjunctive properties to be in A.15 Cp. e.g. Kim 1987, 317f.




property strictly sufficient for that A-property. If A-properties donot strongly supervene on B-properties, A-properties do not strongly

superveneK on B-properties.LEFT TO R IGHT: Suppose that (i) A-properties strongly supervene onB-properties and that (ii) x has some A-property Q at some world w .Let Bx,w be the set of B-properties x has at w . Bx,w B. So, by (Con),there is a P

B, the conjunction of all B-properties x has at w , suchthat

□ z □( z has P ↔ P ′ ( P ′

Bx,w → z has P ′ )).

Call that property ∩Bx,w —the maximal B-property x has at w . Trivially, xhas ∩Bx,w at w . It is easy to see that ∩Bx,w is strictly sufficient for Q.Consider any y with ∩Bx,w at any w ′. Since y has ∩Bx,w at w ′ , (iii) x in wis B-indiscernible from y in w ′ . By (i) and (iii), x in w is A-indiscerniblefrom y in w ′ . So, by (ii), y has Q at w ′ . Since x and w were chosen arbi-trarily and Q was an arbitrary A-property, A-properties strongly su-perveneK on B-properties, provided the former supervene strongly onthe latter.

To see that (iii) holds, consider any B-property P . Either (a) x has P atw or (b) x does not have P at w . If (a), P

Bx,w . Hence,

□ z □( z has ∩Bx,w → z has P ).

So, y has P at w ′ . If (b), by (Neg), there is a P ′ B, the negation of P ,such that

□ z □( z has P ′ ↔ ¬z has P ).

Since, x does not have P at w , x has P ′ at w , and P ′ ∩Bx,w . So, by thesame reasoning as above, y has P ′ at w ′ . Since P ′ is the negation of P , ydoes not have P at w ′ . Since P was an arbitrary B-property, x in w is B-indiscernible from y in w ′ .

The proof is beyond dispute. It is often pointed out, however, thatthe result is too weak to license the claim that strong supervenienceand strong supervenienceK are equivalent notions. It is easy to see

that they are not. For, consider a set of properties, NECESSARY , thatcontains only necessary properties —properties had by everything atevery world —and a set of properties, IMPOSSIBLE, that contains only



STEINBERG108

impossible properties —properties not had by anything at any world.NECESSARY -properties strongly supervene on IMPOSSIBLE-

properties. For, any x at any w is indiscernible from any y at any w ′ with respect to NECESSARY -properties full stop. So, a fortiori , they areindiscernible in these respects, provided they are indiscernible with re-spect to IMPOSSIBLE-properties as well. However, NECESSARY -properties do not strongly superveneK on IMPOSSIBLE-properties,since my coffee mug has a NECESSARY -property but no IMPOSSIBLE-property strictly sufficient for it, since it has no IMPOSSIBLE-property full stop.

This result is not surprising, since the above proof relies on the as-sumption that A-and B-properties are closed under Boolean opera-tions, while Impossible (and Necessary) are not. In fact, the Booleanclosure of IMPOSSIBLE —the smallest superset of Impossible closedunder Boolean operations —simply is the Boolean closure of Neces-sary, so that ‘they’ trivially strongly superveneK . But many sets we areparticularly interested in may not be closed under Boolean operationseither. This may be either so because (i) not every property has a ne-

gation and not every set of properties has a conjunction, or (ii) eventhough they do, negations of A-properties and conjunctions of A-properties need not be A-properties themselves.16

The first worry should perhaps not impress us too much. As dis-cussed in section 1.1 above, the conception of properties typicallyemployed in the supervenience debate is an abundant one. On such aconception it is hard to see how the existence of negations or con-junctions can be denied. In fact, on Lewis’s account, for instance, we

have already seen that it is easily provable that (Neg) and (Con) arealways satisfied. The second worry cannot be so easily dismissed,however. For, suppose that negations of A-properties are always A-properties. Then numbers would have mental properties, for instance,simply because they do not think. Similarly, thoughts would have weight properties, simply because they do not weigh 5 kg. These ex-amples make it likely that virtually no set of properties we are typical-ly interested in will be closed under Boolean operations. But when

the sets are not closed under Boolean operations, the two notionsmay give different verdicts. In fact, since the proof of the right to left

16 See, e.g., McLaughlin 1995.




direction does not appeal to Boolean closure, strong supervenienceK has been shown to be strictly stronger than strong supervenience:

whenever A-properties strongly superveneK on B-properties, theystrongly supervene, but not vice versa .

We should not overrate this result, however.17 It does not show, forinstance, that in characterising some forms of supervenience — weakand strong supervenience as originally defined — we cannot do with-out appeal to possible worlds. Nor does it mean that Kim has simplyadded to the family of supervenience notions his own pair of strict-er-than-usual ones. For, in the immediate vicinity of supervenienceK

there is a characterisation of a notion of strong supervenience that isprovably equivalent to our original one.

In fact, there are two. An obvious variant of (Strong K ) replaces ‘B’ inthe definiens throughout with ‘B( B )’ which designates the Boolean closure of B. The Boolean closure of a set of properties B is the smallestset which contains all properties in B and is closed under (Neg) and(Con). It is easy to see that this characterisation agrees with the origi-nal one, whether or not B itself is closed under Boolean operations. The crucial fact here is that A-properties strongly superveneK on B-properties just in case A-properties strongly superveneK on B( B )-properties.

The second variant is discussed and exploited by Fabrice Correia inhis 2005, chapter 6. Since it will play a role in further developments insection 3, it deserves some more attention. Correia’s variant utilisesthe fact that we can speak of properties in the plural, saying that they

are jointly had by an individual. The idea is that —unlike the definiensof (Strong K ) — we should not require that for every A-property thereis some single B-property strictly sufficient for the A-property. Rather, we should only require that for every A-property there are some B-properties which are collectively sufficient for the A-property.

Let us use double letters as plural variables, making the necessarygrammatical changes in the sentences that contain them. ‘ QQ

( QQ B x has QQ )’, for instance, is to be read as ‘There are some

properties such that they are elements of B and x has them’, where

17 As some of the literature, e.g., McLaughlin 1995, tends to do.




1.4 Global Supervenience

In addition to the local notions of weak and strong superveniencephilosophers have been interested in global supervenience. Sometimes,it is plausible to think, the world-wide distribution of one kind ofproperties B fixes the world-wide distribution of another kind ofproperties A, even when the individual-by-individual distribution ofB-properties does not so fix the distribution of A-properties. Con-sider for instance the set of properties W EIGHT and the propertyMOST W EIGHT. A property is an element of W EIGHT just in case it isthe property of weighing n kg, for some number n. MOST W EIGHT is

the property of weighing at least as much as anything else. Now, intu-itively, worlds that agree in the distribution of W EIGHT-propertiesagree in their distribution of MOST W EIGHT. If both at w 1 and w 2Fred has the property of weighing 80 kg and nothing has the proper-ty of weighing 80+m kg for some positive number m, then Fred hasthe property of weighing at least as much as anything else at both worlds. This generalises: MOST W EIGHT globally supervenes on W EIGHT-properties. However, MOST W EIGHT does not strongly su-

pervene on W EIGHT-properties.19 We can see this by considering afurther world w 3 which is like w 2 apart from containing an extra thing,Frank, that weighs 81 kg. At w 1, Fred weighs at least as much as any-thing else, but Fred has no W EIGHT-properties that are strictly suffi-cient for having MOST W EIGHT. For, at w 3, Fred weighs 80 kg as well,but does not weigh at least as much as anything else, since Frank weighs more than Fred.

A more controversial but (philosophical) real life example in which

global but not individual supervenience may be present is the mentaland the physical. Suppose mental content is partly determined exter-nally. Perhaps, e.g., at w 1, Fred on earth thinks about water whenphysically indiscernible Frank on far-away twin-earth thinks abouttwater.20 Then MENTAL-properties do not even weakly supervene on

19 It is customary in the supervenience debate to speak of the superveni-ence of some property P, when only a single property rather than a plurality

of them is at issue. Strictly speaking, such claims should be understood toconcern P ’s unit set , {P }.20 For this to be plausible Fred and Frank have to be unlike any Freds andFranks we are likely to encounter at the actual world: they cannot themselves




Our intuitive discussion conformed to this understanding of what itis for worlds to agree on their distribution of some properties. When we considered whether MOST W EIGHT supervenes on W EIGHT-properties or whether MENTAL-properties supervene on PHYSICAL-properties, we considered whether there are worlds at which the verysame things have the same W EIGHT/PHYSICAL-properties but differ inMOST W EIGHT viz. MENTAL-properties. However, more recent dis-cussions of global supervenience favour a more lenient understand-

ing of the notion in question, upon which various alternative notionsof global supervenience can be based.

To understand what is at issue consider two worlds w 4 and w 5. At w 4,there are only two individuals a and b , a has P and does not have Q, while b has Q and lacks P . At w 5, there are some other individuals cand d , c has P and lacks Q, while d lacks both P and Q (see figure 1).Do w 4 and w 5 agree on their distribution of P ? Well, they do notagreeK : at w 4, a has P , while at w 5, a does not have P . In another sense,

however, they do agree. For, at both w 4 and w 5, there is exactly onething with P and exactly one thing without P . To be precise, eachthing that exists in one world can be paired up with exactly one P -indiscernible thing at the other.

More formally, let us define the notion of an A-isomorphism be-tween world-domains as follows:21

21 For the sake of brevity, I will often drop mention of the domain in thiscontext and speak about isomorphisms (and bijections generally) between worlds.

a has P¬ b has P

¬a has Qb has Q

w 4

c has P¬ d has P

¬ c has Q¬ d has Q

w 5

Figure 1: w 4 and w 5



STEINBERG114

A -ISOMORPHISM

f is an A-isomorphism between the domains of w and w ′ ↔df.

(i) f is a function that maps each element in the domain of w tosomething in the domain of w′ ( f is a function from D( w ) toD( w′ ))

(ii) each element of D( w′ ) is such that f maps something to it ( f isonto)

(iii) each element of D( w′ ) is such that f maps no more than onething to it ( f is one-one)

(iv) x

D( w ) P

A(at w , x has P ↔ at w′ , f ( x ) has P ).

If conditions (i), (ii) and (iii) are fulfilled, f is a bijection from the do-main of w to the domain of w ′ , i.e. f pairs up each thing that exist atone world with exactly one thing that exists at the other. Condition(iv) ensures that the pairs have the same A-properties at their respec-tive worlds. For this reason, we may also call A-isomorphisms A- preserving bijections .

On the present proposal, worlds w and w agree in their distribution of

A-properties just in case there is an A-isomorphism between them.22 The identity function on D(w) —the function that maps everythingthat exists at w to itself and does nothing else —is a candidate to besuch an A-isomorphism. So, whenever w and w ′ agreeK in their distri-bution of A-properties, they agree in the present sense. But, as w4and w5 show, some worlds agree in their distribution of A-propertiesmerely in the present sense, since, although their domains are not thesame, there is a function that maps them to each other in the right

way. In our example, this is the function f 1 that maps a to c and b to d(and does nothing else). This is so, since (i) f 1 maps each member of{a, b} to some element in {c, d }, (ii) both c and d are the value of ffor some argument, namely a and b respectively (iii) neither c nor d arethe value of f 1 for more than one argument, and (iv) P is exemplifiedby both a at w4 and c, at w 5, and lacked by both b at w4 and d, at w 5. The less mathematically minded reader may picture the inhabitants ofthe two worlds divided by a boundary but connected across theboundary by pieces of string. The f 1-way of tying the string binds a

22 This proposal can be traced back at least to Kim (1988, 115f.) and Paulland Sider (1992, 851).




to c and b to d . In general, w and w ′ will agree in their distribution of A-properties just in case there is a way of tying the string so that each

thing on either side is at the end of exactly one piece of string, nopiece of string is left dangling, and all things connected by a piece ofstring share their A-properties.

Plugging this more lenient understanding into our initial characterisa-tion we get so-called weak global supervenience :

WEAK GLOBAL SUPERVENIENCE

A-properties weakly globally supervene on B-properties ↔df.

w, w ′ ( f ( f is an A-isomorphism between w and w ′ ) → g ( g is a B-isomorphism between w and w ′ )).

In words: A-properties weakly globally supervene on B-propertiesjust in case all A-isomorphic worlds are also B-isomorphic. In ourexample, for instance, P does not supervene on Q, since —as alreadydiscussed —there is a P -but no Q-preserving bijection between w 4 andw 5. f 1 itself is not Q-preserving, since it pairs b with d , and b has Q atw 4 while d lacks Q at w 5. The only other bijection between the two

worlds, the function f 2 which pairs a with d and b with c , is not Q-preserving either, since c lacks Q at w 5. In short: w 4 has one Q-thing, while w 5 has none, so no bijection will be Q-preserving: P does not weakly globally supervene on Q.

As the name suggests, weak global supervenience is rather weak. Its weakness consists in the fact that it requires of worlds between whichthere is an A-preserving bijection only that there also is some or otherB-preserving bijection. It does not require that any A-preserving bi-

jection is itself B-preserving. Consider w 4 and a world w 6 which is justlike w 5 except that c has Q (see figure 2). w 4 and w 6 do not constitute acounterexample to the weak global supervenience of P on Q, sincethere is a Q-isomorphism between w 4 and w 6, namely f

2. However, no

bijection between w 4 and w 6 is both A-and B-preserving. In fact, thedistribution of Q does not seem to be determined by the distributionof P in any particularly strong sense, since, as w 4 and w 6 show, thesame distribution of P allows contrary distributions of Q, i.e. distribu-

tions in which the P -thing plays the Q-role of a non-P -thing. AsLeuenberger (2009, 117) points out, weak global supervenience of A-



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on B-properties merely ensures that the distribution of B-propertiesfixes how many things have A-properties.

For applications in which a little less lenience is required, there arestricter notions of global supervenience that require some or eventotal coordination between A-and B-preserving bijections. These no-tions are intermediate and strong global supervenience:23

INTERMEDIATE GLOBAL SUPERVENIENCE

A-properties intermediately globally supervene on B-properties ↔df.

w, w ′ ( f ( f is an A-isomorphism between w and w ′ ) → g ( g is an A-isomorphism between w and w ′ g is a B-isomorphism between w andw ′ )).

S TRONG GLOBAL SUPERVENIENCE

A-properties strongly globally supervene on B-properties ↔df. w, w ′ ( f ( f is an A-isomorphism between w and w ′ ) → g ( g is an A-isomorphism between w and w ′ → g is a B-isomorphism between w

and w ′ )).In words: A-properties intermediately globally supervene on B-properties just in case whenever there is an A-isomorphism between worlds, some A-isomorphism between them is also a B-isomorphism.

23 Something like weak global supervenience (albeit with a restriction onadmissible bijections) was already suggested in Paull and Sider (1992). Stal-naker (1996, 227) and McLaughlin (1997, 214) seem to be the earliest au-

thors to have distinguished from it the notion of strong global superveni-ence. The notion of intermediate (or middling , as Bennett calls it) global su-pervenience was independently introduced by Shagrir (2002) and Bennett(2004).

a has P¬ b has P

¬a has Qb has Q

w 4

c has P¬ d has P

¬ c has Q¬ d has Q

w 6

Figure 2: w 4 and w 6




A-properties strongly globally supervene on B-properties just in case whenever there is an A-isomorphism between worlds,24 all A-

isomorphisms between them are also B-isomorphisms. Clearly, w 4 andw 6 show that P neither intermediately nor strongly globally superveneson Q, since f

1is the only P -isomorphism between them, while it is not

also a Q-isomorphism.

It is an interesting question which variant of global superveniencephilosophers have in mind when they speak about global superveni-ence without further specification. Bennett (2004) conjectures thatthe notion is closest to intermediate global supervenience, since the

latter shares the former’s commonly recognised strengths and weak-nesses. Leuenberger (2009) argues that it is none of the above, sinceall of the explications have features that global supervenience is notmeant to have. In any case, the notions are sufficiently different for itto seem advisable to keep in mind that there are many relations thatmay be meant by the term ‘global supervenience’.

Let us end this overview of the different forms of supervenience with a quick look at multiple domain supervenience.

1.5 Multiple Domain Supervenience

So far we have been concerned with kinds of supervenience in whoseparadigm examples either (i) the distribution of one kind of proper-ties over an individual determines the distribution of another kind(weak and strong (individual) supervenience), or (ii) the distributionof one kind of properties over a whole world determines the distribu-tion of another kind (global supervenience). Multiple domain supervenience caters for needs in between these two extremes. Consider,for instance, wholes and their parts (e.g. a bicycle and its frame, tiresand so forth) or constituters and constitutees (like, perhaps, lumps ofclay and statues, or bodies and persons). It’s a prima facie plausible view that many if not all properties of wholes supervene on theproperties of their parts. Likewise, if statues are not identical withlumps of clay, then, perhaps, at least many if not all properties of the

24 The ‘

f ( f is an A-isomorphism between w and w ′ ) →’ part of Strong

Global Supervenience is redundant, since ‘ x Fx → x ( Fx → Gx )’ and ‘ x( Fx → Gx )’ are logically equivalent. It is only included for uniformity.



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former supervene on properties of the latter. To give just one exam-ple, weight properties of wholes seem to supervene on the weight

properties of their proper parts. Roughly, no composites have differ-ent weights although the distribution of weight properties amongtheir proper parts is the same. In his 1988, Jaegwon Kim introducedmultiple domain supervenience in order to provide the resources toframe such theses.

Kim’s basic idea is as follows. While in the case of individual supervenience the very same things have A-and B-properties, we may beinterested in A-properties of one kind of things and ask ourselves

whether they are correlated with B-properties of things that stand in acertain relation to the things that have the A-properties, e.g. those thatconstitute the things with the A-properties or those that compose them. The relation in which the bearers of A-properties and the bearers ofB-properties stand is called the coordination relation . The title multipledomain supervenience derives from the typical case in which the coor-dination relation relates different kinds of things, i.e. different domains . As in the case of individual supervenience, there is a weak and

a strong form of multiple domain supervenience, depending on whether only intra-or also inter-world constraints are imposed:25

WEAK MULTIPLE DOMAIN SUPERVENIENCE

A-properties weakly superveneMD on B-properties with respect to R ↔df.

w, x, y, C, D (( z ( z C ↔in w , z stands in R to x )z ( z D ↔in w , z stands in R to y )

C in w is B-indiscernible from D in w ) → x in w is A-indiscernible from y in w ).

S TRONG MULTIPLE DOMAIN SUPERVENIENCE

A-properties strongly superveneMD on B-properties wrt R ↔df.

w, w ′ , x, y, C, D (( z ( z C ↔in w , z stands in R to x )z ( z D ↔in w ′, z stands in R to y )

C in w is B-indiscernible from D in w ′ ) → x in w is A-indiscernible from y in w ′ ).

25 Cp. Kim 1988, 124f. Unlike the present definition proposals, Kim doesnot deal with the potential world-relativity of the relation R there.



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claims, e.g. whether it is always the case that some set of properties A weakly supervenes on a set of properties B, given that A strongly

supervenes on B.26 This is how the entailment questions will be un-derstood in what follows.

Some of these questions have rather obvious answers that can begiven on the basis of logic alone. As a matter of basic predicate logic,for instance, if everything that is B-indiscernible is also A-indiscernible,then, a fortiori , all world-mates that are B-indiscernible are also A-indiscernible. Thus, strong supervenience entails weak supervenience.

Or consider the varieties of global supervenience. Suppose that all B-isomorphisms between worlds are A-isomorphisms whenever there isan A-isomorphism at all. Then, as a matter of basic predicate logic,some B-isomorphism between worlds is an A-isomorphism wheneverthere is an A-isomorphism. And if the latter is the case, then there isa B-isomorphism between worlds whenever there is an A-isomorphism. Consequently, strong global supervenience entails in-termediate global supervenience, which in turn entails weak globalsupervenience.

Finally, strong (individual) entails strong global supervenience. If eve-rything that is B-indiscernible is A-indiscernible, then every bijectionbetween world-domains that only pairs B-indiscernible objects onlypairs A-indiscernible objects.

On the other hand, some entailments obviously do not hold. For in-stance, we have already seen potential cases of weak without strongsupervenience: unsurprisingly, that B-indiscernible world-mates are A-

indiscernible does not guarantee that all B-indiscernible possible ob-jects are also A-indiscernible. Interestingly, though, as Bacon (1986)points out, if A and B satisfy a further condition (being closed underworld-diagonalisation as he calls it), the entailment holds. I provide asimplified variant of Bacon’s result: if A-and B-properties are closedunder world-relativisation and A-properties weakly supervene on B-properties, A-properties strongly supervene on B-properties. Closureunder world-relativisation ensures that if w is a possible world and P

26 Talk of entailment is legitimate if a bit grand, since supervenience itselfis a modal notion, so that the universal claims in question will be necessarilytrue if true at all.




is in A, some property Q is in A as well that satisfies the followingcondition:

WR □ x □( x has Q ↔ at w, x has P ).

Informally, we may think of a given such property as the property ofhaving P at w (as in the case of negation and conjunction, legitimacyof the definite article depends on questions of property individua-tion). The argument is rather straightforward: suppose that A-properties weakly supervene on B-properties and that A and B areclosed under world-relativisation. Let c and d be possible individuals

and w 1 and w 2 possible worlds such that c at w 1 is A-indiscernible fromd at w 2. Since A is closed under world-relativisation, for each propertyP A, there is a property Q A such that □ x □( x has Q ↔ at w 1 , xhas P ). Call a property that corresponds to P in this way P w 1. By defi-nition, for any P A, c has P at w 1 iff c has P w 1 at w 1. By A-indiscernibility and the fact that P w 1 A, d has P w 1 at w 2 iff c has P w 1 atw 1. Again by definition of P w 1, d has P w 1 at w 2 iff d has P at w 1. Puttingthese biconditionals together: for all P A, c has P at w 1 iff d has P at

w 1. In other words: c at w 1 is A-indiscernible from d at w 1. By weaksupervenience c at w 1 is B-indiscernible from d at w 1. By strictly analo-gous reasoning, c at w 1 is B-indiscernible from d at w 2. Thus, A-properties strongly supervene on B-properties.

The remaining entailment questions concerning forms of individualand global supervenience are less straightforward. The history of thequestion of whether global supervenience entails strong individualsupervenience is rather turbulent. Since it has contributed to a better

understanding of what is at issue and how (not) to argue for supervenience claims, the main waypoints of the debate will be sketched in what follows.



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2.1 The Entailment Claim

Kim’s 1984, 168, contains an attempted proof to the effect that Glob- al Supervenience K (see p. ?? above) entails strong individual superveni-ence. The attempted proof, however, is flawed.27 This was shown by acounterexample due to Bradford Petrie:28 Suppose logical space is aspictured in figure 3 —there are exactly two possible objects a and band two possible worlds w 1 and w 2. At w 1, both a and b have Q, while a

does and b does not have P . At w 2, neither a nor b have P , while adoes and b does not have Q. In this case P globally supervenesK on Q,but P does not strongly supervene on Q. For, a at w 1 is P -discerniblebut Q-indiscernible from a at w 2. Thus, strong supervenience fails.But, since b has Q at w 1 while b does not have Q at w 2, w 1 and w 2 donot agreeK in their distribution of Q. A fortiori, they do not agree intheir distribution of Q while disagreeing in their distribution of P .Since w 1 and w 2 are the only two worlds, P globally supervenesK on Q.

Kim (1987, §2) retracts the Entailment Claim, referring to the coun-terexample just presented. However, Paull and Sider (1992) challengethe pertinence of Petrie’s example to the most pressing question in

27 Kim merely shows that the fact that A-properties do not strongly supervene on B-properties does not entail that the former globally supervene onthe latter —the second ‘not’ is in the wrong place. The interested readermight want to see for herself. The point at which things go wrong is ‘sinceB* does not entail F, we can consistently suppose that -F(x) in w#’ (Kim

1984, 168).28 See Petrie 1987, 121. Petrie’s article was most influential. The claim thatKim’s alleged proof must be mistaken predates Petrie’s paper, however. Pe-trie himself mentions Hellman 1985. See also Bacon 1986, n7.

a has P¬ b has P

a has Qb has Q

w 1

¬a has P¬ b has P

a has Q¬ b has Q

w 2

Figure 3: Petrie's example




this respect: whether global supervenience metaphysically entails strongsupervenience, i.e. whether it is metaphysically possible for there to be

sets A and B such that A-properties globally supervene on B-properties without strongly supervening. What Petrie’s exampleshows is merely that there is a (strictly) logical possibility, but not alllogical possibilities are metaphysically possible: if Kripke (1980, 112f.)is right, for instance, it is logically possible but metaphysically impos-sible that Elizabeth II. should be born from any other than her actualparents. More pertinently, it is logically possible but metaphysicallyimpossible that there are just two possible worlds.29

Indeed, Paull and Sider (1992, 837ff.) argue that, given that there are worlds w 1 and w 2 as described by Petrie and both P and Q are intrinsic,a plausible reduplication principle guarantees that there will be further worlds that falsify global supervenience of P on Q. Reduplicationprinciples for possible worlds say that if there are worlds of a certainkind, then there are worlds of some other kind as well, correspond-ing to intuitive judgements about what is possible given that someother things are. One very simple such recombination principle is

what Paull and Sider call the principle of Isolation :ISOLATION

For any world w and individual x , if x exists at w , then there is a worldw ′ and an individual y such that(i) only y ( y ′s parts and objects whose existence is necessitated by

the existence of y or y ′s parts) exists at w ′; and(ii)

y at w ′ is a duplicate of x at w .

29 This is a somewhat charitable reconstruction of the debate. In their pa-per, Paull and Sider claim that Petrie must have intended to answer the ques-tion of metaphysical possibility, albeit using inadequate means (p. 836f.).

However, given that Petrie’s target, Kim (1984), aimed to show that the En-tailment Claim holds drawing only on logical resources and closure condi-tions of the base set, Paull and Sider’s claim about Petrie’s intentions appearsdoubtful.



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independent intrinsic properties, being red and being square , for instance.Let R be any property that is such that, necessarily, a possible object

has R just in case it has P and something has Q, i.e.R □ x □( x has R ↔ ( x has P y y has Q )).

Now, R strongly globally supervenes on {P, Q}, i.e. every {P, Q}-isomorphism between worlds between which there is any such iso-morphism is also an R -isomorphism. For, suppose f is a {P, Q}-isomorphism between some worlds w 5 and w 6. Then

(i) x D( w 5 )(at w 5 , x has P ↔ at w 6 , f ( x ) has P )

and

(ii) y D( w 5 )(at w 5 , y has Q ↔ at w 6 , f ( y ) has Q )

Suppose a has Q at w 5. Then, by the definition of R , whatever has Pat w 5 has R at w 5. By (ii), f ( a ) has Q at w 6. Then, again by the definitionof R , whatever has P at w 6 has R at w 6. Thus, by (i), f is R -preserving.Suppose, on the other hand, nothing has Q at w 5. Then, by (ii), noth-

ing has Q at w 6 . But then, by the definition of R , nothing has R at w 5and nothing has R at w 6. Thus, f is R -preserving on this suppositionas well.

But R does not strongly supervene on {P, Q}. For, let w 7 be a world at which c has P while something other than c has Q and let w 8 be a world at which d has P but nothing has Q. Then c at w 7 is {P, Q}-indiscernible from d at w 8. However, c at w 7 is R -discernible from d atw 8, since, by the definition of R, at w 7, c has R and at w 8, d does not

have R. Consequently, {P, Q} and R are a counterexample to the un-restricted Entailment Claim —Strong Global Supervenience does not en-tail strong individual supervenience, and, therefore, neither does In- termediate Global Supervenience nor Weak Global Supervenience .

2.2 Extending the Base

In the last section we saw that when A and B include only intrinsicproperties, we have strong supervenience as soon as we have weak

global supervenience. On the other hand, when A and B include ex-trinsic properties, we may even have strong global supervenience of A on B without strong supervenience of A on B. Stalnaker (1996,




Appendix) shows, however, that whenever A strongly globally supervenes on B, A strongly supervenes on an extension of B, B, where B

+ is

closed under Boolean operations and maximal-B-structural properties(more on this shortly). This section reproduces the proof for Stal-naker’s thesis. It is the last result about logical relations of di fferentsupervenience relations discussed in this survey. Note that the corre-sponding theses concerning weak and intermediate global superveni-ence do not hold (cf. Bennett 2004, Appendix 3).

The intuitive idea behind Stalnaker’s proof is rather straightforward.Let φB,w be a complete structural description of the instantiation of B-properties

at a world w . That is, let φB,w be the existential closure of a very longexistentially quantified conjunction of open sentences that has thefollowing conjuncts:

1. for every individual x that exists at w and every B-property P : ei-ther an open sentence v x has t P if x has P at w or an open sen-tence ¬v x has t P if x does not have P at w ; where v x is a varia-ble uniquely associated in the conjunction with x and t P is a

name of P ;2. for every distinct individuals x and y that exist at w : v x ≠v y

3. a there-are-no-more-individuals-than-these clause

Intuitively, φB,w specifies which maximal B-properties are instantiated byhow many individuals at w .34 Let φB,w,x be the property that a possibleindividual y has at some possible world w ′ just in case φB,w is satisfiedat w ′ and y is B-indiscernible at w ′ from x at w .35 We may call such

properties maximal B-structural properties. Now let B+

be a supersetof B that contains such maximal B-structural properties for each world w and individual x that exists at w . It can then be shown that whenever A-properties do not strongly supervene on the extendedset of properties B+, A-properties do not strongly globally superveneon B-properties.

34 A maximal B-property is a conjunctive property that includes for everyB-property either it or its negation as a conjunct. Recall p. 8 above.35 Deleting the initial quantifier that corresponds to x in φB,w results in anopen sentence that signifies φB,w,x .



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Before we do so, let us specify a closure condition that ensures thatB+ contains the required properties. Let σ be a sequence of properties

in B+ of any (possibly infinite) length. Then B+ also includes a prop-erty P such that

SD □ x □( x has P ↔ τ ( τ is a sequence in which every object oc-curs exactly once α the α th item of τ has the α th item of σ )).36

Intuitively, closure under (SD) ensures that there are properties in B+

that a possible individual has at a world just in case there is somethingin the domain of that world with the first property in σ, there is

something else in the domain of the world with the second propertyin σ …, and there are no other individuals in the domain. Since B+

is

closed under Boolean operations, B+ includes all maximal B-properties. Therefore, closure under (SD) and Boolean operationsensures that B+

includes a property a possible individual has at a

world w just in case, at w , there are n individuals with B-maximalproperty P 1, another m individuals with B-maximal property P 2 …, forany n , m … and all B-maximal properties. Among these properties

will be properties corresponding to the complete structural descrip-tions of the instantiation of B-properties at worlds.37 Since B+ isclosed under conjunction, there will also be properties that an individual has at a world just in case it has one of the properties justmentioned and it has one of the B-maximal properties. In other words, B+

includes all maximal B-structural properties if it is closed

under Boolean operations and (SD).

We can now reconstruct Stalnaker’s argument. Suppose A-properties

do not strongly supervene on B+-properties. Then there are somepossible worlds w and w ′ and individuals x and y such that x at w isB+-indiscernible but A-discernible from y at w ′. Now, at w , x will havesome maximal B-structural property. Call it P . Since x at w is B+-indiscernible from y at w ′ and P is in B+, at w ′, y has P as well. But, by

36 Strictly speaking, there is no sequence in which every object occurs, forthe familiar set-theoretical reasons. For current purposes I ignore this

presentationally unfortunate fact.37 The properties correspond to the description in the way that everythinghas the property at some world just in case the corresponding description istrue at that world.




the definition of maximal B-structural properties, that means that (i)x has the same B-properties at w that y has at w ′, and (ii) w and w ′ have

the same distribution of B-maximal properties. By (ii) there are bijec-tions between D( w ) and D( w ′ ) that are B-preserving. By (i), there isone such bijection that maps x to y . Call it f . Since x at w is A-discernible from y at w ′, there is at least one A-property that x has atw and f ( x )= y lacks at w ′ or vice versa. Thus, f is not A-preserving.Consequently, if A-properties do not strongly supervene on B+-properties, A-properties do not strongly globally supervene on B-properties.38 Contraposing: If A-properties strongly globally super-

vene on B-properties, A-properties strongly supervene on B+

-properties.

2.3 Philosophical Ramifications

There is considerable debate about the philosophical consequencesthe various entailments and failures thereof may have. This is espe-cially striking in the case of strong and global supervenience. Kim(1984, 168) initially welcomed the putative truth of the Entailment

Claim, since he thought that it attested to the naturalness of bothsupervenience notions that two paths must lead to the same outcome.Stalnaker (1996, 228) takes his result to show that ‘global superveni-ence is the appropriate supervenience concept for the statement ofmany supervenience theses’. Bennett (2004, 501), finally, uses the verysame result in conjunction with the weakness of Weak Global Super- venience and Intermediate Global Supervenience to argue for the view that‘global supervenience [is] little more than a chimera’.

It, thus, seems fair to say that philosophical assessment of the somewhat technical results is not univocal. However, what is clear —if notparticularly surprising —is that the more constraints we place on thetwo sets of properties the more equivalences emerge. Intuitively, whathappens is that the properties in the two sets do the work for weakersupervenience notions that is done by the make up of the strongersupervenience notions themselves. The significance of these results

38 This is the step where proof attempts for Weak Global Supervenience andIntermediate Global Supervenience break down, since only Strong Global Superveni- ence requires that f itself is an A-isomorphism.



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will be relativised by the developments in the next section on explan-atorily strengthened supervenience notions.

3. Grounding Supervenience

So far we have introduced various supervenience notions and investi-gated their logical relationships. All of these notions have in commonthat they can be defined in modal terms. Many philosophers believethat this is as it should be: supervenience is essentially a modal no-tion, and nothing more.39 However, there are also arguments availablethat the so-defined notions are not all a friend of supervenience may

have hoped for and should be supplemented. In the first subsection,a case for such a supplementation will be sketched. For some purpos-es at least, it is worth having stronger notions of supervenience. Thesecond subsection introduces such notions. For reasons of space onlyforms of individual supervenience will be discussed.

3.1 Supervenience and Priority

As Kim (1990) stresses, many philosophical applications of superven-

ience rely on supervenience’s being some kind of dependence or(metaphysical) posteriority relation. How else should the fact that A-properties supervene on B-properties appease someone initially scep-tical of A-properties, for instance? But, the argument continues, itcan be shown that the modal definitions do not define posteriorityrelations. Thus, the supervenience relations we have met with so farare not adequate for one of the main purposes of supervenience.40

One strand of the above argument capitalises on the fact that weakand strong supervenience do not even have the required structural features for being relations of posteriority. Let us start then by listing thestructural features of relations at issue. We will follow common prac-tice and say that a relation R has some structural feature within a given

39 Recall the Lewis quotation on p. ?? above. Lewis adds: ‘A superveniencethesis is, in a broad sense, reductionist. But it is a stripped-down form or

[sic] reductionism, unencumbered by dubious denials of existence, claims ofontological priority, or claims of translatability’ (Lewis 1983, 358). Cp., e.g.,McLaughlin and Bennett 2008, §1, and Horgan 1993, 555.40 For a particularly clear statement of the argument see Correia 2005, §6.3.




set A of relata, suppressing the specification when R has the struc-tural feature universally.

Slightly idiosyncratically, let us read ‘xRy ’ as ‘x bears R to y ’. Then wecan define the structural features relevant for our discussion as fol-lows:

Reflexivity R is reflexive in A ↔df. x A xRx

Irreflexivity R is irreflexive in A ↔df. x A ¬xRx

Symmetry R is symmetric in A ↔df. x, y A ( xRy → yRx )

Asymmetry R is asymmetric in A ↔df. x, y A ( xRy → ¬ yRx )

Antisymmetry R is antisymmetric in A ↔df. x, y A (( xRy yRx ) → x = y )

Transitivity R is transitive in A ↔df. x, y, z A (( xRy yRz )→ xRz )

Ordering R is a strict partial ordering of A ↔df. R is asym-

metric and transitive in A

Posteriority relations, the converses of priority relations, are strictpartial orderings. If something x is posterior to something y , then y isnot posterior to x . And if x is posterior to y , which in turn is posteri-or to z , then x is posterior to z .

The relation of strong supervenience, on the other hand, is not a par-tial ordering, and, thus, not a relation of posteriority, whether meta-

physical or otherwise. For, strong supervenience is not irreflexiveand, thus, not asymmetric either. In fact, it is easy to see that strongsupervenience is trivially reflexive in the set of all sets of properties:if x at w is A-indiscernible from y at w ′, x is A-indiscernible from y atw ′. But asymmetry entails irreflexivity. Thus, strong supervenience isnot a asymmetric. Since strong entails weak supervenience, weak su-pervenience is not asymmetric either (Kim 1990, 13).

In response to this result, one might try to define close relatives of

our old supervenience notions that are partial orderings. Kim (1990,13) considers two such attempts: (i) build in irreflexivity by definition;(ii) build in asymmetry by definition. That neither attempt fixes the



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problem can be seen by considering any set A of modally independ-ent properties P and Q and their negations ( A ={P, Q, P ¯ , Q̄ }) and the

corresponding set of possible binary conjunctions of these proper-ties B ={P ∩ Q, P ∩ Q̄ , P ¯ ∩ Q, P̄ ∩ Q̄ }.41

Re (i): A and B are different sets: since P and Q are modally inde-pendent, one may have P without having P ∩ Q and without havingP ∩ Q̄ , one may have Q without having P ∩ Q and without having P ¯ ∩ Qetc. But A-properties strongly supervene on B-properties and B-properties strongly supervene on A-properties. Thus, strong supervenience between different sets of properties is not asymmetric.

Re (ii): Given transitivity, the relation of non-mutual strong superven-ience is guaranteed to be a strict partial ordering. However, B-properties do not non-mutually supervene on A-properties. But therelationship in which B-stand to A-properties is one of the paradigmcases of supervenience (in fact, it is the one we used in this survey toillicit a pre-theoretical feel for the relations at issue). Thus, non-mutual strong supervenience excludes too much.

Non-mutual supervenience also excludes too little. It is easy to showthat sets that only include properties that are either necessarily exem-plified by everything or are necessarily exemplified by nothing weaklyand strongly supervene on any set of properties. In most cases thissupervenience is one-way. For instance, the property of being a num-ber or not being a number non-mutually supervenes on the propertyof being painted by Leonardo da Vinci.42

In short, neither weak nor strong supervenience nor any of their

close relatives are posteriority relations. For any philosophical applica-tion that requires supervenience to be such a relation, the modallydefined notions will not do. The next section sketches how we maybuild on the modal notions to arrive at supervenience notions thatpick out relations of posteriority.

41 Kim himself uses a different example he borrows from Lombard (1986,225ff.): the sets of perfect sphere volume properties and the set of perfect

sphere surface area properties. However, on an intensional individuation ofproperties the example is problematic, since then we do not have two setsbut one.42 Cp. Correia 2005, 139f.




3.2 Supervenience and Grounding

Weak and strong supervenience are not relations of posteriority. There are two consequences one may reasonably draw from this.First, one may take this to show that it is simply mistaken to take su-pervenience to require posteriority.43 Second, one may try to improveon extant definitions. Some quotations from authors who have ap-pealed to notions of supervenience without subscribing to the defini-tions of section 1 above, indicate an attractive way of pursuing thesecond option.

Thus, Jonathan Bennett writesI shall say that events are supervenient entities, meaning that alltruths about them are logically entailed by and explained or madetrue by truths that do not involve the event concept. (Bennett1988, 12)

Hare, discussing the supervenience of the property of being a goodpicture on natural properties, maintains:

[W]e cannot say ‘[Picture] P is exactly like Q in all respects savethis one, that P is a good picture and Q is not’. If we were tosay this, we should invite the comment, ‘But how can one begood and the other not, if they are exactly alike? There mustbe some further difference between them to make one goodand the other not.’ (Hare 1952, 81)

Lastly, Sidgwick on moral/non-moral supervenience:

There seems, however, to be this difference between our con-ceptions of ethical and physical reality: that we commonly re-fuse to admit in the case of the former — what experiencecompels us to admit as regards the latter — variations for which we can discover no rational explanation. In the variety of coex-istent physical facts we find an arbitrary element in which wehave to acquiesce, […]. But within the range of our cognitionsof right and wrong, it will generally be agreed that we cannotadmit a similar unexplained variation. We cannot judge an ac-tion to be right for A and wrong for B, unless we can find in

43 See, e.g., McLaughlin and Bennett 2008, §3.5.



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the nature or circumstances of the two some difference which we can regard as reasonable ground for difference in their du-

ties. (Sidgwick 1884, 206) All three of these authors seem to work with a supervenience notionthat is stronger than the purely modally defined notions of weak andstrong supervenience. For, Bennett requires truths about other thingsto explain or make true the truths about events, Hare wants some fur-ther property to make a good picture good , and Sidgwick asks for areasonable ground of the difference between right and wrong actions.Given the tight connection between (non-causal) explanation, making

something a certain way (a good picture, true etc.) and the metaphysi-cal notion of ground, the three passages suggest that we should a adda grounding requirement to candidate notions of supervenience.44 Thissuggestion is taken up in Correia 2005, §6. In what follows I intro-duce the resulting notions of weak and strong grounding superveni-ence, and show how they can avoid the charge of not being posteri-ority relations.

The relevant notion of grounding is further discussed in the articleby Kelly Trogdon in this volume, so we may be brief. Let us write ‘φ1 ,φ2 ,... α ’ for ‘φ1 and φ2 … together ground α ’, and ‘[p]’ for ‘the factthat p’. We can now take a simplified version of Correia’s alternativecharacterisation of strong supervenience (recall p. ?? above)45 and adda grounding requirement: instead of only requiring that for every A-property an individual has there are some B-properties that are strict-ly sufficient for having the A-property, the new notion of ground-supervenience additionally requires that these B-properties must

ground the A-property. That is,S TRONG GROUND-SUPERVENIENCE

A-properties strongly ground-supervene on B-properties ↔df.

□ x, P (( P A x has P) → QQ( QQ B x has QQ □ y ( y has QQ → [ y has QQ ] [ y has P ]))).

44 For the connection between grounding and non-causal explanation see,

e.g., the articles collected in Correia and Schnieder 2012. For the connectionbetween making and grounding see Schnieder 2006.45 Unfortunately, Correia (2005, 142ff.) does not explain the need for thesimplification.




We get a corresponding notion of Weak ground-supervenience bydeleting the second occurrence of ‘□’ in the definiens.46 By way of

explaining the workings of Strong ground-supervenience reconsider thetwo sets A ={P, Q, P ¯ , Q̄ }, and the corresponding set of conjunctionsB ={P ∩ Q, P ∩ Q̄ , P̄ ∩ Q, P ¯ ∩ Q̄ }. A-and B-properties mutually stronglysupervene on each other. But B-properties strongly ground-supervene on A-properties without the latter ground-supervening onthe former. For, plausibly, something’s having a property in B is nec-essarily grounded in that thing’s having some properties in A, but not vice versa. Take for instance P ∩ Q, the property of having P and Q.

Necessarily, everything that has P and has Q, has P ∩ Q as well. In fact,something stronger is true: everything that has P and has Q has P ∩ Qbecause it has P , and it has P ∩ Q because it has Q. Stronger still, neces-sarily, whenever something has P and has Q, the fact that it has P andthe fact that it has Q conspire to ground the fact that it has P ∩ Q. This generalises. Therefore, B-properties strongly ground-superveneon A-properties. But A-properties do not ground-supervene on B-properties. For, although, for instance, it is necessary that whateverhas P ∩ Q also has P , if something has P ∩ Q this fact does not ground

the fact that it has P . The direction of grounding goes from the con-juncts to the conjunction, not the other way around.47 For this rea-son, the direction of ground-supervenience goes that way as well.

It can be shown that, generally, strong ground-supervenience is anasymmetric relation that entails strong supervenience. Strong ground-supervenience is, thus, a prime candidate for the job strong superven-ience was initially intended to do. This is due to three features of

grounding: its factivity and the fact that even partial grounding isasymmetric and transitive. Let us start with factivity. Only facts standin the grounding relation, and if it is a fact that p, then p. That is:

46 These definitions correspond to what Correia (2005, 143) calls strongand weak property supervenience1.47 For more on the logic of ground see Fine forthcoming and Schnieder2011.



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F ACTIVITY OF GROUND

□([ p1 ] , [ p2 ]... [ q ]→( p1 p2 ... q )).48

Given Factivity of Ground , the definiens of (StrongC) on p. ?? is astraightforward consequence of the definiens of Strong ground- supervenience .

Let us write ‘φ1 φ2’ for ‘φ1 at least partially grounds φ2’, defined asfollows:

P ARTIAL GROUND

φ1 φ2 ↔df. φ1

φ2 αα φ1 , αα

φ2.Some fact at least partially grounds another if the former grounds thelatter either by itself or with the help of some further facts. Now, inthe debate about grounding it is generally accepted that partialgrounding (and, thus, grounding as well) is asymmetric and transitive:

A SYMMETRY OF P ARTIAL GROUND

□ φ, α □( φ α → ¬α φ )

TRANSITIVITY OF P ARTIAL GROUND □ φ1 ,φ2 ,φ3 □(( φ1 φ2 φ2 φ3 ) → φ1 φ3 ).

Given these two structural features of grounding, it is quite straight-forward to see that strong ground-supervenience must be asymmetric(within the set of sets that include exemplifiable properties).49 For,suppose A-properties strongly ground-supervene on B-properties. Then for every A-property P had by some possible individual x thereare some B-properties QQ that x has such that, necessarily, if any y

48 Strictly speaking, the factivity principle should use quantification intosentence position in the following way to ensure that only facts stand in thegrounding relation:□ x 1 , x 2 ... y ( x 1 , x 2 ... y → p1 , p2 ... q ( x 1 =[ p1 ] x 2 =[ p2 ] ... y =[ q ] p1

p2 ... q )).Since this is non-standard, I leave it at the schema in the main text.

49 The parenthetical remark is necessary to include the trivial case. For, takeany set that includes only unexemplifiable properties. Such a set triviallystrongly ground-supervenes on itself. Arguably, such a case should be –excluded by definition.




has all of QQ, the fact that y has P is grounded in the fact that y hasall of QQ. For each property Q that is one of QQ the fact that y has

all of QQ is at least partially grounded in the fact that y has Q. Thus,by the Transitivity of Partial Ground , for each Q that is one of QQ, thefact that y has Q at least partially grounds the fact that y has P . By the Asymmetry of Partial Ground , finally, P does not even partially ground Q. Since the choice of P and QQ was arbitrary, whenever strongground-supervenience relates an A-property to some B-properties, itdoes not also relate any of the B-properties to properties among which is the A-property. The same holds, mutatis mutandis for the cor-

responding relation of weak ground-supervenience. Let us sum up. The relations of weak and strong supervenience are not partial order-ings and, thus, cannot be relations of metaphysical posteriority. Thecorresponding relations of ground-supervenience entail them andcan be shown to be asymmetric (excluding the trivial case). In virtueof this fact, they have a good claim of capturing interesting supervenience claims. If this is so, two of the main protagonists of thiscollection —supervenience and grounding —are not in competition. To the contrary, grounding may ground supervenience.50

References

Bacon, J. 1986: ‘Supervenience, Necessary Coextension, and Reduci-bility’. Philosophical Studies 49, pp. 163 –76.

Bennett, J. 1988: Events and their Names . Oxford: Clarendon Press.

Bennett, K. 2004: ‘Global Supervenience and Dependence’. Philosophyand Phenomenological Research 68, pp. 501 –29.

Correia, F. 2005: Existential Dependence and Cognate Notions . Munich:Philosophia Verlag.

Correia, F. and B. Schnieder (eds.) forthcoming: Non-Causal Explana- tion . Cambridge: Cambridge University Press.

50 I would like to thank the participants of the Hamburg Colloquium onmetaphysics and the philosophy of language in the summer term 2012 for

helpful discussion. Thanks are also due to Mark Kalderon and the (former)members of Phlox: Nick Haverkamp, Moritz Schulz and particularly MiguelHoeltje and Benjamin Schnieder for discussion and encouragement at vari-ous stages of completion of this material.



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Davidson, D. 1970: ‘Mental Events’. In Foster and Swanson 1970, pp.79 –101.

Fine, K. 2012: ‘Guide to Ground’. In Correia and Schnieder 2012, pp.37 –80.

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Hellman, G. 1985: ‘Determination and Logical Truth’. Journal of Phi- losophy 82, pp. 607 –16.

Horgan, T. 1993: ‘From Supervenience to Superdupervenience: Meet-ing the Demands of a Material World’. Mind 102, pp. 555 –86.

Kim, J. 1984: ‘Concepts of Supervenience’. Philosophy and Phenomeno- logical Research 45, pp. 153 –76.

— 1987: ‘“Strong” and “Global” Supervenience Revisited’. Philosophyand Phenomenological Research 48, pp. 315 –26.

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pp. 129 –50, reprinted in Kim (1993, 109 –30). Page references areto the reprint.

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University Press.Künne, W. 2006: ‘Properties in Abundance’. In Stra wson andChakrabarti 2006, pp. 184 –249.

Leuenberger, S. 2009: ‘What is Global Supervenience?’ Synthese 170,pp. 115 –29.

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— 1986: On the Plurality of Worlds . Oxford: Blackwell.Lombard, L. B. 1986: Events: A Metaphysical Study . London: Routledge

and Kegan Paul.




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http://plato.stanford.edu/archives/fall2008/entries/supervenience/McLaughlin, B. P. 1995: ‘Varieties of Supervenience’. In Savellos and

Yalçin 1995, pp. 16 –59.

— 1997: ‘Supervenience, Vagueness, and Determination’. Noûs 31,pp. 209 –30.

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Putnam, H. 1973: ‘Meaning and Reference’. The Journal of Philosophy

70, pp. pp. 699 –711.Savellos, E. E. and Ü. D. Yalçin (eds.) 1995: Supervenience: New Essays ,

Cambridge: Cambridge University Press.

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— 2011: ‘A Logic for “Because”’. Review of Symbolic Logic 4, pp. 445 –

65.Shagrir, O. 2002: ‘Global Supervenience, Coincident Entities and An-

ti-Individualism’. Philosophical Studies 109, pp. 171 –96.

Sidgwick, H. 1884: The Methods of Ethics . London: Mackmillan.

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Strawson, P. F. and A. Chakrabarti (eds.) 2006: Universals, Concepts and Qualities: New Essays on the Meaning of Predicates , Aldershot: Ash-

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http://plato.stanford.edu/archives/fall2008/entries/intrinsic-extrinsic/







Different Notions of Response-Dependence

Jussi Haukioja

An intuitively compelling distinction seems to exist between thoseareas of discourse in which the facts are in some sense ‘up to us’ andthose in which they are not. For example, it seems that facts concern-ing fashion and humour are in some sense dependent on what wetake to be fashionable or humorous: some x is fashionable, at leastroughly, because we take x to be fashionable. But with respect to manyother areas of discourse, the dependence seems to run in the oppo-site direction. For example, we naturally think that we take things tobe square or solid because they in fact are square or solid. Response-dependence theories were initially proposed as an attempt to sharpen

this distinction. However, the original idea has since been extended in various different ways, with different philosophical aims in mind. As aresult, discussions of response-dependence can sometimes be con-fusing – my hope in the present chapter is to clarify the situation andreduce the risk of misunderstandings, by presenting an overview ofthe main theories and their differences.

1. Introduction

The term ‘response-dependence’ made its entrance into the philo-sophical vocabulary in the late 1980’s, in discussions of values andsecondary properties. During the 1990’s there seems to have beenmuch optimism about using the notion of response-dependence tomake progress with a number of philosophical problems. Response-dependence interpretations of key concepts were proposed in at leastthe following areas: values (Wright 1988, Lewis 1989, Johnston 1989,Smith 1989 and 1994), colours (Wright 1989, Johnston 1992), causali-

ty (Menzies and Price 1993), modality (Menzies 1998), and mathemat-ics (Divers and Miller 1999). Unfortunately, and as we will see, vari-



142 HAUKIOJA

ous notions of response-dependence were proposed, and it is notalways easy to see what presuppositions were being made.

It is, however, easy to point to some shared views. In general, to saythat a concept or a property F is response-dependent is to claim thatthere is an a priori connection between F and our responses (withrespect to F ) in normal, favourable, or ideal conditions.1 Moreover,this connection is characterised by the apriority of some response- dependence biconditional or basic equation of roughly the following kind:

(1) x is F iff x would elicit response R from subjects S in conditions

C . Typically, it is assumed that response R is a cognitive or experientialresponse; thus, concepts of properties which evoke merely bodilyresponses such as nausea or physical well-being are not typically con-sidered as response-dependent. Common examples of response-dependent concepts or properties include redness, fashionableness,amusingness, and so on.

Response-dependence theories are, then, generally committed to theapriority of biconditionals such as (1). Beyond this shared commit-ment, there is room for various options which differ from each otherin important ways. (1) can be thought to express a necessary or a contingent truth; it can be understood as primarily characterizing the property F , or the concept F . Moreover, we’ll see below that one prominent re-sponse-dependence theorist would prefer to give a biconditional witha different scope reading. And, of course, the specifications of R , S ,and C can be fleshed out in a variety of different ways. Response R

has typically been understood as that of x seeming F to S , or of x being judged to be F ; subjects S may be thought to be normal, com-petent, or ideal subjects, conditions C normal, favourable, or idealconditions. I will mostly abstract away from these differences andspeak of standard subjects and conditions. The one thing that every-one would agree with is that R , S , and C should together be specifiedin a substantial or non-trivializing way, that is, in a way which does not

1 An exception to the apriority requirement is Miscevic 1998.



NOTIONS OF RESPONSE-DEPENDENCE 143

make (1) trivially true.2 Beyond this rather obvious requirement, thereis considerable disagreement.

My plan in this paper is to give an overview of the three main ap-proaches to response-dependence: those given by Mark Johnston,Crispin Wright and Philip Pettit. Other authors have used the notionas well, but it is usually not very difficult to locate the notion of re-sponse-dependence that they are assuming as one of these three, or aclose relative. That having been said, it should be obvious that whenthe differences between the different formulations are not firmly keptin mind, misunderstandings will follow.3

The three main notions of response-dependence differ in some keyrespects, as we will see. Perhaps the most important difference con-cerns the aims of the theorists: Johnston and Wright wanted the dis-tinction between response-dependent and response-independentconcepts to mark a difference in the objectivity or mind-independence of the properties that the concepts express. Pettit’snotion of response-dependence, by contrast, was put forward as met-aphysically neutral. Another central disagreement concerns the sourceof the apriority of response-dependence biconditionals. Johnstonand Wright thought that the biconditionals are a priori because therelevant properties are, due to the nature of the concepts in question,somehow conferred or constrained by our responses. Pettit, by con-trast, held that the biconditionals get their a priori status through re-flecting the way our responses fix the reference of response-dependentconcepts. Moreover, Johnston’s and Wright’s versions differed im-portantly in some details of formulation, as well as in their ontologi-

cal consequences.My primary aim in this paper is expository – to point out the maindifferences and connections between the three approaches as clearly

2 Or, as it is sometimes put, we should not give R , S , and C a whatever-it- takes reading. An amusing example of such a reading is given by SimonBlackburn (1993, 273): ‘x is good iff x is such as to elicit astonishment frompolar bears under the ideal circumstances, i.e. those under which polar bears

are astonished at good things’. 3 One example of such a misunderstanding can arguably be found in Mi-chael Devitt’s (2006) criticism of Philip Pettit’s ‘global’ response-dependence view.




some more detail: for colours, the responses mentioned on the righthand side of (2) are plausibly seen as part of the truth condition of the

left hand side: what makes an object red is that it would look red tostandard observers under standard conditions. For shapes, things aredifferent: to the extent that (3) is true, it is true because we are relia-ble detectors of squareness: (3) sustains at most a reading on which thesquareness of an object is part of the causal explanation of why it would look square to standard observers under standard conditions.

Moreover, this difference was thought to be accompanied by a differ-ence in the epistemic statuses of (2) and (3): (2) is plausibly seen as a

priori, while (3) is a posteriori true, if true at all. The term ‘response-dependence’ was coined to denote those concepts for which interest-ing, a priori true biconditionals of this form can be given. Thus, col-our concepts would be response-dependent, while shape concepts would be response-in dependent.

Johnston’s initial idea was to suggest that our moral concepts shouldbe viewed as response-dependent, although he quickly moved to arevisionist position according to which we should adopt an error the-ory regarding our current moral concepts, but could adopt response-dependent moral concepts as ‘surrogates’ (Johnston 1989). Indeed, hesuggested that a similar move should be made in the case of colourconcepts as well (Johnston 1992).

The rationale behind viewing moral concepts (actual or surrogate) asresponse-dependent is that it promises to accommodate our projec-tivist or subjectivist intuitions about morality, while retaining a meas-

ure of realism concerning moral properties. Values, on a response-dependent view, are in a clear sense relative to the kinds of beings weare: values are not properties of the world considered in isolationfrom the ways it affects subjects like us. A response-dependent viewseems promising in that it can fully accommodate this assumption without committing us to non-cognitivism, the view that moraljudgements are not in the business of expressing beliefs (but shouldrather be understood as expressions of emotions, sentiments of ap-proval and disapproval, or something similar). Non-cognitivist viewsdeny the truth-aptness of value attributions, but if moral conceptsare response-dependent, such attributions will obviously be truth-apt:some biconditionals of the form (1) can be used to give us the truth



146 HAUKIOJA

conditions of moral claims. Moreover, response-dependence promis-es to give a ‘cheap’ way of explaining their truth-aptness, without

having to assume an extravagant ontology of values.In general, Johnston thought that when such biconditionals are a pri-ori, the subject matter should be thought of as dispositional. Thisassumption seems to be present already in his early formulations ofresponse-dependence, but it is made explicit in later writings. In par-ticular, in his 1993, Johnston gives an alternative definition of re-sponse-dependence as response-dispositionality : he now takes a conceptF to be response-dependent when and only when an identity of the

following form holds:(4) The concept F = the concept of the disposition to produce R in

S under C ,

where response R ‘essentially and intrinsically involves some mentalprocess’ (Johnston 1993, 103).

Moreover, since Johnston here understands a concept F as a ‘concep-tion or cluster of beliefs de dicto about F s’, it is clear that Johnstonnow understands response-dependent concepts to be ones which arerepresented as expressing dispositional properties, by the agents whopossess them.

If a concept is dispositional in the sense given by (4), it appears that it will ipso facto sustain some a priori biconditional of form (1). Inother words, response-dispositionality entails response-dependence inthe standard sense. But what about the other direction: are there re-

sponse-dependent concepts which are not response-dispositional?Most theorists have assumed that there are, but Johnston disagrees,on the basis of his (in)famous Missing Explanation Argument, to which we will now turn.

3. Johnston: Missing Explanation Argument

With the Missing Explanation Argument ( MEA ), Johnston tried toshow that biconditionals of form (1) can only hold a priori of re-

sponse-dispositional concepts: response-dependent concepts, accordingto Johnston, cannot be concepts of objective properties – properties which can figure in explanations of our cognitive responses. In other




words, the MEA claims that a response-dependent view of, say, ourcolour concepts is incompatible with the compelling view that we

can, relying on the colours possessed by objects, give good empiricalexplanations of our colour judgements. Johnston has presented twodifferent versions of the MEA, which I will here call the ‘old’ and the‘new’ MEA. I will mainly focus on the old MEA.

In fact, even the old MEA was given slightly different formulations in Johnston’s articles (Johnston 1989, 1991 and 1993). What followshere is a reformulation which I think captures the core of the argu-ment.5 The old MEA claimed that the following two claims are incon-

sistent:(5) It is a priori that ( S if and only if S * ).

(6) There can be true empirical explanations6 of the form: S be-cause S *.

If this argument works, it is easy to see how, for example, response-dependent accounts of the colours would be undermined: such anaccount would claim that (5) is true, substituting ‘x is red’ for S * and

something like ‘x would seem red to standard observers in standardconditions’ for S . Yet, it seems intuitively compelling that there can betrue empirical explanations of the form ‘x would seem red to stand-ard observers in standard conditions because x is red’: we wouldnormally not hesitate to explain our colour judgements concerningphysical objects by appealing to the objects’ colours. Yet, if the MEA succeeds, we have to choose between the a priori equivalences andthe empirical explanations. We cannot have it both ways. This is also

the background for Johnston’s revisionist view of colour concepts: our

5 This formulation is similar to the ones given in Menzies and Pettit (1993)and Miller (1995 and 1997).6 Johnston is not operating under any specific theory of what counts as anempirical explanation. The general idea is that ‘a sentence employing the “be-cause” of empirical explanation has a meaning which suits it to be literallyused to convey empirical or epistemically contingent information concerning

a pattern of dependence between facts’ (Johnston 1991, 123). This roughcharacterisation is intended to distinguish the ‘because’ of empirical explana-tion from the ‘because’ of logical explanation and the ‘because’ of concep-tual articulation ( ibid., 123 –4).



148 HAUKIOJA

ordinary colour concepts make incompatible demands on their refer-ents, and should be replaced by explicitly response-dispositional sur-

rogate concepts, which give up on the empirical explanatoriness ofcolours.

The argument for the incompatibility of (5) and (6) is based on thefollowing substitution principle:

(7) Substitution of a priori equivalent expressions cannot turn anempirical explanation into a sentence that is false as an a priorimatter (an explanatory solecism).

Johnston’s reasoning behind (7) is that, although substitution of apriori equivalent expressions may not always preserve the truth ofempirical explanations, such substitution should preserve possible explanatoriness (Johnston 1991, 129 –30). In other words, substitution ofa priori equivalent expressions into a good empirical explanationshould not give us a sentence that can be a priori ruled out as an em-pirical explanation. If (7) is true, the MEA goes through. By (5), S andS * are a priori equivalent; by (7), substitution of S for S * will turn the

empirical explanation mentioned in (6) into an explanatory solecism,‘S because S ’.

The central claim of the MEA is, thus, that a priori equivalent expres-sions cannot function as the explanandum and explanans in an em-pirical explanation. Take colour concepts, as an example. Accordingto the MEA, if it is a priori that:

(2) x is red iff x would look red to standard subjects in standard

conditions,it cannot also be the case that:

(8) x would look red to a standard subject in standard conditionsbecause x is red.

By substituting into explanatory claim (8) on the basis of (2), we would get an explanatory solecism, ‘x is red because x is red’, or ‘x would look red to a standard subject in standard conditions because x

would look red to a standard subject in standard conditions’. Accord-ing to Johnston this shows that, if the a priori equivalence holds, wenever had an empirical explanation to start with, but only the appear-ance of one (‘the explanation goes missing’ ).




The old MEA has received a number of criticisms. One group of crit-icisms focuses on the substitution principle, (7). Alex Miller (1995)

argued persuasively that such a substitution principle may well be trueconcerning definitional equivalences, but that there is no reason tothink it holds for non-definitional a priori equivalences, and that this ishow the response-dependence biconditionals should be interpreted.Moreover, as Miller points out elsewhere (1997), one can arguablyderive (non-definitional) a priori equivalences between instantiationsof natural kinds and reference-fixing descriptions concerning suchkinds. By (7), we should then deny that there can be empirical expla-

nations of the kind ‘ we perceive x as co-instantiating yellowness,heaviness and so on because x is gold’. Cases such as these should atleast make one view (7) with suspicion.7

Another kind of answer to the old MEA is provided by Peter Menziesand Philip Pettit (1993). They claim that the old MEA is based on anequivocation. The right hand sides of response-dependence bicondi-tionals include a dispositional claim concerning how x would look tostandard subjects in standard conditions. Such claims can, according

to Menzies and Pettit, be given two readings: possession readings andmanifestation readings. The a priori equivalences characteristic of re-sponse-dependence theories should be read as concerning the possession of dispositions. Thus, (2) should be read as follows: x is red iff x possesses the disposition to look red to standard subjects in standardconditions. Meanwhile, the explanatory claim (8) should be read asconcerning manifestations of dispositions: when x manifests the dispo-sition to look red to standard subjects in standard conditions, it mani-

fests it because it is red. (2) and (8), on their natural readings, employdifferent readings of the disposition claim, and the argument doesnot go through. The case of redness is in no way special in this re-spect, so we should expect the result to generalise.8

7 Another kind of challenge to the substitution principle is found inMcFarland 1999.8 For completeness’ sake, we can quickly consider three ways of trying toforce the old MEA through, the ambiguity of disposition claims notwith-

standing. First, we might try to read the explanatory claim, (8), according tothe possession reading. This would neutralise the equivocation, but then (8) would claim that x possesses the disposition to look red to standard subjects instandard conditions because x is red. On this reading (8) no longer expresses



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The train of thought leading up to this version of the criterion – Wright is quite clear that this is merely one possible way of drawing

the distinction between detectivist and projectivist concepts, and thusnot the final word10 – is explained in some detail in Wright 1992,108 –24. I w ill here briefly outline Wright’s reasons for the conditionslisted above.

Wright replaced basic equations of type (1) with provisional equationsof type (9). This was done in order to deal with conditional fallacyproblems. These problems were, in the context of response-dependence, raised by Johnston (1993, 119 –121) with the help of

various examples. For instance, we might consider a ‘shy but power-fully intuiti ve chameleon’ which is normally green, but which infalli-bly intuits when it is being viewed, and instantaneously turns tobright red as a result. More generally, these are cases where the satis-faction of C -conditions causes a change in whether F is instantiated. Johnston argued that such cases constitute powerful objections toresponse-dependent accounts which employ basic equations; Wright’sreaction was to replace basic equations with provisional equations

(other reactions are also possible; for a good discussion of condition-al fallacy problems and response-dependence, see Busck Gundersen2006, chapter 8 and Busck Gundersen 2011).

Conditions (i) and (ii) are standard requirements in response-dependence accounts, but the other two conditions require independ-ent motivation. Condition (iii), the independence condition, is neededfor the following reason. If whether the C -conditions for F obtainlogically presupposes facts about the extension of F , then it does not

seem to make sense to view best opinion as constituting F ’s exten-sion; locating the ‘best’ opinions would require that the extension ofF was already determined.11 Condition (iv), the extremal condition, isincluded to rule out cases where (9) is made true, and fulfills condi-

10 Indeed, Wright uses a somewhat different formulation in developing hissuggestion that truths about intentional states should be construed as re-sponse-dependent (Wright 1989). For criticisms of this idea, see Miller 1989,

2007 and 2009.11 Wright (1988) claims that this condition cannot be satisfied in the caseof moral concepts, making a response-dependent account of value impossi-ble.




tions (i)-(iii), because subjects in C -conditions infallibly track the exten-sion of F , although this extension is determined independently of

best opinion. As a putative example of such a concept, Wright con-siders the concept of pain (Wright 1992, 123 –4).

5. Commonalities between Johnston and Wright: Re-sponse-Dependence as a Mark of the Mind-Dependence of Subject Matter

In spite of differences of detail, Johnston’s and Wright’s notions ofresponse-dependence are quite similar in their background and aims – especially compared to Philip Pettit’s notion, to which we will turnin the next section. The most important commonality between Wright and Johnston is that the response-dependence/response-independence distinction is meant to mark a difference in the objectivity of subject matter: it is in the nature of response-dependent con-cepts that they express properties that are in some sense less thanfully objective, while response-independent concepts express objec-tive properties – at least there is nothing about the concepts that

would rule this out. Thus, for both Johnston and Wright, the distinc-tion is meant to have ontological significance, in giving us access to adistinction between the more and the less objective properties, or themore and the less objective subject matters more generally.12

Indeed, in later work Johnston (1998) prefers to understand re-sponse-dependence as a feature of properties rather than concepts, andit appears that nothing of substance is lost in this change of perspec-tive; even the response-dependence biconditionals can remain un-changed. However, caution is needed. While this move may be un-problematic if one is operating under something roughly like John-ston’s or Wright’s notion of response-dependence, we will see in thenext section that on Pettit’s notion, the focus cannot be shifted fromconcepts to properties.13

Another central agreement between Johnston and Wright, which alsosets them apart from Pettit, concerns the source of the apriority ofresponse-dependence biconditionals. Both Wright and Johnston hold

12 For a more recent development of this idea, see Sveinsdóttir 2008.13 As stressed in Brynjarsdóttir 2008.



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that the referents of response-dependent concepts are in some wayrepresented as dispositional or projective, by ordinary speakers. This

is quite explicit in Johnston’s (1993) version: he specifically states thatthe properties picked out by response-dependent concepts are repre-sented as dispositional; they are a priori equivalent with dispositionalconcepts. In Wright, the source of the apriority is not spelled outexplicitly, but Wright clearly thinks that response-dependent conceptsare simply not in the business of expressing objective, mind-independent properties. This is a conceptual matter, and presumably we can find this out by mere reflection on our concepts.

6. Pettit: Response-Dependence and Concept Acquisition

We now turn to the third main conception of response-dependence,that found in Philip Pettit’s work. His view, although it makes use ofbiconditionals similar to those we found in Johnston’s and Wright’s work, is different in some crucial respects.

Like Wright and Johnston, Pettit argues that response-dependencebiconditionals of the form (1) are a priori true for many concepts.However, as we will see below, Pettit’s reasons for thinking that suchbiconditionals are knowable a priori are quite different from Wright’sand Johnston’s. Moreover, Pettit’s understanding of standard condi-tions also differs considerably from that of the other response-dependence theorists, making Pettit-style response-dependence bi-conditionals different in content from Johnston’s and Wright’s equa-tions.

On Pettit’s view, we have to acknowledge a wide-spread response-dependence of concepts to make sense of our ability to acquire con-cepts from examples. Response-dependence is a product of his solu-tion to the Kripkensteinian problem of rule-following, presented inKripke 1982. What follows is a rough outline of his ‘Ethocentric’ theory of rule-following and concept acquisition – for a more de-tailed picture, see Pettit 1990a, 1991, 1998a and 1998b, and Jacksonand Pettit 2002.14

14 For critical responses to Pettit’s theory of rule-following, see Sommer-field 1990, Hindriks 2004 and Boghossian 2005. For a response to Sommer-




Pettit is concerned with the question of how an agent could pick up adeterminate rule – in particular, acquire a determinate concept –

from a finite array of examples. According to Pettit, one preconditionfor an agent S to be able to accomplish this is that the examplesshould appear similar to each other, in such a way that S can developa disposition to classify new things as being relevantly similar to theexemplars or not. That is, having been exposed to a range of objects which are F , S begins to somehow treat objects as F or non-F in nov-el situations.

But more needs to be said. The mere inclination to classify things

according to whether they seem F or not is not sufficient for attrib-uting the concept F to the subject. In order for S to possess the con-cept F , S ’s applications have to have correctness conditions. That is,something about S (possibly in conjunction with facts external to S )must determine what entities F correctly applies to, such that correctapplication can diverge from S ’s actual applications of F . Appealingmerely to S ’s extrapolative dispositions will only give us the distinc-tion between those things that seem F to S and those that do not, so

possession of such dispositions cannot be all there is to possessingthe concept F .

To account for correctness conditions, Pettit appeals to his novelspecification of normal or favourable conditions: favourable condi-tions are determined through corrective practices . When we find discrep-ancies in judgements, either between the judgements made of thesame situation by different agents or between judgements made byone individual at different times, we take them to signal errors. That

is, we have higher-order dispositions to react to discrepancies betweenmanifestations of our first-order, extrapolative dispositions. Roughly, when one and the same x has been judged both F and non-F , wehave the inclination to resolve this discrepancy by looking into theconditions in which those judgements were made. To the extent that we are able to locate, in the circumstances in which the conflictingjudgements were made, factors which explain the discrepancy, we canstart to treat judgements of F -ness made in such conditions as unfa-

vourable. Pettit’s novel idea is to define favourable conditions for ap- field, see Pettit 1990b; for a response to Hindriks, see Haukioja 2005; for aresponse to Boghossian, see Pettit 2005.



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plying concept F functionally, as those kinds of conditions which areapt to survive such corrective practices with respect to F .15

Given this account of favourable conditions, it follows, according toPettit, that it is a priori that:

(10) x is red iff x would seem red to standard subjects in favourableconditions.

The reason that (10) will be knowable a priori is that, on the Etho-centric account, our responses regarding F -ness in favourable condi-tions fix the reference of F . In other words, F expresses that property,

whichever it happens to be, that fits our inclinations to judge thingsas F in favourable conditions. The apriority of (10) follows for famil-iar Kripkean reasons.16 We should note that Pettit is not claiming that(10) would be in any way obvious to those who possess the concept ofredness, far less that an agent should believe (10) in order to possessthe concept. Rather, the claim is that (10) is knowable merely on thebasis of reflection on how the extension of the concept of redness isfixed. The role of responses as reference-fixers also has another im-

portant consequence. On Pettit’s version of response-dependence,biconditionals such as (10) – where the specifications of standardsubjects and standard conditions are not rigidified – are not necessarybut contingent.17 As we saw above, this makes Pettit-style response-dependence fall outside the scope of Johnston’s Missing Explanation Argument.

15 For a detailed exposition of this definition of normal conditions, see

Pettit 1999; for further discussion and defence, see Haukioja 2007.16 Suppose we stipulate as follows: let ‘Jack the Ripper’ refer to the uniqueperson, if such exists, that murdered the following women in 1888: Mary Ann Nichols, Annie Chapman, Elizabeth Stride, Catherine Eddowes, andMary Jane Kelly. Having made this stipulation, we can know a priori (accord-ing to Kripke 1980), that ‘Jack the Ripper (if he existed) killed Annie Chap-man’ is true, even if we don't kno w who Jack the Ripper was. We can knowsuch truths merely on the basis of understanding how the reference of ‘Jackthe Ripper’ is determined. We can, according to Pettit, know (10) a priori for

similar reasons: it is knowable merely on the basis of understanding how thereference of ‘red’ is determined. 17 As stressed by Pettit (1991). For further discussion of the modal statusof Pettit-style biconditionals, see Haukioja 2001.




For Pettit, response-dependence follows from the explanation ofexemplar-based concept acquisition. Since we apparently can and do

acquire concepts for wholly objective properties from examples, it isimportant that his notion of response-dependence not mark a differ-ence in the objectivity of subject matter, in the sense that the proper-ties picked out by response-dependent concepts would thereby beshown to be somehow subjective or mind-dependent. Pettit (1991)has argued in detail that there are no entailments from the response-dependence of a concept, in his sense, to any strong claims of mind-dependence (or, for that matter, mind-independence) concerning the

property it expresses. Indeed, Pettit mentions in passing that evennatural kind concepts such as WATER can be response-dependent. This may seem quite counter-intuitive at first blush; I will return tothis issue in the next section.

If Pettit is right, then all basic concepts – concepts that we have ac-quired from examples – are response-dependent. Response-dependence is, then, a global phenomenon, applicable concepts of arange of properties, from subjective ones such as fashionableness to

objective ones such as being water. This puts Pettit in sharp opposi-tion to Johnston and Wright, for whom the very reason for formulat-ing a notion of response-dependence was to draw a distinction be-tween concepts for the objective and concepts for the subjective.

7. Pettit: ‘Global’ Response-Dependence

The doctrine of Global response-dependence has not gained wide-spread acceptance, although not very many detailed arguments have

been presented against it.18 I suspect – and this suspicion gets someconfirmation from my experiences of informal discussions about thisquestion – that the resistance stems, at least in part, from a kind ofnagging feeling that there just has to be something wrong with the view, even if people are not quite able to put their finger on the prob-lem. Since such reactions have not been articulated in print, I willhere slightly diverge from my expository aims, look at what I think

18 The most prominent arguments against global response-dependence areSmith and Stoljar 1998 and Devitt 2006. Pettit’s response to Smith andStoljar is Pettit 1998a.



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are two of the main sources of discomfort with the view, and try tomake the view more palatable.

First worry: ‘Global response-dependence is just mad: there are obviously response-independent concepts!’ Pettit claims that all conceptsare response-dependent – but if response-dependence means theapriority of a relevant response-dependence biconditional, the view issimply false, and obviously so. Take the concept of being an electron,for example. How could anyone think that something like (11) is truea priori?

(11) x is an electron iff x would seem to be an electron to standardsubjects in favourable conditions.

Electrons aren’t the kind of thing we encounter and which seem tous to be anything! There simply cannot be any a priori connectionbetween electrons and our electron-responses.’

Reply: Pettit claims that all basic concepts are response-dependent, inthe sense of supporting a priori biconditionals. Even if our non-basicconcepts are somehow built from, or in some weaker way dependenton, our basic concepts, it does not follow that the non-basic conceptsare response-dependent in this sense. The subjects or conditions thatare standard or favourable for the application of one concept maynot be standard or favourable for another. Thus, even a simple con-junction of two response-dependent concepts, F and G, might notsupport a response-dependence biconditional, if it turns out that theconditions which are favourable for judging F -ness are not favourablefor judging G-ness, and vice versa.19 Hence, there is no reason to ex-

pect a priori biconditionals to hold of all concepts, even if globalresponse-dependence is accepted – and since the concept of an elec-

19 Consider, for example, the conjunctive concept YELLOW ANDPHOSPHORESCENT (supposing both YELLOW and PHOSPHORES-CENT are basic for an agent). The favourable conditions for judging yel-lowness are, presumably, something like statistically normal lighting at noonon a cloudy day. The favourable conditions for judging phosphorescence are,

by contrast, conditions in which the relevant object is brought to darkness after having been exposed to light. Obviously, no circumstances are favoura-ble for both, and the conjunctive concept will not sustain an a priori re-sponse-dependence biconditional.




tron is obviously not acquired from examples, global response-dependence is not committed to the apriority of (11).

Second worry: ‘How could WATER be response-dependent?!? Mostof us have, it seems plausible to assume, acquired the concept of wa-ter from examples: we have been exposed to samples of water, wehave participated in corrective practices where judgments of the type“x is water” have been subjected to comparison, and so on. It fol-lows, on Pettit’s view, that it should be a priori that:

(12) x is water iff x would be judged to be water by standard subjects

in favourable conditions.Pettit (1991) himself suggests this (if only in passing). But have wenot learned from Kripke (1980) and Putnam (1975) that there are nosuch a priori connections between natural kinds and our judgementsconcerning them? The extension of our concept of water is deter-mined by our causal interactions with our local kinds, not by the man-ifest properties that they happen to have. For example, would it notfollow from (12) that Putnam’s XYZ would be water?’

Reply: no, it does not follow. In the case of colours, favourable condi-tions turn out to be pretty much the kinds of conditions in which wemuch of the time actually do ascribe colours to objects – such condi-tions are usually fairly easy to achieve. But we should note there is noreason to expect this to generalise to all response-dependent con-cepts: for some concepts, favourable conditions may be very unlike the normal, everyday conditions of application, they may even bequite difficult to achieve.

If Pettit’s theory of concept acquisition is to apply to the concept of water, something roughly like the following story would have to hold.First, agents develop an extrapolative inclination from being exposedto samples of water. These inclinations, it seems to me, should haveto be primarily sensitive to the kinds of causal relations that the sam-ples of water can stand in towards other substances, objects, and en- vironmental variables. That is, the extrapolative inclination should notbe merely to categorise as water anything that superficially looks like

water – though that may be a good enough rule of thumb in normal,everyday situations – but rather to focus on how samples of waterinteract with features of reality external to them. Favourable condi-



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tions could then turn out to be circumstances in which such causalinteractions of putative samples of water, and other substances, can

be compared. Ultimately, if the story is to work, favourable condi-tions for judging whether a given sample of a substance is watershould be identified as ones in which we gain access to the micro-structure of the sample of liquid in question – whether it shares itsmicrostructure (presumably, H2O) with the uncontroversial samplesof water or not.

No one, to my knowledge, has seriously tried to fill in the details ofhow such a story could be told, and one may be pessimistic about its

prospects. Whatever may be the case, it appears that the question ofresponse-dependence, and the apriority of (12), is something of a redherring here. What really matters is whether the Ethocentric theoryof rule-following and concept acquisition really can explain exemplar-based acquisition of natural kind concepts – in particular, whetherPettit’s functionalist account of favourable conditions really can havethe outcome that, for some concepts, fully favourable conditions areconditions in which we can have evidence of underlying structures. If

the Ethocentric theory can do this, global response-dependence, andthe apriority of (12), should not cause any further problems. Howev-er, a critical examination of Pettit’s theory of rule-following falls out-side the scope of this article.

8. Conclusion

As we have seen, the central works on response-dependence are agood twenty years old today. The enthusiasm about response-

dependence as an independent object of study has seemed to wane agreat deal since the 1990’s. However, response-dependence has defi-nitely become part of the standard philosophical machinery, and con-tinues to get new applications.20 It is therefore all the more importantfor philosophers to pay close attention to the differences between thedifferent notions of response-dependence that are being used. Thedifferences are well known and largely agreed on by theorists whohave been working explicitly on the phenomenon of response-

dependence, rather than only the applications of one or another of20 Such as Zangwill 2001 for aesthetic properties, Hindriks 2005 for socialinstitutions, and Howat 2005 for pragmatism.




the versions. But outside this fairly limited circle of philosophers, theavailability of the different notions is apt to cause confusions. My

hope is that this article, along with other recent works where the im-portance of the differences has been stressed (Busck Gundersen2006, Brynjarsdóttir 2008, Howat forthcoming) will play a role inpreventing such misunderstandings.21

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Some Varieties of Metaphysical Dependence

E. J. Lowe

In this paper, I shall first of all (in section 1) define various kinds ofontological dependence, motivating these definitions by appeal toexamples. My contention is that whenever we need, in metaphysics,to appeal to some notion of existential or identity-dependence, oneor other of these definitions will serve our needs adequately, which one depending on the case in hand. Then (in section 2) I shall re-spond to some objections to one of these proposed definitions inparticular, namely, my definition of (what I call) essential identity-dependence. Finally (in section 3), I shall show how a similar ap-proach can be applied in the theory of truthmaking, by offering an

account of the truthmaking relation which defines it in terms of atype of essential dependence. I shall also say why I think that thisapproach is preferable to one which treats the truthmaking relation asprimitive. More generally, my view is that accounts of dependence or‘grounding’ which treat these notions as primitive are less satisfactory than my own position, which is that in all cases a suitable definition isforthcoming if we look hard enough.

1. Necessary and Essential Ontological DependenceIn my view, there are two broad species of ontological dependence

necessary dependence and essential dependence and within eachspecies there are three fundamental varieties: rigid existential depend-ence, generic existential dependence, and identity -dependence.1 Each va-riety of essential dependence is stronger than (entails but is not en-tailed by) the corresponding variety of necessary dependence. Withineach species of dependence, identity-dependence is stronger than

1 The account that I am about to give is a refinement of one to be foundin Lowe 1998, 136 –53.



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rigid existential dependence. Furthermore, essential identity-dependence is asymmetrical (or, perhaps, anti-symmetrical, though

the difference is unimportant for present purposes), whereas rigidexistential dependence (of either variety) is merely non -symmetrical.

1.1 The Definitions

ND1 x is rigidly existentially necessarily dependent on y ↔df. Nec( x exists only if y exists).

ND2 x is generically existentially necessarily dependent on F s ↔df. Nec( x exists only if some F s exist).

ND3 x is necessarily identity-dependent on y ↔df. There is somefunction such that Nec( x = ( y )).

ED1 x is rigidly existentially essentially dependent on y ↔df. Ex ( x exists only if y exists).

ED2 x is generically existentially essentially dependent on F s ↔df. Ex ( x exists only if some F s exist).

ED3 x is essentially identity-dependent on y ↔df. There is somefunction such that Ex ( x = ( y )).

1.2 Notes on the Definitions

The operator ‘Nec’ is to be read as ‘it is metaphysically necessarythat’. The operator ‘Ex ’ is to be read as ‘it is part of the essence of x that’. The expression ‘ ( y )’ is to be read as ‘the of y ’. Note also thatthe definitions have been simplified by treating rigid existential de-pendence and identity-dependence as one-to-one relations, whereasin fact in some cases they may be one-to-many. It is easy enough tosee how the definitions could be modified to accommodate cases likethe latter. I should also remark at this point that my own view is thatall necessary truths – in the metaphysical sense of ‘necessary’ – derivefrom essential truths, rather than vice versa.2 This is not to say thatthe class of necessary truths is coextensive with the class of essential

2 Compare Fine 1994 and see further Lowe 2008.



VARIETIES OF METAPHYSICAL DEPENDENCE 167

truths: rather, the latter form only a proper sub-class of the former.‘Ex ( p )’ entails ‘Nec( p )’, but the reverse entailment does not hold.3

1.3 Preliminary Remarks on Essence

An entity x ’s essence is the sum of all the parts of its essence and isexpressed by x ’s so-called real definition.4 Importantly, however, x ’sessence is not a further entity in addition to x .5 We should not reifyessences. Not being an entity, x ’s essence does not literally containany entities as parts or constituents, since only entities can have otherentities as parts. (By an ‘entity’, I simply mean something that does or

could exist.) However, the proposition expressing x ’s real definitionmay well, and normally will, make reference to entities other than x .For example, the real definition of a circle is that it is the locus of apoint moving continuously in a plane at a fixed distance from a givenpoint (its centre). This definition makes reference to two points and adistance between them. There is, incidentally, no contradiction be-tween speaking of an essence as having ‘parts’ and yet denying thatessences have entities as parts. The ‘parts’ of an essence should be

understood as parts of the real definition which expresses that es-sence. For instance, it is part of the real definition of a circle that it isa planar figure, and also part of its real definition that it has a centre.In that sense, then, it is part of the essence of a circle that it is a pla-nar figure and also part of its essence that it has a centre. I shall saymore about essences and parts of essences (or ‘partial’ essences, ifthat expression is preferred) later.

3 There is a case for saying that ‘Ex ( p )’ entails only the weaker conditionalizedmodal proposition ‘Nec(if x exists, p )’. I shall set aside debate over this issuefor the purposes of the present paper. But note that I have not stipulatedthat ‘Nec( p )’ is to be interpreted as meaning ‘In every possible world, p’.‘Ex ( p )’ could uncontroversially be taken to entail ‘Nec( p )’ if the latter wereinterpreted as meaning ‘In every possible world in which x exists, p’—aninterpretation which I have not ruled out.4 Compare Fine 1994.5 I explain why I make this claim in Lowe 2008. To condense matters,since every entity has an essence and no entity is to be identified with its ownessence, to regard essences as entities is to commit oneself to a problematicinfinite regress of essences.



168 LOWE

1.4 Some Examples of Essential Dependence

(a) An event is rigidly existentially essentially dependent on its sub-ject(s) or participant(s): thus, it is part of the essence of the death ofSocrates that it exists only if Socrates exists.

(b) An Aristotelian (or ‘immanent’) universal, U, is generically existen-tially essentially dependent on instances of U: thus, it is part of theessence of redness that it exists only if some instances of redness(some red tropes or modes) exist, and it is part of the essence of thenatural kind horse that it exists only if some individual horses exist.

(c) (i) A unit set or singleton is essentially identity-dependent on itsmember: thus, it is part of the essence of singleton Socrates, {Socra-tes}, that it is the set whose sole member is Socrates. (ii) A trope ormode is essentially identity-dependent on its bearer (the ‘individualsubstance’ to which it belongs) and its time of existence: thus, if r is ared trope of apple a existing at time t , then it is part of the essence ofr that it is the particular redness of a at t .6

1.5 Essential Identity-Dependence Entails Rigid Existential EssentialDependence

Thus, since it is part of the essence of singleton Socrates that it is theset whose sole member is Socrates, it is also part of the essence ofsingleton Socrates that it exists only if Socrates exists. And since it ispart of the essence of red trope r that it is the particular redness of a at t , it is also part of the essence of r that it exists only if a exists.

1.6 The Asymmetry of Essential Identity-Dependence

For example, since it is part of the essence of singleton Socrates thatit is the set whose sole member is Socrates, it is not part of the es-sence of Socrates that he is the sole member of singleton Socrates.

6 It may be disputed whether the time at which it exists is part of the es-

sence of a trope or mode, though I shall not enter into this debate here; butit is indisputable, I take it, that it is part of the essence of any trope or modeof a concrete individual substance that it exists at, and only at, some time (ortimes) during the existence of that substance.




Two distinct entities cannot depend essentially for their identity oneach other.7

1.7 Accidental Dependence

If x is generically existentially dependent on F s but not rigidly exis-tentially dependent on any F in particular, then I say that x is acci-dentally existentially dependent on the actual F s. For example, an Ar-istotelian universal is accidentally existentially dependent on its actualinstances, and an essentially coloured individual substance is acci-dentally existentially dependent on its actual colour trope or mode.

Similarly, a bronze statue is accidentally existentially dependent on thebronze particles actually composing it. It is quite clear that in meta-physics we need sometimes to speak of accidental existential depend-ence, as in the foregoing examples, and that none of the six defini-tions listed earlier captures, on its own, any such notion of depend-ence. However, as has just been made clear, the notion of accidentalexistential dependence is apparently definable in terms of the notionsof generic existential dependence and rigid existential dependence

(of either the necessary or the essential variety, as the case may be),and so does not rely on any notions that are not used in defining thesix varieties of ontological dependence listed earlier. For complete-ness, indeed, we can add the following to the foregoing six defini-tions:

AD x is accidentally existentially dependent on the actual F s ↔df. (i) x is generically existentially dependent on F s but (ii) x is notrigidly existentially dependent on any F in particular.

Of course, the types of existential dependence figuring in clauses (i)and (ii) of (AD) may be construed in either a necessitarian or an es-sentialist manner.

Just to make clear how (AD) works in a specific case, consider againthe case of the bronze statue, b , and the bronze particles actuallycomposing it, the actual P s. Evidently, b is generically existentiallydependent on P s (clause (i)), since it is part of the essence of b that itexists only if some bronze particles composing it exist. Hence, given

7 I defend this claim in Lowe 1998, 150, and more fully in Lowe forth-coming. I shall consequently say no more about it here.



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that b actually exists, some P s —the actual P s —exist. Equally, though,b is clearly not rigidly existentially dependent on any P in particular

(clause (ii)), since it is not the case that, for any given one of the P s, itis part of the essence of b that it exists only if that P exists. Thethought is that the bronze particles that actually compose b just hap-pen to do so, since b could have been composed of different bronzeparticles. Nonetheless, b has to be composed of some bronze parti-cles or other in order to exist. And this means that b stands in an on-tological dependence relation to the particular bronze particles thatdo happen to compose it, even though it could have stood in that

very same relation to some other bronze particles, had they insteadcomposed b . It is this kind of relation that I call ‘accidental existentialdependence’. And I believe that (AD) adequately captures this kindof relation.

Accidental existential dependence is a highly significant kind of rela-tion in metaphysics, since there are very many important examples ofit. Indeed, many cases that metaphysicians are apt to describe interms of a relation of ontological ‘grounding’ are, I believe, explica-

ble in terms of (AD). The fact that none of the six earlier definitionsof ontological dependence serves, on its own, to capture the kind ofdependence involved in such cases does not, then, indicate that weneed to appeal to a primitive or undefined notion of ‘grounding’ inthese cases. For, if I am right, this additional species of dependenceis readily definable in terms of the earlier defined varieties.

1.8 More on Parts of Essences

I now need to supplement my earlier remarks on parts of essences. Any purely logical consequence of an entity’s essence is part of itsessence —or so I would like to contend, since saying this makes itmuch clearer what is meant by speaking of ‘parts’ of essences (or‘partial’ essences) and hence how we are to understand the importantoperator ‘it is part of the essence of x that’. But there are apparentdifficulties attending this view. It follows, for example, that it is partof the essence of any entity e that everything —not just e —is self-

identical, since the real definition of any entity trivially has this purelylogical consequence. This in itself is not objectionable, as far as I cansee. However, in standard first-order predicate logic, the purely logicaltruth that everything is self-identical, ‘ x ( x = x )’, entails ‘a = a ’,




where ‘a ’ is any individual constant. Thus, it entails, for example, ‘2 =2’, which in turn entails ‘ x ( x = 2)’, and the latter is standardly read

as ‘2 exists’. Hence, by the lights of this system of logic, it is part ofthe essence of any entity e that 2 exists, and thus part of e ’s essencethat it exists only if 2 exists, thereby making e rigidly existentially es-sentially dependent on 2 (or indeed any other object, such as the Eif-fel Tower). This is plainly absurd. However, as I see it, the fault herelies entirely with the inference rules of standard first-order predicatelogic with identity and with the standard interpretation of the tenden-tiously named ‘existential’ quantifier—the particular quantifier, I pre-

fer to call it —‘ ’, which is wrongly, in my view, taken to express exist-ence. My own view is that the existence predicate is a ‘first-level’predicate —a predicate of objects rather than of properties —and thatits meaning is primitive and indefinable.8 Pure logic, I consider,should be existentially neutral —and thus not presuppose a non-empty ‘domain of quantification’—and have no concern with anyparticular object, whether that object be concrete and contingent (likethe Eiffel Tower) or abstract and necessary (like 2). Once this is made

clear, I believe that an explication of partial essences in terms of log-ical consequence will not lead to a grossly over-inflated characterisa-tion of essences.

1.9 Natural Laws and the Essences of Natural Kinds

If K is a natural kind, then there will be natural laws governing K ofthe form ‘K s are F ’ and, in at least some cases, it is very plausible tosay that such laws (or the propositions expressing them) are essential

truths concerning the kind K . For instance, it is plausible to say that itis part of the essence of the kind tiger that tigers are quadrupedal.Propositions of the form ‘K s are F ’ are known as generic proposi-tions, and many natural laws are expressible by propositions of thisform. Now, ‘K s are F ’ does not entail ‘ x (if x is a K , then x is F )’,since K may have abnormal instances which are non-F .9 For example,a particular tiger, t , might be born with only three legs. Clearly, then, t is not essentially quadrupedal, since t is not quadrupedal at all. How isthis possible, given that (as we have just said) tigers are essentially

8 I say more about this in Lowe 2009, 54 –5.9 See further Lowe 2009, 141 –63.



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quadrupedal? The answer, as I see it, is that we must distinguish care-fully between the essence of a kind and the essence (the so-called

individual essence) of any individual belonging to that kind. The les-son is that the essence of a kind K does not necessarily transmit wholly to every individual instance of K : so, even though it is part ofthe essence of K that K s are F , it doesn’t follow that it is part of theessence of every individual K that it is F .

2. Response to Some Objections

In an excellent recent book, Fabrice Correia presents a systematic

account of various subtly different notions of existential depend-ence.10 In the course of doing so, he critically examines some otherapproaches, including my own. He identifies three main alternativeaccounts, which he calls the ‘modal-existential’ approach, the ‘purelyessentialist’ approach, and the ‘essentialist-existential’ approach. Thefirst of these approaches has had numerous advocates. The secondCorreia attributes to me and the third he attributes, independently, toKit Fine and to Kevin Mulligan, Peter Simons and Barry Smith. In

each case, Correia argues that the approach in question fails to cap-ture certain strong pre-theoretical intuitions concerning relationshipsof existential dependence between putative entities of various onto-logical categories.

Correia’s own ‘foundational’ approach, as he calls it, appeals to a gen-eralized notion of grounding — which he takes to be primitive —along with various more specific notions of grounding. Correia elucidatesthese notions and their use in defining what he calls the ‘simple foun-

dation’ of one entity in another, with the help of detailed illustrativeexamples. This is his proposed definition:

x is [simply] founded in y iff it is impossible that x exists with-out being based on y .

where ‘An object x is based on an object y ... when the fact that x ex-ists is partly grounded in some fact about y ’ (Correia 2005, 66).

I shall now examine Correia’s objections to my own approach, the so-

called ‘purely essentialist’ approach (although, as will be clear from

10 See Correia 2005.




earlier parts of the present paper, I am by no means averse to mod-al —that is, necessitarian —definitions of ontological dependence, but

just think that these do not capture the only, or indeed the most im-portant, varieties of ontological dependence). In particular, I shallexamine his objections to my account of what I call essential identity- dependence . As can be seen from (ED3) above, I characterise this asfollows:11

x is essentially identity-dependent on y iff there is some func-tion such that it is part of the essence of x that x is the of y.

Now, I claim that essential identity-dependence entails what Correiacalls ‘m -necessitation’—that is, that if x is essentially identity-dependent on y , then it follows that necessarily, if x exists, then y ex-ists or, equivalently, that necessarily, x exists only if y exists. (WhatCorreia calls ‘m -necessitation’ is just what I call ‘rigid existential nec-essary dependence’, defined by (ND1) above.) In support of this en-tailment thesis, I have offered illustrative examples which seem per-suasive. Thus, for an assassination to exist, there must be some par-ticular assassination that it is —and which assassination it is will dependon which person is assassinated, because assassinations are essentiallyidentity-dependent on their victims (the persons assassinated). But ifthere is no such person , then it is undetermined which assassination it sup-posedly is, and so no such assassination can exist. Correia, however,thinks that there are credible counter-examples to my entailment the-sis. At the same time, he maintains that, according to his own defini-tion of simple foundation , ‘unlike identity -dependence foundation has

the desired property of entailing m -necessitation’ (Correia 2005, 67). Here is one such putative counter-example.12 Correia suggests thatthe property of being identical with Socrates , which he calls I S , is essen-tially identity-dependent on Socrates and yet can exist even thoughSocrates does not exist, given that I S is a necessary existent and Socra-tes is a contingent existent. However, in my view, properties are not , ingeneral, necessary existents: being an ‘immanent realist’, I hold thatthey exist only in worlds in which they are instantiated. And, certainly,

11 See also Lowe 1998, 149, to which Correia refers.12 See Correia 2005, 48.




(Correia 2005, 49), even though Pegasus does not exist. However, I would say that, if there really is such a thought, then in fact it is either

a purely descriptive thought or else one containing as a constituentPegasus’s individual concept, where the latter is taken not to be essen-tially identity-dependent on Pegasus. If it really were an object-dependent thought, then it couldn’t exist unless Pegasus did. (Of course, it mayseem to me that I am having such an object-dependent thought whenreally I am not, as in the case of apparent demonstrative thoughtsabout hallucinatory objects.)

All of Correia’s alleged counterexamples to my entailment thesis are

indeed, as he concedes, ‘somewhat baroque’ (Correia 2005, 49). Hetakes these examples to defeat my ‘premise that where F is a function,for every x , the F of x cannot exist unless x exists’ (Correia 2005, 48n.13). But this premise simply appeals to the standard conception ofa function, according to which a function is undefined for values for which it lacks an argument. (What is the length of Santa Claus’sbeard, given that Santa Claus, and hence his beard, doesn’t exist?) It is worth remarking here that Correia has already made it clear that his

quantifiers are possibilist , not actualist ,15 which rather stacks the cardsagainst my position from the outset. On my own (actualist) view,something doesn’t exist at all unless it actually exists. For me, a sing u-lar term which lacks a referent in this, the actual world, cannot haveone in some other, merely possible, world.

I should also mention that Correia thinks that the force of his allegedcounter-examples doesn’t depend on our accepting that they really are genuine counter-examples, but only on our accepting that some met-

aphysician could reasonably take them to be counter-examples. This is inline with his general aim to explicate the notion(s) of existential de-pendence in a metaphysically neutral fashion (though how his preferencefor possibilist quantifiers can be taken to be consistent with such neu-trality is not entirely clear to me). In his view, ‘[A]ny account of the various notions of existential dependence should be compatible withany viable, i.e. non-absurd, i.e. dialectically possible metaphysical view’ (Correia 2005, 10). And he acknowledges that my own account

of existential dependence does not aim at such neutrality and hencethat he ‘will not take [his] objections to establish that Lowe’s charac- 15 See Correia 2005, 19.

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terisation is inadequate given his particular purposes’ (Correia 2005,46n12). In defence of my own non-neutrality in this matter, I would

only say that, unlike Correia,16 I take the explication of existentialdependence not to be a mere exercise in conceptual analysis, but asubstantive contribution to fundamental metaphysics: and, concern-ing the truths of fundamental metaphysics we cannot, if we are real-ists, adopt a neutral stance.17

Concerning Correia’s own positive proposals, I would further askonly this: is it really satisfactory to take the notion of ‘metaphysicalgrounding’ as primitive , as Correia does?18 The reason why I aban-

doned my own earlier attempts along such lines is precisely that leav-ing such a notion undefined seems intolerably obscure, even after allof the various elucidatory points have been made and illustrative ex-amples have been provided.19 And, as I indicated before, my belief isthat the definitions of the various types of ontological dependencepresented earlier in this paper are, taken together, fully sufficient tomeet all the needs of metaphysics. I have yet to come across a com-pelling counter-example to this claim.

3. Truthmaking and Dependence

In this third and final section, I turn to the topic of truthmaking,concerning which notions of dependence are also widely held to playan important role. One very well-known account of truthmaking isthe necessitarian account , according to which:

NT e is a truthmaker for if and only if and only if it is meta-

physically necessary that is true if e exists.

16 Correia proclaims at the very outset of his book, that his ‘investigation isa conceptual one... not one of metaphysics ... [but] of meta -metaphysics’ (Cor-reia 2005, 9).17 I readily concede that there is much more to be said about the methodo-logical issues at stake here, and that Correia is right to try to reach as broad aconsensus as possible about how to define or characterise a key metaphysicalnotion like that of existential dependence. I am just more sceptical than he

is about the possibility, and even the desirability, of achieving complete neu-trality in this sort of exercise.18 See Correia 2005, 57.19 For one of those attempts, see Lowe 1994.

In (NT), ‘’ denotes the proposition that P . It is a familiar factthat ( NT ) has various counterintuitive consequences, such as that any

entity whatever is a truthmaker for any necessary truth.20 One of theimplications of (NT) is a principle known as the entailment principle :

EP If e is a truthmaker for and entails < Q>, then e is atruthmaker for < Q>.

Why? Well, according to (NT), if e is a truthmaker for , then, inevery possible world in which e exists, is true. So, suppose that e is indeed a truthmaker for and hence that in every possible

world in which e exists, is true. Now, given that entails< Q>, every possible world in which is true is a world in which< Q> is true. Hence, in every possible world in which e exists, < Q> istrue. But, according to (NT), this implies that e is a truthmaker for< Q>. QED

One immediate implication of (EP) is the principle that a truthmakerfor any conjunctive proposition is a truthmaker for each of its con-juncts —the conjunction principle :

CP If e is a truthmaker for , then e is a truthmaker for and e is a truthmaker for < Q>.

Both (EP) and (CP) are accepted by many truthmaker theorists, whether or not they accept (NT), but Gonzalo Rodríguez-Pereyra hasargued in a recent paper that any satisfactory theory of truthmakingmust reject (EP) and (CP).21 He brings out very clearly many of thedrawbacks of theories that are committed to these principles, such as

the necessitarian account (NT). And in place of that account, he advocates the following, which we may aptly call the in virtue of account ,maintaining that it is committed to neither (EP) nor (CP):

VT e is a truthmaker for if and only if is true in virtueof e.

Rodríguez-Pereyra dismisses the charge that the locution ‘in virtue of ’in (VT) is unduly obscure. And I agree that very often our use of thislocution is sufficiently clear for the purposes in hand. However, I

20 I discuss some of these consequences in Lowe 2006, 202 –3.21 See Rodríquez-Pereyra 2006.

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have serious doubts as to whether it is the right locution in terms of which to couch an illuminating account of truthmaking.

One of my worries is that the ‘in virtue of’ locution has a very wideand disparate usage in philosophical contexts. We say, for instance, that ared apple is red in virtue of having a red skin, that I am touching thetable in virtue of touching the leg of the table, that the statue is heavyin virtue of being made of solid bronze, and that David Cameron isPrime Minister of the UK in virtue of being the leader of the coalitionmajority in the House of Commons —and so on. In some of thesecases, the ‘in virtue of’ locution seems to be in play because a part –

whole relation obtains between certain entities (the apple and its skin,the table and its leg), but in other cases this is not so: sometimes aconstitution relation or a role/occupier relation is at issue, and so on.Nothing seems to unify all the various uses of the ‘in virtue of’ locu-tion, in short.

But there is another and perhaps more serious worry. Don’t we say,and quite properly, that the conclusion of a sound argument is true ‘in virtue of ’ the truth of the its premises—that, for instance, <Socratesis mortal> is true in virtue of the truths <Socrates is a man> and<All men are mortal>? After all, we say that a sound argument is‘truth-preserving’, or that the truth of its premises is ‘transmitted’ toits conclusion. But this would imply that the conjunction of any setof true propositions which together entail another is a truthmaker ofthat other proposition, according to the ‘in virtue of’ account oftruthmaking, (VT). It seems perfectly acceptable to say, for example,that <Socrates is mortal> is true ‘in virtue of’ the truth <Socrates is

a man and all men are mortal>. And, that being so, the truth <Socra-tes is a man and all men are mortal> is, according to (VT), a truth-maker of <Socrates is mortal>. But Rodríguez-Pereyra surely cannotintend (VT) to have this consequence. For one thing, it threatens toreinstate the conjunction principle, (CP). For now it seems that wemust say, quite generally, that if is true, then is atruthmaker of both and < Q>, whence it is hard to see why atruthmaker of the former should not also be a truthmaker of each of

the latter. Rodríguez-Pereyra might perhaps reply that the locution ‘in virtue of ’ as it appears in (VT) is not to be understood in the foregoing way —not, that is, in the way in which it is used in saying that the

conclusion of a sound argument is true ‘in virtue of’ the truth of itspremises. But then it would seem that the ‘in virtue of’ locution must

be assigned a more specific sense than Rodríguez-Pereyra has yetmade clear, in order to figure in a satisfactory account of truthmak-ing.

Incidentally, since we seem equally happy to say that the conclusionof a sound argument is true because its premises are true, or because of the truth of its premises, the foregoing considerations also put pres-sure on those philosophers who prefer to use the locution ‘because’,or ‘because of’, rather than the locution ‘in virtue of’, to express thekind of dependence involved in truthmaking.22 My own preferred account of truthmaking once again appeals to thenotion of essence and, more particularly, to the notion of essential dependence —in contrast with the notion of necessary dependence invoked bythe necessitarian account, (NT).23 Thus, the locution that I prefer touse instead of Rodríguez-Pereyra’s ‘in virtue of’ locution is, onceagain, the locution ‘it is part of the essence of’, which has alreadyserved us well in accounting for certain varieties of existential andidentity-dependence: but now I want to put it to use in the service ofa theory of truth and truthmaking. So, for example, I want to say thatit is part of the essence of any proposition, , that it is a proposition andalso that it is either true or false . Accordingly, the following, at least to afirst approximation, is my preferred account of truthmaking, which we may call the essentialist account :24

22 I once considered the idea of appealing to the ‘because’ locution to ex-

plicate the notion of ontological dependence, in Lowe 1998, 145 –6, butabandoned it as insufficiently perspicuous. For a more thorough explorationof the idea, see Schnieder 2006. I am happy to concede that the advocatesof the ‘because’ locution are considerably better placed to answer my wor-ries than are the advocates of the ‘in virtue of’ locution, since they are in aposition to draw a well-motivated distinction between an ‘evidential’ and a‘non-evidential’ (or ‘objective’) sense or use of ‘because’. See, in particular,Schnieder 2011.23 See further Lowe 2006, 202 –4.24 It appears to be an implication of (ET) that since, for instance, it is plau-sibly part of the essence of the proposition that Vulcan exists that it is trueif Vulcan exists, Vulcan is therefore a truthmaker for that proposition. Andyet Vulcan does not exist. Is this a problem for (ET)? Well, remember that I



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Loux, M. J. and D. W. Zimmerman (eds.) 2003: The Oxford Handbookof Metaphysics , Oxford: Clarendon Press.

Lowe, E. J. 1994: ‘Primitive Substances’. Philosophy and PhenomenologicalResearch 54, pp. 531 –52.

— 1998: The Possibility of Metaphysics: Substance, Identity, and Time . Ox-ford: Clarendon Press.

— 2003: ‘Individuation’. In M. J. Loux and D. W. Zimmerman (eds):The Oxford Handbook of Metaphysics , Oxford: Clarendon Press, pp.75 –98.

— 2006: The Four-Category Ontology: A Metaphysical Foundation for Natu- ral Science . Oxford: Clarendon Press.

— 2008: ‘Two Notions of Being: Entity and Essence’. In Le Poidevin2008, pp. 23 –48.

— 2009: More Kinds of Being: A Further Study of Individuation, Identity,and the Logic of Sortal Terms . Malden, MA and Oxford: Wiley-Blackwell.

— 2012: ‘Asymmetrical Dependence in Individuation’. In Correia andSchnieder 2012, pp. 214 –33.


Rodríquez-Pereyra, G. 2006: ‘Truthmaking, Entailment, and the Con-junction Principle’. Mind 115, pp. 957 –82.

Rosenkrantz, G. S. 1993: Haecceity: An Ontological Essay . Dordrecht:Kluwer.


— 2011: ‘A Logic for “Because”’. Review of Symbolic Logic 4, pp. 445 –65.

Tomberlin, J. E. (ed.) 1994: Philosophical Perspectives 8: Logic and Lan- guage , Atascadero, CA: Ridgeview.



Explanation and Fundamentality

C. S. I. Jenkins

1. Introduction

Members of a wide range of ontological categories can apparently bedescribed as (at least putatively) metaphysically ‘fundamental’. Onexamining a selection of work by contemporary metaphysicians, onefinds that the adjective ‘fundamental’ is being applied to (among oth-er things) all of the following:

truths (e.g. Williams 2010, Sider 2011),

facts (e.g. deRosset 2010),

states of affairs (Armstrong 1997),

layers or levels of reality (e.g. Schaffer 2003, Cameron 2008,Paseau 2010),

reality’s structure (e.g. Lowe 1998, Hall 2010, Sider 2011),

things (e.g. Fine 2001),

individuals (e.g. deRosset 2010),

entities (e.g. Cameron 2008, Hall 2010),

objects (e.g. Cameron 2008),

qualities (e.g. Schaffer 2003),

properties and relations (e.g. Lewis 1986, Armstrong 1997),universals (e.g. Armstrong 1997),



184 JENKINS

quantifiers (e.g. Sider 2011),

laws (e.g. Lewis 1986, Armstrong 1997),

languages (e.g. Sider 2011),

and theories (e.g. Sider 2011).

And I haven’t even started on uses of the adverb ‘fundamentally’.

Setting aside some no-doubt-important differences, for current pur-poses I shall take it that metaphysical fundamentality is generally sup-posed to amount to something reasonably similar regardless of the on-

tological category of that to which it is being attributed. My purposein this paper is to explore the question: what are metaphysicians do-ing when they describe something as ‘metaphysically fundamental’? There is influential recent work in metaphysics arguing about whetherthere exists anything fundamental (see e.g. Markosian 2005, Cameron2008). The fundamentality or otherwise of particular things is also arich source of metaphysical debate (see e.g. Schaffer 2010). And this work taps into a venerable tradition plausibly dating back at least to

Aristotle. This paper asks: what kind of question is being disputed here? I con-sider the following hypothesis by way of an answer:

H YPOTHESIS H When metaphysicians describe something as ‘fundamental’, thatmeans approximately the same in their mouths as if they had called it‘(part of) that by appeal to which all the rest can be explained’. Corre-

spondingly, ‘x metaphysically depends upon y

’ and other cognatephrases should be understood as expressing roughly the same thingas ‘(salient things about) x can be explained by appeal to y ’.

According to H, the connection between fundamentality and depend-ence is that something counts as fundamental just in case it is part ofthat on which the rest depends. (Notice that I don’t say that the fun-damental is that which depends on nothing; the reasoning behind thisis discussed on p. 7 below.)

Notice that H is deliberately generic. I do not mean to suggest thatevery metaphysician who uses the phrase ‘metaphysically fundamen-tal’ uses it as H suggests. Some explicitly define the phrase in such a



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Relatedly, note that the quality of a putative explanation can affectour willingness to label it ‘an explanation’, at least in some contexts.1 I

think this impacts upon our willingness to use ‘dependence’-talk and‘fundamentality’-talk. One explanatory virtue that seems particularlyimportant here is the omission of irrelevant or unnecessary material. You might think that if the fundamental can ‘explain’ all the rest, thenso can: the fundamental together with a number of extraneous addi-tions, in which case H will deliver incorrect results. But the inclusionof unnecessary extras (especially if they interfere with the tidiness oruniformity or informativeness of the envisaged explanation) could

well be enough to make the putative explanation bad enough not tocount as ‘an explanation’ in the relevant contexts.

The phrase ‘that by appeal to which’ is also to be understood as con-text-sensitive, like many other definite descriptions. I want to allowthat there could be more than one thing which is such that all ‘therest’ can be ‘explained’ by appeal to it, and that context of utterancecan serve to select a salient one (just as ‘the teacher’ can, in context,pick out one particular teacher even though many teachers exist).

What might be special about the salient thing, in this sort of scenar-io? Various things, I imagine. Perhaps, for example, it is salient be-cause it is of a particular kind, and/or possesses a particular property,that is currently under discussion or otherwise of interest. In a situa-tion where either (say) the collection of all the physical facts or thecollection of all the physical things could serve as something by ap-peal to which all ‘the rest’ (i.e. the rest of the facts or the rest of thethings, depending on which we choose) can be ‘explained’, but we are

having c conversation about facts and are only interested in facts, we will be able to pick out the collection of physical facts with thephrase ‘that by appeal to which all the rest can be explained’.

Another thing to note about H is that ‘by appeal to’ is imprecise: itdoesn’t tell you anything very specific about the kinds of role(s) thatthe thing appealed to will be playing in the relevant explanations. That too is deliberate; my view is that calling something ‘fundamen-tal’ does not give that much information as to what sorts of roles that

thing plays in the relevant explanations. In a similar vein, H avoids

1 See Jenkins 2008, 68 – 70, for further discussion.



EXPLANATION AND FUNDAMENTALITY 187

difficult questions as to whether the various things which can becalled ‘fundamental’ or said to ‘depend’ on one another belong to the

correct ontological categories to be explanations or do any explainingthemselves. All it requires is that they can be appealed to in explana-tions. (For brev ity, I’ll sometimes talk as if, according to H, explana-tion constitutes grounding or dependence, but this ‘constitution’ talkisn’t meant to imply anything more or less than H.)

I also want to draw attention the parenthetical ‘part of’ in H. This isthere because it is not typical to believe that each fundamental thingis explanatory of all of the rest by itself. It is more usual to believe

that the fundamental, taken all together, can explain ‘the rest’.H is a claim about meaning. But that doesn’t mean that it must beeither false or obvious. Often, we use words competently but withouta thorough reflective grasp of their meaning. And although my pro-ject is interpretative – I want to find out what the ‘fundamentality’debates are all about – that does not mean I am not also pursuing theproject of finding out what fundamentality is (at least, assuming thatI write this sentence in a similar context to some of those in whichmetaphysicians use their word ‘fundamentality’). I take it that thistechnical term is owned by the metaphysicians who deal in it at leastto the extent that if I find out what metaphysicians are discussing when they talk their ‘fundamentality’-talk, then I know what meta-physical fundamentality is. That’s not to say I know all there is toknow about the nature of metaphysical fundamentality; there may bemore to it than one can discover just by learning what the wordmeans. But it’s a start.

2. Key Features of Fundamentality

Many suggestive words and phrases are employed by philosophers inthe process of characterising metaphysical fundamentality. Some ofthese appear to import some pretty substantial assumptions about what fundamentality amounts to. These include:

‘degrees of reality’,

‘structure’,‘objectivity’,



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‘smallness’,

‘composition’,

and ‘featuring in the best and/or minimal metaphysically com-plete language or theory’.

The idea that dependence and fundamentality are to be cashed out interms of degrees of reality, with the fundamental being most real andthat which merely depends upon it being somewhat less real, is dis-cussed by e.g. Cameron (2008, 9 –10) and Schaffer (2003, 498). Unlessthis is simply the view that the non-fundamental is unreal (which I

shall discuss below), I find it difficult to make sense of it. I don’tknow what it would be for reality to have more than two ‘degrees’,unless that’s a way of cashing out the idea of something’s existing vaguely or otherwise indeterminately. I assume that a commitment tothe non-fundamentality of a thing ought not entail a commitment tothat thing’s existing vaguely or otherwise indeterminately.

Fundamentality is particularly associated with structure by Sider(2011). He says, for example, that ‘the ultimate goal [of metaphysics]is insight into this structure itself —insight into what the world is real-ly like, at the most fundamental level’ (1). As I understand it, this as-sociation is intimately connected to Sider’s belief in an objective struc-ture to reality: a structure created by the joints in nature, such that thedifference between non-electrons and electrons marks such a joint,but the difference between things which are electrons-or-cows andthings which are neither electrons nor cows does not. UnderlyingSider’s association of fundamentality with structure, there may be a

ghost of the assumption that the fundamental, and only the funda-mental, is objective . Although Sider does reject this assumption explicit-ly in his 2011, it would, in conjunction with his desire to establish thatstructure is objective, explain why he is at pains to argue that the kindof ‘structure’ he’s talking about is fundamental.

But I don’t see why non-fundamental reality, if any such there is,should not count as structured, and objectively so. For the sake ofneutrality on this issue, I think we should understand the notion of

fundamentality in such a way that it is not obviously mistaken tothink that non-fundamental reality has a structure just as objective asthat of non-fundamental reality.




More generally, I do not endorse ways of characterising fundamental-ity which force us to associate fundamentality (or the lack of it) too

closely with objectivity (or the lack of it); again, there is nothing obviously wrong with the idea that there are objective but non-fundamental things. Non-empty sets are often taken to be paradigmsof non-fundamentality. Consider the singleton of the natural number9. It metaphysically depends upon 9 in a way that seems to render thesingleton non-fundamental. But I don’t see that this gives us any rea-son to deny objectivity to {9}; it seems about as objective as anythingcould be. Plausibly, one way for some things to be non-fundamental is

for them to depend metaphysically on our minds . (Maybe humour facts,for example, are non-fundamental for this reason.) But we obviouslyshouldn’t assume that depending on something is the same as depend-ing on our minds.

The connections between smallness, composition and fundamentalitymake sense if it is assumed that, if anything is fundamental, thesmallest parts out of which everything else is mereologically com-posed (and/or the facts about those smallest parts, and/or their

properties, or whatever) are fundamental. This view is in evidence ine.g. Schaffer 2003 and Markosian 2005, and in both cases it appearsthat, as a result, mereological notions are being imported into the very characterisation of fundamentality and/or dependence. But do-ing this automatically rules out the view that the whole universe isfundamental and its smaller parts are dependent upon it (see e.g.Schaffer 2010; by 2010, Schaffer is declining to analyse the metaphys-ical ‘priority’ relation he appeals to), and may also problematize views

on which (e.g.) the physical is fundamental and the mental is ground-ed in it. Regardless of whether such views are correct, it seems inap-propriate to rule them out by giving a definition of fundamentality which makes them impossible.

It’s sometimes proposed that fundamentality is closely associated withbeing part of, and/or expressible in, a certain language: some sort ofideal and/or minimal language adequate for description of the world.Sider (2011), for example, associates fundamentality with an optimal

(though not minimal) language for describing the world. Relatedly,fundamentality might be associated with appearance in an idealand/or minimally adequate theory of the world. Though I don’t know



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of anyone who explicitly does this, some of Lewis’s work comesclose: see Lewis 1983, 42, where it is claimed that the perfectly natural

properties are the only properties which appear in the basic axiomsof the ‘ideal system’ or theory. (For Lewis, minimality or non-redundancy is a requirement on such a theory.) And the perfectly nat-ural properties are the properties which, according to some commen-tators, Lewis takes to be limning the ‘fundamental structure of reality’(see Hall 2010, §3), though Lewis himself doesn’t explicitly describethem as ‘fundamental’ in his 1983.

Perhaps some associations of this kind are warranted; perhaps, for

example, appearance in such a language or theory is symptomatic offundamentality. However, it would seem inappropriate to attempt todefine metaphysical fundamentality in terms of languages or theories.(I don’t mean to implicate here that Sider or Lewis does so.) I take itthat those who defend a fundamentality thesis may also want the rel-evant fundamentality structures to be wholly metaphysical, mind-independent, and objective. And that won’t sit well with their beingsimply a matter of how things are with our languages or theories. I’m

not even sure we should take either of these symptoms as a necessaryand sufficient condition for fundamentality.2 What happens if there ismore than one ideal or minimally adequate language or theory? Whatif there are none? I’m not sure how to go about addressing thesequestions.

Many other words associated with fundamentality are relatively neu-tral with respect to what fundamentality actually is , but are still suggestiveregarding the kind of structure associated with fundamentality. These

fall into two groups, the first of which includes words like:‘priority’,

‘dependence’,

‘hierarchy’,

2 Except if we link these symptoms explicitly to H: if (for example) we say

that appearance in the relevant kind of theory is necessary and sufficient forfundamentality, and also that the relevant kind of theory is simply: that theo-ry which states the facts by appeal to which the rest of the facts are to beexplained.




‘depth’,

‘derivativeness’,

‘shallowness’,

‘reduction’,

and ‘inheritance’.

The second group includes words like:

‘foundations’,

‘elementariness’, ‘ground’,

‘ultimate’,

‘basis’/‘basic’

‘primitiveness’

and ‘primariness’.

The association with so many words suggestive of ordering – the words in the first group – strongly indicates that the existence ofsome kind of ordering is (or at least: is considered) absolutely crucialfor fundamentality. I will hereafter refer to this ordering as the ‘de-pendence’ ordering. However, although some of the order-suggesting words in the first group (e.g. ‘hierarchy’) may be considered sugges-tive of a stratified ordering, it is not at all obvious that just becausethere is an ordering there must be stratification. Fundamentality doesnot obviously require ‘layers’ or ‘levels’ of reality; there might insteadbe a continuous scale from the less fundamental to the more funda-mental. At least, nothing about the idea of fundamentality as requir-ing some sort of ordering obviously rules that out.

The association with words in the second group indicates that theordering needs to have a minimal end: the fundamental end. Butthere is no apparent need for it to have a maximal end. And we

should make room (at least in conceptual space) for the possibilitythat there is some vagueness, indeterminacy and contextual shiftinessas to whether some particular thing counts as being ‘at the minimalend’ (i.e. falls in the extension of ‘fundamental’). Compare: being dry



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is being at the minimal end of the wetness spectrum, but there maybe some vagueness, indeterminacy, and contextual shiftiness as to

exactly how dry something has to be to fall in the extension of ‘dry’.By analogy, we should allow that we might sometimes use ‘fundamen-tal’ in such a way that it’s vague or otherwise indeterminate whether(say) all physical things count as ‘fundamental’ or only the smallestones. And we should allow that sometimes ‘fundamental’ might shiftin (relatively determinate) extension between (say) the collection ofall physical things and the collection of the smallest physical things,depending on context.

There is also another kind of sophistication to this notion of a min-imal end: it is compatible with the existence of a ‘minimal end’ to thedependence ordering that the ‘end’ itself be dependent on something , andeven that this dependence itself leads to a further endless chain ofdependence. One could, for example, regard the physical world asmetaphysically fundamental, meaning that the rest – i.e. the mental, thespiritual, the normative, etc. – metaphysically depends on the physical world, whilst simultaneously allowing that there are chains of de-

pendence amongst physical things , and even whilst allowing that these chains of dependence never bottom out. So for example, one couldthink that physical wholes metaphysically depend on their properparts, and that physical objects are ‘gunky’ (in the sense that each ofits parts has proper parts), so that the physical world depends on itsproper parts which depend on their proper parts and so on all the way down, and yet also sensibly describe the physical world as meta-physically ‘fundamental’ because it is that on which every other aspect

of reality depends. This is a feature of the relation between dependence and fundamen-tality which H allows for. H does not require that fundamental thingsdepend on nothing. Although this may happen in some cases of fun-damentality, it should not be imposed as a condition on fundamental-ity, as this would prevent the physical world from being fundamentalon the view just considered: the physical world is a physical thing, soit has parts, upon which – according to the view in question – it de-

pends. My best guess as to why such dependence doesn’t affect at-tributions of ‘fundamentality’ in cases like this is that the dependencein question is in some sense internal to the thing which is being la-




belled as ‘fundamental’ (in this case, the physical world). Because it’sinternal, this kind of dependence doesn’t interfere with the physical

world’s adequacy for explaining ‘the rest’: the things on which thephysical world depends (i.e. the physical world’s proper parts) are in-ternal to it and so aren’t part of ‘the rest’ (which consists of the men-tal, the spiritual, the normative etc.), and therefore the physical worlddoesn’t have to help explain them in order to count as ‘fundamental’. Thus it’s no problem if they are involved in the explanation of thephysical world (i.e. if the physical world depends on them).

Were we to change context such that the world’s proper parts did

start to count as part of ‘the rest’, then plausibly we would no longerbe able truly to describe the physical world as ‘fundamental’. What H allows is that what is ‘fundamental’ may yet depend on something,but only if that something doesn’t count as part of ‘the rest’.

3. The Need for H

It is sometimes suggested that fundamentality and/or dependence are‘unanalysable’ or ‘primitive’, without much detail as to what would berequired for an analysis and why one cannot be provided (see e.g.Cameron 2008, 3; Schaffer 2009, 364). This sort of move runs a fa-miliar kind of risk: in saying that something of interest to philoso-phers (but few others) is sui generis or otherwise not amenable to sig-nificant explication, we risk making it appear mysterious. We alsoraise questions about its respectability as a subject of enquiry, such as: what sorts of epistemic resources are we using when we enquireabout fundamentality? And: how do we know that it is epistemically

accessible to us at all?But it is also fairly common for philosophers to assume that we havesome grasp of what fundamentality and dependence amount to, whichis adequate (at least as a starting point) to enable us to make use ofthe notions in serious philosophy (see e.g. Williams 2010, 107; Cam-eron 2008, 3; Schaffer 2010, 36). Maybe we do, but I think it’s risky toproceed on that assumption, lest when pressed we turn out not tohave a decent grasp at all, or to have a variety of different grasps. And again, leaving matters there risks casting a shroud of mystery, orat least fails to dispel any such shrouds that may have already beencast.

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If we had a secure grasp of dependence, we would be in decentshape: we could then hope to understand fundamentality in terms of

dependence (as discussed on p. 2 above). Modal characterisations ofthe dependence notion as some kind of supervenience are familiar,but also (since at least Fine 1995) familiarly hopeless. Issues includethe unwanted dependence of the necessary upon everything, and thefact that supervenience can be symmetric and this makes it difficultto see how it could generate the kind of ordering required for de-pendence. There is widespread recent consensus is that such modalcharacterisations just don’t work for these reasons. (See e.g.

McLaughlin and Bennett 2005, §3.5; Correia 2008, §1.4; and Koslickiforthcoming; a similar point to the second is made in Lowe 2009.)

I was deliberately careful about stating the second worry (the worrygenerated by symmetries in supervenience). It’s tempting to cash itout (as McLaughlin and Bennett, Correia and Koslicki do) by statingthat dependence is asymmetric , but I have put the point in terms of theneed to ‘generate the kind of ordering required for dependence’. Iexplain why in Jenkins 2011: although it is very natural to treat meta-

physical dependence as irreflexive and asymmetric, there are other ways in which one could accommodate the data responsible for theappearance of irreflexivity and asymmetry. However, the modal char-acterisations of dependence fail even to account for the appearance ofirreflexivity and asymmetry.

Given that modal characterisations of dependence won’t work, Ipropose that H take their place. Explanation talk is everywhere in thisliterature. It’s strikingly common to see words associated with expla-

nation (particularly ‘because’ and ‘in virtue of’) dropped into discus-sions of dependence and fundamentality as if the connection be-tween explanation and dependence were a very obvious or naturalone. Here, for example, is Schaffer (2010, 35; emphasis in the origi-nal):

There is also the metaphysical structure of prior and posterior,reflecting what depends on what, and revealing what are thefundamental independent entities … Consider Socrates. Giventhat he exists, the proposition <Socrates exists> must be true. And conversely, given that the proposition <Socrates exists> istrue, there must be Socrates. Yet clearly there is an asymmetry.




The proposition is true because the man exists and not vice ver-sa. Truth depends on being …

Less often, but still fairly frequently, explanation isn’t merely droppedinto the discussion in passing; it is explicitly stated that metaphysicaldependence (or some cognate notion) is closely connected with ex-planation. Here is deRosset (2010, 74):

The priority theorist holds that the existence and features ofall macroscopic concreta are fully explicable solely by referenceto the existence and features of other things. Those other

things are in this sense prior to the familiar macroscopic individuals. Ultimately, the explanation bottoms out in a relativelysparse inventory of entities, whose existence and features haveno further explanation.

And here is Fine (2001, 15; emphases in the original):

We take ground to be an explanatory relation: if the truth that Pis grounded in other truths, then they account for its truth; P ’sbeing the case holds in virtue of the other truths’ being the case.

(I think the ‘we’ here is the academic first person singular ‘we’,but maybe Fine intends to express the view that this is whatphilosophers in general take ground to be.)

Clearly, both deRosset and Fine at least think that belief in metaphys-ical grounding/priority relations commits one to some correspondingclaims about explanation. That by itself, though, is weaker than thehypothesis H that I’m interested in, which says that there’s nothing

more to calling something ‘fundamental’ than calling it ‘(part of) thatby appeal to which the rest can be explained’. (A similar point is not-ed by Correia; see his 2005, 56.) According to H, attributions of thekind of ‘dependence’ that g enerates the ordering required for funda-mentality just are attributions of (a certain kind of) explanatory de-pendence. It isn’t that there’s something else, metaphysical depend-ence, which goes along with or gives rise to explanations.

I suspect that Fine and deRosset probably endorse something strong-

er than the weak claim that dependence goes along with explanatoryconnections. DeRosset (2010, 75) enjoins us to ‘[ c]all a fact fundamental if it is not explained by any other fact’; although this precise con-



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ception of the relationship between fundamentality and explanationis not one that that H recommends, DeRosset may well be intending

to convey commitment to an identity between fundamentality andsomething to do with explanation. Fine says (2001, 16) that ground-ing is ‘the ultimate form of explanation’, which also suggests an iden-tification of grounding with (a certain kind of) explanation.

But even assuming that deRosset and/or Fine do or would endorsesomething in the vicinity of H, neither of them provides much com-mentary on how to understand such a thesis, nor a sustained assess-ment of the merits and demerits of such a characterisation of fun-

damentality.Correia’s 2005 notion of ‘metaphysical grounding’ is more obviouslya pre-cursor of to the dependence notion characterised by H. He de-scribes (p. 53) a notion of priority such that:

a is prior to {a } insofar as the existence of a explains , or helpsexplain , the existence of {a } — while the converse is false. …Metaphysical grounding is an explanatory link of the kind un-

der consideration.However, Correia doesn’t offer an argument to the effect that thissort of characterisation in terms of explanation is a good characterisa-tion of the thing metaphysicians have been interested in all this time.(He does offer objections to some alternative characterisations ofnotions in the vicinity, but that doesn’t do all the required work, sincethere could be others.)

My view contrasts with that of Koslicki (forthcoming), whose posi-tion is that ontological dependence is something which merely ‘under- writes’ explanations:

As a number of writers have noted, it is plausible to think thatdependence and explanation are related in something like thefollowing way: when the presence of one type of phenome-non Ø explains that of another type of phenomenon Ψ, thisexplanatory relationship is underwritten by a dependence rela-

tion of some sort. For example, it is plausible to think that thecausal, probabilistic or logical dependence relations mentionedearlier in this paper underwrite causal, probabilistic or logicalexplanations, respectively. It would certainly be attractive to ex-




tend this idea to the realm of ontological dependence, so that we may similarly take ontological dependence relations to give

rise to ontological explanations. There are other accounts of notions that are at least in the vicinity ofmetaphysical dependence and which assign some crucial role to ex-planation. One such account may be found in Lowe 1998. Lowe’sproposal is considerably less straightforward than H, but it is sugges-tive that explanation is an important part of his picture. Schnieder(2006), rehabilitating a simpler proposal which was considered butrejected by Lowe, also suggests that explanation is crucial for de-

pendence (at least of things on other things). He characterises suchdependence thus (p. 409):

x depends upon y ↔df . F ( x exists, because y is F ).

However, Schnieder also says that the relevant kind of explanation is‘conceptual’, and says that conceptual explanations are ‘based on cer-tain conceptual relations which they in turn illuminate’ (p. 404). Hestresses the ‘objectivity’ of the explanations, notwithstanding their

conceptual nature. But whether conceptual explanations count as‘objective’ in the relevant sense or not, I think Schnieder’s focus onthe conceptual is misplaced. One reason why is that it seems desirableto allow for the possibility that some interesting dependence relationshold entirely a posteriori, and in ways that have nothing particularlyto do with concepts. For example, one might want to claim that factsabout water are metaphysically dependent upon facts about hydrogenand oxygen and the way they bond. Or that facts about my mental

states are grounded in facts about the distribution and fundamentalproperties of the subatomic particles in my brain.

Let me conclude this section by noting that H differs from all theprecursors described here by being metalinguistic . I think this is im-portant, because I think ‘explains’ is highly context sensitive (see Jen-kins 2008) and consequently I suspect that ‘depends’ and ‘fundamen-tal’ exhibit the same sort of behaviour. The non-metalinguistic pre-cursors of H can’t deliver this feature as they stand; a proper explana-

tion of the meaning of context-sensitive language requires that onetake a metalinguistic stance. (By analogy, I can’t properly explain what



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‘I’ means just by saying that I am Carrie Jenkins. I have to go metalin-guistic: for example, I could say that ‘I’ refers to whomever utters it.)

Let me give an example of the sort of context sensitivity for ‘de-pends’ that I’m trying to capture. The following utterances soundgood to me. (Maybe they’re true. They’re at least plausible.)

(1) The funniness of joke J depends upon its reception by normalaudiences.

(2) The funniness of joke J depends upon its reference to ducks.

But this one sounds strange:(3) The funniness of joke J depends upon its reception by normal

audiences and its reference to ducks.

This, I conjecture, is because ‘depend’ in (1) is used to gesture at theobtaining of one of the relations that can (in certain contexts) countas playing the metaphysical ‘explanation’ role,3 whereas in (2) it isused to gesture at a different relation, which can also (albeit in a dif-ferent set of contexts) be so described. Perhaps the operative relationin (1) is constitution – the idea being that the funniness of joke J is constituted by something about its reception by normal audiences – whereas in (2) the operative relation is something more like influenceor (non-causal) generation – the idea being that J’s funniness is influ-enced or generated by J’s reference to ducks.

This difference gives rise to two different (though related) meaningsfor ‘depends’, and (3) sounds odd because it attempts to ignore thisdifference. The trio (1), (2), (3) is in that respect analogous to:

(a) Sarah called Teri a cab.

(b) Sarah called Teri a fool.

(c) Sarah called Teri a cab and a fool.

Also suggestive is the fact that it can sound OK to say ‘The funninessof J depends only upon its reception by normal audiences’, eventhough it is also true to say ‘The funniness of J depends upon its ref-

3 I am attracted to a kind of functionalism about explanation, described in Jenkins 2008.




erence to ducks’. This is analogous to the acceptability of saying ‘Theonly thing Sarah called Teri was a fool’, even though it is also true to

say ‘Sarah called Teri a cab’.4 Even readers who are not convinced by these particular examplesmay agree that it is advantageous for an account of what metaphysi-cians are doing when they talk the ‘fundamentality’-talk to be capableof accommodating shiftiness of this kind. If such behaviour is evenon the cards, we are better off taking a metalinguistic approach. There is no particular disadvantage to doing so, except the additionof a manageable amount of extra complexity in the statement of the

account.

4. Assessing H: Pros

In this section I look at what considerations can be marshalled insupport of H … in addition, that is, to the existence all the aforemen-tioned associations between fundamentality/dependence and expla-nation, which I think constitute one of the primary reasons for ac-cepting something in the vicinity of H.

One noticeable feature of H is that it renders fundamentality and de-pendence relatively unmysterious. There is nothing terribly metaphys-ically weird about them; they can be understood in terms of explana-tion, which is a notion that we all know and some of us love. Ofcourse, H is to be understood as referring to particular metaphysicallyinteresting kinds of explanation (on which more later), and so there isscope for caution about the existence or obtaining of some or all of

the kinds of metaphysical relations which might give rise to thosesorts of explanations. But the weirdness of fundamentality and de-pendence per se is at least potentially reduced if we can make senseof them without requiring either to consist in something sui generis.

Correspondingly, epistemic worries that could arise if one thoughtfundamentality and dependence were strange sui generis metaphysicalfeatures of the world should be allayed by H, to at least some extent. Those who like to think of metaphysical enquiry as continuous with

other kinds of enquiry should find this particularly reassuring: the

4 Thanks to Jonathan Ichikawa for discussion of this point.



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practice of thinking about and looking for explanations is ubiquitousin all kinds of intellectual endeavour.

Then there is the fact that commonly-assumed features of metaphys-ical dependence include irreflexivity, asymmetry and transitivity (seee.g. Cameron 2008, 3; Schaffer 2010, 37). Explanation relations arealso often taken to have some or all of these features. (See e.g.Nozick 1981, 116 –17.) I’m not actually sure we should endorse theclaim that metaphysical dependence is an irreflexive relation (see Jen-kins 2011), but that needn’t matter; I’m not sure that explanation is anirreflexive relation either. What matters is that they both seem to be.

(They both at least exhibit what I call ‘quasi-irreflexivity’: it soundsbad to say ‘x explains x ’ and it sounds bad to say ‘x metaphysicallydepends upon x ’.) If H is correct one would expect various (appar-ent) features of explanation to have echoes in (apparent) features ofmetaphysical dependence.

It is also noteworthy that arguments in favour of fundamentality (thatis, in favour of there actually being something which is fundamental) tendto make play with the feeling that something or other needs to be ‘gotoff the ground’.5 This feeling is, I think, plausibly related to the feel-ing that explanations have to ground out somewhere in order to besatisfying, a feeling sometimes expressed by saying that one has mere-ly ‘pushed the question back’ if one’s explanations do not ground out.Some authors explicitly connect the need for fundamentality with theneed for metaphysical explanation to begin somewhere: for example,Cameron (2008, 3) says that ‘there is a problem if metaphysical ex-planation never ‘grounds out’ at some fundamental level’. This point

needs to be handled with some care owing to the possibility of de-pendence within the fundamental; see p. 7 above. But, as with irre-flexivity and asymmetry, my point doesn’t require that either explana-tion or dependence really does need to ‘get off the ground’, merelythat we tend to think this way about both explanation and fundamen-tality.

Also worth mentioning is that fact that modal connections can besymptomatic of the presence of explanation, and particularly of cer-

5 Caution is needed in interpreting this sort of feeling though, as indicatedon p. 7 above.




tain kinds of explanation. Modal connections are strongly associated with explanations that trade on identities, for example. We can ex-

plain why there are moral facts by saying that there are facts about themaximisation of utility, if we believe the two kinds of facts are iden-tical. And, if we believe that, we may well also think that the obtain-ing of certain utility maximisation facts is necessary and sufficient forthe obtaining of corresponding moral facts. Similarly, we can expectmodal symptoms to be associated with explanations which trade onmereological relations, constitution relations, and other relations thatare distinctively of interest to metaphysicians (of which more later).

So it is not too surprising that modal characterisations of metaphysi-cal dependence have been suggested, if explanation is in fact what’sgoing on, particularly if the explanations in question are at least rea-sonably often of these kinds associated with modal connections.6

Two final advantages of H. Firstly, since pretty much anything can beappealed to in an explanation, pretty much anything can be sensiblycalled ‘fundamental’ if H is correct. This makes sense of the lengthof the (long but still very incomplete) list in §1 above of kinds of

things to which the term is being applied in contemporary metaphys-ics.

Secondly, the lack of any serious philosophical interest in questionslike whether there exists anything maximally un fundamental, and whatif anything has that property, is also suggestive. For one thing, we aregenerally more likely to be interested in getting hold of somethingthat we think could serve satisfying explanation of all the rest thanfinding out exactly how far the explanatory reach of that explanans

extends. (I don’t propose to explain that fact about us here; I merelynote that it is a fact.) For another, it is less intuitive to think that thatthe explanatory reach of some explanans will have any ‘end’ than it isto think that there will be a ‘starting point’ to the explanatory chain,

6 The fact that dependence is associated with identity (or explanationsinvolving identity) is not enough by itself for modal characterization of de-pendence to seem plausible; nor are its being associated with mereology, its

being associated with constitution, etc. What could lead to a modal charac-terization of dependence seeming plausible is that modal connections aresymptomatic of all these various kinds of explanation that are associated withdependence.



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of the kind required for fundamentality. (Again, I don’t propose tooffer an explanation of why this is less intuitive; it’s enough for cur-

rent purposes that it is.)

5. Assessing H: Cons

The flip side of the first advantage I mentioned in §4 above – that H renders metaphysical fundamentality and dependence unmysterious – is the concern that it inappropriately ‘deflates’ them. How best toaddress this concern will depend on exactly what sort of inflated no-tions the objector would prefer. But I anticipate that much of the

discomfort may come from the feeling that explanation is humano-centric, whereas metaphysical fundamentality and dependence shouldnot be: they should be metaphysically weighty, mind-independent,matters.

This sort of objection might be spelled out along roughly the follow-ing lines. What makes for an explanation (or at least, a good explana-tion) depends on things like what the audience already knows, and what the hearer is interested in. And the goal of an explanation, atleast sometimes, is to produce understanding in the audience. Noneof this is relevant to metaphysical dependence relations, which obtainmind-independently and have nothing to do with what people knowor are interested in or understand. (See also passing remarks in Lowe1998, 146, and Lowe 2009, §3, to the effect that there is a risk, onsuch approaches, of conflating metaphysics and epistemology.)

I here set aside cheap answers to this objection which concede that

metaphysical dependence is simply less mind-independent than(most) people previously thought. Koslicki (forthcoming) discussesthis type of concern for her own view, and addresses it as follows:

… if at the end of the day we want to be left with a substa n-tive notion of ontological dependence (as well as related con-cepts, such as those of priority, primacy, basicness, non-derivativeness, fundamentality, and the like), the type of expla-nation at work here cannot be viewed as one that is to be un-

derstood in primarily subjective, pragmatic or epistemic terms. Although it is very common these days to think of explanationin this way, other approaches to explanation, which are more




conducive to a realist understanding of this notion, are availa-ble. For example, one might hold that any explanatory connec-

tion between a phenomenon, Ø, and a phenomenon, Ψ, canbe traced back to there being a law connecting Ø and Ψ. Andeven to those who have a relatively easy time hearing the ex-planatory ‘because’ as a highly pragmatic, subjective, epistemicand/or context-sensitive connective, it is perhaps somewhatmore difficult to swallow that what counts as a law should sim-ilarly be tailored to interests or other occasion-dependent fea-tures. Aristotle’s famous doctrine of the four causes or explan-

atory factors also allows for a realist approach to explanation:matter (material cause), form (formal cause), telos (final cause)and source of change (efficient cause), in Aristotle’s view, arereal and privileged constituents of the world, even though which of these aspects is of particular importance to us, when we ask a specific ‘why’-question, may of course vary from oc-casion to occasion.

I think this answer is on the right track, but can be made more ap-

pealingly general. I’m not sure whether it is ‘very common’ (amongphilosophers? among the folk?) to think of explanation as primarilysubjective, pragmatic and/or epistemic. But the important point tonote is that one needn’t believe that explanations require coveringlaws, or that Aristotle was right about explanation, in order to arguethat explanation is not always humanocentric in such a way as to ren-der it unsuitable for cashing out what metaphysical dependenceamounts to.

In Jenkins 2008, 66 –7, I describe several dimensions of variation inthe things that we are ordinarily happy to call ‘explanations’. I suggestthat sometimes ‘explanation’ is used in such a way that little more isrequired of something to count as ‘an explanation’ than that a f eelingof understanding be produced in the recipient. Such uses express what I call an ‘all-in-the-mind’ conception of explanation. On otheroccasions of use, how things stand in (mind-independent) reality ismuch more important for determining what falls within the extension

of ‘explanation’ than are feelings of understanding. This notion of‘real’ explanation is in play when we say things like: ‘There must besome explanation of the existence of the universe but nobody could




we cite in reply can be taken as explaining all the rest; there will always be something else (i.e. whatever X itself is explained by) that is

not explained by X . So characterising fundamentality in terms of ex-planation, as H does, appears to beg the question against views ac-cording to which there is something fundamental.

There are four responses to consider here. Firstly, one could arguethat this doesn’t beg the question but rather moves the debate along.Maybe recognising that fundamentality is all about explanation, andexplanation never bottoms out, is (at least sometimes) a way of find-ing out that nothing is fundamental. I find this somewhat methodo-

logically unsatisfying; if we characterise fundamentality in such a wayas to make it too obvious whether there is anything fundamental, werisk being subject to a modus tollens manoeuvre, and told that sincethat is not that obvious, the characterisation must be wrong.

Secondly, maybe explanation does bottom out. The fact that one canalways ask another explanation-seeking why-question doesn’t meanthere is any answer to be had. Maybe there are just some explanatorily‘brute’ facts, truths, objects or whatever. Thirdly, even if explanationin general does not bottom out, maybe certain kinds of explanationdo. Even if one can always ask ‘why?’ and reasonably expect an answer , itcould be that there won’t be an answer of the right kind for a meta-physical dependence relation to be in place. Fourthly, even if there isan answer of the right kind for a metaphysical dependence relation tobe in place, even this will not necessarily interfere with fundamentali-ty provided there is no dependence on ‘the rest’, for the reasons dis-cussed on p. 7 above.

Another possible objection to H is that fundamentality is sometimesassociated (at least in the Aristotelian tradition, at least according tosuch commentators as Schaffer 2009) with the thought that the non-fundamental is ‘no addition to being’. Armstrong (1982 and elsewhere) introduced this phrase in connection with what he called ‘su-pervenience’. Could we make sense of the thought that whatever isnon-fundamental is ‘no addition to being’, if fundamentality werecashed out in terms of explanation in the way H suggests?

There are two broad groups of ways to understand the claim that thenon-fundamental is ‘no addition to being’. On the first group of in-terpretations, the non-fundamental is ‘no addition to being’ because it



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is either non-real or identical to something fundamental. (Jenkins(2011) explains why I think it needn’t automatically be contradictory

to make claims of the form ‘x = y , yet x is fundamental and y is non-fundamental’.)

Holding that the non-fundamental is unreal, along with H, amountsto holding that when we have an explanation of the rest , the rest is forsome reason non-real. Something Fine says (2001, 4) suggests that hemight find this combination of views problematic:

Now it may be conceded that there is a sense in which certain facts

are more fundamental than others; they may serve to explain the oth-er facts or perhaps, in some other way, be constitutive of them. Buthow does this provide a ground for denying reality to the other facts?Indeed, that they had an explanation or constitution in terms of thereal facts would appear to indicate that they themselves were real.

There is nothing inconsistent about the position under consideration,but Fine challenges it on motivation. What is it about this kind ofexplicability that supposedly makes for non-reality?

I share Fine’s intuitions here to some extent, but I also note that wecould construct a possible motivation for denying existence to thenon-fundamental on the grounds that it doesn’t do the kind of ex-planatory heavy lifting done by the stuff that is fundamental. Thethought here would be, roughly, that pulling one’s explanatory weight,in the sense of being a member of that-by-appeal-to-which-the-rest-is-to-be-explained, is a necessary condition for being worthy of ad-mission to one’s ontology. The idea that there is some connection be-

tween something’s playing an explanatory role and being worthy ofadmission to one’s ontology is not an uncommon one (see e.g. Baker2005 for a good recent discussion of such connections in the case ofmathematical entities).

What if, on the other hand, the (supposedly) Aristotelian claim is in-terpreted as saying that everything non-fundamental is simply identi-cal to something fundamental? According to H, that amounts to the view that those things of which a certain kind of explanation can be

given are identical to the things that are appealed to in the relevantexplanations. This is not inconsistent either; indeed, it could be thatthe kinds of explanation that are relevant for grounding include a




kind that arises from identity. For example, a certain kind of explana-tion of why there are minds could appeal to the fact that there are

brains (which are identical to minds). The second group of interpretations of the phrase ‘no addition tobeing’ takes it slightly less seriously. On such interpretations, theclaim that the non-fundamental is no addition to being, instead ofmeaning that the non-fundamental adds nothing to reality at all , justmeans that it adds nothing to fundamental reality (and is therefore isnot significant, metaphysically speaking). Schaffer, for example, sug-gests reading ‘no addition to being’ as ‘no addition to the sparse basis’(Schaffer 2009, 353).Of course, if that is what’s meant, then once again the view can beconsistently held together with H. It can even be motivated by H,since one might feel that methodologically it is much less of a bigdeal to posit things for which the right kinds of explanations can begiven (i.e. non-fundamental things) than it is to posit things that lacksuch explanation. The former are certainly no addition to inexplicable reality; explicable reality, it might be felt, is relatively philosophicallycheap.

One final worry: can H allow for emergence?9 That is to say, if H istrue, can it happen that (say) consciousness depends on fundamentalphysical facts and yet is not fully explicable by appeal to them? I thinkso. To accommodate such cases, ‘all the rest’ may need to be read in arestricted way, so as to allow for the possibility that some non-fundamental things are in some respects inexplicable. But it wouldn’t

solve this problem to suggest that ‘by appeal to which all the rest canbe explained’ be read as something like ‘by appeal to which ever y-thing that can be explained about the rest can be explained’: I take itthat the fundamental has to be doing some significant explanatory work, even it isn’t doing quite all that one might want, and the formu-lation just considered doesn’t deliver that in cases where nothingabout the rest can be explained. A form of words that gets closer to what we’re after would be: ‘by appeal to which sufficiently muchabout the rest can be explained’.

9 Thanks to Dave Chalmers and Elizabeth Barnes for discussion of thisquestion.




along with modal connections between explanandum and explanans).I’m not sure we should expect that the relevant explanations will al-

ways be associated with non-distinctness, however. It seems metaphys-ically respectable to say that {9} depends on 9, but the two entitiesare wholly distinct. They are, nevertheless, undeniably somewhat in-timately related. Perhaps there is some way of spelling out ‘tight’nessof explanation to cover this kind of case as well as the non-distinctness kinds, and all other cases of metaphysical dependence.But I don’t at present know what it is.

Koslicki (forthcoming) believes there are different varieties of onto-

logical dependence: one associated with ‘real definition’, one associat-ed with being ‘a constituent in a proposition expressing [the] acci-dental nature’ of the grounded thing at a particular time, and at leastone other kind of which she does not give a theory. Each kind ofgrounding is, on Koslicki’s view, associated with explanations of thegrounded in terms of its grounds. But consistently with H we couldhold a variant of her view on which the explanation relations wereconstitutive of dependence rather than just associated with it. Real def-

inition gives rise to explanations, Koslicki says; then she goes on toidentify the dependence relation with the relation of being a constitu-ent in a proposition expressing a real definition. We could acceptmost of Koslicki’s story but then identify the dependence relation with the relevant explanation relations instead.

However, I am not sure that it is methodologically desirable to havebelief in dependence relations commit one to believing in such thingsas real definition, propositions expressing accidental natures (with

constituents) and/or whatever particular theoretical commitmentsturn out to be necessary to account for Koslicki’s further kind(s) ofgrounding. One of the attractions of H is that one can believe in de-pendence and fundamentality while remaining pretty neutral about what sorts of metaphysical mechanisms give rise to the explanationsthat constitute grounding.

In discussion, Koslicki has suggested to me that her postulation ofthe different varieties of grounding makes her view more contentfulthan H alone. That is true, but I don’t think that increasing quantityof content is necessarily a good thing in an interpretative project. And if we want to say more than H does, we can do so not by chang-



210 JENKINS

ing what H says (unless we have independent reason to do that), butby adding further claims by way of elucidation of H. We could, for

example, recapture much of what Koslicki says (if we wanted to) byreclassifying her varieties of grounding as varieties of things that canbe described as ‘metaphysical explanations’. This would enable us tocapture a lot of her view without splintering the notion of dependenceor building any of Koslicki’s more controversial metaphysics into thatnotion.

Let me now offer couple of suggestions of my own as to what kindsof explanation are relevant. These comments fall short of a theory,

but I hope they may nonetheless be illuminating.Firstly: transitivity seems important. It seems to be a generally ac-cepted principle of grounding that if A grounds B and B grounds C , A grounds C , and I can’t think of any reason to doubt that this iscorrect. (Not so for the equally common irreflexivity assumption; see Jenkins 2011.) But plausibly, not all explanation works in a transitive way; it’s not implausible to say that the arrangement of particles inmy brain explains my feeling pain, and my feeling pain explains mytaking painkillers, but that we can’t explain my taking painkillers interms of the arrangement of particles in my brain, because that sortof attempted explanation would be ‘at the wrong level’ (see e.g.Campbell 2010, §2 for a recent discussion of this idea).

But will any old metaphysically interesting transitive relation associat-ed with explanation give rise to the right kind of explanations? Per-haps not. DeRosset (2010, 7 –8) for example, doubts whether causal

explanations can be the kind of explanations to which what he calls‘priority theorists’ are committed. He says that appealing to causalexplanations in this context doesn’t sit at all comfortably with the ideathat the non-fundamental is ‘no addition to being’. On some of theless serious construals of that phrase described in §5 above, there isno obvious tension. Nevertheless, it does sound somewhat odd to myears to describe an event as metaphysically fundamental merely on thegrounds that it can be appealed to in a causal explanation of the restof the events.

So what kinds of explanation are relevant for H? The suggestion I want to float here is that there may be no particularly tidy answer tothis question. I’m not sure why we should expect there to be anything




more to say here than: the kinds of explanation that have been ofinterest to metaphysicians working in the tradition of thinking about

dependence and fundamentality (such as the kinds of explanationthat identity, constitution and parthood give rise to). While theremight be some unity to these kinds of explanation, the grouping couldbe in part due to historical accident, much like the subdiscipline ofmetaphysics itself.

7. Some Rivals

In addition to the cousins of H described in §3 above, it is worth

briefly considering a couple of alternative views as to what metaphy-sicians are up to when they talk about fundamentality. These two arenot chosen because they are the only credible alternatives, but be-cause discussing them helps reveal more of the dialectical advantagesof H itself.

Firstly, I’ve assumed that there is something reasonably unified to besaid about what ‘fundamental’ means in the mouths of metaphys i-cians. One rival of my view states that multiple different things canbe expressed by that word and there is no unity of the kind H postu-lates between these multiple meanings. However, I don’t think weshould postulate such ambiguity unless it demonstrably helps us makebetter sense of what metaphysicians are saying. I think the burden ofproof is upon the ambiguity view. And H does already allow for ahealthy amount of flexibility as to exactly what gets expressed by‘fundamental’ in the mouths of different metaphysicians, while stillmaintaining an appealing unity.

A second alternative view 10 is that to call a thing fundamental is just tosay that it belongs to a fundamental kind . Fundamental kinds mightthen be characterisable roughly as H suggests, but on this view thereneed be no requirement that fundamental things play any particularexplanatory role. I don’t have much against this sort of alternative view, according to which kinds are privileged for the purposes of un-derstanding fundamentality and things get to be fundamental only (asit were) derivatively. But I don’t see much motivation for it either. Why should some kind – say, the kind electron – be especially explana-

10 Thanks to Ned Hall for suggesting I discuss this here.



212 JENKINS

torily interesting, unless the electrons themselves (at least qua elec-trons) are too? Until this question is answered, I prefer the more uni-

fied account of what it means to call something ‘fundamental’ that H provides.11

References

Armstrong, D. 1982: ‘Metaphysics and Supervenience’. Critica 14, pp.3 –18.

— 1997: A World of States of Affairs . Cambridge: Cambridge Universi-ty Press.

Baker, A. 2005: ‘Are There Genuine Mathematical Explanations ofPhysical Phenomena?’. Mind 114, pp. 223 –38.

Cameron, R. 2008: ‘Turtles All The Way Down: Regress, Priority andFundamentality’. Philosophical Quarterly 58, pp. 1 –14.

Campbell, J. 2010. ‘Control Variables and Mental Causation’. Proceed- ings of the Aristotelian Society 110, pp. 15 –30.


Cornwell, J. (ed.) 2004. Understanding Explanation , Oxford: OxfordUniversity Press.

Correia, F. 2005: Existential Dependence and Cognate Notions . Munich:Philosophia Verlag.

— 2008: ‘Ontological Dependence’. Philosophy Compass 3, pp. 1013 –32.

11 I am grateful to the editors of the present volume for many substantialcomments on an earlier draft of this paper, and to those present at the Colo-rado Dependence Conference in 2009, especially Daniel Nolan, for help with thinking about this topic. I am also indebted to my audiences at theCarolina Metaphysics Workshop in June 2010, particularly Antony Eagle,Daniel Korman, Kathrin Koslicki and Jessica Wilson, at the Phlox BecauseII Conference in Berlin in August 2010, particularly Elizabeth Barnes, Kit

Fine and Stephan Leuenberger, at the Institute of Philosophy Logic andMetaphysics Forum in November 2010, especially Nick Jones and Lee Wal-ters, and at a PERSP seminar at the University of Barcelona, particularlyDan Lopez de Sa, Tatjana von Solodkoff and Rich Woodward.




Correia, F. and B. Schnieder (eds.) forthcoming: Non-Causal Explana- tion , Cambridge: Cambridge University Press.

DeRosset, L. 2010: ‘Getting Priority Straight’. Philosophical Studies 149,pp. 73 –97.

Fine, K. 1995: ‘Ontological Dependence’. Proceedings of the AristotelianSociety 95, pp. 269 –90.

— 2001: ‘The Question of Realism’. Philosophers Imprint 1, pp. 1 –30.

Hall, N. 2010: ‘David Lewis’s Metaphysics’. In Zalta, E. (ed.) Stan- ford Encyclopedia of Philosophy . URL:

http://plato.stanford.edu/entries/lewis-metaphysics/. Jenkins, C. 2008: ‘Romeo, René and the Reasons Why: W hat Explana-

tion Is’. Proceedings of the Aristotelian Society 108, pp. 61 –84.

— 2011: ‘Is Metaphysical Dependence Irreflexive?’. The Monist 94, pp.267 –76.

Koslicki, K. forthcoming: ‘Varieties of Ontological Dependence’. Toappear in Correia and Schnieder forthcoming.

Lewis, D. 1983: ‘New Work For a Theory of Universals’. The Australa- sian Journal of Philosophy 61. Repr. in his Papers in Metaphysics and Epistemology , pp. 8 –55.

— 1986: On the Plurality of Worlds . Oxford: Blackwell.

— 2003: ‘Things Qua Truthmakers’. In Lillehammer and Rodríquez-Pereyra 2003, pp. 25 –38.

Lillehammer, H. and G. Rodríquez-Pereyra (eds.) 2003: Real Metaphys-

ics: Essays in Honour of D. H. Mellor , London: Routledge.Lipton, P. 2004: ‘What Good is an Explanation?’. In Cornwell 2004,pp. 1 –21.

Lowe, E. J. 1998: The Possibility of Metaphysics . Oxford: Oxford Univer-sity Press.

— 2009: ‘Ontological Dependence’. In Zalta, E. (ed.) Stanford Encyclo- pedia of Philosophy . URL: http://plato.stanford.edu/entries/ de-pendence-ontological/.

Markosian, N. 2005: ‘Against Ontological Fundamentalism’. FactaPhilosophica 7, pp. 69 –83.

http://plato.stanford.edu/entries/%20dependence-ontological/






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McLaughlin, B. and K. Bennett 2005: ‘Supervenience’. In Zalta, E.(ed.) Stanford Encyclopedia of Philosophy . URL:

http://plato.stanford.edu/entries/supervenience/. Nozick, R. 1981: Philosophical Explanations . Cambridge, MA: Harvard

University Press.

Paseau, A. 2010: ‘Defining Ultimate Ontological Basis and the Fun-damental Layer’. Philosophical Quarterly 60, pp. 169 –75.

Schaffer, J. 2003: ‘Is There A Fundamental Level?’. Noûs 37, pp. 498 –517.

— 2009: ‘On What Grounds What’. In Chalmers, Manley and Was-serman 2009, pp. 347 –83.

— 2010. ‘Monism: The Priority of the Whole’. The Philosophical Review 19, pp. 31 –76.


Sider, T. 2011: Writing The Book of the World . Oxford: Oxford Univer-

sity Press. Williams, J. R. G. 2010: ‘Fundamental and Derivative Truths’. Mind 119, pp. 103 –41.

http://plato.stanford.edu/entries/supervenience/

http://plato.stanford.edu/entries/supervenience/



216 DEROSSET

containing a hydroxide group. Diamond is hard because each carbonatom in its crystalline structure is bonded to each of its neighbours.

Theorists who claim that grounding explanations provide an ‘onto-logical free lunch’ have concentrated their efforts on defending anovel view of ontological commitment. They argue that we shouldreject a familiar version of Ock ham’s Razor

Do not multiply entities beyond necessity!

in favour of a less familiar variant

Do not multiply fundamental entities beyond necessity!

3

where an entity is fundamental iff it is not derivative: either its exist-ence or one of its other features is explanatorily basic. If they areright, then grounding explanations are not (or not just) causal: theavailability of a complete causal explanation of an explosion in termsof causal laws, initial conditions, and the ignition of a fuse does notshow that the explosion is ‘no addition to being’, given the laws, con-ditions, and ignition.

The dispute over the proper application of Ockham's Razor has in-terest only if the fundamental entities are a subclass of all of the enti-ties. If every entity is fundamental, then the application of the famil-iar version of Ockham's Razor yields the same results as the applica-tion of its restriction to the fundamental. As one might expect, the

3 See esp. Schaffer 2009, 361, from which the formulation in the text isadapted. Schaffer’s view differs from Cameron’s 2008. Cameron argues thatthe ontological commitments of a theory are given by an inventory of fun-damental entities; Schaffer, that ontological commitments are given by aninventory of the existent entities, but that only commitments to fundamentalentities count when applying Ockham’s Razor. See Schaffer 2008 for a de-fense of Schaffer’s side of the dispute. Though the exposition in the maintext fits Schaffer’s view better than Cameron’s, this dispute about the proper

characterization of the technical notion of an ontological commitment is irrelevant for present purposes. Schaffer and Cameron agree that ( i ) existenceclaims concerning deriv ative entities are an ‘ontological free lunch’, and ( ii )the class of derivative entities is large and diverse.



NO FREE LUNCH 217

theorists in question claim that the fundamental entities are an eliteclass.4

Here I argue that they are wrong: barring reduction, every entity isfundamental, in the sense that either its existence or its possession ofat least one other feature is explanatorily basic. Thus, the claim

EXPLANATION Many entities are derivative: their existence and other features can beexplained solely by reference to the existence and properties of otherthings.

should be rejected. An upshot is that, whatever form Ockham’s Ra-zor should take, grounding explanations on their own do not providean ‘ontological free lunch’.5

Here’s the plan. §1 sets out and defends the premises of the argu-ment against EXPLANATION. The argument itself is outlined in §2,and its import clarified in §3. §§4 –5 discuss responses that might bemade to the argument. I close with some remarks on the significanceof the result in §6.

4 Schaffer (2010), for instance, argues that every concrete entity other thanthe entirety of the concrete cosmos is derivative. Another example is Arm-strong’s (1997) contention that that most universals are derivative. Melia(2005) goes further, outlining a defence of the idea that all universals arederivative.5 Schaffer (2009 and 2010b) has suggested that the basic idea for priority

theorists is not explanation but grounding . We explain facts by reference toother facts, but, by Schaffer’s lights, grounding may obtain between items ofany category, including objects, facts, and properties. Schaffer, however,agrees that grounding requires explanation: the existence and other featuresof the entities that ground an entity completely explain its existence andother non-relational features (private correspondence). See, for instance, theclaim at Schaffer 2009, 364 –5, that grounding ‘... is the notion the physicalistneeds to explicate such plausible claims as “the fundamental properties andfacts are physical and everything else obtains in virtue of them”’ (Loewer

2001, 39) [citation and emphasis in original]. Cameron, 2010, 257, also en-dorses this link between grounding and explanation. The argument in thispaper against EXPLANATION thus applies to views which rely on groundingrather than explanation to distinguish fundamental and derivative entities.



218 DEROSSET

1. Determination, Diversity, Irreducibility

Consideration of a standard way proposals for grounding explana-tions may fail motivates a constraint on this sort of explanation: theexplanation of the existence and other features of a given entity musttrace how those facts are determined. A complete explanation of aderivative entity d ’s having a certain feature F in terms of facts g 1, g 2 ,... should show why d had to be F , given g 1, g 2 , ... . The explanans thereby provides means for distinguishing d from entities which arenot F , and thus showing why d , unlike those other things, is F . There’s something wrong with or missing from a proposed explana-

tion if there is something just like d so far as the explanans goes, but which lacks F . Call any entity which lacks F but is just like d so far asthe explanans goes, a confounding case for the proposed explanation. Forinstance, a confounding case for the explanatory claim

(1) This diamond is hard because it has such-and-such crystallinestructure

would be an entity which has the crystalline structure in question but

is not hard. An explanatory proposal is at best incomplete if there is a confoundingcase for it: the proposal is either off on the wrong foot entirely, orrequires supplementation. ‘At best incomplete’ is awkward to negate.So, for reasons of style I'll call an explanation good if it is not at bestincomplete; good explanations are not off on the wrong foot entirely,and do not require supplementation. Note that explanations that are‘good’ in this sense may fail to qualify as what we would ordinar ily

call ‘a good explanation’: they may be complicated, long -winded, un-enlightening, difficult to understand, etc .

Here is an intuitive way of appreciating the point that confoundingcases indicate that an explanatory proposal is at best incomplete. Astandard strategy for criticizing a proposed explanation of the form‘x is F in virtue of being G’ is to identify a confounding case: anotherobject that’s G but not F . Thus

(2) x is a stable nucleus in virtue of being an oxygen nucleusis a transparently inadequate explanation, given the existence ofshort-lived radioactive oxygen isotopes. Even the mere possibility of



NO FREE LUNCH 219

a confounding case shows that a proposed explanation is at best in-complete. Suppose now that there happen not to be any short-lived

radioactive oxygen isotopes, but it is possible to make some in a cer-tain kind of research reactor. The proposed explanation is still at bestincomplete. Explanatory proposals are thus subject to what I will callthe determination constraint :

DETERMINATION CONSTRAINT

An explanatory proposal of the form, ‘d has feature F because ( d ,x 1, ..., x n )’ is at best incomplete if there is or might have been a con-founding case for it: an entity e and some entities a 1, ..., a n such that e (together with a 1, ..., a n ) satisfies ( y , x 1, ..., x n ) but lacks F .6

EXPLANATION requires that there be many derivative entities. Sup-pose that d is one of them, and that F is one of d ’s features. The ar-gument against EXPLANATION will also use two further assumptions. The first is:

DERIVATIVE DIVERSITY There is a derivative entity e that lacks F .

DERIVATIVE DIVERSITY is innocuous: it’s a natural concomitant ofany view which proposes to use EXPLANATION to mitigate its onto-logical commitments. Without DERIVATIVE DIVERSITY , such a viewhas a severely limited scope: it can only claim an ‘ontological freelunch’ with respect to a class of qualitatively indiscernible entities.

The second assumption is:

IRREDUCIBILITY

d ’s being F and e ’s not being F are irreducible.

The explication of the notion of reduction is highly contested. Forpresent purposes I resort to stipulation: what I am calling a reduction of one fact to another involves the identification of those facts. Noparticular epistemological status is indicated, since an identity thatundergirds a reduction, like many other identities, may not be a priori .

6 Two technical notes. First, here and throughout, I am sloppy about useand mention whenever it is convenient and does not materially affect theargument. Second, I am not assuming that any formula of the form ( d , x 1,…, x n ) contains d (or, for that matter, any of the x s).



NO FREE LUNCH 221

being F ultimately obtains in virtue of facts which do not involve d at all . We get some explanation of the form, ‘d is F because ( t 1, ..., t n )’,

where may mention certain entities and features, but doesn’t men-tion d . That means that e meets exactly the same conditions: it will beequally true of e that (together with t 1, ..., t n ) it satisfies . Since e isnot F , it presents a confounding case for the proposed explanation. Application of the determination constraint implies that the pro-posed explanation is at best incomplete.

Some technical notions are required to state the more formal and

more general version of the argument. For present purposes, let’sthink of a fact as a distribution of certain properties and relationsover certain entities, which I will term the entities involved in the fact.For instance, being male is possessed by George Bush; this is a verysimple way in which this property is distributed over the individual inquestion. Likewise, Bush bears being the husband of toward his spouseLaura; this is a somewhat less simple way in which this relation is dis-tributed over those two individuals. The latter fact involves bothspouses; the former involves only George. An explanatory proposal

for the fact that d has some feature F says that this fact obtains in virtue of certain further facts, each of which is to be identified with adistribution of certain properties and relations over certain entities. Thus, a proposal to explain d ’s having F can be expressed by a claimof the form,

Prop d is F because ( d , t 1, ..., t n )

where all of the entities involved in the explanans are denoted by ex-

actly one term among d , t 1, ..., t n , and says how the properties andrelations in question are distributed over those entities. When an ex-planatory proposal is expressed by a claim of this sort, I will say thatthe claim perspicuously articulates the proposal. A perspicuous articula-tion of an explanatory proposal names names: it specifies exactly which entities are involved in the proposed explanans and explanandum . Thus, the claim, ‘the diamond d is hard in virtue of the arrangementand bonding of certain carbon atoms’ fails to be a perspicuous ar-

ticulation of any explanatory proposal; on the other hand, if c 1, …, c n name the carbon atoms in question, then ‘d is hard in virtue of thearrangement and bonding of c 1, ..., c n ’ is a perspicuous articulation of

222 DEROSSET

an explanatory proposal. I will assume that every explanatory pro-posal that meets the needs of EXPLANATION has a perspicuous artic-

ulation.8

As a final bit of stage-setting, let’s note a consequence of the deter-mination constraint. The determination constraint implies that goodexplanations don’t have confounding cases. Consider again a perspic-uously articulated explanatory proposal of the form

Prop d is F because ( d , t 1, ..., t n ).

A confounding case for this explanatory proposal will be a situationin which some object d *, along with some other objects a 1, ..., a n , hasthe properties required to satisfy the explanans clause , but in whichd * lacks F . Thus, d *, together with a 1, ..., a n , witnesses the truth of

(3) ( y 1, ..., y n )(

x )( ( x , y 1, ..., y n ) Fx ).

So, the determination constraint implies that any perspicuously ar-ticulated explanatory proposal of the form (Prop) is associated with auniversal generalization

(4) ( y 1, ..., y n )( x )( ( x , y 1, ..., y n ) → Fx ).

According to the determination constraint, if the explanatory pro-posal is good, then its associated universal generalization is true.

Here, then, is the argument. Assume EXPLANATION for reductio. Re-call our ancillary assumptions: d is a derivative entity, F is one of its

8 This assumption might be resisted on a variety of grounds. (For in-stance, it might be held that some facts concerning the existence and otherfeatures of derivative entities can be adequately explained only by facts involving infinitely many entities, and that no infinitary perspicuous articula-tion exists.) If the assumption fails, then the argument of this paper willhave to be made at the level of facts. This can be done by representing a fact(in the actual world) by a pair containing the set of entities I it involves andthe set of properties and relations P it involves. The fact represented by <h I ,P > is the distribution of the properties and relations in P over the entities in

I . These representations can, in effect, play the role of perspicuous articula-tions of explanatory proposals. This is not the place to work out the detailsof this alternative approach, so for present purposes I will rely on the as-sumption.



NO FREE LUNCH 223

features, and d and F satisfy IRREDUCIBILITY and DERIVATIVE DI- VERSITY . Since d is derivative, its possession of F has a good explana-

tion perspicuously articulated by a claim of the form,(5) d is F because R ( t 1, ..., t n ),

where R stands in for some (possibly very complex) relation, andnone of the terms t 1, ..., t n denote d .9 But the explanans clause R ( t 1,..., t n ) is also of the form, ( d , t 1, ..., t n ) (see the second remark of n.6).So the explanation in question is also of the form

(7) d is F because ( d , t 1, ..., t n ).

The determination constraint implies that this explanation is goodonly if its associated universal generalization

(8) ( y 1, ..., y n )( x )( R ( y 1, ..., y n ) → Fx )

is true. Since R ( y 1,... , y n ) is x -free, standard quantificational logicyields

(9) (( y 1, ..., y n )R ( y 1, ..., y n ) → ( x )Fx ).

An explanatory proposal is good only if the explanans clause is true.In this case, that requires that R ( t 1, ..., t n ) be true. But then the ante-cedent in (9) is satisfied, and so e is also F . DERIVATIVE DIVERSITY implies that e is not F . Contradiction.

3. Clarifications

Once this argument is stated, it is not difficult to see what’s missing

from the proposal to explain d ’s being F by R ( t 1, ..., t n ). We need onlyadd explanatorily basic facts which indicate what the t ’s have to do with d . Suppose, for instance, that d is a diamond, and we are tryingto explain its hardness in terms of the arrangement and bonding ofcertain carbon atoms. Then we could add the claim that d is com-

9 This is where IRREDUCIBILITY comes in. If d ’s being F is reducible, then,for all we’ve said, it just comes to the obtaining of some relation S among t 1,

…, t n . Then, one might object that (5) misrepresents the form of the explan-atory proposal at hand, which is really(6) S ( t 1, …, t n ) because R ( t 1, …, t n ). This explanatory proposal does not succumb to the reductio.



224 DEROSSET

posed of those carbon atoms; d is hard not just because some carbonatoms are arranged and bonded in such-and-such a way, but because

its carbon atoms are arranged and bonded in that way. This proposaldoes not succumb to our argument; it is crucial for the argument thatthe explanans not involve d . If the explanans clause mentions d , thenthe argument is invalid.10

But our choice of derivative entities d and e and of feature F was en-tirely arbitrary. Thus, admitting explanatorily basic facts involving d means giving up on EXPLANATION entirely. Our argument shows thatthere is a gap in any proposal for explaining any derivative entity’sfeatures that meets the demands of EXPLANATION, so long as DE-RIVATIVE DIVERSITY and IRREDUCIBILITY are satisfied. But fillingthis explanatory gap in the most obvious way, by admitting explanato-rily basic facts involving d , means giving up EXPLANATION. The mor-al of our argument is: barring reduction, there do not exist two derivativeentities x and y that differ on some feature F.

Our argument might be thought to show too much, on the groundsthat it implausibly requires that every fact be explanatorily basic. Butthe argument allows non-basic facts involving d . For instance, theargument does not show that we must accept that

(10) d is a diamond.

is explanatorily basic. (10) imputes a sortal, ‘diamond’ to our friend d .It is plausible to think that d ’s diamondhood is explicable in terms ofthe arrangement of its parts. But the argument does not establish that(10) appears among the explanatorily basic facts. The argument only

shows that, among facts involving d , at least one is explanatorilybasic; it does not show that any particular fact involving d is explana-torily basic. For this reason, the argument cannot show that there isno metaphysical utility in pursuing the explanation of such facts as(10) in, say, partly microphysical terms. For the same reason, theremay even be a reasonable sense in which d might be said to be ‘lessfundamental’ than the particles of which it is made: certain featuresof d are, perhaps, explicable in part by reference to the particles, but

not vice versa. In sum, our argument does not provide any reason to10 To be precise, the step from the analogue of (8) to the analogue of (9) isblocked.



226 DEROSSET

the determination constraint is that a complete explanation of anentity x ’s having some feature F must show why that entity, unlike,

say, some non-F entity y , is F . It must therefore mention what distin-guishes x from y in respect of F -ness; more colloquially, together with the explanation for y ’s lacking F , it must provide the means forsaying what makes them different in this respect.

The determination constraint is also motivated as a generalizationfrom cases. Consider again the explanatory proposal, concerning aparticular oxygen nucleus x ,

(2) x is a stable nucleus in virtue of being an oxygen nucleus. This proposal is transparently inadequate, given that there are radio-active oxygen nuclei. The proposal does not suffice to explain whythis nucleus, unlike those radioactive nuclei, is stable; it doesn't tell us what makes this nucleus different from them with respect to radioac-tivity. Its inadequacy is a direct result, then, of its failure to meet thedetermination constraint.

This is no isolated phenomenon. Read any substantial swath of phi-losophy, and you will encounter explanatory proposals of the form

EXP x is F because ( x ).

You will also encounter arguments against such proposals of theform:

y is not F , but y is such that ( y )( EXP ) is at best incomplete.

The determination constraint says, in effect, that these arguments are valid. Consider a crude example. A utilitarian ethicist might proposethat certain courses of action, like giving a substantial proportion ofyour income to OXFAM, are obligatory in virtue of the fact that theymaximize utility. Others have objected that there are confoundingcases for this explanatory proposal: courses of action, like framingand punishing an innocent person to stop a crime wave, that maxim-ize utility but are not obligatory.12 The utilitarian may dispute the

premise, arguing, for instance, that framing the innocent in such cir-

12 See Carritt 1950.



NO FREE LUNCH 227

cumstances is obligatory. The utilitarian may amend the original ex-planatory proposal, arguing, for instance, that giving to OXFAM is

obligatory in virtue of being enjoined by a rule the adoption of which maximizes utility.13 The utilitarian may not blithely accept thepremise and stick with her explanatory proposal. The argument is valid, just as the determination constraint requires.

To take a less crude example, consider the state of the debate overmaterial constitution. In the standard test case, a lump of clay Lumpland a statue Goliath are coincident throughout the entirety of theircareers. They are made of the same particles, subject to the same

physical pushes and pulls, etc. Pluralists about material constitutionhold that Lumpl and Goliath are nevertheless distinct, typically on thegrounds that they differ in their sortal and modal properties. For in-stance, a pluralist typically argues that Lumpl differs from Goliath inthat Lumpl, unlike Goliath, can survive being squashed. A commonobjection14 to pluralism is that the pluralist cannot explain the sortaland modal differences he alleges between Lumpl and Goliath. Thisargument, called the grounding problem , uses an instance of the determi-

nation constraint. The idea is that Lumpl and Goliath are indiscerni-ble with respect to all of the salient explanans . Lumpl, like Goliath, iscomposed of certain particles, in certain arrangements, and bearingcertain causal and spatiotemporal relations to other things. Thus, onthe pluralist’s view, any perspicuously articulated explanatory proposalof the form

(12) Goliath cannot survive squashing because it is composed ofparticles p1, ..., pn in such-and-such arrangement

will find a confounding case presented by Lumpl, which can survivesquashing. This is a reason, as the determination constraint says, tothink that any such explanation is at best incomplete.15

13 See the discussion in Smart 1973.14 In fact, Wasserman 2002 dubs it ‘the standard objection’.

15 Thus, Fine 2008, 107:‘For if I use the fact that a given object ’s, for example, to explain why ithas the modal profile that it does, then I had better be sure that a coincidentobject with a different modal profile does not also satisfy .’



228 DEROSSET

Faced with this problem, pluralists either supplement the explanatoryproposal (see, for instance, Fine 2008), suggest that the salient sortal

and modal features of Lumpl and Goliath are fundamental (see, forinstance, Bennett 2004b), or deny that Lumpl and Goliath are dis-cernible in the relevant ways (see Sider 2008). But if the determina-tion constraint is rejected, they needn’t bother: they can just blithelyaccept that the explanans clause fits Lumpl as well as Goliath, eventhough Lumpl lacks the modal and sortal features in question. Thisresponse is evidently unreasonable. The determination constraintshould not be rejected.

Perhaps, however, there is an alternative constraint on good explana-tions that captures the inadequacies of the explanations we have beendiscussing, but cannot be used to establish the failure of EXPLANA-

TION. Consider once again the transparently inadequate explanatoryproposal

(2) x is a stable nucleus in virtue of being an oxygen nucleus.

I have diagnosed the failure of this explanatory proposal as a failure

to meet the determination constraint. But it might be suggested that abetter diagnosis appeals instead to a failure of entailment: The sug-gested diagnosis of the inadequacy of (2) is that its explanans does notentail its explanandum .16 The idea is that the explanation fails on thegrounds that it is possible that x be an oxygen nucleus that's unstable,and so the fact that x is an oxygen nucleus does not entail that x isstable. In general, the suggestion is that explanatory proposals aresubject to what I will call the entailment constraint :

ENTAILMENT CONSTRAINT An explanatory proposal of the form, ‘d has feature F because ( d ,x 1, ..., x n )’ is at best incomplete if it is possible that ( ( d , x 1, ..., x n )

Fd ).

Notice that the entailment constraint is strictly weaker that the de-termination constraint. If the possibility that something or other is a con-founding case suffices for the inadequacy of a proposal to explain

16 The sense of entailment in question is strict modal entailment: P entails Q in this sense iff □( P → Q ). Thanks to Chad Carmichael and an anony-mous referee for emphasizing the need to discuss this suggestion.



NO FREE LUNCH 229

some feature of d , then the possibility that d itself is a confoundingcase will also suffice. But an explanatory proposal can meet the en-

tailment constraint without meeting the determination constraint.Consider yet another proposal to explain the fact that diamond d ishard:

(13) d is hard because R ( p1, p2 , … )

where R ( p1, p2 , … ) exhaustively specifies the arrangement and otherphysical features of the totality of fundamental particles in the universe. Nothing in the argument of §2 rules out the idea that R ( p1, p2 ,

… ) entails all of the facts, including the fact that d is hard. So, noth-ing in that argument tells against the contention that (13) passes theentailment constraint. But the argument did establish that (13) failedthe determination constraint. Since it is so weak, the entailment con-straint cannot be used to show the falsity of EXPLANATION.

But the entailment constraint is also too weak to cover the cases plau-sibly diagnosed by the determination constraint. It is plausible tothink that the entailment constraint explains why (2) is not a good

explanation only if it is also plausible to think that x ’s stability ismerely contingent: if x is necessarily stable (if it exists), then it is im-possible for x to be radioactive, and so also impossible for x to beradioactive and an oxygen nucleus. Truth be told, I suspect that anyoxygen nucleus that is in fact stable is necessarily so, though, ofcourse, the idiosyncrasies of my modal opinions are no sound basisfor the determination constraint. Still, it is easy to come up with ex-planatory proposals with the same kind of inadequacy as (2) which

pass the entailment constraint. Even sceptics about the necessarystability of x may accept the necessity of x ’s being an oxygen nucleus.If so, then

(14) x is an oxygen nucleus in virtue of the fact that x contains atleast two protons

will pass the entailment constraint. Still, given the existence of, e.g.,lithium nuclei, this explanatory proposal is obviously inadequate. Sim-ilarly, notice that the entailment constraint won’t help us pose the

grounding problem for the pluralist. Consider again the explanatoryproposal



230 DEROSSET

(12) Goliath cannot survive squashing because it is composed ofparticles p1, ..., pn in such-and-such arrangement.

The feature of Goliath whose explanation is in question is typicallytaken to be a feature that Goliath had to have. Being unable to survive squashing is no merely contingent feature of Goliath; Goliathnot only cannot survive squashing, it necessarily cannot survivesquashing. If this plausible view is correct, the entailment constraint will not correctly diagnose the inadequacy of this explanatory pro-posal.

In general, explanatory proposals that are, intuitively, at best incom-plete but meet the entailment constraint can be generated using thisrecipe:

1. Find a case in which some necessary feature F of an individual x isplausibly explained by facts G1x , G2 x , ….

2. Make sure the case is also one in which there might have beensome individual y which has G1 but lacks F and any of the other Gs.

3. The explanatory proposal that meets the entailment constraint byis at best incomplete will, then, be:

(15) x is F in virtue of the fact that it is G1.

Here's one last example, derived using this recipe. Consider the pa-perweight sitting on the desk in front of me. This paperweight has, asa matter of necessity, both a rest mass and a location. Now considerthe explanatory proposal

(16) This paperweight has both a rest mass and a location in virtueof having a location.

This proposal is obviously at best incomplete, since the paperweight’srest mass is not accounted for at all. The determination constraintsays why, given the possible existence, e.g., of particles that have loca-tions, but no rest mass (as photons actually do, according to somephysical theories). The entailment constraint will not deliver this re-sult, because the paperweight’s necessary features are trivially entailed

by any feature that suffices for its existence. By virtue of its weak-ness, the entailment constraint is not an acceptable replacement forthe determination constraint.



NO FREE LUNCH 231

In summary, abandoning the determination constraint presents twochallenges. First, we must state a plausible alternative constraint on

adequate explanation with two features: ( i ) like the determinationconstraint, it correctly diagnoses the inadequacy of the explanatoryproposals discussed in this section; but ( ii ) unlike the determinationconstraint, it cannot be used to establish the failure of EXPLANA-

TION. Second, we must deny the plausible view that the completegrounds for one entity’s being F , together with the complete groundsfor another entity’s lacking F , provides the means for saying whatmakes these two particular entities different in this particular way.

5. Explaining Existence

I have, from the very beginning, been calling an entity derivative iffneither its existence nor any of its other features is explanatorilybasic. The argument so far has been carried out in terms of this no-tion of derivativeness. An objector might contend that this notion ofderivativeness is not the notion relevant to the application of Ock-ham’s Razor in ontology. The relevant notion of ‘derivative’ is weak-

er: where the notion I have been working with requires that both theexistence and other features of a derivative entity be explicable in otherterms, the objector’s notion requires only that its existence be so ex-plicable. To avoid terminological confusion, I will keep using derivative (and fundamental ) as I have been, and call an entity existentially derivative iff its existence can be completely explained solely by reference to theexistence and properties of other things. Call an entity existentially fundamental iff it is not existentially derivative. The objector may then

contend that we should reject EXPLANATION in favour ofEXPLANATION

Many entities are existentially derivative: their existence can be ex-plained solely by reference to the existence and properties of otherthings.

Further, existentially derivative entities are an ‘ontological free lunch’,so we should endorse an even weaker form of Ockham’s Razor

Do not multiply existentially fundamental entities beyond ne-cessity!



232 DEROSSET

When this objection is stated in this raw, unvarnished way, it mightappear ad hoc . But this appearance can be dispelled by attending to a

particular case. Consider a group of marbles g , whose constituentsare exactly the marbles m 1, ..., m n . It is plausible to think that

(17) g exists because m 1, ..., m n are marbles grouped together

is a good explanation. Nothing more, it might seem, is required for g to exist than for its constituents to be grouped together.17 But, if thisexplanation is good, then g is existentially derivative. The objector issuggesting that there is a large and diverse array of entities that are

like g in this respect, and that commitment to them is ‘no addition tobeing’, given commitment to the existentially fundamental entities.

Let’s turn our attention to EXPLANATION . Is it true? There are two ways of defending EXPLANATION against the sort of argument Ihave given against EXPLANATION. The first defence is to notice that,as it stands, the argument of §2 does not generalize to show that EX-

PLANATION fails. Consider again

(17) g exists because m 1, ..., m n are marbles grouped together.Notice that no analogue of DERIVATIVE DIVERSITY for this sort ofexplanation is true: there is no entity e that lacks existence. For thesame reason, there is no (actual) confounding case for this explanato-ry proposal. There is nothing that does not exist, and so a fortiori nothing that is just like g so far as the arrangement of m 1, ..., m n goes,but lacking existence. In fact, there’s not even a possible confoundingcase for (17), given the impossibility of there being something that

lacks existence. In the case of explanations of existence, the argu-ment of §2 gets no purchase.

It turns out that a variant of the old argument can be mountedagainst EXPLANATION . The new argument relies on two new as-sumptions. The first new assumption is that the explanation of theexistence of an existentially derivative entity like g should also provide

17 This particular case is due to Mark Moyer, but a similar case has beensuggested independently by Fabrice Correia and Benjamin Schnieder. Thanks to Correia, Moyer, and Schnieder for suggesting the line of responseexplored in this section.



NO FREE LUNCH 233

fodder for the explanation of the actual existence of g . Consider againthe proposed explanation of g ’s existence in terms of the grouping

of m 1, ..., m n . This explanatory proposal can be perspicuously articu-lated by a claim of the form

(18) g exists because R ( m 1, ..., m n )

This explanation concerns the existence of g in the actual world. Wecan therefore generate an explanation for the actual existence of g from the fact that it is actually the case that R ( m 1, ..., m n ). In brief, ifthe explanatory proposal (18) is good, then so is

(19) g actually exists because actually R ( m 1, ..., m n )Call this assumption actualization .

The second new assumption constrains the range of candidates forexplaining g ’s existence. Let g , e , etc., exhaust the actual existent enti-ties. The second assumption, which I'll call permissiveness , is that thefacts (if any) that explain g ’s existence do not entail that the only enti-ties are g , e , etc.18 The assumption of permissiveness implies that no

explanation for g ’s existence rules out a world in which all facts in theexplanans obtain and yet there are some aliens : some objects whichdon’t actually exist.19 For instance, if (18) is good, then permissive-ness says that there is a possible world in which a non-actual entityexists and m 1, ..., m n are grouped in the way specified by R . Permis-siveness is very plausible in this case. The grouping of m 1, ..., m n doesnot necessitate the nonexistence, for instance, of alien concrete ob-jects elsewhere.

18 Strictly speaking, the assumption needed for the argument is that there isat least one existentially derivative entity whose existence does not have anexplanatory basis which entails that there are no entities other than g , e , etc. But it is plausible that g fits the bill if anything does.19 Permissiveness will be rejected by anyone who rejects the possibility ofaliens ( e.g. Linsky and Zalta 1994). It will also be rejected by anyone who

thinks that the explanation for g ’s existence includes a ‘that’s all’ fact, to theeffect that there are no entities other than the actual entities; see Chalmersand Jackson 2001. So the explanatory basis for g ’s existence, according topermissiveness, does not entail the non-existence of aliens.



234 DEROSSET

Here, then, is a sketch of the variant of the argument. Suppose forreductio that EXPLANATION is true. Then some claim with the same

form as (18) perspicuously articulates a good explanation of g ’s exist-ence. Apply actualization: an explanatory proposal with the sameform as

(19) g actually exists because actually R ( m 1, ..., m n )

is also good. Now apply permissiveness. There is a world w contain-ing an alien a , and in which R ( m 1, ..., m n ). The alien a , together withm 1, ..., m n present a possible confounding case for (19): at w , m 1, ..., m n

actually stand in R , but a does not actually exist. The determinationconstraint says an explanation is at best incomplete if it has possibleconfounding cases, so (19) is not good. Contradiction.

Given actualization and permissiveness, the determination constraintimplies that EXPLANATION faces the same sort of problem as EX-PLANATION. Though the argument can be avoided by denying eitheractualization or permissiveness, both of the new assumptions haveconsiderable plausibility in the present case. We have, however, an-

other defence of EXPLANATION close to hand: deny the relevantapplications of the determination constraint. This is the second wayto defend EXPLANATION against the argument of §2. I have alreadyargued that the determination constraint is supported as a generaliza-tion from cases. But none of the cases in question concerned expla-nations of existence. Thus, those cases can be accommodated if wedeny applications of the determination constraint to explanations ofthe existence of entities (and to their actual existence), but accept its

applications to explanations of other features. The argument againstEXPLANATION crucially depends on the application of the determi-nation constraint to the explanation of g ’s (actual) existence. If thatapplication fails, then the argument is unsound.

My worry about this way of defending EXPLANATION is that deny-ing the application of the determination constraint to explanations ofexistence threatens to trivialize its application to explanations of oth-

er features; call this the trivialization worry . Suppose we are confronted with an explanatory proposal of the form

(20) x has F because P



NO FREE LUNCH 235

that fails the determination constraint. If the determination con-straint’s applications to explanations of existence are rejected, then

this explanatory proposal can be rehabilitated by claiming that what’sbeing explained is instead an existential claim. For instance, the pro-posal to explain the obligatoriness of giving a substantial proportionof your income to OXFAM can be recast as an explanation of theexistence of a duty to give:

(21) There exists a duty for you to donate a substantial portion ofyour income to OXFAM in virtue of the fact that doing so would be utility-maximizing.

Similarly, a proposal to explain Goliath’s modal or sortal features canbe recast as a proposal to explain the existence of a certain essence forGoliath. More generally, a proposal to explain any entity’s havingsome feature F can be recast as a proposal to explain the existence ofa certain F -ness trope possessed by it. Such an explanatory proposal,on the view under consideration, can be good despite there being aconfounding case. But it’s obvious that the new explanation has justthe same problem as the old one: recasting the explanation in existen-tial terms makes the proposal no better. The applications of the de-termination constraint to explanations of (actual) existence say why.

A defender of EXPLANATION should agree that these explanationsof existence facts are at best incomplete, even though the restricted version of the determination constraint doesn’t, by itself, deliver this verdict. But, the defender might urge, there is reason to deny that theproblematic explanatory proposal can avoid the determination con-

straint by being recast as explanations of existence facts. Consideragain the proposal to ground the existence of a duty to donate a sub-stantial portion of your income to OXFAM in the fact that such adonation would be utility maximizing. The defender may argue thatthe existence of a duty is to be explained by reference to the obliga-toriness of courses of action: if you have a duty to donate, then thatduty exists in virtue of it being obligatory for you to donate. Theproposed explanation of the existence of the duty in terms of utilitymaximization must, then, be understood as resulting from two ex-planatory claims:



238 DEROSSET

should be restricted so as not to apply to such explanations. Response( i ) faces a version of the original argument. Response ( ii ) either falsely

implies that recasting bad explanations as explanations of existencefacts improves them, or won’t secure the result that existentially de-rivative entities are an ‘ontological free lunch’.

This still leaves unresolved the question of what, if anything, is wrong with the proposal to explain the existence of the group ofmarbles g in terms of the grouping of its constituent marbles m 1, ...,m n . To tell the truth, I am unsure what to say about such a case. Inparticular, I am unsure what is entailed by the claim that g exists. If it

turns out that g ’s existence does not tolerate replacement of its con-stituents over time, then I am tempted to think that its existence isreducible to m 1, ..., m n ’s being grouped together. If it turns out that g ’sexistence does tolerate replacement of constituents, so that there canbe Ship of Theseus-style cases,22 then matters are more complicated.I suspect that Ship of Theseus-style cases show that the proposedexplanation is inadequate,23 but I am unsure how to supplement theproposal.

Perhaps we need to add the claim that g is composed of those mar-bles; g exists not just because some marbles are grouped together, butbecause its marbles are grouped together. It is tempting to character-

22 See Salmon, 1979 and Noonan 1985 for discussion. The Ship of The-seus is a ship S 1 that was originally constructed from some planks p1, p2 , …, pn . These have all been replaced one-by-one with completely different planks pn+1, pn+2 , …, p2n . It is plausible to think that in some such case, it is possiblethat the post-replacement and pre-replacement ships are identical. If g toler-ates replacement of its constituent marbles in a similar manner, then it isplausible to think that m 1, …, m n can be traded out one-by-one, and thengrouped to form a second group of marbles g* .23 Argument : if a Ship of Theseus-style case is possible for g , then m 1, …, m n can be grouped together to form an alien group g* . It is plausible that, ifthose marbles explain g ’s existence, then they also explain its existence atevery time at which it in fact exists. But, if they can be grouped to form g* ,

then there can be a time at which the marbles are grouped as they actuallyare, and yet g does not exist. This strikes me as a compelling objection to theoriginal explanatory proposal: the grouping of marbles at a given time failsto necessitate g 's existence at that time.



NO FREE LUNCH 239

ize this proposal by appeal to some notion of essence.24 The idea would be that the existence of a material thing is explained by some

congeries of facts involving other things, together with some specifi-cation of the essence of the thing. In the case at hand, the claim isthat the essence of g is given by the fact that it is composed of m 1, m 2 ,..., m n . The existence of g is explained by the fact that g has this essen-tial feature, together with the fact that those marbles are grouped to-gether. A notion of essence suited to play this role might be helpfullycharacterized in a variety of ways. For instance, if the argument of §2succeeds, we can define a notion of essence that will do the trick: the

essence of a thing is the totality of its features that are explanatorilybasic. It is often held that the essential features of a thing play an im-portant role in explaining its further features. This suggestion en-shrines this claim as definitive of essence.25

So far I have suggested that g ’s existence be explained in part by ap-peal to its essence. Perhaps, instead, we should accept that g ’s exist-ence is explanatorily basic. After all, given analogues of IRREDUCIBIL-ITY and DERIVATIVE DIVERSITY , the application of the determination

constraint to the explanation of any of g ’s features other than exist-ence implies that some of the facts involving g are explanatorily basic. Why not its existence? It should be noted that the argument of §2can be adapted to show that g ’s existence is not the only fact involving g that is explanatorily basic. Consider, for instance, a perspicuouslyarticulated explanatory proposal of the form

(24) d is F because d exists and R ( t 1, ..., t n ),

where none of the terms t 1, ..., t n denote d .DERIVATIVE DIVERSITY

ensures that e is a confounding case for this explanatory proposal: e exists, is such that R ( t 1, ..., t n ), but is not F . So, if the argument issound, it shows not only that some fact involving d is explanatorilybasic, but also that some fact involving d other than the fact that d exists is explanatorily basic.

24 Thanks to Benjamin Schnieder.25 The exploration of this notion of essence is a task for another day. Fortwo further alternatives, see Almog 1991 and Fine 1994 and 2008.



240 DEROSSET

6. Conclusion

The argument of this paper has a general result: barring reduction,there do not exist two non-fundamental, qualitatively discernible enti-ties. I have focused on the consequences of this result for ontology.In particular, I have argued that EXPLANATION cannot be used toclaim that grounding explanations provide an ‘ontological free lunch’. But the general result bears on a more popular conception of reality.On this conception, reality comes in layers: at the bottom are (per-haps) the physical entities. Higher up, we find chemical, biological,geological, psychological, sociological, economic, etc., entities: mole-

cules, human beings, diamonds, mental states, nations, interest rates,and so on. We might eliminate certain of these alleged higher-levelentities from our ontology, denying their existence altogether; and wemight hold that certain facts involving others are reducible. But, onthe layering conception, after we have eliminated and reduced asmuch as we can, the features of the remaining higher-level entities areto be explained entirely in terms of the existence and features of en-tities at lower levels.26

If the argument of this paper is correct, this conception faces a prob-lem. Barring reduction and elimination, the features of molecules,human beings, diamonds, etc., cannot be explained solely in terms ofother things. Grounding explanations still allow us to acknowledgethat some facts are more basic than others. But if there is any suchthing as a diamond, then, barring reduction, some facts involving di-amonds are explanatorily basic. Whether all of the explanatorily basicfacts concerning erstwhile derivative entities are physical facts, or fit

into any interesting category, is a matter for further investigation.27

26 See Kim 1993 for a seminal critical discussion of this conception; inKim's discussion, the higher-level entities in question are mental propertiesand the lower-level entities are physical properties.27 Thanks to Fabrice Correia, Tyler Doggett, Mark Moyer, and BenjaminSchnieder for comments on earlier drafts of this paper. Thanks also to RossCameron, Chad Carmichael, Andrew Cortens, Jonathan Schaffer, Ted Sider,and Jason Turner for discussion.



NO FREE LUNCH 241

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— 2004b: ‘Material Coincidence and the Grounding Problem’. Philo- sophical Studies 118, pp. 339 –71.

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— 2010: ‘How to have Radically Minimal Ontology’. PhilosophicalStudies 151, pp. 249 –64.

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242 DEROSSET

Linsky, B. and E. N. Zalta 1994: ‘In Defense of the Simplest Quanti-fied Modal Logic’. In Tomberlin 1994, pp. 431 –58.

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and Contemporary Readings , 3rd ed., Oxford: Oxford University Press.

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NO FREE LUNCH 243

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Metaphysical Grounds and Essence

Fabrice Correia

Is it possible to provide an account of metaphysical grounding interms of essence? E. J. Lowe (2009) addresses a similar questionabout truth-making and essence, and makes a suggestion whichpoints towards a positive answer. Kit Fine (2012) addresses the origi-nal question and answers negatively. I argue that the prospects for anaccount of metaphysical grounding in terms of essence are not asbad as one might have thought.

1. Introduction

Philosophers traditionally distinguish between the essential and theaccidental. A feature is said to be essential to a thing if it pertains towhat the thing is, in a specifically metaphysical sense; and a feature issaid to be accidental if it is a feature the thing has, but which merelycharacterises how the thing is, without telling us anything about what itis.

The concept of metaphysical grounding (hereafter, simply ‘ground-ing’) has perhaps been less visible than the concept of essence in the

history of philosophy, but it has constantly been used. A fact isgrounded in other facts provided that the former obtains in virtue of the latter, where ‘in virtue of’ is understood as having metaphysicalforce. The concept of grounding is involved in many important phil-osophical theses, like for instance the following:1

Mental facts obtain in virtue of neurophysiological facts;

Dispositional properties are grounded in categorical proper-

ties;1 See e.g. Fine 2001, Correia 2005, Schnieder 2006a and 2006b, Correia2010 and Rosen 2010.



METAPHYSICAL GROUND AND ESSENCE 245

Legal facts are grounded in non-legal, e.g. social, facts;

Morally wrong acts are wrong in virtue of non-moral facts;

Determinables are exemplified in virtue of corresponding de-terminates being exemplified;

Universals exist in virtue of their having exemplifiers;

A whole exists in virtue of the fact that its parts exist and arearranged in such and such a way;

Every truth is made true, i.e. given any truth, there is an entity

x such that this truth is true in virtue of the existence of x . According to many, the concept of essence is central to metaphysics,insofar as one of the main tasks of the metaphysician is to identifythe essential features of all things. Some also take the concept ofgrounding to be equally central, and hold that one of the main tasksof the metaphysician is to determine what grounds what. Along thisline of thought is the venerable tradition which holds that one of thegeneral aims of metaphysics is to unveil the layered structure of reali-ty, which consists of a level of basic, i.e. ungrounded, facts, and a(perhaps itself structured) level of facts grounded in the formerfacts.2

Granted that both essence and grounding are legitimate concepts,there arises the question how each is to be understood, and how theyare related. Each concept has sometimes been characterised in termsof modality (and truth-functions). Thus, for instance, it has beensuggested that for a feature to be essential to a given thing is for it tobe the case that as a matter of metaphysical necessity, the thing hasthat feature if it exists. And a natural thought is that for a fact to begrounded in other facts is for it to be the case (i) that all the latterfacts obtain, and (ii) that as a matter of metaphysical necessity, theformer fact obtains if the latter facts do.

2 See e.g. Fine 2001, and also Schaffer 2009 (although Schaffer takes enti-ties of any kind, not just facts, to be capable of being tied by the relation ofgrounding).



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In recent years, many have voiced scepticism about the availability ofsuch accounts of essence and grounding.3 Consider for instance the

accounts just mentioned. Holding both accounts at once yields trou-ble. For if we take both of them to be correct, we will have to saythat whenever a feature F is essential to a given existing thing x , thefact that x has F is grounded in the fact that x exists. Yet, it may bedoubted that the fact that Socrates is human obtains in virtue of thefact that he exists, even on the assumption that Socrates is essentiallyhuman. Each account is also problematic in isolation. As Kit Fine(1994) argues, although it is plausible to say that as a matter of meta-

physical necessity, Socrates belongs to {Socrates} if Socrates exists, we don’t want to say that it is essential to Socrates that he belongs to{Socrates}. And although it is plausible to say that as a matter ofmetaphysical necessity, the fact that Socrates exists obtains if the factthat {Socrates} exists does, we don’t want to say that the former factobtains in virtue of the latter fact. These are objections to particularmodal accounts of essence and grounding. But other such accountsare subject to similar objections, and it is reasonable to think that allaccounts of that sort are bound to fail.

Granted that no satisfactory modal account of essence or groundingcan be found, what are the available options? A fairly liberal move, which we may dub ‘double primitivism’, is to take both notions to beprimitive. The view is forcefully expounded in Fine 2012 (§11 on es-sence and ground):

I think it should be recognized that there are two fundamental-ly different types of explanation. One is of identity, or of what

something is; and the other is of truth, or of how things are. Itis natural to want to reduce them to a common denominator – to see explanations of identity as a special kind of explanationof truth or to see explanations of truth as a special kind ofexplanation of identity or to see them in some other way as in-stances of a single form of explanation. But this strikes me asa mistake.

3 On essence, see e.g. Dunn 1990 and Fine 1994, and on grounding e.g.Correia 2005 and Rosen 2010.




and starting with a sentential operator one can define a predicate inthe following way:

[ p ] is grounded in [ p1 ], [ p2 ], … iff df p because p1, p2, ….

In this case, there arises the question which mode of formulation ismore basic. I will leave this question aside, as well as the question whether facts or other suitable entities should be countenanced. As we shall see, unlike the difference between taking facts and takingpropositions to be the relata of the grounding relation, the differencebetween the two modes of expression matters in the present context.

I will call those who reject facts ‘anti-factualists’ and their opponents‘factualists’. And I will call those factualists who take the basic modeof formulation to be predicational ‘predicationalists’ and those whotake it to be operational ‘operationalists’.

3. The Simple Accounts

Let a be my laptop, b be a red ball, a+b be the mereological fusion ofa and b , and {a , b } be the set whose sole members are a and b .

Consider first the following list of putative cases of grounding ties:

(1) [ a+b exists] is grounded in [ a exists], [ b exists];

(2) [{a , b } exists] is grounded in [ a exists], [ b exists];

(3) [ b is a red ball] is grounded in [ b is red], [ b is a ball];

(4)

[The proposition that b is red is true] is grounded in [ b is red].

Then consider the following list of essentialist claims:It is part of the nature of [ a+b exists] that it obtains if both [ a exists] and [ b exists] do;

It is part of the nature of [{a , b } exists] that it obtains if both[ a exists] and [ b exists] do;

It is part of the nature of [ b is a red ball] that it obtains if both[ b is red] and [ b is a ball] do;

It is part of the nature of [the proposition that b is red is true]that it obtains if [ b is red] does.



250 CORREIA

It seems to me that many of those who would take items from thefirst list to be true would also take the corresponding items from the

second list to be true (barring a negative attitude regarding the con-cept of essence). And I suspect that some among them would takethe following account of grounding in terms of essence to be partic-ularly attractive (here and throughout the rest of the paper I use ‘---→ ...’ for ‘if ---, then ...’):

SPRED f is grounded in f 1, f 2, … ↔df. (i) f 1 obtains f 2 obtains …, and (ii) It is part of the nature of f that: f 1 obtains f 2 obtains… → f obtains.

I myself toyed with this account in the past before getting convincedthat it is problematic.

A similar account can be formulated if the target concept is ex-pressed by means of a sentential operator rather than by means of apredicate:

SOP p because p1, p2, … ↔df. (i) p1 p2 …, and (ii) It is part of what it is for it to be the case that p that: p1

p2 … → p.

In contrast with (SPRED ), (SOP ) is formulated with the help of an un-common essentialist notion. The most common notion of essence isthe notion of what a given thing – e.g. Mont Blanc, Socrates, or thenumber 7 – is. This is the notion alluded to in the introduction to this

paper. A less common notion is the notion of what it is to be suchand such – e.g. a mountain, human, or prime. An even less commonnotion is the one at work in (SOP ), i.e. the notion of what it is for it tobe the case that blah – e.g. what it is for it to be the case that MontBlanc is a mountain, what it is for it to be the case that Socrates ishuman, or what it is for it to be the case that 7 is prime. I have arguedelsewhere (2006) that the second notion (which I dubbed ‘generic’)cannot be reduced to the first (which I dubbed ‘objectual’), in par-

ticular that ‘what it is to F ’ cannot be understood as ‘what the proper-ty of being F is’ and the likes. Likewise, I think that the third notion – which we may dub ‘alethic’ – cannot be reduced to the first, and inparticular that ‘what it is for it to be the case that p’ cannot be under-




stood as ‘what the proposition that p is’. I am aware that some will besceptical about the third notion (and probably most of them also

about the second), but I will not here enter into a debate. 6 (SPRED ) and (SOP ) are intended to be accounts of the most basic con-cept of grounding. One can think of other such accounts, similar to(SPRED ) and (SOP ), namely:

S′OP p because p1, p2, … ↔df. (i) p1 p2 …, and (ii) It is part of the nature of [ p ] that: p1 p2 … → p.

S′′OP p because p1, p2, … ↔df. (i) p1 p2 …, and (ii) It is part of the nature of [ p ] that: [ p1 ] obtains [ p2 ] ob-tains … → [ p ] obtains.

Only (SOP ) can be available to an anti-factualist. In the case of factual-ists, we must distinguish between the predicationalists and the opera-tionalists. Only (SPRED ) is available to a predicationalist. In contrast, in

principle an operationalist can adopt either of (SOP ), ( S′OP ) and ( S′′OP ).But notice that going for ( S′′OP ) would be a bit odd. For by acceptingthe account, one would have the required resources for defining apredicate for grounding, along the lines of (SPRED ), and it is not clearhow one could then justify the claim that the most basic concept ofgrounding should be expressed by means of an operator rather thanby means of a predicate so defined. Similar considerations may beraised against ( S′OP ). For the sake of simplicity I will leave both ( S′OP )

and ( S′′OP ) aside, but it will nevertheless be clear how the discussioncould be extended to these accounts.

Let me turn now to some objections to the proposed accounts. E. J.Lowe (2009) examines an account of truth-making which bears acertain resemblance to the proposed accounts of grounding, andraises an objection against the former which can be raised, mutatismutandis , against the latter. The account of truth-making runs as fol-lows:

6 In the context of discussing the connections between essence andgrounding, Fine (2012, n23) stresses that ‘there is something to be said’ infavour of the concept of alethic essence.



252 CORREIA

TM The proposition that p is made true by x ↔df. (i) x exists, and

(ii) It is part of the nature of the proposition that p that: y exists → the proposition that p is true.

Lowe’s objection to (TM) consists in proposing a counterexample tothe left-to-right direction of the bi-conditional (pp. 213 –4). Considerred ball b and the redness trope t which inheres in b . It is plausible tosay – and many friends of truth-making would be willing to say – thatthe proposition that b is red is made true by t .7 If this is taken forgranted, then by (TM) we should conclude that it is part of the na-

ture of that proposition that it is true if t exists. But according toLowe, this conclusion is problematic. For the proposition could exist without the trope, while – Lowe argues – nothing can be essentiallydependent on (i.e. have as part of its essence a relation to) something without which it could exist.

The objection can be turned in an obvious way into an objection to(SPRED ). It is perhaps plausible to say that:

(a) [ b is red] is grounded in [ t exists]. Taking this and (SPRED ) for granted, we must say that it is part of thenature of [ b is red] that it obtains if [ t exists] obtains, and thereforethat the former fact is essentially dependent upon the latter. Butgranted that [ t exists] could not exist without t while [ b is red] could,[ b is red] could exist without [ t exists], and we face the same problemas above.

One can also indirectly extract from Fine (2012) two further candi-date counterexamples to the left-to-right direction of (SPRED ). Thefollowing two claims are plausible:

(b) [Someone is a philosopher] is grounded in [Socrates is a philos-opher];

(c) [ b is coloured] is grounded in [ b is red].

By (SPRED ), the first claim entails that [someone is a philosopher] is

essentially dependent upon [Socrates is a philosopher], and the se-cond claim that [ b is coloured] is essentially dependent upon [ b is red].

7 See Mulligan, Simons and Smith 1984.




But [Socrates is a philosopher] is essentially dependent upon Socratesand [ b is red] upon the colour red, and so by (SPRED ) and the transitivi-

ty of essential dependence, [someone is a philosopher] is essentiallydependent upon Socrates and [ b is coloured] upon the colour red. Yet, the objection goes, there are no such dependencies. Fine puts itin a colourful way by saying that [someone is a philosopher] ‘knowsnothing’ of Socrates, and likewise that [ b is coloured] ‘knows nothingof’ specific colours.

Unlike (a) –(c), claims (1) –(4) above cannot be used to provide coun-terexamples to (SPRED ) – at any rate, using them to this effect would be

much less effective. For in each case, the derived dependencies arequite plausible.

Let us turn to (SOP ). Consider the operational statement of groundcorresponding to (b):

(b′) Someone is a philosopher because Socrates is a philosopher.

By (SOP ), the statement entails that it is part of what it is for it to bethe case that someone is a philosopher that someone is a philosopherif Socrates is. Here, no reference is made to [someone is a philoso-pher]. In fact, the expression ‘what it is for it to be the case thatsomeone is a philosopher’ does not contain any sub-expression whichhas a reference, and accordingly no statement of type ‘x essentiallydepends upon y ’ is entailed. As a consequence, one cannot object to(SOP ) as in the previous case via a denial of essential dependency. YetI guess that a similar kind of objection can be put forward: instead ofdenying that a given entity is essentially dependent upon Socrates,

one will deny that what it is for it to be the case that someone is aphilosopher has anything to do with Socrates.

Similar objections to (SOP ) can be raised starting from the operational versions of (a) and (c). In contrast, like in the case of (SPRED ) the op-erational versions of (1) –(4) cannot be used to provide counterexam-ples to the account.

4. Generalisation

Consider again the second objection against (SPRED ). Granted that[someone is a philosopher] is grounded in [Socrates is a philosopher],



254 CORREIA

the account entails that the grounded fact is essentially dependentupon the grounding fact, and this is taken to be problematic. Now, if

we grant that there is such a link of grounding, then we will likewisegrant that the following generalisation holds as well: [someone is aphilosopher] is grounded in any fact of type [so and so is a philoso-pher]. This remark naturally leads one to modify (SPRED ) as follows:

GPRED f is grounded in f 1, f 2, … ↔df. (i) f 1 obtains f 2 obtains …, and (ii) There is a condition Φ such that Φ( f 1, f 2, …) and it ispart of the nature of f that: for all g 1, g 2, … such that Φ( g 1, g 2, …), g 1 obtains g 2 obtains … → f obtains.8

An important difference between (GPRED ) and (SPRED ) is that while inthe latter what follows the essentialist operator ‘it is part of the na-ture of f that’ is a singular sentence about f 1, f 2, …, in the former it isa general sentence which makes no reference to any of these facts(unless condition Φ does make reference to some of them, ofcourse). Lowe’s final suggestion for an essentialist account of truth-

making results from such a generalisation move (2009, 215), as well asthe essentialist account of grounding presented and criticised by Fine(2012, §11) I will introduce later.

(GPRED ) nicely escapes the objections raised against (SPRED ). For sup-pose we assume again that (a) holds. Then by the new account wemust take the following to hold as well:

There is a condition Φ such that Φ([ t exists]) and it is part ofthe nature of [ b is red] that: for all g such that Φ( g ), g obtains

→ [ b is red] obtains.

This existential statement follows from the sentence which resultsfrom replacing both occurrences of the variable in the embeddedopen sentence by the condition ‘is the fact [ x exists], for some x which is a redness trope inhering in b ’, namely the conjunction:

[ t exists] is the fact [ x exists], for some x which is a rednesstrope inhering in b

8 Here and below, ‘there is a condition Φ’ is to be understood as a non-objectual quantifier into predicate position.




It is part of the nature of [ b is red] that: for all g such that ( g isthe fact [ x exists], for some x which is a redness trope inheringin b ), g obtains → [ b is red] obtains.

We can certainly accept this sentence as true without being commit-ted to accepting unwanted dependencies, since the condition in ques-tion does not make reference to objects that would yield such de-pendencies. Examples (b) and (c) can be handled in a similar way.

The new account also fares well with respect to cases (1)-(4), which

were not problematic. Consider for instance:(1) [ a+b exists] is grounded in [ a exists], [ b exists].

By (GPRED ), accepting (1) requires accepting:

There is a condition Φ such that Φ([ a exists], [ b exists]) and itis part of the nature of [ a +b exists] that: for all g 1, g 2 such thatΦ( g 1, g 2 ), g 1 and g 2 obtain → [ a +b exists] obtains.

This statement follows from the sentence which results from replac-ing both occurrences of the variable in the embedded open sentenceby the condition ‘are two facts, one identical with [ a exists] and theother one with [ b exists]’. Accepting this sentence is once again notproblematic given that the condition does not refer to problematicentities: as previously stressed, it is quite plausible to hold that [ a+bexists] is essentially dependent upon both [ a exists] and [ b exists].Cases (2) –(4) are similar.

Let us turn to (SOP ). Since here we do not have facts to generalisefrom, the account cannot be modified in exactly the same way. But asimilar manoeuvre suggests itself, yielding an account I will call‘( GOP )’. Consider a statement of type ‘ p because p1, p2, …’. There aretwo cases two distinguish. The first is the case where none of ‘ p1’, ‘ p2’,… makes reference to any object. Then there is no need to modify(SOP ). The account must be modified only in the second case, i.e. thecase where some of ‘ p1’, ‘ p2’, … makes reference to some object(s).

For the sake of simplicity, I illustrate how the modification must bemade in the simple case where each of ‘ p1’, ‘ p2’, … either makes no



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Let me start with the third objection. Let x be something which existsin time, and suppose that:

( ) It is part of the nature of x that x exists simpliciter iff x existsat a time.

In order for (GOP ) to predict what Fine says it does, we should be ableto derive from ( ) certain truths which hold in virtue of what it is forit to be the case that x exists simpliciter and of what it is for it to bethe case that x exists at a time. Presumably, the essentialist statementsthat should be derivable are:

( ) It is part of what it is for it to be the case that x exists simplicit-er that: x exists at a time → x exists simpliciter

and

( ) It is part of what it is for it to be the case that x exists at a timethat: x exists simpliciter → x exists at a time.

But ( ) is an objectual essentialist statement which tell us something

about what x is, whereas ( ) and ( ) are alethic essentialist statements which tell us something about what it is for it to be the case that x exists simpliciter, and something about what it is for it to be the casethat x exists at a time, respectively, and accordingly I do not see that( ) or ( ) follows from ( ). Consider the principle that one can alwayscorrectly infer ‘it is part of what it is for it to be the case that F ( x )that F ( x ) if G( x )’ and ‘it is part of what it is for it to be the case thatG( x ) that G( x ) if F ( x )’ from ‘it is part of the nature of x that F ( x ) iff

G( x )’. I take it to be subject to counterexamples. For instance, con-sider an Aristotelian view of universals according to which it is partof the nature of humanity that it exists iff something exemplifies it. Itake it that, consistently with this view, it can be maintained that it isnot part of what it is for it to be the case that something exemplifieshumanity that something exemplifies humanity if humanity exists. Ithus take the general principle to fail, and I do not see that the partic-ular instance of the principle concerning ( ), (

) and ( ) is in any bet-

ter position.




Now for the second objection. The distinction between constitutiveand consequential essence was first made in Fine 1995a, §3, which

discusses exclusively the objectual notion of essence: An essential property of an object is a constitutive part of theessence of that object if it is not had in virtue of being a con-sequence of some more basic essential properties of the ob-ject; and otherwise it is a consequential part of the essence. [...] The constitutive essence is directly definitive of the object, butthe consequential essence is only definitive through its connec-tion with other properties.

This characterisation is not altogether clear (to me, at least), but animportant point to retain is that the consequential essence of an ob-ject is closed under a certain consequence relation.11 Clearly, if thereis such a distinction for objectual essence, it (or a very similar distinc-tion) will also apply to alethic essence. If this is conceded, then wemay grant that on a consequential conception of alethic essence it will be correct to say that it is true in virtue of what it is to be thecase that p that p if ( p p )

(on the grounds that ‘ p if ( p p )

’ is a con-

sequence, in the appropriate sense, of anything whatsoever), and inso doing we will agree with Fine that if the concept of essence ex-pressed by the essentialist operator in (GOP ) is consequential, then theaccount will predict that ‘ p because ( p p )’ is true.

If all this is conceded, then why not take the concept of essence involved in (GOP ) to be constitutive? Fine tells us that on his view aboutthe relationships between constitutive and consequential essence, the

former is to be defined in terms of the latter and of the concept ofgrounding, and clearly on this view (GOP ) cannot be understood in theproposed way. But why should one accept Fine’s view, rather than themore natural view, mentioned and flatly rejected by him (2012, §11),that consequential essence is the closure of constitutive essence un-der (an appropriate relation of) logical consequence?

I believe that the Finean distinction between constitutive and conse-quential essence is sound, both in the objectual and in the alethic case

11 Fine elaborates a bit on the kind of consequence relation he has in mindin his 1995a, §4. See also Fine 1995c and 2000.



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(and also in the generic case, for that matter).12 I construe constitutiveobjectual essence in such a way that a proposition belongs to the con-

stitutive essence of an object just in case it correctly tells us some-thing which pertains to what the object is, and similarly I take a prop-osition to be constitutive of what it is for it to be true that blah just incase it correctly tells us something which pertains to what it is for itto be true that blah . And I take it that consequential concepts of es-sence are, in both the objectual and the alethic case, to be defined asclosures of the constitutive concepts under appropriate consequencerelations. This being said, in response to Fine’s second objection I

recommend to understand (GOP ) as involving constitutive alethic es-sence – more generally, I recommend to understand the essentialistconcepts in the four accounts of grounding we met so far as beingconstitutive rather than consequential.

Before moving to the next section, let me mention a further objec-tion to (GOP ). In a nutshell, the objection is that by (GOP ), partialgrounds must be full grounds. Consider a statement of ground oftype

12 I should perhaps mention that I have not always been of that opinion(see Correia 2007, fn. 14). Fine (1995a, 58) stresses that it is difficult to see where and how to draw the line between constitutive and consequential es-sence, and that before we get clear on these issues ‘it seems advisable to work as far as possible with the consequentialist notion’. I agree that thequestion of where and how to draw the line is difficult. In particular, consti-tutive essences are certainly not ‘logically inert’, to use Fine’s (1995a, 57)expression, and it is not clear which closure principles for constitutive es-

sence should be accepted (see the end of this section for some thoughts).But even if it is granted that it is ‘advisable to work as far as possible withthe consequentialist notion’, we should not refrain from working with theconstitutive notion if we believe that this is what is needed. I should perhapsmention here that in my 2012, I present a theory of essence in the spirit ofFine (the ‘rule-based’ account), which distinguishes between basic essentialtruths – which would correspond, at least extensionally, to the Finean consti-tutive truths – and derivative essential truths, which result from the interactionof basic essential truths and the nature of logical concepts. The derivative

truths are not obtained by closure under a consequence relation, though, thederivations involving, so to speak, more fine-grained mechanisms. In thatpaper I do not give a recipe for identifying constitutive essences, nor do I tryto theorise on the closure principles for constitutive essences.




(I) p because F ( a ), G( a ).

By (Gop ), it follows that F ( a ) G( a ), and that(II) There is a condition Φ such that Φ( a ) and it is part of what it is

for it to be the case that p that: for all x such that Φ( x ), F ( x )G( x ) → p.

Let Φ witness the truth of (II). We then have:

(III) Φ ( a ) and it is part of what it is for it to be the case that p that:for all x such that Φ ( x ), F ( x ) G( x ) → p.

Now define condition H ( x ) as Φ ( x ) F ( x ). The first conjunct of(III) and the fact that F ( a ) allow us to infer that H( a ). In addition, bythe second conjunct of (III), it is part of what it is for it to be thecase that p that for all x such that H ( x ), G( x ) → p. So we have:

(IV) There is a condition Ψ such that Ψ( a ) and it is part of what it isfor it to be the case that p that: for all x such that Ψ( x ), G( x ) → p.

But then by (GOP ) again, it follows that

(V) p because G(a).

But there are many statements of type (I) which we may take to betrue while rejecting the corresponding statement of type (V).

At a crucial point, this objection – call it the reduction objection – involved the transition from the second conjunct of (III),

(t1) It is part of what it is for it to be the case that p that: for all x ,Φ ( x ) → ( F ( x ) G( x ) → p ),

to

(t2) It is part of what it is for it to be the case that p that: for all x ,Φ ( x ) F ( x ) → ( G( x ) → p ).

Clearly, if the conditional involved in (t1) and (t2) is the material con-

ditional, then the transition from the embedded universal statementin (t1) to the embedded universal statement in (t2) is classically logi-cally valid. And even without this assumption about the conditional,it is plausible to hold that the transition is in an intuitive sense logical-



262 CORREIA

ly valid. Now, it might be stressed, once it is granted that the essen-tialist operator in (t1) and (t2) expresses a constitutive concept of es-

sence, it is not obvious that the transition from (t1) to (t2) is legitimate. At this point some might wish to simply deny that the transition islegitimate, on the grounds that constitutive essences are ‘logically in-ert’. But this view about constitutive essences is too extreme to beplausible. For although constitutive essences are not closed underarbitrary consequence relations – in particular, they are certainly notclosed under classical logical consequence – they are arguably closedunder certain non-trivial consequence relations which are ‘more tight’than classical logical consequence. For instance, it seems that we canleg itimately infer ‘it is part of the constitutive nature of Socrates thathe is both G and F ’ from ‘it is part of the constitutive nature of Soc-rates that he is both F and G’. My impression is that the inferencefrom (t1) to (t2) is just as legitimate as the one just mentioned.

Here is an argument to the effect that the inference is legitimate if‘→’ stands for the material conditional. Contexts of type ‘it is part of what it is for it to be the case that p that ---’, even understood as ex-pressing constitutive essence, must be closed under some equivalencerelation of ‘meaning the same’. Plausibly, this relation should satisfythe following general principles:

¬( ) ¬ ¬ ;

( ) ( );

If , then ;

If , then ;

If , then x

x

.

Once this is granted, it can be proved that the transition from (t1) to(t2) is truth-preserving.

It is perhaps possible to agree on the previous argument, and at thesame time defend the view that if ‘→’ is understood as expressing

something else than the material conditional (say, a ‘relevant’ condi-tional), we get an account of grounding which is both plausible andimmune from the previous objection. Perhaps. I leave it up to those




who wish to put forward such a view to come up with an appropriateconditional, and argue that the resulting account does escape the re-

duction objection. To conclude this section, let me stress that (GPRED ) is immune fromthe indiscrimination objection, but not from the reduction objectionif the latter is effective at all against (GOP ). The details are straight-forward.

5. Escaping the Unwanted Dependencies and the Indis-crimination Objections

As previously stressed, the indiscrimination objection affects (SOP ) as well as (GOP ). But it affects neither (SPRED ) nor (GPRED ). Also, the simpleaccounts are immune from the reduction objection. The whole situa-tion can be summed up in the following table, where ‘ ’ signifies thatthe objection applies, ‘ ’ that it does not, and ‘ ?’ that the objectionapplies if the conditional expressed by ‘ ’ is the material conditional,and perhaps does not apply otherwise:

(SPRED ) (SOP ) (GPRED ) (GOP )

Unwanted dependencies

Indiscrimination

Reduction ? ?

In this last section I wish to suggest a modification of the two opera-tor accounts and give a final verdict on the viability of these and theother two accounts.

Let us first focus on the indiscrimination objection to (SOP ). The ob-jection states that the account cannot do justice to the distinctionbetween plural grounds and conjunctive grounds. The account, as

well as each of the other accounts we have met so far, involves incondition (ii) of its analysans the standard dyadic conditional ‘if …,then …’. The source of the indiscrimination problem is that the list‘ p1, p2, …’ in (Sop )’s analysandum is represented in the antecedent of



264 CORREIA

the conditional by the conjunction ‘ p1 p2 …’. In order to escapethe problem I suggest that the account be modified by replacing the

standard conditional by a new conditional, ‘IF …, THEN …’, whosefirst position can be filled in with a list of one or more sentential ex-pressions, and which is defined as follows:

IF p1, p2, …, THEN p iff df if it is the case that p1 it is the casethat p2 …, then it is the case that p.

Of course, it is crucial for this proposal that ‘it is the case that ---’should not be taken to be a mere notational variant of ‘ ---’, for oth-

erwise ‘IF p1, p2, …, THEN p’ would just be a notational variant of ‘if p1 p2, …, then p’ and thus nothing would be gained. For the pro-posal to be of any help, I must not only insist that ‘ it is the case that ---’ and ‘---’ are not mere notational variants; I must also argue that thepresence of ‘it is the case that’ in the definition of the new cond i-tional makes the difference I want it to make.

Now, it will be asked, how could ‘it is the case that ---’ and ‘---’ fail tobe mere notational variants? I simply reply that they are not. I agreethat all the (truth-evaluable) instances of ‘it is the case that p iff p’ are(perhaps logically) necessarily true. Accordingly, I agree that in exten-sional contexts and many intensional contexts, occurrences of ‘it isthe case that’ can be eliminated without affecting truth-value. But thisis compatible with the view that the use of ‘it is the case that’ issometimes non-redundant. For instance, the use of the phrase ‘it isthe case that’ allows one to make informative claims about pieces oflogical vocabulary, whereas dropping the occurrences of the phrase

removes (some of) the informative aspect of what is said. This canactually be seen by comparing the following two principles:

p1 p2 (if it is the case that p1 it is the case that p2, then it isthe case that p1 p2 ).

p1 p2 (if p1 p2, then p1 p2 ).

Both can be argued to be true, perhaps even logically necessary. But

while the first principle records an important feature of conjunction(it is a version of the inference rule of conjunction introduction for-mulated as a statement rather than a rule), the second merely reflectsa general property of the conditional and tells us nothing about con-




junction. What is more, there are arguably true statements involving‘it is the case that’ which become falsehoods if the occurrences of

the expression are eliminated. For instance, it is plausible to hold thatthis is the case for

It is a fundamental fact about conjunction that: p1 p2 (if it isthe case that p1 it is the case that p2, then it is the case that p1

p2 ),

and

It is part of the nature of conjunction13

that: p1 p2 (if it isthe case that p1 it is the case that p2, then it is the case that p1 p2 ),

which is closer to the focus of this paper.14

What I suggest in place of (SOP ) is thus the following account:

OP p because p1, p2, … ↔df. (i) p1 p2 …, and (ii) It is part of what it is for it to be the case that p that: IF p1, p2, …, THEN p.

The previous considerations make it plausible to hold that the transi-tion from

It is part of what it is for it to be the case that p that: IF p1, p2,…, THEN p

to

It is part of what it is for it to be the case that p that: if p1 p2 …, then p

is not legitimate, and accordingly that a case can be made for the viewthat ( OP ) escapes the indiscrimination objection. (GOP ) was also sub-

13 Or perhaps of conjunction and other items, among them e.g. the condi-

tional.14 Ke vin Mulligan (2010, 568) defends the view that ‘it is the case that p because p’ must hold in case ‘ p’ is true. This view, if correct, provides a fur-ther example, granted that no instance of ‘ p because p’ can be true.



266 CORREIA

ject to the objection, and I recommend that it be modified in thesame way. The resulting account will be labelled ‘( OP )’. Since ( SPRED )

and (GPRED ) were not affected by the objection, there is no need tomodify them.

Let me now turn to the unwanted dependencies objection to thesimple accounts (SPRED ) and (SOP ). Of course, if the objection is effec-tive at all against (SOP ), it will affect equally well (

OP ). But I think thatthe objection can be resisted.

Recall the form of the objection as stated against (SPRED ): from a plau-

sible claim of ground, one derives, using the account, the conclusionthat a certain fact is essentially dependent upon another fact, and onerejects the conclusion – the rejection being just flat (Finean rejection)or based on the assumption that essential dependence entails existen-tial dependence (Lowean rejection).

As stressed en passant in section 3, the notion of essential dependence which is at work here can be defined as follows:

DEP x essentially depends upon y ↔df. for some condition Φ, itis part of the nature of x that Φ( y ),

where the essentialist operator is the operator involved in the accountand so, given my previous recommendation, should be understood asexpressing constitutive objectual essence. Now for one thing, pace Lowe, I do not think essential dependence so defined entails existen-tial dependence – where to say that an object existentially depends onanother object is to say that the former (metaphysically) cannot exist

without the latter. For instance, suppose there is such a thing as theproperty of being identical to Socrates.15 It is then plausible to saythat the property is essentially dependent, in the sense of (DEP), up-on Socrates, on the grounds, say, that it is part of the nature of theproperty that Socrates exemplifies it if he exists. Yet one can consist-ently maintain that the property necessarily exists, while Socrates ex-ists only contingently. Thus, in my view, if the inferred dependenciesin the objection against (SPRED ) are to be rejected, the rejection shouldnot be of the Lowean sort.

15 See Fine 1995b, 274, and Correia 2005, 52.




Taking this for granted, is it so clear that these dependencies shouldbe rejected? Consider for instance the case of [someone is a philoso-

pher] and [Socrates is a philosopher]. We reached the conclusion thatthe former is essentially dependent upon the latter on the basis of theassumption that:

(#) It is part of the nature of [someone is a philosopher] that it ob-tains if [Socrates is a philosopher] does,

which itself was derived from the assumption that [someone is a phi-losopher] is grounded in [Socrates is a philosopher]. It does not strike

me as intuitively incorrect to accept (#), and accordingly it does notstrike me as intuitively incorrect to hold that the existential fact essen-tially depends, in the sense of (DEP), upon the singular fact. To thecontrary, I find (#) quite plausible, and I am therefore happy to holdthat there is this dependency link between the two facts.

The other proposed counterexamples to (SPRED ) do not impress memore than the one just discussed, and, likewise, I am not impressedby the unwanted dependencies objection against (SOP ) / ( OP ).

6. Concluding Remarks

We ended up with four essentialist accounts of grounding, (SPRED ),( OP ), (GPRED ) and ( OP ), and if the arguments I proposed in this paperare correct, their behaviour with respect to the unwanted dependen-cies, the indiscrimination and the reduction objections can be repre-sented by modifying the table from section 5 as follows:



268 CORREIA

That is to say: the simple accounts (SPRED ) and (

OP ) escape all threeobjections; (GPRED ) and ( OP ) escape the first two objections but not

the third if they are understood as formulated in terms of the mate-rial conditional; they may escape this objection if another conditionalis taken to be at work, but this needs to be argued for.

I favour the simple accounts over any versions of (GPRED ) and ( OP ),and among the simple accounts I favour ( OP ). I prefer the simpleaccounts because they are simpler than any versions of (GPRED ) and( OP ). And I favour ( OP ) over (SPRED ) because the former, but not the

latter, requires accepting an ontology of facts, whereas I believe thatan account of grounding should be as far as possible neutral on thequestion whether there are such entities. Whether ( OP ) – or any otheraccount presented in this paper, for that matter – can stand furtherexamination is something I do not want to bet on at the present time. Yet I hope to have shown that some accounts of grounding in termsof essence have some plausibility.16

16 I wish to thank Benjamin Schnieder and Alex Steinberg for their veryextensive and valuable comments on an earlier draft of this paper, and alsoto Kathrin Koslicki and the audiences at the Goethe Universität FrankfurtResearch Colloquium in philosophy (February 2011), the Ontological DependenceWorkshop at the University of Bristol (February 2011) and the Grounding and Modality Workshop at the University of Glasgow (April 2011) for helpful dis-cussion. This work was carried out while I was a Swiss National ScienceFoundation professor (projects PP001-114758 and PP00P1-135262), and incharge of the Swiss National Science Foundation sinergia project ‘Intention-

ality as the Mark of the Mental’ (project CRSI11-127488). The research lead-ing to these results has also received funding from the European Communi-ty’s Seventh Framework Programme FP7/2007-2013 under grant agreementno. FP7-238128.

(SPRED ) ( OP ) (GPRED ) ( OP )

Unwanted dependencies

Indiscrimination

Reduction ? ?




References

Bolzano, B. 1837: Wissenschaftslehre , Sulzbach: Seidel.


Correia, F. 2005: Existential Dependence and Cognate Notions . Munich:Philosophia.

— 2006: ‘Generic Essence, Objectual Essence, and Modality’. Noûs 40, pp. 753 –67.

— 2007: ‘(Finean) Essence and (Priorean) Modality’. Dialectica 61, pp.63 –84.

— 2010: ‘Grounding and Truth-Functions’. Logique et Analyse 211, pp.251 –79.

— 2012: ‘On the Reduction of Necessity to Essence’. Philosophy andPhenomenological Research 84, pp. 639 –53.

Correia, F. and B. Schnieder (eds.) 2012: Metaphysical Grounding: Under- standing the Structure of Reality . Cambridge: Cambridge University

Press.Dunn, J. M. 1990: ‘Relevant Predication 3: Essential Properties’. In

Dunn and Gupta 1990, pp. 77 –95.

Dunn, J. M. and A. Gupta (eds.) 1990: Truth or Consequences , Dor-drecht: Kluwer.


— 1995a: ‘Senses of Essence’. In Sinnott-Armstrong, Raffman and Asher 1995, pp. 53 –77.

— 1995b: ‘Ontological Dependence’. Proceedings of the Aristotelian Soci- ety 95, pp. 269 –90.

— 1995c: ‘The Logic of Essence’. Journal of Philosophical Logic 24, pp.241 –73.

— 2000: ‘Semantics for the Logic of Essence’. Journal of Philosophical

Logic 29, pp. 543 –84. — 2001: ‘The Question of Realism’. Philosopher’s Imprint 1, pp. 1 –30.



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Hale, B. and A. Hoffmann (eds.) 2010: Modality: Metaphysics, Logic, and Epistemology , Oxford: Oxford University Press.

Lowe, E. J. 2009: ‘An Essentialist Approach to Truth-Making’. InLowe and Rami 2009, pp. 201 –16.

Lowe, E. J. and A. Rami (eds.) 2009: Truth and Truth-Making , Stocks-field: Acumen.

Mulligan, K. 2010: ‘ The Truth Connective vs the Truth Predicate. On

Taking Connectives Seriously ’. Dialectica 64, pp. 565 –84.Mulligan, K., P. Simons and B. Smith 1984: ‘Truth-Makers’. Philosophy

and Phenomenological Research 44, pp. 287 –321.

Rosen, G. 2010: ‘Metaphysical Dependence: Grounding and Reduc-tion’. In Hale and Hoffmann 2010, pp. 109 –35.

Schaffer, J. 2009: ‘On What Grounds What’. In Chalmers, Manley,and Wasserman 2009, pp. 347 –83.

Schnieder, B. 2006a: ‘ A Certain Kind of Trinity: Dependence, Sub-stance, Explanation’. Philosophical Studies 129, pp. 393 –419.

— 2006b: ‘ Truth-Making without Truth-Makers’. Synthese 152, pp.21 –46.

Sinnott-Armstrong, W., D. Raffman and N. Asher (eds.) 1995: Modal- ity, Morality, and Belief: Essays in Honor of Ruth Barcan Marcus . New York: Cambridge University Press.



The Dependence of Truth on Being: Is There A Problem for Minimalism?

Stefano Caputo

1. The Dependence of Truth on Being and Minimalism There are things we believe and assert. Some of those things are true,others are not. Whether such a thing is true or not seems to dependon just one thing: whether the world is the way we say and believe itis.

This common-sense intuition goes hand in hand with another one:how the world is does not depend on whether the things we say are

true. How the world is, in a certain respect, rather depends on howthe world is in other respects, provided it depends on anything.

The previous facts can be summed up, perhaps with a more meta-physical flavour, by the following slogan: truth is grounded in beingbut not the other way around.

Since the dependence-relation between the truth of what we believeand assert and the way the world is is asymmetrical, it cannot be justcounterfactual dependence: assume that I believe that Nicola is talland that what I believe is true, surely if Nicola had not been tall whatI believe would not have been true, but it is also the case that if whatI believe had not been true Nicola would not have been tall. The de-pendence pointed at here rather seems to be an explanatory depend-ence: it is not because I truly believe that Nicola is tall that Nicola istall; rather it is because Nicola is tall that I believe something true inbelieving that he is tall.1

1 Aristotle (Metaphysics, 10, 1051b 6 –9) stresses this intuition. Künne(2003, 150 –4) has drawn new attention to this remark by Aristotle.



272 CAPUTO

Generalising from the preceding example, and using the word ‘prop-osition’ as a noun for the things we believe and assert, the asymmet-

rical dependence between truth and how things are can be expressed with this general principle

PRINCIPLE OF THE GROUNDEDNESS OF TRUTH (GT)If a proposition is true, it is true because the world is a certain way;but if the world is that way, it is not so because the proposition istrue.

Assuming that ‘that’-clauses are canonical singular terms for proposi-

tions and that the sentence embedded in the that-clause specifies the way the world must be in order that the proposition be true the par-ticularizations of the previous principle are instances of the schema:

(B) If (it is true that p ), (it is true that p ) because p, but it is not thecase that (if p, p because (it is true that p )).2

Our disposition to assent to ( GT ) and to the (non-paradoxical) in-stances of (B) manifests what can be called the intuition of theasymmetrical dependence of truth on being, for brevity TDB.

The variant of deflationary conceptions of truth by far most dis-cussed in the last twenty years is Horwich’s Minimalism (Horwich1990). Minimalism is the conception of truth according to which theMinimal Theory (MT), the theory comprising all, and solely, thepropositions which are expressed by non-paradoxical instances ofschema

(T) (It is true that p ) iff p

is an adequate theory of truth, that is to say one which explains anyfact involving truth, eventually in conjunction with other theories, incase the fact that must be explained involves not only truth but alsosomething else (this is what Gupta (1993) calls the ‘Adequacy The-sis’).

Now, TDB provides this powerful argument against Minimalism:3

2 I use parentheses as a means of syntactic disambiguation.3 If not exactly the argument, the line of reasoning it makes explicit canbe found in Vision 1997, 2010, David 2002, Rodríguez-Pereyra 2005. Theargument is also presented (but not endorsed) in Künne 2003, 151.



274 CAPUTO

(BT) (It is true that p ) because p

obtained by substituting ‘p’ with a true sentence are false if they areunderstood as expressing explanatory claims. In the next paragraph Iset out three ways by which a minimalist could defend this claim andI argue that they are flawed.

2. Some Arguments against TDB

The first argument, put forward by Douven-Hindriks (2005), is basedon the idea that sentences which are immediately recognized as logi-

cally equivalent by any competent speaker are substitutable, salva ex-planatory force , in explanatory contexts. If this is true, then the in-stances of (BT) have the same explanatory force as those of theschema

(BT*) (It is true that p ) because it is true that p

since any competent speaker of English accepts the T-equivalencessolely on the basis of her understanding of them. But the instancesof (BT*) are no explanations at all, so neither are those of (BT).

What justifies the first premise of the argument? Douven-Hindriks’idea is that, since explaining something involves providing infor-mation which improves understanding of it, nothing is gained andnothing is lost in substituting in an explanation the explanans sen-tence with another one which does not differ from it in informative-ness. If, moreover, it is granted that sentences which are immediatelyrecognized as logically equivalent by any competent speaker do not

differ in informativeness, it follows that they are substitutable as ex-planantia salva explanatory force of the explanation.

The main problem I see with the latter argument is that it is very hardto find a notion of informativeness whereby both its premises (thesubstitutivity principle and the claim that sentences which are a-prioriequivalent carry the same information) come out true.

To begin, if one equates the informativeness of a sentence with itstruth-conditions, understood as sets of possible worlds, any pair oflogical equivalent sentences will carry the same information. Howeverthere are a lot of sentences which are quite trivially logically equiva-lent which are not substitutable, salva explanatory force , in explanato-



THE DEPENDENCE OF TRUTH ON BEING 275

ry contexts. For instance, ‘Romeo died’ and ‘Romeo died and it israining or it is not raining’ are quite trivially logically equivalent but

‘Juliet killed herself because Romeo died’ is true whether ‘Juliet killedherself because Romeo died and it is raining or it is not raining’ isfalse.

Even to resort to a more fine grained notion of informativeness,such as one which identifies the information provided by a sentence with the structured proposition it expresses, won’t do. Provided thatproper names are directly referential expressions, ‘Clark Kent is ClarkKent’ and ‘Clark Kent is Superman’, express the same structured

proposition but, as Douven and Hindriks themselves stress, ‘Lois hasnothing to fear because Clark Kent is Superman’, unlike ‘Lois hasnothing to fear because Clark Kent is Clark Kent’, seems to be agood explanation.

So perhaps the notion of informativeness at stake here is still morefine-grained and we should take differences in cognitive value of anexpression into account. But this creates the following problem forthe argument. A criterion for establishing the difference in cognitive value among expressions is the so-called Frege criterion : two expres-sions e and e’ differ in cognitive value if they are not substitutablesalva veritate in belief-ascriptions. Now, consider the following sen-tences:

(8) It is true that snow is white.

(9) Snow is white.

(10) (It is true that snow is white) because snow is white.(11) (It is true that snow is white) because it is true that snow is

white.

(12) Benjamin believes that ((it is true that snow is white) becausesnow is white).

(13) Benjamin believes that ((it is true that snow is white) because itis true that snow is white).

Since Benjamin, like many other people, is disposed to assent to (10)and not to (11), (12) is true and (13) is false. But (13) differs from (12)solely for the fact that (8) has been substituted to the second occur-



276 CAPUTO

rence of (9). So the two sentences are not substitutable salva veritatein belief ascriptions. Can we conclude, by the Frege Criterion, that (8)

and (9) differ in cognitive value?

Here Douven and Hindriks face a dilemma. One option one has is todeny that this application of the Frege-criterion is legitimate, pointingto the fact that it cannot be ruled out from the start that ‘because’-contexts are similar to quotational contexts, that ‘because’, like quota-tion-marks, operates on features of the expressions it bounds whichare different from their content (individuated in whatever fine-grained way). If this were the case then from the fact that someone

believes that p because q but does not believe that p because r it couldnot be inferred that ‘q ’ and ‘r ’ have different cognitive value in thesame way that it cannot be inferred that ‘snow’ and ‘neige’ differ incognitive value from the fact that someone believes that ‘snow’ hasfour letters and does not believe that ‘neige’ has four letters. There-fore what can at most be concluded from the application of Frege-criterion is that (10) and (11) (and not their constituent sentences)have different cognitive value. But if one take this route, one must

also grant that ‘because’ creates hyper-opaque contexts, i.e. contextsin which substitution salva veritate of expressions which are cognitivelyequivalent does not hold, so the premise of the argument accordingto which sentences which have the same cognitive value are substitut-able in because-contexts, is false. The other option one has is to claimthat ‘because’ does not create such hyper-opaque contexts. However,if ‘because’ does not create hyper-opaque contexts, the Frege-criterion is legitimately extensible from these contexts to sentences

embedded in them and therefore from the failure of substitutivity in(12) and (13) it can be inferred that (8) and (9) do not have the samecognitive value, and in this case the other premise of the argument isfalse.

Since there seems to be no way to make true both its premises, theargument which should support one premise of Douven-Hindriksargument against TDB is unsound and therefore this premise remainsin need of justification. Therefore, until such a justification is provid-

ed, the argument should be rejected. The second argument starts by observing that if one asks ‘Why is ittrue that p?’ the answer ‘Because p’ will not normally count as a good




explanation.4 From this fact it is concluded that what is said by theinstances of (BT) is not an explanation at all.5 In order to see why the

argument is unsound, one must be clear about the distinction be-tween an act of explaining, a kind of assertion which consists of as-serting propositions typically expressed by sentences of the form ‘ p because q ’ and the proposition which is thereby asserted.6 Since, asLewis (1986) observed, giving an explanation is providing an answerto a question which is a request for some kind of information, anexplanatory act can be unsuccessful in all the manners in which an actof providing information can be: the information provided must in

fact be of the right kind and of the right amount given the practicaland cognitive goals of the person asking for the explanation. Thefirst basic condition that an explanatory act must satisfy in order tobe successful is that the proposition asserted be true, otherwise noinformation will be provided. But there seem to be at least two otherconstraints: in the first instance that the information provided be thekind of information requested in the context (the relevance constraint )and in the second instance that the information be new for the agentsseeking the explanation (the novelty of information constraint ). From thisit follows that if the explanatory proposition asserted in an answer toa why-question is a proposition knowledge of which is considered asbackground knowledge in a given context, the explanation will beevaluated as a bad explanation since it violates the novelty of infor-mation constraint, although the proposition asserted is evaluated astrue. These are cases in which the explanation will sound trivial sincethe pieces of information provided by the explanation sound trivial.But trivial information and explanations are still information and ex-

planations. Therefore the reason why, in normal contexts, whensomeone asks ‘Why is it true that p?’ the answer ‘Because p’ is consid-ered a bad one could be the following: since the information provid-

4 Künne (2003, 150) points out this fact.5 Considerations of this kind can be found in Douven-Hindriks 2005 andLiggins 2010 (concerning explanations such as ‘he is a bachelor because he isan unmarried man’).6 The distinction is accepted by philosophers who have very different views about the nature of explanation, such as Van Fraassen (1980), Achinstein (1983), Lewis (1986), Ruben (1990). On this see also Schnieder2006.



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ed by the proposition that it is true that p because p is one that anycompetent speaker is supposed to know, someone asking why it is

true that p is seeking a further explanation of this fact, namely anexplanation of the fact that p, which, via the trivial explanation that itis true that p because p, will also count as an explanation of why theproposition that p is true.7 The information provided by the instancesof (BT) will not therefore be, in such contexts, the relevant infor-mation since the relevant information was about the fact that p. Thisis the reason why the answer provided by uttering an instance of(BT), if we somehow manage to seriously consider it as an answer to

this request for information, will be considered at best as an utteranceof the proposition that p because p, which is no explanation at all.However, that the proposition that p because p is not an explanationdoes not entail that a different proposition, namely the propositionthat it is true that p because p, is not an explanation (although a trivialone). So the argument is invalid since the conclusion does not followfrom the premise.

The last argument against TDB says that even granting that there are

contexts where speakers are disposed to assent to instances of (BT),is not sufficient to show that they believe in TDB, since in these con-texts the expression ‘because’ could be used not to express an ex-planatory connection between propositions but just to signal thepresence of an inference, whereby the speaker is providing justifica-tions or reasons for what he believes.8 I think that this proposal facesproblems. Notice, first of all, that in contexts where the speakers arecompetent with ‘true’, someone seeking a reason for believing that it

is true that p will be someone asking for a reason to believe that p. Therefore, in such contexts, uttering ‘ p’ to provide a reason to believethat it is true that p should be seen as at least as question begging asuttering ‘ p’ for giving an explanation of why it is true that p. Moreo- 7 For the claim that an explanation of the form ‘it is true that p because r ’may be such in virtue of the fact that there is an explanation in which ‘r ’ isthe explanans and which is a step in a chain of explanations whose first stepis ‘it is true that p because p’ see Schnieder 2006, Caputo 2007.8 Liggins (2010) put forward this argument against Schnieder’s (2006)claim that sentences like ‘Pietro is a bachelor because he is an unmarriedman’ express explanations. I think the argument could also be employedagainst the purported truth-explanations.




ver the proposal faces the following problem: if one accepts thestandard analysis of what a reason is, according to which a reason for

r is a premise of a sound argument which has r as conclusion it fol-lows that, since ‘It is true that p’ and ‘ p’ are mutually inferable (assum-ing the corresponding instance of (T)), either sentence can express areason to believe the other. But then, on this account of what a rea-son is, one hasn’t accounted in any different way from the explana-tion-account for the intuitions of asymmetry between ‘It is true that p’ and ‘ p’: one is simply denying these intuitions and this revisionarystance should be based on some independent reason to reject TDB,

such as those provided by the first two arguments which, if I’m right,are flawed. The advocate of the reasons-account could reply thatthere are more fine-grained accounts of what a reason is according to which ‘ p’ expresses a reason for ‘It is true that p’ but not the other way around; for instance, she can appeal to a notion of a canonicalreason , that is to say a reason for asserting a sentence which is part ofthe basic assertibility conditions for that sentence, where basic assert-ibility conditions for a sentence are those constitutive of the compe-tence with it. According to this interpretation ( GT ) expresses the cor-rect intuition that in order to decide whether a proposition is true wemust first decide whether the world is a certain way (but not the other way around). Moreover, she can stress that the minimalist can agree with the claim that ‘ p’ expresses the basic assertibility conditions for‘it is true that p’ but not the other way around, so that the reasons-account provides the minimalist with a good way out of the Because-argument.

Although I think that there is some truth in this line of reasoning(see §5 below), what it entails is at most that there is an interpretationof the sentences expressing TDB according to which these sentencesdo not express explanations but true claims of a different kind andthat this interpretation is in some contexts the correct way to under-stand utterances of ( GT ) and instances of (B). But that a sentencesays something in some contexts does not exclude that it says some-thing else in other contexts and that what is said by it in these lattercontexts is true.

So not even the reasons-argument provides conclusive reasons tobelieve that TDB (understood as an explanatory claim) is false.




follows is a situation where the word ‘bachelor’ is involved; I will thenextend the conclusions drawn from this case to the truth predicate.

The reason for doing so is that I think that explanations expressed bysentences such as (14) and (15) below are paradigmatic cases of thekind of explanations to which truth-explanations belong.

(14) John is a bachelor because John is an unmarried man.

(15) A bachelor is a bachelor because he is an unmarried man.

So, imagine a child, Nicola, who hears the word ‘bachelor’ used bycompetent speakers around him for the first time: speaking to a

friend, Nicola’s mother says things like ‘John is a bachelor’, ‘Bachelorsare nice people’. Nicola trusts his mummy and defers to her, so byassenting to what his mother is saying he comes to believe that Johnis a bachelor and that bachelors, whatever else they are, are nice peo-ple; therefore Nicola is disposed to accept ‘John is a bachelor’ and‘Bachelors are nice people’ but he has no disposition to accept ‘Johnis an unmarried man’, or ‘Unmarried men are nice people’: these pairsof sentences aren’t therefore cognitively equivalent for him. Nicola

begins to wonder about bachelors, about what being a bachelor con-sists in. And wondering about such things he asks his mother thingslike ‘Why is someone a bachelor Mum?’ The mother, provided shesucceeds in satisfying Nicola’s request for information, will answer with (15). The moral to be drawn from this kind of situation is that,in contexts of these kinds, sentences like (14) and (15) express ex-planatory information concerning , in Schnieder’s (2010) words, whatmakes something thus and so.12

As far as property talk is considered as legitimate as talk in whichpredicates are used, given the trivial equivalence of a sentence like(14) to ‘John has the property of being a bachelor because he is anunmarried man’, it is safe to say that these kinds of explanations provide information concerning what it is for something to have a givenproperty, what having this property consists in. Therefore from nowon I will speak of these kinds of explanations using the propertiestalk, without assuming that it is in some way conceptually or meta-

physically more fundamental than properties-free talk. So what islearnt by Nicola is what being a bachelor consists in, what it is for

12 Schnieder (2010) calls these explanations ‘Analytical’.



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something to exemplify this property. Although this information andthese explanations are about the world and not the words, there is

also a sense in which they convey semantic information and explana-tions. In fact believing that bachelors are unmarried men is what isneeded for Nicola to become a competent speaker with ‘bachelor’:accepting the sentence ‘Bachelors are unmarried men’ is in fact thebasic regularity of use which endows the word ‘bachelor’ with itsmeaning. This is just implicit knowledge of meaning, it is not explicitknowledge of propositions such as the proposition that ‘bachelor’applies to x iff x is an unmarried man. Explicit semantic information

can be extracted by implicit knowledge in several ways: one way isthrough disquotational principles such as ‘If the F s are the Gs then“F ” applies to x iff x is a G’. Another way is through answers toquestions concerning the proper extension of a predicate: imagineNicola asking his mother, ‘Mum, why are only unmarried men, andnot little kids like me, bachelors?’ An appropriate answer to this ques-tion would seem to be ‘ There is no “because” here Nicola! Only un-married men are bachelors since this is what “bachelor” means!’13

Explicit semantic information grounds semantic explanations, such as‘”bachelor” applies to x because x is an unmarried man’.

Something similar to what has been said for ‘bachelor’ holds also for‘true’. When someone doesn’t know the meaning of the word ‘true’the proposition that it is true that snow is white because snow is white is an explanation which gives information concerning theproperty of being true: what is learned, in this case, is not what beingtrue consists in, what it is for an arbitrary thing to exemplify the

13 Since understanding ‘since’ here as a variant of the explanatory ‘because’ would make the mother inconsistent (she would be asserting both that thereis no explanation of the fact that only men can be bachelors and that thereis such an explanation), it seems more charitable (as suggested by Burge(1978a)) to interpret it as signaling the presence of an inference: the reasonto believe that only unmarried men are bachelors is that ‘bachelor’ meansunmarried man . This is right but I think that there is also an explanatory un-derstanding of ‘since’ in this context that is consistent with the first ‘no “be-

cause”’: the fact that ‘bachelor’ means unmarried man is not presented asexplaining the fact that only unmarried men are bachelors; it is rather putforward as an explanation of why this fact is a primitive fact, that is to sayone for which no explanation is available.




property of being true, but just what it is for the proposition thatsnow is white to exemplify this property, the conditions which, pro-

vided they are satisfied, make that particular proposition true (what isusually called truth-conditions). From this information one can ex-tract semantic information concerning the application conditions ofthe truth-predicate to a particular proposition.

Since being a competent speaker with respect to ‘true’ amounts toknowing these pieces of information, these explanations are trivialfor competent speakers; but trivial explanation is still explanation,although pragmatically unsatisfactory. Further evidence for this claim

is provided by the following facts. In the first place, in a context where speakers are competent with ‘true’ the degree of perceivedunsuccessfulness of asserting an instance of (BT) seems to be lowerthan that of asserting an instance of (BT*) as an answer to the ques-tion ‘Why is it true that p?’: while in fact the evaluation of the secondanswer will be to consider it no explanation at all, it seems to me thatthe more natural reaction to the first answer would be to say ‘Yes ofcourse, but why p?’ In the second place, while competent speakers are

never disposed to accept as a good explanation the instances of(BT*), they are disposed to assent to instances of (BT) provided thatthe right sentential context is provided, as for instance in:

(16) (Is it true that snow is white) because snow is white, or is snow white because it is true that snow is white?

which invites the addressee to choose between two different explana-tions. I think that no philosophically unbiased ordinary speaker would

reply ‘Neither’ or ‘Both’. They would reply ‘The first one is true!’ The explanation of these facts is precisely that while answers whichare instances of (BT*) and of ‘ p because it is true that p’ violate allthree norms governing acts of explanation (truth, novelty and relevance), answers which are instances of (BT) violate just the last twonorms, so although they are evaluated as bad answers they are stillconsidered as better answers than the former.

4. Conceptual Explanations?Künne (2003, 155) and Schnieder (2006) claim that the precedingexplanations are conceptual explanations. Is this right? The answer



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depends on what one means by ‘conceptual’. There are at least threepossible understandings of this expression: 1) a conceptual explana-

tion is one which concerns concepts; 2) a conceptual explanation is anexplanation that we know just by virtue of the possession of someconcepts; 3) a conceptual explanation is one which is true in virtue ofconcepts and relations between them. It seems to me false that thepreceding explanations are conceptual in the first sense. In fact theyprovide information concerning what it is for something to have aproperty. Explanations of this kind are those given in philosophy(sometimes but not always in the form of analyses) but, as far as the

topic of such explanations is concerned, there seems not to be anysubstantial difference between them and explanations based on theo-retical reductions such as ‘This is water because it is H2O’. As far astheir topic is concerned, all these explanations are better described asmetaphysical and not conceptual explanations, since they are concernedmore with why things are what they are rather than with how we rep-resent things.

Rather, it seems to be true that these explanations are conceptual in

the second, epistemic sense, although I think that one gains both inevidential sources and in empirical adequacy in speaking of linguisticcompetence instead of concepts and concept possession. And it isindeed just by virtue of our linguistic competence that we are justi-fied in asserting explanations such as (14), (15) or the instances of(BT).14 Since we have a priori knowledge of these metaphysical ex-planations I will call them metaphysical-a priori explanations . On the con-trary, we need empirical enquiry to gain knowledge of the fact that

something is water because it is H2O: this is however, as King (1998)stresses, just an epistemological difference, not a difference concern-ing the kind of information involved. There are properties, like beinga bachelor and being true, which seem to be more language-shapedthan others, since our linguistic competence provides us withknowledge of what it is for something to possess them, whereas oth-er properties, like being water, are such that their nature completelytranscends our linguistic competence. A plausible way to explain this

14 As David Liggins pointed out to me, linguistic competence providesjustification of (14) and of the instances of (BT) provided one knows factssuch as the fact that John is a bachelor and that a given proposition is true.




difference is by pointing to the different ways in which predicates canbe introduced in language: through explicit or implicit definitions or

by ostensive definitions which point to concrete samples of things to which the predicates apply. When a predicate is introduced in lan-guage through explicit or implicit definitions it is endowed with itsmeaning simply by virtue of the fact that speakers regard as truesome sentences in which it occurs (as, for instance, ‘Bachelors areunmarried men’);15 in such cases therefore one’s linguistic compe-tence provides knowledge of what having the corresponding proper-ty consists in. Properties like bachelorhood and truth seem to have

both a language-dependent feature and a language-independent one:on the one hand the linguistic practices by which the correspondingpredicates are introduced provide empirically non revisable infor-mation concerning the nature of such properties; on the other handthe exemplification of these properties is not language- or mind-dependent since the definitions, explicit or implicit, or the inferentialrules by which the use of corresponding predicates is governed, linkthe exemplification of the properties to mind- and language-independent matters, such as being unmarried or snow’s being white(as far as the exemplification of truth by the proposition that snow is white is at stake).16

Metaphysical-a priori explanations are conceptual explanations also inthe third sense, with the qualification that I think that facts involvingconcepts are grounded in facts involving linguistic competence. Andthis is the reason why we can gather knowledge of these explanationsso easily, solely on the basis of linguistic competence. The reasons for

this claim are the following. These explanations, and the facts theypoint to, involve asymmetries like the following: it is a fact that Johnis a bachelor because he is an unmarried man but not the other wayaround. But these asymmetries seem to me correctly explainable onlyon the basis of the features of linguistic competence with the expres-sions occurring in the sentences by which we express them. Let meexplain this point starting from what Schnieder (2010) claims about

15 On this see Horwich 1997.16 These ideas clearly draw on those developed by Neo-Fregeans such asHale and Wright (2000) as well as on Schiffer’s (1996, 2003) pleonastic Pla-tonism.



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the asymmetries involved in these explanations, since I am in partsympathetic with him but I part company with him in some respects.

He claims that the connective expressed by ‘because’ operates in the-se explanations not on the propositions which are expressed by thesentences connected by ‘because’ when they are taken in isolation,but on these propositions under linguistic modes of presentation. This seems to me convincing, but it implies that the asymmetries inthese explanations are explained by facts involving both concepts,taken as the constituents of propositions, and linguistic expressions.For instance, what explains the asymmetry involved in (14) and (15) is

that the expression ‘unmarried man’ represents the concept BACH-ELOR in a more informative way than the expression ‘bachelor’does, in so far as it represents how that concept relates to more prim-itive concepts such as the concept MALE and the concept UN-MARRIED.17 But in the first place if one grants this one must recog-nise, as Schnieder does, that what is tracked by the asymmetry of ‘be-cause’ is a diff erence between expressions in their intended interpre-tation and I think that facts concerning the intended interpretation ofexpressions are determined by facts concerning linguistic compe-tence, by facts concerning how competent speakers use words. In thesecond place I think that the facts concerning the concept BACHE-LOR and its relations to more primitive concepts as well as featuresof concepts such as their primitiveness or relative simplicity aregrounded in facts involving linguistic competence. For instance, whatit is for the concept MAN to be more primitive and more simple thanthe concept BACHELOR is for the competence with ‘bachelor’ (and with translations of it) to depend on the competence with ‘man’ (and

with translations of it). What it is for the concept BACHELOR to bethe concept consisting of the conjunction of the concepts MAN andUNMARRIED is for the competence with ‘bachelor’ to consist ofthe competence with ‘unmarried man’ (and not the other wayaround). This explanatory dependence of facts involving concepts onfacts regarding linguistic competence could be further advocatedstressing, in the first place, that whatever concepts are, the possessionand structure of concepts is manifested by our linguistic competence

with the corresponding words; in the second place that it is difficult17 Expressions of the form ‘the concept F ’, are singular terms which de-note the concept expressed by ‘F ’.




to state identity conditions for concepts which are free of referenceto facts involving language and linguistic competence. A plausible

statement of identity conditions for concepts could take the follow-ing form: the concept Q is the concept P iff ‘Q’ REL ‘P’ where ‘REL’ de-notes an appropriately chosen relation holding between linguistic ex-pressions (such as the relation of interpretation or a suitable relationbetween the linguistic competences with the expressions).

In the next paragraph this picture will be applied to the account ofthe asymmetry in the truth-explanations and I will argue that thiskind of account should be congenial to the minimalist.

5. Minimalism and TDB

If, all things considered, there are good reasons to consider TDB as atrivial common-sense truth, how can the minimalist resist the Be-cause-argument?

The best way to do it is not by denying that TDB is a fact, but ratherby denying that TDB is a fact which involves only truth. Although in

fact the truth predicate is the only one which appears in the instancesof the schema (B) , there is another linguistic expression which isshared by all of them: the connective ‘because’. This is an expressionthat, at least in some contexts, is used to express explanations, there-fore it is not a surprise that the facts to which instances of (B) pointcannot be explained solely on the basis of MT; we must also considerfacts concerning explanations of a specific kind: metaphysical-a prioriexplanations. To think so does not commit one to the implausible

claim that the propositions expressed by sentences of the form ‘ p because q ’ involve the concept of explanation, but just to the muchmore plausible claim that these propositions are true just in case theproposition expressed by ‘ p’ is explained by the proposition expressedby ‘q ’. The Because-argument pointed to a feature of many (and per-haps all) explanations: that they exhibit an asymmetry of the explana-tory relation holding between explanans and explanandum. I havemoreover claimed that, as far as metaphysical-a priori explanationsare concerned, these asymmetries must be traced back to asymmetriesconcerning linguistic competence with the corresponding predicates.How can the minimalist put together these claims and Minimal theo-ry to provide an account of TDB?



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The kind of account of TDB I recommend to the minimalist is closeto proposals made by Schnieder (2006) and Barker (2007).

According to Schnieder (2006) explanatory asymmetry between ‘it istrue that p’ and ‘ p’ in schema ( BT ) depends on the fact that ‘masteryof the concept of truth is constituted by the ability to relate state-ments involving it to statements involving only conceptual resourcesalready at hand’ (Schnieder 2006, 33), where the relation at stake isthe logical relation ‘iff’ which connects the left and right-hand sidesof the T-biconditionals. I think this is basically right with the qualifi-cation that since facts involving concepts are grounded in facts in-

volving linguistic competence, what more fundamentally explains thisexplanatory asymmetry is that, in the first place, the disposition toaccept sentences of the form ‘It is true that p iff p’ is what the lin-guistic competence with ‘true’ consists in; in the second place, alt-hough our competence with ‘true’ is not exhausted by the dispositionto accept any single sentence of this form, this disposition is a neces-sary and sufficient condition to correctly use the correspondingtruth-ascription and the same disposition is not needed to correctly

use, and therefore to understand, the sentences which appear on theright hand side of the T-biconditionals.

Can the minimalist appeal to these facts? Of course she can! In factaccording to the minimalist MT is an implicit definition of truth andthis means that the disposition to accept T-biconditionals is the basicregularity governing our use of the word ‘true’, which endows the word with its intended meaning. Moreover, as in any definition, thedefinition may work only insofar as the definiens (in explicit defini-

tions) and the matrixes in which the defined expression is inserted (inimplicit definitions) are antecedently and independently understood.18

According to Barker (2007) the fact that the explanatory relation ineach T-biconditional goes from the right-hand side to the left-handside, and not the other way around, is explained by the fact that theright-hand sides are the premises in the introduction rules governingthe use of the truth-predicate and not the other way around. In other words: while the canonical justification to assert a sentence of the

form ‘It is true that p’ is provided by ‘ p’ the converse is not the case.

18 Horwich (2009, 199f.) seems to agree.



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6. Objections and Replies

I think there are two main objections, the translation objection and thecontingency objection , to my claim that metaphysical-a priory explana-tions are grounded in facts involving linguistic competence.19

The translation-objection , which goes back to Church’s (1950) criticismof Carnap’s (1947) metalinguistic analysis of belief -ascriptions, takesits start from the norm governing translation according to whichgood translations should preserve truth value. So if (17) were true(18), its translation in German, should also be true:

(17) (A bachelor is a bachelor because he is an unmarried man) because of how competent speakers use the word ‘bachelor’.

(18) (Ein Junggeselle ist ein Junggeselle, weil er ein unverheirateterMann ist) auf Grund dessen, wie kompetente Sprecher das Wort‘bachelor’ verwenden.

But (18) will be evaluated as false by whoever understands it: whyshould how Anglophone people use a word of their own language

have any import for what explains why bachelors (regardless of theirnationality!) are what they are? Therefore (17) is false too.

I think that this argument is flawed because its premise according to which (18) is a correct translation of (17) assumes the so-called Lang-ford-test for translation, according to which quoted material is not tobe translated. But this assumption has been disputed by several au-thors (since Burge 1978b).

The idea behind criticisms to the Langford-test is that quotationsoften do more than just referring to a word-shape type and that inthose cases understanding of the quoted material is relevant to theunderstanding of the quotation itself. There are plenty of cases ofthis kind like so-called mixed quotation, hybrid quotation and directdiscourse. For instance the correct German translation of

(19) John said to Jill ‘I love you’.

is

19 Both these objections were pointed out to me by the editors of this vol-ume.




(20) John sagte zu Jill ‘Ich liebe dich’.

The claim that (20) is the correct translation of (19) is supported bythe ordinary practice of translation, and by the constraint on transla-tion according to which good translation should preserve what is saidby a sentence. In fact the more correct answer in German to a ques-tion concerning what someone said by uttering (19) seems to be:

(21) Sie hat gesagt, dass John zu Jill sagte ‘Ich liebe dich’.

Similarly it seems to me that the intuitively more correct report inGerman of what someone said by uttering (17) is

(22) Sie hat gesagt, dass ((Ein Junggeselle ein Junggeselle ist, weil erein unverheirateter Mann ist) auf Grund dessen, wie kompetenteSprecher das Wort ‘ Junggeselle’ verwenden).

To appreciate this fact it is sufficient to think of (22) as an answer bya bilingual (German and English) speaker to a monolingual Germanspeaker who asks what Mary said by uttering (17). Therefore the whatis said-report test provides a reason to think that the more correct

German translation of (17) is(23) (Ein Junggeselle ist ein Junggeselle, weil er ein unverheirateter

Mann ist) auf Grund dessen, wie kompetente Sprecher das Wort‘ Junggeselle ’ verwenden

The reasons why (23) is the correct translation of (17) are similar tothose in virtue of which (20) is the correct translation of (19). In di-rect discourse reports quoted material gets translated because in thiskind of discourse we are primarily interested in representing the ut-terances of other people, that is to say their tokening of words withtheir intended meanings, and meaning-properties are shared by ex-pressions and their translations. So, in this kind of discourse, quota-tions refer not to mere shape-types but to more abstract types, whichcan be represented as the class of all expressions with the samemeaning of the expression quoted.20 The same is true of sentenceslike (17) since the features of ‘bachelor’ to which (17) points areshared by all the words of other languages which are translations of

it: these features are the inferential and referential aspects of the

20 See Recanati 2001.



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competence. So ‘bachelor’ in (17) must be interpreted as referring notto the shape-type but to the more abstract type which can be repre-

sented as the set of all words, in whatever language, which share therelevant features which constitute the competence with them.

Another account of the fact that quoted material in direct discoursegets translated, which can be extended to the translation of sentenceslike (17), is to claim with Burge (1978b) that direct discourse carries with it a hidden self-referentiality either embedded in its semantics orin some pragmatic convention governing its use. For instance, if thefirst alternative (which is not the one Burge prefers) is chosen, (19)

should be paraphrased as(24) John said to Jill ‘I love you’, taken as a sentence of the language

of this sentence.

Given this hidden self-referentiality, at the semantic or pragmatic lev-el, the behavior of direct-speech report in translation becomes a spe-cific instance of the more general phenomenon that sometimespreservation of self-reference in translation matters more than

preservation of reference.21 If one takes this route one can point out that (17) is, semantically orpragmatically, hiddenly self-referential and that therefore the properunderstanding of it should be:

(25) Someone is a bachelor because he is an unmarried man becauseof the features of the competence on ‘bachelor’, understood asit is used in this very sentence.

Finally one may observe that in translating (17) the preservation ofself-referentiality is to be preferred to the preservation of referenceof the quotation, since a translation like (18), where reference of thequotation is preserved, loses, for a speaker of the target language, animportant piece of information: that the asymmetry of ‘because’ inthe explanatory sentence which is the explanandum in (17) stemsfrom nothing but some use-properties of the expression occurring init, use properties which it shares with the expressions of other lan-

21 Burge (1978b) stresses that this is what happens in translating a text ofmetamathematics where the very starting point of some theorem is the con-strual of a self-referring sentence.




guages which count as their translations, including the expressions heis actually using.

What could be objected against this line of argument is that it resiststhe translation-objection only conceding that metaphysical-a prioriexplanations are grounded, if not on facts involving only this or thatlanguage, on the generic existence of linguistic facts. But also thisgeneric dependence seems to be false and this is stressed by the contingency objection which runs as follows.

Since I claim that TDB and, more generally, metaphysical-a priori ex-

planations are grounded in facts involving linguistic competence, I’mcommitted to the truth of sentences like

(26) It is true that snow is white because snow is white because somefacts involving linguistic competence are thus and so.

But (26), as far as it is an explanatory claim, should support the coun-terfactual

(27) Had it not been the case that the relevant facts involving linguis-

tic competence are thus and so then it would not have been thecase that it is true that snow is white because snow is white.

But take a possible world which differs from our world just in thatthere are no speaking creatures in it. In this world, as in our world,snow is white; so the proposition that snow is white is true as evalu-ated at this world and it seems also to be true, at this world, that thisproposition is true because snow is white. Therefore (27) is false andso (26) is also false.

This is an instance of the general pattern of objection that is usuallyput forward against conventionalist or constructivist positions onspecific subject matters (for instance modality, ontology, morality)according to which facts which seem to be language or mind inde-pendent are explained by facts that are mind or language dependent(as linguistic, social, or cognitive facts).22

22 Boghossian (1996) put forward this objection against the conception ofanalyticity according to which there are sentences which are true simply by virtue of their meaning.



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My reply to this objection follows what recent conventionalists suchas Einheuser (2006) and Sidelle (2009) have said concerning this gen-

eral pattern of objections to conventionalism: the truth of explana-tions such as (26) does not involve the truth of the correspondingcounterfactuals although there is some other kind of dependencybetween the facts to be explained and the facts by which the conven-tionalist want to explain them (in this case the facts involving linguis-tic competence).

Here the right thing to say is reminiscent of K ripke’s (1980) consid-erations concerning counterfactual reasoning, in particular his claim

that possible worlds are stipulated via counterfactual hypotheses whose content depends on the ways we actually use words. Startingfrom these kind of considerations one can claim that if possible worlds are scrutinized at all, they are always scrutinized with the lensof the language we actually speak and, taking a step further, that ouractual linguistic practices shape the space of possibilities themselves,so that if we had been engaged in other practices the set of possible worlds accessible to us would have been different.23 Given the way in

which we actually speak facts such as the fact that if it is true thatsnow is white this is true because snow is white and that whoever is abachelor is so because he is an unmarried man are necessary andprimitive facts, in the sense that there is no fact in the possible worldsat which these facts obtain which grounds them, and what our actuallinguistic practices explain is just the necessity and primitiveness ofthese facts. Remember Nicola and imagine him asking again ‘Why?’,after his mother has said that bachelors are bachelors because they

are unmarried man. Faced with this new request for an explanationthe mother could repeat ‘There is no “because” Nicola, bachelors arebachelors because they are unmarried man because “bachelor” meansunmarried man’. This kind of answer would not be inconsistent sincethe first ‘because’ is the one which supports counterfactuals, and sothat there is no ‘because’ entails that there is no counterfactual sup-porting explanation of the explanatory fact about which Nicola is

23 The relevant worlds for the evaluation of this latter hypothesis are notmetaphysically possible worlds, relative to our actual linguistic practices, sothe intended reading of this hypothesis is what Einheuser calls the ‘counte r-conventional’ reading distinct from the counterfactual one.




asking, since this is a primitive and necessary fact which covaries withnothing; on the other hand the second ‘because’ is the one which

does not support counterfactuals since linguistic facts explain justthis, the necessity and primitiveness of such facts, their being, so tosay, brute, although trivial, explanatory facts.

The last objection I want to discuss runs as follows. Metaphysical-apriori explanations seem to point to facts involving some kind ofasymmetrical metaphysical dependence, e.g., in the case of truth thefact that the truth of a proposition is grounded in the world being ina certain way. But how do these facts emerge from asymmetries

which concern just our concepts or, as I claim, just the structure ofour linguistic competence? As Liggins (2010) correctly observes, rela-tions of relative conceptual simplicity and primitiveness do not always mirror relations of metaphysical priority. In a similar way, focus-ing on the importance I give to the inferential asymmetry between (8)and (9), it could be stressed that this involves taking sides with those who think that the ‘because’ in TDB is reason-giving instead of beingreally explanatory, where explanations, differently from inferences,

track objective relations among facts. The answer to these concerns is to point to the fact, highlighted inthe previous paragraph, that properties like bachelorhood and truthare such that the linguistic practices governing the use of the corre-sponding predicates provide non-revisable information concerningtheir internal structure and their exemplification-conditions. In thesecases canonical reasons for ascribing the predicates count also asbasic explanations of why the property is exemplified so what having

a given property is an inferential consequence of (Jenkins 2008) countsalso as an objective ground for having such a property and what Jen-kins (2008) calls ‘explication’ of the concept is also an explanation of what it takes for something to have the corresponding property. Insupport of this claim it should be noted that the difference betweenreasons and explanations comes to the fore when there is space fordivergence between the criteria by which one recognises the exempli-fication of a property and the objective conditions that must be satis-

fied for the property to be exemplified: but this happens just withproperties like water not with properties like bachelorhood and truth.



296 CAPUTO

7. Conclusions

I hope to have vindicated the following claims: first, TDB

is a com-monsense truth; second, TDB is true in virtue of facts concerning thenature of our linguistic competence with the truth-predicate; third, aminimalist can perfectly explain, in his framework, these facts andthereby why TDB is true.24

References

Achinstein, P. 1983: The Nature of Explanation . Oxford: Oxford Uni-

versity Press. Aristotle 1991: The Complete Works of Aristotle . 4th edn, Barnes, J. (ed.).Princeton, Guildford: Princeton University Press.

Barker, S. 2007: Global Expressivism: Language Agency without Semantics,Reality without Metaphysics. URL: http://eprints.nottingham.ac.uk/696/1/BOOKGE.pdf.

Beebee, H. and J. Dodd (eds.) 2005: Truthmakers. The Contemporary De- bate . Oxford: Oxford University Press.

Boghossian, P. A. 1996: ‘Analyticity Reconsidered’. Noûs , 30, pp. 360 –91.

Boghossian, P. and C. Peacocke (eds.) 2000: New Essays on the A-priori ,Oxford: Clarendon Press.

Burge, T. 1978a: ‘Belief and Synonymy’ . Journal of Philosophy 75, pp. 119 –38.

— 1978b: ‘Self-Reference and Translation’. In Guenthner andGuenthner-Reutter 1978, pp. 137 –53.

24 This paper owes a lot to the conversations I had with Diego Marconi.Many thanks also to all the people which contributed with their commentsto make this paper better than it was. In this respect I’m particularly in debtto the editors of this volume, Miguel Hoeltje, Benjamin Schnieder and AlexSteinberg which, with their careful and illuminating comments, helped me torevise in many important respects the first draft of this paper. This research

has been carried on as part of the research-project ‘Truth, Explanation andContextual Dependence’ under the supervision of Alfredo Paternoster, to which I’m grateful, and thanks to the funding of the Banco di Sardegna Foun-dation.

http://eprints.nottingham.ac.uk/696/1/BOOKGE.pdf

http://eprints.nottingham.ac.uk/696/1/BOOKGE.pdf




— 1979: ‘Individualism and the Mental’. Midwest Studies in Philosophy 4,pp. 73 –121.

Caputo, S. 2007: ‘ Truth-making: What it Is Not and What it Couldbe’. In Monnoyer 2007, pp. 275 –311.

Carnap, R. 1947: Meaning and Necessity . Chicago: The University ofChicago Press.

Church, A. 1950: ‘On Carnap’s Analysis of Statements of Assertionand Belief’. Analysis 10, pp. 97–9.

David, M. 2002: ‘Minimalism and the Facts about Truth’. Schantz

2002, pp. 161 –75.Douven, I. and F. Hindriks 2005: ‘Deflating the Correspondence Intui-

tion’. Dialectica 59, pp. 315 –29.

Einheuser, I. 2006: ‘Counterconventional Conditionals’. PhilosophicalStudies 127, pp. 459 –82.

Guenthner, F. and M. Guenthner-Reutter (eds.) 1978: Meaning andTranslation , London: Duckworth.

Gupta, A. 1993: ‘Minimalism’. Philosophical Perspectives 7, pp. 359 –69.Hale, B. and C. Wright 2000: ‘Implicit Definition and the A priori’. In

Boghossian and Peacocke 2000, pp. 286 –319.

Horwich, P. 1990: Truth . Oxford: Basil Blackwell.

— 1997: ‘Implicit Definition, Analytic Truth, and AprioriKnowledge’. Noûs 31, pp. 423 –40.

— 2009: ‘Being and Truth’. In Lowe and Rami 2009, pp. 185 –200.

King, J. C. 1998: ‘What is a Philosophical Analysis ?’. Philosophical Stud- ies 90, pp. 155 –79.

Kripke, S. 1980: Naming and Necessity . Oxford: Basil Blackwell.

Künne, W. 2003: Conceptions of Truth . Oxford: Clarendon Press.

Jenkins, C. S. 2008: ‘Romeo, René, and the Reasons Why: What Ex-planation Is’. Proceedings of the Aristotelian Society 108, pp. 61 –84.

Lewis, D. K. 1986: ‘Causal Explanation’. In his Philosophical Papers,

Volume II, Oxford: Oxford University Press, pp. 214 –40.Liggins, D. 2010 (Draft): ‘Truthmakers and Dependence’.



298 CAPUTO

Lowe E. J. and A. Rami (eds.) 2009: Truth and Truth-Making , Durham: Acumen.

Monnoyer, J. M. (ed.) 2007: Metaphysics and Truthmakers , Frankfurt:Ontos Verlag.

Recanati, F. 1997: ‘Can We Believe what We Do not Understand?’. Mind and Language 12, pp. 84 –100.

— 2001: ‘Open Quotation’. Mind 110, pp. 637 –87.

Rodríguez-Pereyra, G. 2005: ‘ Why Truth-makers’. Beebee and Dodd2005, pp. 17 –31.

Ruben, David-Hillel 1990: Explaining Explanation. London: Routledge.Schantz, R. (ed.) 2002: What is Truth?, New York: De Gruyter.

Schiffer, S. 1996: ‘Language-Created, Language-Independent Enti-ties’. Philosophical Topics 24, pp. 149 –67.

— 2003: The Things We Mean . Oxford: Clarendon Press.

Schnieder, B. 2006: ‘ Truth-making without Truth-makers’. Synthese 152, pp. 21 –46.

— 2010: ‘A Puzzle about ‘Because’’. Logique et Analyse 211, pp. 317 –43.

Sidelle, A. 2009: ‘Conventionalism and the Contingency of Conven-tions’. Noûs 43, pp. 224 –41.

Van Fraassen, B. C. 1980: The Scientific Image. Oxford: Oxford Univer-sity Press.

Vision, G. 1997: ‘ Why Correspondence Truth Will Not Go Away’. Notre Dame Journal of Formal Logic 38, pp. 104 –31.

— 2010: ‘Intensional Specifications of Truth-Conditions: ‘Because’,‘In Virtue of’, and ‘Made True By…’’. Topoi 29, pp. 109 –23.



300 LEUENBERGER

consequence that whenever x is in the domain and y in the conversedomain of R , then Rxy . To see this, note that for any binary predicate

R expressing a relation, monadism entails the truth of a biconditionalof the following form:

(M1) Rxy ↔ Fx Gy .

Suppose now that x is in the domain of R , such that Rxz for some z . Then Fx holds by the left-to-right direction of (M1). If y is in theconverse domain of R , then Rz'y for some z' , and thus Gy by the left-to-right direction of (M1) again. Hence, Fx Gy , and Rxy by the

right-to-left direction of (M1). This consequence is unacceptable,since many relations do not relate everything in their domain witheverything in their converse domain. That I am taller than someoneand someone is taller than you does not entail that I am taller thanyou, after all.2

Monism has the consequence that every relation is symmetric. It en-tails a biconditional of the following form for every binary R :

(M2) Rxy ↔

H ( x + y ). If Rxy , then H ( x + y ) by the left-to-right direction of (M2). Hence,H ( x + y ), and Rxy by the right-to-left direction of (M2). This argumentassumes that the function + is commutative. But unless told otherwise by the monist, we can assume that + is just ordinary mereologi-cal summation, which is commutative.3 Since taller than is not sym-metric, monism can account for it no more than monadism can.

It is tempting to pool the resources of monadism and monism, andhold that the true logical form of Rxy is Fx Gy H ( x + y ). We maycall that view monadicism .4 Neither of the two previous objections ap-

2 For a similarly unacceptable consequence of crude monadism, see Mates1986, 217.3 This argument against monism is given in Russell 1903, 225: the wholea +b ‘is symmetrical with regard to a and b , and thus the property of the whole will be exactly the same in the case where a is greater than b as in the

case where b is greater than a ’. Russell claims that Leibniz was already awareof the argument.4 Its negation is called ‘the doctrine of external relations’ by Russell (1924,373).



SUPERVENIENCE AMONG RELATIONS 301

plies. Nonetheless, the view has the unacceptable consequence thatany relation is symmetric among those entities that are in both its

domain and its converse domain. For it entails for a biconditional ofthe following form for any R :

(M3) Rxy ↔ Fx Gy H ( x + y ).

Suppose that for some z and z' , Rzx and Ryz' . Then Fx Gy by theleft-to-right direction of (M3). Now suppose Rxy . Then H ( x + y ) bythe left-to-right direction of (M3) again, and H ( y +x ) by the commu-tativity of +. Hence Fy Gx H ( y +x ), and Ryx by the right-to-left

direction of (M3). But again, you may be taller than me, but not vice versa, even though we are both in the domain and the converse do-main of being taller than .

If the project of showing relations to be reducible requires a transla-tion scheme of the kind suggested by (M1)−(M3), its prospects aredim.5 But perhaps there is another sense in which relations – or atleast some of them – are reducible. Intuitively, it seems that whatever we think about whether all relations are reducible, surely being taller

than is. The question what constitutes reducibility has received a great deal ofattention in other areas. When looking for a pertinent concept ofreducibility for relations, we could do worse than consider work donein the philosophy of mind. As is well known, the concept of supervenience has occupied centre stage there. Typically, philosophers acceptthat supervenience – of one variety or another – is necessary for re-ducibility. It is widely acknowledged that the supervenience of a class A on a class B is not by itself sufficient for reducibility. Whether it issufficient when conjoined with certain other claims is a difficult ques-tion that I will not address here.

Whatever the exact relationship between supervenience and reducibil-ity, the question whether some relations are reducible to propertiesnaturally leads to the question whether the former supervene on thelatter. What would it take for relations to supervene on properties?

The extant literature does not contain a sustained and systematic ex- 5 For a sophisticated discussion of technical aspects of that question, seeHumberstone 1984.



302 LEUENBERGER

amination of this question, at least as far as I am aware. This is sur-prising, given that a great deal of work has been done on distinguish-

ing various concepts of supervenience, supplying exact characteriza-tions for them, and finding applications. It is even more surprising inlight of the fact that the concept of supervenience is eminently suit-able to be applied to relations, as I shall argue.

As noted above, supervenience is useful in discussing the relationshipbetween mental and non-mental properties. One reason for this is theputative multiple realizability of the former. If the multiplicity is infi-nite, then what is realized is not finitely definable in terms of the real-

izers, and hence not definable in a language like English in which noinfinite disjunctions can be formed. Nonetheless, the realized proper-ties supervene on the class of realizers. Some relations can also besaid to have an infinite multiplicity of realizers. Again, being taller than serves as an example. That relation cannot be finitely defined interms of height properties, where those are understood as propertiesthat never differ among things that are of the same height. To putthis in the formal mode: no two-place predicate that expresses the

relation of being taller than can be defined in the language of predicatelogic whose only non-logical terms are unary predicates. Nonetheless,being taller than supervenes on heights. We can spell out precisely whatthis means. Let x , y

and x' , y'

be two ordered pairs that are indis-cernible with respect to height properties – that is, for every heightproperty H , x has H if and only if x' has H , and y has H if and onlyif y' has H . Then x , y and

x' , y' are indiscernible with respect tobeing taller than – x is greater than y just in case x' is greater than y' ,

and y is greater than x just in case y' is greater than x' . An argumentfor the truth of that supervenience claim will be given in section 3.

As this example shows, the intuitive idea of supervenience is easilyapplied to relations. My aim in this paper is not to introduce a newconcept; rather, it is to explicate a concept that we already have, anddiscuss a couple of applications.

2. Global versus Local Supervenience among Relations

The neglect of relations has not been total. Some authors have de-ployed supervenience when theorizing about relations. For example,supervenience has been invoked in the classification of relations into




internal, external and extrinsic, a topic to be discussed in sections 4and 5. Occasionally, even the general question what it is for classes of

relations to be related by supervenience has been raised. However,those who considered the question tended to give up on providing ananswer rather quickly. After observing that ‘[as] Kim (1993) notes, itis far from trivial to apply the individual notions of superveniencedirectly to relations’, Shagrir (2009, 419) claims that ‘[i]t is more natu-ral to convert relations to properties of individuals that express theserelations’. But by and large, theorists of supervenience did not evenraise the question in the first place, and have followed the metaphysi-

cal tradition in neglecting relations. What explains such lack of attention? I suspect that it is partly due tothe erroneous belief that the work has already been done. The re-ceived view, it seems to me, is that supervenience claims involvingrelations are global supervenience claims, at least implicitly. Since ex-tant accounts of global supervenience are designed to apply to prop-erties and relations alike, they might be thought to provide a satisfac-tory account of supervenience among classes of relations.6

It is hardly an accident that relations tend to be associated with globalsupervenience. To see whether a certain global supervenience claimholds, we typically need not only compare two things, but also con-sider other things besides them. Likewise, to see whether certain rela-tions supervene, we typically need to not only compare two things,but also consider other things besides them. Hence both relationsand globality point us beyond simple pairwise comparisons of things.On reflection, though, it is clear that the contrast between monadic

and non-monadic is different from the contrast between non-global – or local – and global. There is a clear intuitive difference betweenglobal and local supervenience claims. Many relational or extrinsicproperties globally, but not locally, supervene on intrinsic ones.7 Forexample, the property of being the oldest person merely globally supervenes on ages of people. However, not only monadic properties canbe relational. Intuitively, a relation is extrinsic or relational if whether

6 The received view is rarely articulated explicitly. But it seems to be sug-gested in footnote 6 of Shagrir 2009, 419.7 I am using ‘relational’ loosely here. For a proposal about what distinctionto mark by the pair ‘extrinsic’ and ‘relational’, see Humberstone 1996.



304 LEUENBERGER

it holds or not between its relata depends on other things than therelata. The relation of being adjacent in age – of being such that nobody

has an intermediate age – globally supervenes on ages, but does notdo so locally. It is a relational relation, as it were. For a philosophicallymore interesting example, consider the relation of reference, holdingbetween mental and linguistic tokens on the one hand and objects onthe other. Reference is a broadly intentional relation, and as such widely taken to be globally supervenient on non-intentional proper-ties and relations. However, it arguably does not locally supervene onthem, since whether something is a referent of a given token may

depend on what other candidates are available. Global and local su-pervenience thus seem to come apart. In some theoretical contexts, we may be interested in the global concept, and in others in the localone.

In addition to the intuitive difference, there are two further reasons why we may not wish to construe all supervenience claims involvingrelations as global supervenience claims. First, the concept of globalsupervenience is not understood as well as the concept of strong su-

pervenience, and the project of explicating it has faced severe diffi-culties.8 Second, we may wish to consider supervenience claims involving so-called ‘transworld relations’ or ‘crossworld relations’. Ex-tant accounts of global supervenience only apply to relations whoserelata are in the same possible world.9 It is true that most garden- variety relations are intraworld relations, and only relate worldmates.Presumably, any relation that requires spatiotemporal or causal relat-edness will be in that category. But other relations of philosophical

interest are crossworld relations. Most famous among them is therelation of identity. Some puzzles about transworld identity raise thequestion whether it supervenes on qualitative properties, or indeed onany properties that do not in some way involve identity itself. Theo-rists who deny that there are any true claims of transworld identityhave invoked other crossworld relations in the analysis of de re modal-ity, such as counterparthood and representation de re . We can likewise

8 Some of these are discussed in Leuenberger 2009 and in the works re-ferred to there.9 I do not wish to claim that accounts of global supervenience could notbe modified to apply to crossworld-relations.




ask whether these relations supervene on other properties or rela-tions. David Lewis (1986, 221) defined haecceitism as the claim that

representation de re does not supervene on qualitative character, againusing our implicit understanding of supervenience as it applies torelations.10 Depending on how much we are including in the class ofqualitative properties – in particular, whether or not we are includingextrinsic properties – we get stronger or weaker versions of haeccei-tism.

But discussions of crossworld relations are not restricted to theoriesof de re modality. Similarity is a crossworld relation, and we can ask

whether it supervenes on intrinsic properties. Mental representationgives rise to other putative cases of crossworld relations. I stand inthe relation of thinking about the species of to any other-wordly human.Further, one might argue that any other-worldly human stands in therelation of making true to my mental tokening of the proposition thathumans are possible. Last but not least, the relation of indiscernibilityused to define strong supervenience is a crossworld relation.

The earlier literature on supervenience occasionally distinguished be-tween possible-worlds versions and modal-operator versions. The versions are not equivalent, although they are co-extensive if we re-strict ourselves to classes of properties that have certain closureproperties. By and large, philosophers have preferred to work withthe possible-worlds versions. But in ignoring crossworld relations,they have failed to exploit one important advantage of those versions. As is well known, the standard language of modal operators does nothave the power to express claims about crossworld relations, while

the possibilist language does.In this section, I hope to have provided some motivation for extend-ing the standard definition of supervenience to relations. In the nextsection, I will formally define such a notion.

3. Defining Strong Supervenience for Classes of Relations

The familiar definition of strong supervenience, which applies to

classes of monadic properties, can be broken down into three steps.10 Lewis formulated it as a global supervenience claim. He was not fullyexplicit about how that claim ought to be understood.



306 LEUENBERGER

First, an equivalence relation of indiscernibility is defined relative toevery property F . The field of the relation of indiscernibility consists

of ordered pairs x , w , with x an individual and w a world. The pairx , w

is F -indiscernible from x' , w'

just in case x has F in w iff x' has F in w' . Given the assumption that individuals are world-boundand only have properties in worlds where they exist, we could takethe field to consist of individuals. But despite the simplification thatit would offer, I will not make this assumption in this section. Se-cond, indiscernibility relative to a class A of properties is defined interms of indiscernibility relative to each of its members: x , w

is A-

indiscernible from x' , w'

just in case it is F -indiscernible for every F A. Since we may identify indiscernibility relations with classes of

ordered pairs, as is customary in formal logic, we can define A-indiscernibility to be the intersection of the relations of F -indiscernibility for every member F of A. Third, supervenience of A on B is defined by comparing the relations of indiscernibility generat-ed by A and B, respectively. That is, A strongly supervenes on a classB just in case B-indiscernibility is a sub-class of A-indiscernibility. In

other words, A strongly supervenes on B just in case the partitiongenerated by B is a refinement of the partition generated by A. Or inyet other words: A strongly supervenes on class B just in case all B-indiscernible elements are A-indiscernible.

When we generalize this definition to apply to classes that may in-clude monadic properties as well as relations of any finite adicity – henceforth just ‘classes of relations’ – the second and the third step will be exactly the same. A-indiscernibility will be the intersection of

all the relations of R -indiscernibility, for any R A, and A will besaid supervene on B if the partition generated by B is a refinement ofthe partition generated by A. Only the first step requires modifica-tion. We need to define a relation of R -indiscernibility for a givenrelation R , of any adicity.

The field of indiscernibility relations used in the definition of strongsupervenience for properties consists of ordered pairs. However, the

question whether x , w and x' , w'

are indiscernible relative to a dy-adic relation R does not immediately seem to make sense.11 Rather,

11 Kim (1993) discusses different ways in which we might give it a sense.




we need to consider pairs of such ordered pairs, and ask whether x ,w , y , v

is R -indiscernible from x' , w'

, y' , v'

. Clearly, it is a nec-

essary condition for their R -indiscernibility that x in w bears R to y inv if and only if x' in w' bears R to y' in v' . But for the notion of R -indiscernibility pertinent here, that condition is not sufficient: it isalso required that y in v bears R to x in w if and only if y' in v' bears R to x' in w' .

That is, if R is admiration and @ the actual world, then John,@ , Mary, @ is R -indiscernible from Peter, @ , Martha, @

only if John admires Mary just in case Peter admires Martha, andMary admires John just in case Martha admires Peter. Of course,though, it is not required for the R -indiscernibility of those pairs that John admires Mary just in case Martha admires Peter.

What is it for two such ordered pairs of ordered pairs to be F -indiscernible for a monadic property F ? This case has in effect al-ready been considered by Kim (1993, 161), and I can adopt his sug-gestion: x , w

, y , v

is F -indiscernible from x' , w'

, y' , v'

iff x in

w has F just in case x' in w' has F , and y in v has F just in case y' in v'has F . That is, elements at corresponding places in the sequence needto be F -indiscernible in the sense familiar from the definition ofstrong supervenience.

We can now generalize the foregoing to sequences that have morethan two members. Let an n -selector be a function that takes in adenumerable sequence and yields a sequence of length n whose

elements are all in , and that operates on all such sequences in thesame way: for any and ' , any natural number j and any i ≤ n , if( )i = j , then ( ' )i = ' j (( )i is the i -th element of the sequence

, and j is the j -th element of We can represent by the n-tuple 1 , …, n of natural numbers determined by the conditionthat ( )i = i

for all and all 1 ≤ i ≤ n . For example, if is the de-

numerable sequence Socrates, @ , Plato, @ Aristotle, @ 4, @ 5, @

, and the triple Plato, @

, Socrates, @ Aristotle, @ , then can be represented by 2, 1, 3 .



308 LEUENBERGER

The class of elements on which R -indiscernibility is to be definedincludes all denumerable sequences of ordered pairs of individuals

and worlds.12 Such sequences and ' are R -indiscernible, for -aryR , iff for all n -selectors = 1, …, n , =

1, …,

n exemplifies

R iff ' = ' 1, …, '

n does. This relation is easily verified to be an

equivalence relation. (In my terminology, R -indiscernibility is not thesame as agreement on R : n -tuples agree on n -ary R iff either both orneither exemplify R .)

This completes the first step in the definition of strong superveni-

ence for classes A and B that may include relations. The second stepis predictable: sequences and ' are A-indiscernible iff they are R -indiscernible for every R A. The third step, defining strong supervenience, is again familiar.

STRONG SUPERVENIENCE

A strongly supervenes on B iff any two B-indiscernible sequencesand ' are also A-indiscernible.

This explication of a concept of strong supervenience that applies torelations has a number of welcome features. First, it is a proper gen-eralization of the familiar explication of strong supervenience, whichit entails as a special case. Second, it equips the defined concept withthe formal features that we expect a concept of supervenience tohave. Third, it yields the welcome verdict that relations strongly su-pervene on their converses, and vice versa. Fourth, it classifies para-digm cases correctly. Fifth, it is discriminatory, avoiding the conse-

quence that the non-contingent supervenes on everything.I shall elaborate on these five features in turn.

Generalization. The biconditional standardly used to define strong su-pervenience for monadic A and B is entailed as a special case. Sup-pose that there are pairs x , w and x' , w'

that are B-indiscernible but A-discernible according to the standard definition, for some A and B that have only monadic members. Then the two sequences which

12 A generalization to deal with relations with infinitely many relata will notbe given here, and neither will a generalization to relations whose relata donot belong to any one particular world (transworld fusions, for example).




respectively have those pairs in all places are likewise B-indiscerniblebut A-discernible, and hence A fails to strongly supervene on B ac-

cording to the above definition. For the other direction, suppose nowthat A does not strongly supervene on B according to the above def-inition. Then there are B-indiscernible sequences and ' that are A-discernible. Since A has only monadic members, there is some F A and a natural number i such that i

and i

' do not agree on F . Itfollows that the pairs i and ' i are B-indiscernible but A-discernibleaccording to the standard definition.

Formal features. It turns out that strong supervenience has many for-mal features that we normally want supervenience to have: it is transi-tive, monotonic (if A strongly supervenes on B and B is a subclass ofB' then A strongly supervenes on B' ) and accumulative (if A and A' both strongly supervene on B, then so does the union of A and A' ). All these results are immediate from the above definition and the factthat A-indiscernibility is an equivalence relation for every A. We alsoobtain the result that any relation strongly supervenes on its nega-tion.13

Converses. The fact about negations just mentioned is familiar fromthe case of properties. But there are also specific consequences forrelations. Notably, it turns out that every binary relation strongly su-pervenes on its converse.14 This is a welcome result, since it has longbeen recognized that relations and their converses are intimately re-lated. Indeed, it has been argued that this intimate relation is identity(Williamson 1985). In this case as in many others, we could consider a

supervenience claim as a fall-back position if the corresponding iden-

13 Strictly speaking, this is a result about the corresponding unit classes. Iomit the phrase ‘the unit class of’ when there is no danger of confusion. Infact, something slightly stronger holds: replacing some or all members of A and B with their negations never changes the truth-value of the superveni-ence claim.14

Proof: Suppose and ' are R ˘ -discernible, where R

˘ is the converse of

R . Then for some pair = 1 , 2 , and ' do not agree on R ˘ . It followsthat if ' = 2 , 1 , '

and '

' do not agree on R , and hence and ' areR -indiscernible as well.



310 LEUENBERGER

tity claim turned out to be untenable. The result about converses ex-tends straightforwardly to any permutation of a relation.15

Paradigms. In section 1, we encountered the relation of being taller than as a paradigm of a relation that is intuitively reducible to monadicproperties. We can now verify that according to the above definition,that relation does indeed supervene on the class of height propertiesB. For suppose that and ' are B-indiscernible. Then for any i andany H B, i has H (i.e. the first member of i has H in the world which is the second member of i ) just in case ' i has H . Let = j, k

be any 2-selector. We distinguish three jointly exhaustive cases, andshow that in each of them, j is taller than k iff ' j is taller than ' k.Case (i): j is taller than k. Then these elements have height proper-ties, say H 1 and H 2 respectively, such that everything with H 1 is tallerthan anything with H 2 . Due to the B- indiscernibility of and ' , ' j also has H 1 and ' k also has H 2 . It then follows that ' j is taller than

' k. Case (ii): j and k both have heights, but the former is not tallerthan the latter. By reasoning parallel to that in case (i), we can show

that ' j is not taller than ' k Case (iii): at least one of j and k doesnot have a height, such that it is not the case that j is taller than k.Due to the B-indiscernibility of and ' , one of ' j and ' k alsolacks a height, and hence it is not the case that ' j is taller than ' k.

Discrimination. It is often claimed that relations of supervenience failto make discriminations in the realm of the non-contingent, sinceeverything non-contingent trivially supervenes. Such claims are in

need of qualification. It is true that necessarily universal relations andnecessarily empty relations supervene on all classes. But not all intui-tively non-contingent relations do. There is a good sense in which therelation of identity is non-contingent, according to orthodoxy: if x = y is true, it is necessarily true, and if it is false, it is necessarily false.

15 Kit Fine (2000) argued that there are neutral relations, which lack a direc-tion or sense, and explored so-called ‘positionalist’ and ‘anti-positionalist’

accounts of them. Relations that have converses distinct from them are ‘b i-ased’, in his terminology. The account of supervenience given here appliesto biased relations. I shall not discuss whether and how it could be adaptedto apply to neutral ones.




However, identity does not trivially supervene. For let be the se-quence with Socrates, @ in all places, and ' the sequence that is

like in all places except the first, where it has Plato, @ . Thenand ' are discernible with respect to identity, but indiscernible withrespect to the universal relation. Hence identity does not stronglysupervene on the universal relation.16

4. Internal Relations

In the first section, I suggested that a notion of supervenience that

applies to relations may be of help in formulating broadly reduction-ist theses about relations – theses that have at least a fighting chanceof being true for important classes of relations, unlike monadism,monism, and monadicism. After having defined such a notion of su-pervenience, I will now explore such an application.

The words ‘internal’ and ‘external’ have notoriously been used tomark various different distinctions among relations. Some of them were prominent in debates between British idealists and their oppo-

nents.17 More recently, one such distinction has been revived by Da- vid Lewis. Relations that are internal in his sense may be consideredas those that are reducible to monadic properties. Here, I will focuson his account. For ease of exposition, I will follow Lewis in assum-ing that individuals are world-bound.

In his analysis of internality, Lewis helps himself to the notion of anintrinsic property – roughly speaking, a property that a thing has in virtue of how it is in itself. Intuitively, internal relations are those that

are particularly intimately bound up with intrinsic properties. Again,our paradigmatic example is being taller than : whether one thing bearsthat relation to another is entirely a matter of how these things areintrinsically. In contrast, being two meters apart and having a common friend are not internal, since whether one thing bears them to another is notjust a matter of the intrinsic properties of the two things.

16 The proposal for defining strong supervenience among classes of rela-

tions in Leuenberger 2008b has the first four of these features, but is lessdiscriminating: it entails that identity strongly supervenes on every class ofrelations. For this reason, the present proposal now seems to me superior.17 For a survey of ten different distinctions, see Ewing 1934, 117−42.



312 LEUENBERGER

According to Lewis (1986, 62), an internal relation ‘is one that supervenes on the intrinsic properties of its relata ’. Prima facie, there is

more than one way to cash this out precisely. Two different analysan-da can be distinguished: first, the notion of an internal relation; andsecond, the notion of a relation being internal to given relata. Thisdistinction is analogous to the one that Humberstone (1996) drewbetween global intrinsicality – a property of properties – and localintrinsicality – a relation between a particular and a property. (Theselabels should not be taken to suggest an interesting connection to thecontrast between local and global supervenience.) If R is any dyadic

relation, and I the class of (globally) intrinsic properties, we obtainthe following biconditionals:

R is globally internal iff for all x , y , x' and y' , if x and x' are I -indiscernible and y and y' are I -indiscernible, then Rxy iff Rx'y' .

R is locally internal to x and y iff for all x' and y' , if x and x' are I -indiscernible and y and y ' are I -indiscernible, then Rx'y' .

It is a consequence of these definitions that a relation is globally in-

ternal iff it is locally internal to all x and y that are related by it.18 However, a relation may be locally internal to some things but not toothers, and hence not globally internal. Let R be any contingentlyexemplified globally internal relation. Presumably, the relation of be-ing twice as massive is as good a candidate as any. Consider the rela-tion R' that holds between worldmates x and y if R is exemplified inthe world that they inhabit. Then R' is locally internal to any worldmates that stand in R , but is not globally intrinsic, presumably:

two things may stand in R in one world, while their intrinsic dupli-cates in another world do not. To be sure, this example is contrived.But there may be more natural ones as well. One could argue that therelation of representation holds in some cases in virtue of resem-blance in intrinsic matters, and in other cases in virtue of a causal

18 The left-to-right direction is straightforward to verify. For the right-to-left direction, suppose that R is not globally internal. Then there are x , y , x' ,

and y' such that x and x' are I -indiscernible and y and y' are l -indiscernibleand yet Rxy but not R x'y' . Then x and y are related by R , but R is not locallyinternal to them.




relationship. Since resemblance is internal, representation may be lo-cally internal to cases of the first sort, but not globally internal. Fur-

ther, consider the relation that holds between x and y iff x is disposedto open y if x is turned. That relation is locally internal to some keyand some door, perhaps, and may hold between some switch andsome door without being locally internal to them.

In the rest of this section, I will only discuss global internality, and will drop the qualifier ‘global’. Internality, as characterized above, canbe captured in a simple way using the notion of strong supervenienceformally defined in section 3. The first of the above biconditionals is

equivalent to the claim that a dyadic relation R is globally internal iffR supervenes on I .19 Moreover, this account of global internality canbe straightforwardly generalized from dyadic ones to relations of anyfinite adicity: a relation is globally internal iff it supervenes on theclass of intrinsic properties.20

Is this account of internal relations plausible? One might suspect thatit will be vulnerable to a number of standard objections to explica-tions in terms of supervenience.

First, all relations that relate universally come out as internal. Suppos-ing that arithmetical facts are necessary, the relation R that holds be-

19 This is established by showing that the supervenience of R on I is equiv-alent to the claim that for all x , y , x' , y' , if x and x' are I -indiscernible and x' and y' are -indiscernible, then Rxy iff Rx'y' .Left-to-right: To show the contrapositive, suppose that there are x , y , x' , y'

such that x and x' , and y and y' , are respectively I -indiscernible, but Rxy andnot Rx'y' . Let ' be the sequence starting with x followed by y in all otherplaces, and ' the sequence with x' in the first and y' in all other places. Then

and ' are I -indiscernible but R -discernible, and hence R does not supervene on I .Right-to-left: Suppose that R does not supervene on I . Then there are de-numerable sequences and ' that are I -indiscernible but not R -indiscernible, and there is a 2-selector = 1 , 2 such that it is not the casethat =

1

,2

exemplifies R iff ' = '

1

, '

2

exemplifies R . Since1

is I -indiscernible from ' 1

and2 is I -indiscernible from '

2 , the claim on

the right-hand side is false as well.20 Leuenberger (2008b) touches on this point briefly.



314 LEUENBERGER

tween x and y just in case x is such that there are infinitely manyprime numbers supervenes on every class of properties or relations,

and is thus internal according to the proposal. Prima facie, it mightnot seem internal. Second, internality comes out as intensional ratherthan hyperintensional. As a consequence, a dyadic relation R' is inter-nal just in case R R' is, where R is universal. Again, intuitions maydisagree, wishing to classify R and R R' differently. Third, the ac-count does not guarantee a certain asymmetry – in this case, betweeninternal relations and intrinsic properties. For the supervenience ofinternal relations on intrinsic properties is compatible with the super-

venience of intrinsic properties on internal relations.I will not discuss the first two objections, since the relevant consider-ations seem to be the same as in the discussion of broadly modalaccounts of intrinsic properties. The third objection merits separatediscussion here, though. We should note that not only is there noguarantee of asymmetry, but indeed a guarantee of symmetry, underthe assumption that relations are relatively abundant: intrinsic proper-ties supervene on internal relations, as well as the other way round. In

the case of dyadic relations, the required assumption of relativeabundance is that for any intrinsic property F , there exists a relationR that x bears to y iff both x and y are F .21

Why is the lack of asymmetry of supervenience thought to be objec-tionable? Some authors have tried to press supervenience into servicefor explicating relations such as metaphysical explanation, or ground-ing, or metaphysical priority. Such attempts have met with criticism.For present purposes, we need not settle the question whether its lackof asymmetry disqualifies supervenience from deployment in expli-cating those relations. What matters here is that some uses of supervenience do not require it to be asymmetric. To me, the present oneseems to be among them.

The thesis that a given relation is internal may be accompanied by theclaim that its holding is metaphysically explained, or grounded, by

21 To show that every intrinsic property supervenes on dyadic internal rela-tions, suppose that H is any intrinsic property. Let R hold between x and y just in case both x and y have H . It is easy to verify that R supervenes on H ,and is thus internal. Likewise, it is easy to verify that H supervenes on R .




intrinsic features of the relata. For example, Bernard Bosanquet(1911, 277) takes it to be characteristic of internal relations that they

are grounded in the relata (albeit by their nature rather than their in-trinsic properties): he has a discussion of ‘what have been called “in-ternal relations”, i.e. relations grounded in the nature of the relatedterms’. Moreover, it would arguably be in the spirit of David Lewis’metaphysical system to say that internal relations hold in virtue of theexemplification of some more natural intrinsic properties. Nonethe-less, internality need not involve grounding by the intrinsic propertiesor the nature of the relata. The notion characterized here is available

even to philosophers who are sceptical of the intelligibility of talkabout grounding, or those who wish to remain neutral about the di-rection of explanation in that particular case. More interestingly, it isavailable to philosophers who take the intrinsic features of the relatato be metaphysically explained, or grounded, by the holding of theinternal relation. Such a thesis may be in the spirit of certain structur-alist or structural realist views – although I am not aware that theterm ‘internal relations’ is used in the pertinent literature. Possibly,such a thesis can even be found in the idealist tradition, which madeextensive use of the term. At any rate, some formulations do suggestit. As Ewing (1934, 130) puts it in his survey of that tradition, ‘aninternal relation is often described as a relation which “makes a dif-ference to” its terms’. On one reading of that phrase, it entails thatthe relata have their intrinsic nature at least partly in virtue of the factthat the relation holds between them. Such a claim would be compat-ible with the supervenience of the relation on intrinsic properties.Perhaps the holding of the relation modifies the relata in such a way

that they are intrinsically different from any entities not standing inthe relation. If so, the relation supervenes on the intrinsic properties.

In light of this, it seems to me that the third of the above objectionscan be answered: there is at least one useful notion of internality which does not require an asymmetry between intrinsic propertiesand internal relations, and it is a virtue of the explication that it failsto entail asymmetry. I conclude that an analysis of internality in termsof supervenience has promise.



316 LEUENBERGER

5. External Relations

Even if we suppose that internal relations are those that superveneon intrinsic properties, there remains the question what external rela-tions are. Intuitively, external relations are those whose exemplifica-tion is not a matter of how the relata are intrinsically. A first stab would be to say that a relation is external iff it is not internal. How-ever, this may be too liberal, since it allows relations with internalconjuncts or disjuncts to be external. A second stab is due to Lewis:external relations are those that are not internal but still intrinsic ra-ther than extrinsic. What, then, are intrinsic relations? The concept of

intrinsicality, familiar in the domain of properties, can be applied torelations too. Intuitively, a dyadic relation is intrinsic if it such that whenever x bears it to y , it does so in virtue of how things stand withrespect to x and y , independently of how the rest of the world is; andmutatis mutandis whenever x does not bear it to y . There is no needto discuss the concept of an intrinsic relation in detail here. For ourpurposes, it is enough to assume that the class of intrinsic relationsincludes all internal ones, and is closed under supervenience.

Paradigmatic examples of external relations are spatial ones, such asbeing two meters apart, as well as temporal and spatiotemporalones —at least as these relations are typically conceived of by meta-physicians.22 What is distinctive of such relations is that they are in-dependent of the intrinsic nature of the relata: the masses and charg-es of two point particles neither metaphysically necessitate nor pre-clude any particular distance between them. It is natural to take thisas a general account of external relations: they are those that are in-

dependent of the intrinsic properties. This would be consistent withhow earlier authors conceived of external relations. For example, Taylor (1903, 141) seems to have an independence account in mind when he asks ‘whether there are or are not merely external relations(i.e. relations which are independent of the special qualities of theirterms)’.

22 Bricker (1993) contends that this conception is wrong. He draws on theGeneral Theory of Relativity to argue that actual spatiotemporal relationsare extrinsic, not external.




When Lewis defined external relations as those that are intrinsic butnot internal, he did so in a context in which it was dialectically useful

for him to have internality, externality and extrinsicality to come outtrichotomous. However, if we follow him in taking every intrinsicrelation to be either internal or external, we fail to do justice to theidea that external relations are independent of intrinsic properties. IfR is internal and R' any other relation, then neither their conjunctionnor their disjunction enjoy such independence. However, if R is in-ternal and R' external in Lewis’ sense—weakly external , from nowon —then either their conjunction or their disjunction is also weakly

external.23

There is a more demanding sense of externality such that certainconjunctions or disjunctions of an internal and an external relationcome out as neither internal nor external, since they are not suitablyindependent from intrinsic properties.24 However, it turns out thatsuch a demanding notion of externality cannot be defined in termsof supervenience. Full independence implies lack of supervenience,but lack of supervenience does not imply full independence. Howev-

er, it can be defined from the same conceptual tools that have beenused to define supervenience. Lewis (1998, 117) introduced a notionof orthogonality of subject matters: ‘Two subject matters M 1 and M 2 are orthogonal iff, roughly, any way for M 1 to be is compatible with any way for M 2 to be.’ Orthogonal subject matters are independent ofeach other. We can define a notion of orthogonality that stands tostrong supervenience like Lewis’ orthogonality stands to global su-pervenience. Say that n -ary R and m -ary R' are orthogonal iff for any

sequences and ' , there is a sequence '' that is R -indiscernible23 Both R R' and R R' are intrinsic: they supervene on the intrinsic R and R' , and the class of intrinsic relations is closed under supervenience.Moreover, at least one of R R' and R R' fails to be internal. For reduc-tio, suppose they are. Then R , R R' and R R' are all internal. Since R' iscointensional with a truth-functional combination of those three relations, itsupervenes on the class consisting of them. Using the closure of internalrelations under supervenience, we can conclude that R' is also internal, con-

trary to the assumption that it is weakly external.24 There is a precedent for this in the analogous case of intrinsic proper-ties: Lewis (1999) was happy to allow for properties which are neither intrin-sic nor extrinsic, but intermediate.



318 LEUENBERGER

from and R' -indiscernible from ' . If R and R' are orthogonal, any way to be with respect to R is compatible with any way to be with

respect to R' . The following definition of strong externality then sug-gests itself: R is strongly external iff it is orthogonal to the class of in-trinsic properties.25

Since any intrinsic relation is either internal or weakly external, it istrivially the case that any intrinsic relation supervenes on the internaland the weakly external relations together. However, it is a substan-tive metaphysical question whether any intrinsic relation supervenes – strongly or even only globally – on the internal and the strongly ex-ternal relations together. It is conceivable, after all, that there are weakly external but no strongly external relations. Imagine that dis-tance relations are intrinsic, but constrained with metaphysical neces-sity by some intrinsic property of the relata. Perhaps very massivepoint-particles cannot be very close to each other. If so, distance rela-tions are not strongly external. Since they are generally taken to be aprime candidate, we may doubt whether there are any strongly exter-nal relations. Furthermore, some philosophers might think that being

abstract is an intrinsic property, and that abstract objects cannot standin spatial relations.26

If we take some relations to be uncontroversially external, we maythink that the above analysis undergenerates. However, there is an-other respect in which it might be thought to overgenerate: it entailsthat if R' supervenes on a strongly external R , then R' is likewise

25 Given this formal explication of independence in hand, we can nowprove that independence is not definable from supervenience, by describingtwo models M 1 and M 2 that agree on all supervenience claims but not on allorthogonality claims. In M 1, a has F and G, b has F but not G, and c has G but not F . M 2 is just like M 1, except that there is an additional element d thathas neither F nor G. It is easy to verify that in both models, {F } fails to su-pervene on {G}, and {G} fails to supervene on {F }. It follows that themodels agree on all supervenience claims. However, {F } and {G} are or-

thogonal only in M 2, but not in M 1.26 To be sure, metaphysicians with Humean inclinations will be disposed todismiss such scenarios, on the grounds that they involve a brute necessaryconnection. But Humeanism is itself a substantive metaphysical claim.




strongly external.27 For if and ' are any sequences, then the strongexternality of R guarantees that there exists a sequence '' that is R -

indiscernible from and I -indiscernible from ' . Since R' superveneson R , '' is also R' -indiscernible from , and thus also orthogonal toI . As a consequence, relations that supervene on any relation turn outto be strongly external as well as internal. Surprisingly, then, the clas-ses of internal and of strongly external relations are not disjoint.Moreover, the proposal may yield intuitively questionable results forsome relations that hold between more than two things. Considerequidistance, i.e. the relation R that holds between x , y , and z iff the

distance between x and z is equal to the distance between y and z .Since equidistance supervenes on distance, it is strongly external ifdistance is. However, there is a sense in which that three-place rela-tion is not fully external – it is determined by intrinsic relations hold-ing between some but not all of its relata. For that reason, we maydefine a relation of adicity n +1 as purely external iff it is orthogonal toall intrinsic properties and relations of adicity at most n .

I will not try to settle the question whether external relations are ade-quately analysed in terms of orthogonality and intrinsicality. Howev-er, I hope to have made it plausible that both supervenience and therelated concept of orthogonality can fruitfully be applied to rela-tions.28

References

Bosanquet, B. 1911: Logic, or the Morphology of Knowledge . Vol. II. 2ndedition. Oxford: Clarendon Press.

27 This is not to say that the class of strongly external relations is closedunder supervenience. Supervenience on a more than one-membered class ofstrongly external relations does not guarantee strong externality. Perhaps acertain profile of intrinsic properties is compatible with two things being atany spatial distance from each other, and compatible with them being at anytemporal distance from each other, but incompatible with them having acertain spatial distance and a certain temporal distance together.28 Many thanks to the editors for their helpful comments on an earlier ver-sion. I also benefitted from the discussion at the workshop ‘Grounding andModality’ at the University of Glasgo w, and would like to thank its partici-pants.



320 LEUENBERGER

Bricker, P. 1993: ‘The Fabric of Space: Intrinsic vs. Extrinsic DistanceRelations’. Midwest Studies in Philosophy 18, pp. 271−94.

Ewing, A. C. 1934: Idealism. A Critical Survey . London: Methuen & CoLtd.

Fine, K. 2000: ‘Neutral Relations’. The Philosophical Review 109, pp.1−33.

Humberstone, L. 1984: ‘Monadic Representability of Certain BinaryRelations’. Bulletin of the Australasian Mathematical Society 29, pp.365−75.

— 1996: ‘Intrinsic/Extrinsic’. Synthèse 108, pp. 205−67. Kim, J. 1993: ‘Postscripts on Supervenience’. In Supervenience and Mind.

Selected Philosophical Essays. Cambridge: Cambridge UniversityPress, pp. 161−71.

Leuenberger, S. 2008b: ‘Supervenience in Metaphysics’. PhilosophyCompass 3, pp. 749−62.

— 2009: ‘What is Global Supervenience?’. Synthèse 170, pp. 115−29.

Lewis, D. 1999: ‘Extrinsic Properties’. In his Papers in Metaphysics and Epistemology. Cambridge: Cambridge University Press, pp. 111−15.Originally published in Philosophical Studies 44, pp. 197−200.

— 1986: On the Plurality of Worlds. Oxford: Blackwell.

— 1998: ‘Relevant Implication’. In his Papers in Philosophical Logic. Cambridge: Cambridge University Press, pp. 111−24. Originallypublished in Theoria 54, pp. 161−74.

Mates, B. 1986: The Philosophy of Leibniz. Metaphysics and Language. Ox-ford: Oxford University Press.

Muirhead, J. H. 1924: Contemporary British Philosophy. London: Allenand Unwin.

Russell, B. 1903: The Principles of Mathematics. Cambridge: CambridgeUniversity Press.

— 1912: The Problems of Philosophy. London: Williams & Norgate.

— 1924: ‘Logical Atomism’. In Muirhead 1924, pp. 356−83. Shagrir, O. 2009: ‘Strong Global Supervenience is Valuable’. Erkennt- nis 71, pp. 417−23.




Taylor, A. E. 1903: Elements of Metaphysics. London: Methuen & Co.Ltd.

Williamson, T. 1985: ‘Converse Relations’. The Philosophical Review 94,pp. 249−62.



Multiple-Domain Supervenience for Non-Classical Mereologies

Ralf M. Bader

1. Introduction The properties of complex entities generally stand in determinationand dependence relations to the properties of the components from which they are made up.1 This plausibly holds for material objectsand the parts that compose them, for states of affairs and their con-stituents, for structural universals and the simple universals from which they are combined, for sets and their members, as well as forother complex entities, such as propositions, facts and properties.

The relations that hold between these complexes and their constitu-ents can be considered as falling under the category of parthood rela-tions and can be characterised by means of different mereologicalsystems, whereby many of these complex entities require non-classical mereological systems since they have much more structurethan classical extensional mereology can capture.2 The determination

1 Which direction the determination and dependence relations go may

well differ. Supervenience relations will be provided both for cases in whichthe direction of determination coincides with the direction of compositionand for cases in which it coincides with the direction of decomposition (cf.section 4).2 Those who are uncomfortable with such a liberal notion of parthoodcan reinterpret the claims about parthood relations as claims about constitu-tion, combination or concatenation relations. For the purposes of this papernothing hangs on whether the different relations connecting complex enti-ties and their constituents are all species of a common genus or whether

they are fundamentally heterogeneous. All that matters is the formal featuresthat characterise these relations and the dependence and determination rela-tions to which they give rise. (For a pluralistic account of parthood that sub-sumes all these cases cf. Fine 2010.)

MULTIPLE-DOMAIN SUPERVENIENCE 323

and dependence relations that hold between properties of complexentities and their constituents can be helpfully modelled by means of

co-ordinated multiple-domain supervenience relations.3 Making mer-eological supervenience claims when dealing with non-classical par-thood relations requires taking into consideration additional featuresabout the ways in which entities are composed. This paper is con-cerned with developing multiple-domain supervenience relations fora number of non-classical parthood relations, allowing us to capturethe determination and dependence relations that hold in non-classicalmereological systems.

2. Classical Mereological Supervenience

2.1 Classical Extensional Mereology

Classical extensional mereology ( CEM ) is structurally identical to acomplete Boolean algebra without the null element. It is characterisedby a number of commitments that are rejected by the non-classicalsystems that we will be considering:

UNIQUENESS OF COMPOSITION CEM is an extensional system insofar as sameness of parts impliessameness of whole, ensuring that any collection of parts can onlycompose a single whole that has all of them as parts:

z ( z << x ↔ z << y ) → x = y .

NON-HIERARCHICAL CEM is a ‘flat’ mereological system. Objects do not have any interest-ing mereological structure. They only differ in terms of the numberand nature of parts of which they are composed, but not in the wayin which they are composed. CEM does not recognise different waysin which parts can compose objects. The resulting mereological hier-archy consists of levels that are specified via the mereological com-plexity of objects, which is determined by the number of parts thatthey have.

3 It is worth keeping in mind that the supervenience apparatus is limited inthat it only allows us to model features concerned with property variation,leaving out important hyperintensional elements involved in determinationand dependence relations that can only be captured by grounding relations.




2.3 R-related Pairs

We can appeal to this co-ordination relation to partition (in the non-technical sense) the members of the subvening and supervening do-mains into R -related ordered pairs, in such a way that the first entryof each pair is a non-empty collection taken from the subvening do-main whilst the second entry is a non-empty collection taken fromthe supervening domain, whereby these collections are connected bythe co-ordination relation. In the case of mereological supervenience,the subvening domain is the domain of parts, the supervening do-main is the domain of wholes and the co-ordination relation is the

composition relation. We then end up with pairs consisting of partsas well as of the wholes that they compose. That is, an R -related pairhas the following structure: xx ’s y

, where the xx ’s are the parts thatcompose y .

We can then say that two pairs xx ’s y and

xx *’s y * are B-indiscernible iff there is a B-preserving mapping from the xx ’s on-to the xx *’s, such that any x that is one of the xx ’s has any B-property

F iff the image of x under also has F .7 Two pairs are A-indiscernible iff y has any A-property G iff y * also has G. Given thesenotions of indiscernibility for pairs, we can use the standard accountsof weak and strong supervenience, i.e. A-properties supervene on B-properties iff:

weak-mds For all worlds w , and all pairs P and P * in w , if P andP * are B-indiscernible in w , then they are A-indiscernible in w .

strong-mds For all worlds w and w *, and all pairs P in w and P * inw *, if P in w and P * in w * are B-indiscernible, then P in w and P * in w * are A-indiscernible.

This account is thus analogous to the single-domain case, with thedifference that in the multiple-domain case we map R -related pairs

7 If the set of B-properties includes irreducibly plural properties, then the

notion of B-indiscernibility must be supplemented by the condition that anysub-plurality of the xx ’s has any plural B-property F iff the image of thesub-plurality under also has F (where the image of a sub-plurality is theplurality of the images of the members of the sub-plurality).



326 BADER

rather than individual objects, where B/ A-indiscernibility of pairs isunderstood in terms of the first/second members of the pairs being

B/ A-indiscernible. Mereological supervenience then holds if R -related pairs consisting of parts and the wholes that they composeare such that if the parts are B-indiscernible then the wholes are A-indiscernible.

2.4 Associated Isomorphisms

The strong version of single-domain global supervenience requiresthat all B-preserving isomorphisms are A-preserving. This criterion

does not make sense when applied to the multiple-domain case since we have different mappings for the subvening domain and for thesupervening domain. As a result, we have to provide criteria as tohow B-preserving mappings of the subvening domain have to be re-lated to A-preserving mappings of the supervening domain if multi-ple-domain supervenience is to hold.

nc-mds For all worlds w and w *, if there is a B-preserving mappingof the members of the subvening domains of w and w *,

then there is an A-preserving mapping of the membersof the supervening domains of w and w *.

This non-co-ordinated version, (nc-mds), is too weak to be of inter-est. We can see this by considering the example of a Cartesian dualist who wants to claim that the mental and the physical constitute twodifferent domains, but that the mental nonetheless supervenes on thephysical. Let us consider a case in which we have two worlds eachconsisting of four objects {a ,b ,c ,d } and {a ,b ,c

,d

}, where c ( c

) is thesoul correlated with a ( a ) and d ( d

) is the soul correlated with b ( b ).In this case, a and a have B-property F 1, b and b have B-property F 2,c and c have A-property G1, and d as well as d have A-property G2.Now, if we map a onto a and b onto b

, then we have ensured thatthe mapping of members of the subvening domain is B-preserving.If we map c onto c and d onto d

, then we also get a mapping of themembers of the supervening domain that is A-preserving. (nc-mds)

consequently holds. Yet, this relation would also hold if c

were to beG2 and d

were to be G1 since we could then map c onto d and d ontoc to get an A-preserving mapping of the members of the superven-




ing domain. Accordingly, we can see that it is too weak, given that adetermination relation should not be compatible with a permutation

of the supervening properties whilst the base properties are beingheld fixed.8

To make substantive supervenience claims, we need to connect thedomains and connect the mappings. We can do this by appealing tothe notion of an associated isomorphism, which uses the co-ordination relation to connect mappings of members of the differentdomains.

ASSOCIATED ISOMORPHISM A one-to-one mapping of members of the supervening domainfrom D S onto D S * counts as an associated isomorphism of a mappingof members of the subvening domain from D B onto D B*, if it isthe case that if any collection of members x 1…x n from D B is mappedonto x 1*…x n* from D B* by , then maps the images of x 1…x n un-der R in D S , i.e. y 1… y n, onto the images of x 1*…x n* under R in D S *,i.e. y 1*… y n*.

This notion allows us to specify a co-ordinated version of global mul-tiple-domain supervenience:

c-mds For all worlds w and w *, every B-preserving mapping ofthe members of the subvening domains of w and w * issuch that the associated mapping of the members of thesupervening domains of w and w * is A-preserving.9

This co-ordinated version is sufficiently strong to capture depend-

ence and determination relations. In particular, we can use this ver-sion to make mereological supervenience claims, i.e. every B-

8 This permutation problem affecting the non-co-ordinated multiple-domain supervenience relation is analogous to the kind of problem affecting weak global supervenience (cf. Bennett, 2004).9 This version of co-ordinated multiple-domain supervenience presuppos-es that there is only one associated mapping of the members of the super-

vening domain, which amounts to presupposing that R always picks out aunique image. This presupposition is satisfied in the case of CEM insofar ascomposition is unique, but as we will see below there are non-classical sys-tems in which it fails to be satisfied.



328 BADER

preserving mapping of parts is such that the associated mapping ofthe wholes that they compose is A-preserving.

3. Non-Classical Mereological Supervenience

Non-classical mereological systems reject various features of CEM.Such systems allow us, for instance, to characterise objects that aretreated as hylomorphic compounds, to make sense of coinciding ob-jects, as well as to describe the mereological makeup of complexstructured entities such as propositions and states of affairs. In orderto make mereological supervenience claims within these systems, we

need to modify the multiple-domain supervenience principles that wehave developed so far. In particular, we need to (i) change the do-mains, (ii) impose restrictions on mappings, (iii) modify the co-ordination relation, and (iv) alter the things that are being mapped.

Non-classical systems that reject extensionality allow for there to bedifferent wholes that are composed of the same parts. This leads tosituations in which the R -relation will not pick out a unique image inthe supervening domain, allowing for failures of standard mereologi-cal supervenience insofar as indiscernibility of parts need not yieldindiscernibility of wholes. We will be considering five kinds of non-extensional mereologies, namely non-hierarchical mereologies thatincorporate (i) order-sensitive composition relations, (ii) repetition-sensitive composition relations, and (iii) many-many composition re-lations, as well as hierarchical mereologies that contain (iv) composi-tion relations that give rise to compositional structure, and (v) hylo-morphic composition relations that combine form and matter.

3.1 Order-Sensitivity

Order-sensitive composition relations allow for there to be objectsthat are composed of the same parts but are nonetheless distinctsince they are composed of these parts in different ways. In particu-lar, the order in which the parts compose the objects can differ. Thiskind of composition can be found when dealing with structured enti-ties, such as structural universals, facts, states of affairs and proposi-

tions. For instance, the states of affairs Rab and Rba both have astheir constituents particulars a and b , as well as a non-symmetric rela-tion R , but are nonetheless distinct states of affairs that have differ-

330 BADER

properties.10 (At least this can happen if the set of A-properties in-cludes properties with respect to which Rab and Rba differ – as long

as the A-properties are restricted to only those properties that areshared by all the wholes composed of the parts in question, e.g.properties shared by Rab and Rba , then mereological supervenience will hold even given the standard supervenience relation that is notorder-sensitive.)

If we impose the constraint that mappings also have to be order-preserving, then the associated mappings of B-preserving isomor-phisms will be A-preserving. There will be no order-preserving map-

ping that is B-preserving yet has an associated mapping that fails tobe A-preserving. This is because there is no order-preserving map-ping from the parts of Rab onto Rba . The difference in the order ofcomposition can thus explain the differences in properties betweenRab and Rba , i.e. even though they are made up of the same partsthere is no failure of supervenience since the differences betweenthem can be explained in terms of the order in which they are com-posed out of the parts that they share. The difference between Rab

and Rba that gives rise to their A-discernibility is the order in whichthe B-indiscernible parts compose these different wholes. In the onecase a whole is composed out of a , b , and R by having them as partsin one order, i.e. [ a > b ] << Rab , while in the other case the whole iscomposed by having them as parts in a different order, i.e. [ b > a ] <<Rba .

3.2 Repetition-Sensitivity

Repetition-sensitive composition relations are not extensional sincethey allow for there to be objects that are composed of the sameparts but that are nonetheless distinct since they are composed ofdifferent numbers of occurrences of these parts. Repetition-sensitiveparthood relations are important when dealing with structural univer-sals, in particular if one wants to specify ratio structures for quanti-ties.11 If one wants to say that the properties of a structural universalare determined by the properties of the simple universals from which

10 This ensures that only (wg-mds) but not (sg-mds) holds (cf. section 3.3).11 For an account of quantities in terms of structural universals cf. Arm-strong 1988.




it is combined, then one has to make a supervenience claim that issensitive to repetitions.

Here it might be suggested that repetitions show up in the decompo-sition and that while there is a sense in which objects can be distincteven though they are made up of the same parts (namely insofar asthere is some level of decomposition at which they have the sameparts), there is another sense in which these objects will be made upof different parts (namely insofar as there will be decompositions ofone object that are such that the other object lacks correspondingdecompositions). There are accordingly two senses of what it means

for objects to be made of the same parts.SAME PARTS 1x and y are made of the same parts if there is some level of decom-position at which they have the same parts. Being made of the sameparts in this sense is compatible with there being some level of de-composition at which the objects are made of different parts.

SAME PARTS 2

x and y are made of the same parts if every decomposition of x has acorresponding decomposition of y , i.e. if there is a bijection fromdecompositions of x onto decompositions of y such that any part p features in any decomposition d of x iff p features in the decomposi-tion of y that is the image of d under . Being made of the sameparts in this sense is clearly not compatible with there being somelevel of decomposition at which the objects are made of differentparts.

When one is dealing with cases in which objects are made up of thesame parts only in the former but not the latter sense, then the repeti-tion shows up in the decompositions.

E.g., the universals being-3-grams and being-2-grams are both com-posed of the universal being-1-gram , though they are composedof different numbers of occurrences of this universal, i.e. being- 3-grams can be decomposed into three occurrences of the universal being-1-gram while being-2-grams can be decomposed intotwo occurrences of the universal being-1-gram . Yet, there exists adecomposition of being-3-grams into being-2-grams and being-1-gram ,



332 BADER

though there is no analogous decomposition for the universal being-2-grams .

The fact that repetitions can show up in this way can be used whenmaking supervenience claims, i.e. one can specify the mereologicalsupervenience principle such that if x and y are made of B-indiscernible parts at all levels of decomposition, then x and y are A-indiscernible. More precisely, if the decompositions of x and y can beput into one-to-one correspondence whereby there will be B-preserving mappings between the corresponding decompositions,then x and y will be A-indiscernible.

This proposal faces the problem of providing an account as to howdecomposition is to be understood. In particular, it seems that oneneeds to appeal to non-classical decomposition principles specified interms of occurrences since the standard account of a complete de-composition (according to which the xx ’s are a collection of non-overlapping parts of y that are such that there is no z that is a part of y but that does not overlap the xx ’s) is not applicable to these cases. Yet, once one needs to bring in occurrences for making sense of thedecomposition principles one can also appeal to occurrences to di-rectly specify repetition-sensitive supervenience principles.

However, it is sometimes possible to specify mereological principlesindirectly by mapping objects standing in non-classical parthood rela-tions onto suitably related entities that have a classical mereologicalstructure. For instance, when dealing with structural universals we canappeal to the classical mereological structure of their instances to

specify decomposition principles for the universals, rather than hav-ing to appeal to non-classical decomposition principles for the prop-erty parts that are the constituents of these universals. This is possi-ble in the case of structural universals because the parts that com-pose the structural universal are instantiated by the parts of the ob-jects that instantiate the structural universal.

E.g., a structural universal F can be completely decomposed intooccurrences of universals G1…Gn iff every x instantiating F has

a complete decomposition into parts p1… pn, where (i) each part pi instantiates exactly one of the universals that occurs inG1…Gn, and where (ii) there is a bijection from parts p1… pn

onto the occurrences of universals G1…Gn such that any part pi instantiates universal Gi iff the image of pi under is an occur-

rence of Gi. While certain forms of repetition-sensitive composition relations canbe accounted for in this way, there seem to be cases where a differentapproach is required. In particular, if one is dealing with a restrictedrepetition-sensitive mereology which holds that it is not possible tofuse fusions but only to fuse simples, then there will only be one levelof decomposition consisting of decompositions into occurrences ofsimples, ensuring that all wholes that are made of the same parts willdiffer only in the number of occurrences and will not differ in termsof intermediate levels of decomposition since no such levels exist.

E.g., if we only have one simple, namely x, then the ontology will consist of: x , fu ( x ,x ), fu ( x ,x ,x ), fu ( x ,x ,x ,x ) etc. However, theontology will not include fu ( x , fu ( x ,x )) etc. Every whole will ac-cordingly have a unique decomposition consisting of a numberof occurrences of x .

In such cases repetitions will not show up unless one distinguishesdifferent occurrences of the same parts. Accordingly, one cannotsimply impose the condition that every decomposition must have acorresponding B-indiscernible decomposition if wholes are to be A-indiscernible. Instead, one must specify mappings that preserve oc-currences.

When dealing with repetition-sensitive composition, the subveningdomain cannot be understood as a set but must instead be conceived

of as a multi-set.12 Property-preserving mappings then have to pre-serve occurrences of parts. There must be a bijection between theoccurrences of parts whereby any occurrence of x that is one of the

12 It should be noted that only the subvening domain has to be a multi-set. As in the case of order-sensitive composition, a modified uniqueness claimholds for repetition-sensitive composition (<<n represents the number ofoccurrences of a part in a whole in an analogous way that the number of

occurrences of a member in a multi-set are represented by n ):z ( z <<n x ↔ z <<n y ) → x = y .

This uniqueness principle ensures that we only have repetitions in the subvening domain and not in the supervening domain.



334 BADER

xx ’s is mapped onto an occurrence of the image of x under . Putdifferently, for every x that is one of the xx ’s, each occurrence x i of x

has an image, namely x i*, that is an occurrence of the image of x ,namely of x *.

3.3 Many-Many Composition

Coincident objects are distinct yet made up of the same parts (atsome level of decomposition). There are two ways of understandingcases of coincidence. On the one hand, coinciding objects can beconceived of as structured entities that have a formal component that

distinguishes them and explains their distinctness. Such hylomorphicaccounts of composition will be considered in section 3.4 below. Onthe other hand, they can be understood as unstructured entities thatresult from many-many composition relations. It is this latter account,on which coinciding objects are composed of the same parts and on which composition lacks hylomorphic or compositional structure andis neither order-sensitive nor repetition-sensitive, that is at issuehere.13

Cases of coincidence arise if the xx ’s compose a plurality of yy ’s. These cases can be modelled either by having a unique many-manyco-ordination relation or by having a non-unique many-one co-ordination relation. In the former case, the composition relation con-nects a plurality of parts to a plurality of composite wholes. We thenhave R -related pairs that are such that both members of the pairs arepluralities, i.e. xx ’s yy ’s . In the latter case, the composition relationconnects a plurality of parts to individual composite objects but fails

to be unique, which means that the same plurality in the subveningdomain can have multiple images under R in the supervening domain. We then have a plurality of R -related pairs that are such that it is onlythe first member of any pair that is a plurality, but this plurality ofparts can be the first member of different pairs, i.e. xx ’s y 1 …xx ’s y n . Strong supervenience principles for coinciding objects can

be devised by adopting the former option, modelling many-manycomposition relations by means of many-many co-ordination rela-

13 For a more detailed account of the considerations presented in this sec-tion, as well as for a discussion of the philosophical ramifications and un-derpinnings, cf. Bader manuscript.




tions rather than understanding R as a many-one relation that fails topick out a unique image in the supervening domain. That way one

will get a unique image, namely the plurality of objects composed bythe parts.14

R -related pairs xx ’s yy ’s and xx *’s yy *’s that are co-ordinated by amany-many composition relation are B-indiscernible iff there is a B-preserving mapping from the xx ’s onto the xx *’s, such that any xthat is one of the xx ’s has any B-property F iff the image of x under

also has F , while they are A-indiscernible iff there is an A-

preserving mapping from the yy ’s onto the yy *

’s, such that any y thatis one of the y ’s has any A-property G iff the image of y underalso has G. Given this understanding of mereological supervenience,the properties of coinciding objects will supervene on the propertiesof their parts. Both (weak-mds) and (strong-mds) will hold if a many-many co-ordination is used to pick out the members of the R -relatedpairs.

Analogous results can be established when appealing to associated

isomorphisms to devise global multiple-domain supervenience rela-tions. We can note that the co-ordinated global version (c-mds) that was defined earlier presupposes that R picks out a unique image inthe supervening domain. This presupposition is met in CEM since thecommitment to the uniqueness of composition that is integral toclassical mereology ensures that the composition relation always picksout a unique image. Yet, when we are dealing with non-extensionalmereologies, a collection of members of the subvening domain can

have multiple images under R in the supervening domain. In suchcases we can distinguish two kinds of global multiple-domain supervenience relations.

wg-mds For all worlds w and w *, every B-preserving mapping ofthe members of the subvening domains of w and w * hasan associated A-preserving mapping of the members ofthe supervening domains of w and w *.

14 When dealing with accounts of coinciding objects that allow for mutualparthood, the subvening domain, i.e. the domain of parts, should be re-stricted to include only parts that satisfy the weak supplementation principle.(Thanks to Gabriel Uzquiano on this point.)



336 BADER

sg-mds For all worlds w and w *, every B-preserving mapping ofthe members of the subvening domains of w and w * is

such that all its associated mappings of the members ofthe supervening domains of w and w * are A-preserving.

These co-ordinated versions differ only if the co-ordination relationfails to be unique, i.e. if x 1…x n has a plurality of images under R inthe supervening domain. In such cases, a particular mapping of thesubvening domain will have a plurality of associated mappings, allow-ing us to distinguish between a weak version of multiple-domain su-pervenience that requires only that one of these associated mappings

be A-preserving and a strong version that requires that all of them be A-preserving.15

When dealing with coinciding objects, (wg-mds) will hold but (sg-mds) will fail if a many-one co-ordination relation is used. Yet, whenappealing to a many-many co-ordination relation both (wg-mds) and(sg-mds) will hold.

3.4 Hierarchical Mereologies

Wholes in CEM only differ in terms of the parts of which they arecomposed, but do not differ in terms of the ways in which they arecomposed. This means that classical mereology does not recogniseany interesting mereological structure. Hierarchical mereologies, bycontrast, allow for there to be different ways in which parts can com-pose wholes. In such cases, properties of wholes do not superveneon properties of parts considered by themselves, but on the proper-ties of the parts together with the manner of composition, i.e. theproperties of wholes are determined by the properties of parts to-gether with their mereological structure. There are two ways of con-ceiving of mereological structure.

COMPOSITIONAL STRUCTURE Wholes can have internal structure that results from the way in whichthey are composed out of their parts. Different wholes can be com-

15 The distinction between the three kinds of global multiple-domain su-pervenience relations, namely non-co-ordinated (nc-mds), weak co-ordinated(wg-mds) and strong co-ordinated (sg-mds), corresponds to that between weak, intermediate and strong global single-domain supervenience.




posed of the same parts due to the way that the parts are structured,due to the way in which they go together to compose the different

wholes.16 For instance, if one rejects the principle that fusing some-thing with a fusion is identical to fusing that thing with the parts ofthe fusion, then one can have four different wholes composed of x , y , and z since fu ( x , y ,z ) fu ( x , fu ( y ,z )) fu ( y , fu ( x ,z )) fu ( z , fu ( x , y )).17

HYLOMORPHIC STRUCTURE Hylomorphic compounds have structure that derives from their for-mal elements, allowing for wholes to differ in the way that form andmatter are combined in composition.18 We can represent a hylomor-phic compound of material parts x 1…x n and form F as fu ( x 1…x n F ). We can then have different wholes that are composed of the samematerial parts but have different formal components, e.g. fu ( x 1…x n F )

fu ( x 1…x n G ). Moreover, we can have different wholes that arecomposed of the same material parts and that have the same formalcomponents but that are such that the form binds the matter in dif-ferent ways, e.g. fu ( fu ( x 1…x i F ), fu ( x j…x n G ) H ) fu ( fu ( x 1…x i G ),

fu ( x j…x n F ) H ). In such a case we have distinct wholes, even thoughthe wholes have the same material parts, namely x 1… x n, as well asthe same formal components, namely F , G, and H , since they differin the ways in which form binds matter. That is, there are different ways of composing wholes out of parts resulting from differentform-matter combinations.

Compositional structure can be accounted for in a relatively straight-forward manner when making mereological supervenience claims. All

that needs to be done is to restrict the co-ordination relation R to therelation of immediate composition, thereby ensuring that any collec-

16 It should be noted that the compositional order at issue here is distinctfrom the order of constituents that is at issue when dealing with order-sensitive composition. These two forms of non-extensional compositioncan be combined as well as kept separate.17 If supplementation principles are rejected as well, then one can get a

significant further increase in the number of ways in which objects can becomposed since in that case x fu ( x ) fu ( fu ( x )) etc.18 For contemporary hylomorphic accounts cf. Fine 1999, Johnston 2006,Koslicki 2008.



338 BADER

tion of parts has a unique image under R in the supervening domain.For instance, even though fu ( x , fu ( y ,z )) and fu ( y , fu ( x ,z )) have the same

mediate parts, namely x , y and z , they have different immediate parts,the former being immediately composed of x and fu ( y ,z ), while thelatter is immediately composed of y and fu ( x ,z ).19

The strategy of restricting the co-ordination relation to the relationof immediate composition runs into problems when dealing withdense parthood orderings since such orderings allow for objects tohave mediate parts without having immediate parts. In these kinds ofcases additional conditions need to be imposed to ensure that com-

positional structure is preserved. In particular, mereological structuremust be preserved at all the intermediate levels of composition.

R-RELATED PAIRS

B-indiscernible R -related pairs xx ’s y and

xx *’s y * have the samecompositional structure iff the B-preserving bijection from the xx ’sonto the xx *’s is such that any sub-plurality of the xx ’s has an imageunder R that is a part of y iff the image under of the sub-plurality

has an image under R that is a part of y *

. ASSOCIATED ISOMORPHISMS

A bijection of members of the subvening domain from D B ontoD B* preserves compositional structure if the xx ’s are mapped ontothe xx *’s by only if it is the case that any sub-plurality of the xx ’sthat has an image under R that is a part of y (i.e. of the image underR of the xx ’s that is being mapped by the associated isomorphism )is mapped onto a sub-plurality of the xx *’s that has an image under R that is a part of y * (i.e. of the image under R of the xx *’s that is theimage under of y ).

Hylomorphic structure can be accounted for in an analogous way. There are again two options for preserving hylomorphic structure.One can either restrict R to the relation of immediate composition orimpose the condition that the mappings are such that intermediate

19 If we want to say that A-properties of wholes do not just supervene onB-properties of their immediate parts but also on B-properties of their me-diate parts, then problems arise unless the set of B-properties is a proper orimproper subset of the set of A-properties, cf. section 4.




structure is preserved. In either case, the additional requirement mustbe satisfied that formal components be preserved as well. This can be

done by specifying that the corresponding images under R always beimages that have the same formal components. In particular, B-indiscernible pairs P and P * have to be A-indiscernible only if y and y * have the same formal component. Similarly, an associated isomor-phism preserves hylomorphic form if it maps y onto y * (wherethese are images under R of the pluralities mapped by the base iso-morphism ) only if they have the same formal component. When itcomes to preserving intermediate mereological structure the modified

condition in both cases is that any sub-plurality of the xx ’s has animage under R that is a part of y and that has any formal componentF iff the image under of the sub-plurality has an image under R that is a part of y * and that also has formal component F .

4. Priority of Parts/Wholes

In some cases we might want to say that certain properties of wholes,such as distributional properties, fix certain properties of parts. For-mal mereological systems are neutral regarding questions of priority. They characterise parthood structure but are silent on questions ofontological priority. Accordingly the idea that wholes are prior totheir parts is not in conflict with CEM. In other words, one can adoptclassical mereology yet identify the direction of determination not with the direction of the composition relation but with the directionof the decomposition relation.

In cases in which the direction of determination runs from wholes toparts rather than from parts to wholes, we need to appeal to the de-composition relation rather than the composition relation to co-ordinate the domains and let the subvening domain consist of wholesand the supervening domain of parts. Since most wholes have multi-ple decompositions, it follows that the members of the subveningdomain will have multiple images in the supervening domain. The co-ordination relation R , which in this case is the decomposition rela-tion, will not pick out a unique collection of parts but will pick out

multiple decompositions. Since there are multiple decompositions,these must be appropriately mapped if a supervenience claim is tohold.



340 BADER

FIRST PASS: one can restrict R such that it picks out not all decompo-sitions but only atomic decompositions. If this is done then any

whole will have a unique image under R consisting of the collectionof atoms into which the whole can be decomposed. Accordingly, themereological supervenience claim then states that if y and y * are B-indiscernible, then their atomic decompositions will be A-indiscernible, i.e. R -related pairs that are B-indiscernible will be A-indiscernible (the pairs have the form y

xx ’s , where the xx ’s are theatoms into which y can be decomposed).

The xx ’s are an atomic decomposition of y ↔df. (i) all of the xx ’sare parts of y , (ii) all of the xx ’s are mereological atoms, and (iii)there is no z that is a part of y that does not overlap the xx ’s.

This account is problematic when one is dealing with gunky mereo-logies that allow for objects to be composed from atomless gunk.Moreover, it fails to capture the idea that properties of wholes fixproperties of all of their parts and not just properties of their atomicparts. Accordingly, intermediate parts need to be included as well andR should not be restricted to pick out atomic decompositions.

SECOND PASS: one can try to take intermediate levels of the mereo-logical hierarchy into consideration yet retain a unique image under R by restricting R to the immediate decomposition relation.

The xx ’s are an immediate decomposition of y ↔df. (i) all of thexx ’s are immediate parts of y , and (ii) there is no immediate partof y that is not one of the xx ’s.20

Appealing to immediate parthood, however, does not provide us witha general solution since this is not applicable when one is concerned with dense parthood orderings. Additionally, this proposal facesproblems in accounting for the idea that the A-properties of wholesfix the B-properties of all their parts and not just of their immediateparts. One might try to circumvent this problem by bringing in chainsof immediate parthood relations. Yet this only works when the set ofB-properties is a proper or improper subset of the set of A-

20 It should be noted that the xx ’s will not classify as a complete decomposi-tion of y in the traditional sense since the immediate parts of y will in mostcases overlap.




properties since otherwise it will only be the case that the A-properties of the mediate parts (at one remove) of y supervene on

the B-properties of the immediate parts of y and not on the B-properties of y itself. That is, unless the B-properties and not just the A-properties of immediate parts supervene on the B-properties of wholes, this way of making supervenience claims will not capture theidea that the A-properties of mediate parts also supervene on the B-properties of wholes.21

THIRD PASS: if y and y * are B-indiscernible, then every decompositionof y has a corresponding A-indiscernible decomposition of y *, i.e. if

the xx ’s are a complete decomposition of y , then there exists a com-plete decomposition of y * into the xx *’s, such that the xx ’s and thexx *’s are A-indiscernible.

The xx ’s are a complete decomposition of y ↔df. (i) all of thexx ’s are parts of y , (ii) the xx ’s do not overlap each other, and(iii) there is no z that is a part of y that does not overlap the xx ’s.

While an improvement over the other proposals insofar as all parts

of wholes are considered, rather than just atomic or immediate parts,and insofar as there is no restriction to atomistic or non-dense mer-eologies, this account is nonetheless problematic since it does notpreserve mereological structure. The different decompositions mustbe adequately connected. In particular, one needs to connect the dif-ferent decompositions in such a way as to preserve mereological rela-tions amongst them.22

FINAL PASS: if y and y * are B-indiscernible, then the images of y under

R , i.e. the complete decompositions of y , will be A-indiscerniblefrom the images of y * under R , i.e. the complete decompositions of y *, whereby the A-indiscernible decompositions are connected in

21 Analogous problems also affect the above-discussed attempts of account-ing for compositional and hylomorphic structure by restricting R to the rela-tion of immediate composition.22 Failure to preserve mereological structure also undermines the attempt

to appeal to total decompositions to ensure that any whole has a uniqueimage under R in the supervening domain.

The xx ’s are a total decomposition of y ↔df. any z is one of the xx ’s if f z is a part of y .




Bennett, K. 2004: ‘Global Supervenience and Dependence’. Philosophyand Phenomenological Research 68, pp. 501 –29.

Fine, K. 1999: ‘Things and Their Parts’. Midwest Studies in Philosophy 23, pp. 61 –74.

— 2010: ‘Towards a Theory of Part’. The Journal of Philosophy 107, pp.559 –89.

Johnston, M. 2006: ‘Hylomorphism’. The Journal of Philosophy 103, pp.652 –98.

Kim, J. 1993: Supervenience and Mind . Cambridge: Cambridge Universi-

ty Press.Koslicki, K. 2008: The Structure of Objects . Oxford: Oxford University

Press.



CONDITIONAL FALLACY PROBLEMS 345

where Q □→ P is true while P is in fact false, or where Q □→ P istrue but P is in fact true.1

The problems are best illustrated by examples. The most famous ex-amples of conditional fallacy problems are probably the counterex-amples to the simple conditional analysis of dispositions,

(2) x is disposed to give response r to stimulus s iff, if x were sub-jected to s , x would respond with r .

One type of counterexample to this analysis is based on finkish dis-positions: dispositions that would be lost if their manifestation condi-

tions ( s ) came about so the expected manifestation ( r ) would fail tomaterialise. An often cited example is a fragile vase protected by anangel who would render it solid if it were struck (Johnston 1993,120). While unstruck, this vase remains fragile, so the analysandum ofa (very simplified) conditional analysis of fragility is true. But if the vase were struck, it would become solid, and hence fail to break, sothe analysans is false. A non-supernatural example of a finkish dispo-sition is Martin’s (1994) example of an electric fuse. The finkish lack

of a disposition creates a complementary problem: x lacks the dispo-sition, but if s came about, x would acquire the disposition and re-spond with r . For example, imagine an evil sorcerer who has decidedto make a solid stone vase fragile if it is struck so that in fact anystriking would lead to breaking. Such counterexamples are generallythought to refute the simple conditional analysis of dispositions(though see Gundersen 2002 and Choi 2008 for defences of theanalysis).

Response-dependence theses have traditionally been formulated ei-ther in terms of dispositions or in terms of biconditionals with con-ditional right-hand-sides – biconditionals exactly like those employedby a simple conditional analysis of dispositions. So, not surprisingly,they face conditional fallacy problems too. A response-dependencethesis about a certain kind of concepts (or properties) says that theconcepts (or properties) depend in a certain way on certain cognitiveresponses in appropriate observers in favourable conditions. This

idea has been fleshed out in different ways by different authors. Ac-

1 Thanks to Benjamin Schnieder for advice on this section.



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cording to one authoritative account, Crispin Wright’s ( 1992), re-sponse-dependent concepts are concepts whose extensions are partly

determined by judgements in favourable conditions. For response-independent concepts, by contrast, judgements in favourable condi-tions merely track independently constituted extensions. Others un-derstand response-dependence differently; the main varieties are de-scribed in Jussi Haukioja’s contribution to this volume. Despite theirdifferences, most authors state their views in terms of a priori truebiconditionals of roughly the following form:

(3) Something, x , is F (falls under the concept ‘F ’ or has the proper-

ty F ) ↔ x would elicit response R from subjects S in conditionsC .

As it stands, (3) does not have exactly the same form as (1). But whenunpacked a little, it has a similar form. What the consequent says isroughly that if C-conditions were to apply to a subject S in appropriate contactwith x, x would elicit response R from S. This is a form that renders theequations vulnerable to conditional fallacy problems.

How should R , S and C be specified? This is a notoriously difficultquestion. Different specifications will yield very different kinds ofresponse-dependence views. The responses could be e.g. judgements,emotions, or perceptual experiences. The subjects and conditionscould be statistically typical, statistically typical in the actual world, oridealised in various ways. Whatever the detail of the specifications,there is general agreement that trivialising whatever-it-takes-formulations must be avoided, and that the specifications must be

compatible with the a priority of the biconditionals. In the following, we shall use the label C -conditions for the stand-ard/idealised/favourable conditions. Where appropriate, we shall as-sume that the requirements on the relevant subjects are built into theC -conditions. While many hard questions about C -conditions can bebracketed for current purposes,2 we shall have more to say aboutsome aspects of appropriate specifications of C -conditions.

2 One pressing problem is how to reconcile the prima facie conflictingrequirements of substantiality and a priority. See e.g. Blackburn 1993, 270f(on a problem) and Pettit 1999 (on a solution).




To fix ideas, let us focus on the following simple response-dependence thesis of colour concepts:

(4) x is white iff x would be judged to be white by (or: look whiteto) standard subjects in standard conditions.3

For present purposes, we can conceive of standard subjects as hu-mans whose visual abilities are statistically typical in the actual world,and who are competent with colour concepts, etc. We can conceiveof standard conditions as including normal daylight, proper distanceto the object, etc. The simplifications will not matter for current pur-

poses, as analogous problems will arise for any response-dependencethesis of similar form.

Consider a piece of photosensitive paper, waiting to be used for mak-ing photographs in a darkened lab. The paper has a surface structurethat, given C -conditions, would usually make a surface look white. Inthe dim red lab light, it looks the same colour as the lab assistant’suncontroversially white coffee mug. However, if the paper were to beexposed to daylight, the light would change its surface in such a way

that it would come to look more like the coffee than like the mug. Sothe right-hand-side of (4) is false. Yet intuitively the paper is white aslong as it is kept out of daylight; the left-hand-side is true. This lookslike a counterexample to the left-to-right direction of (4). (For thecorresponding biconditional for black – substituting ‘black’ for‘white’ in (4) – we get a counterexample to the right-to-left direction. The paper is not black, but it would look black to, and be judged tobe black by, subjects in C -conditions.)

Another standard example is Johnston’s shy but intuitive chameleon.4 This creature is uniformly green as it rests on a leaf in the dark. Or,in less question-begging terms, it has a surface structure normallyfound in objects that look green. It is also shy and very perceptive; ifa being with a suitable visual system were to spot it, it would immedi-ately notice and blush bright red. We would like to say that the cha-meleon is green (and disposed to turn red). But the (4)-style bicondi-

3 Or, in the more explicit form: x is white iff (if standard conditions wereto apply to a subject S looking at x , S would judge that x is white (or: x would look white to S )).4 Johnston 1992, 231 and 1993, 119.



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tional for green has a false right-hand-side, even while the creature isunobserved, and thus fails in the left-to-right direction. Correspond-

ingly, the biconditional for red has a true right-hand-side and a falseleft-hand-side, yielding a counterexample to the right-to-left direction.

Counterexamples of this type threaten whenever we have an x that isoutside C -conditions and intuitively has quality F (appears in the relevant way, corrected for any known perturbing factors; has the physi-cal properties usually connected with F ), but where some finkishmechanism ensures that, on coming into C -conditions, x wouldchange in such a way as to lose F , or conversely.

2. How Much is at Stake?

Yow much damage will be done if response-dependence bicondition-als are vulnerable to conditional fallacy problems? In the case of theconditional analysis of dispositions, many philosophers have takenthe counterexamples to be knockdown objections. Some may drawthe same conclusion in the case of response-dependence accounts.Of course, the biconditionals were never intended as analyses of re-sponse-dependent concepts; their suitability for this purpose wouldbe questionable indeed, as terms of the disputed class occur on theright hand side. But the biconditionals are intended to say somethinginteresting and a priori true about the concepts. So any counterexam-ples would be bad news for response-dependence theorists.

However, the counterexamples need not be seen as knockdown ob-jections. First, it may be possible to show that something is wrong

with the counterexamples, so the equations are left undamaged. Theadvertised suggestion about relativising the C -conditions is an in-stance of this strategy, as is one component of Blackburn’s view.Gundersen (2002) pursues this strategy in defence of a conditionalanalysis of dispositions.

Secondly, even if the counterexamples pose a real problem, it may bea problem with the equations rather than with the intuitive distinctionthey are employed to capture. Perhaps the equations can be adjusted

in a way that allows them to avoid conditional fallacy problems andstill do their job. This line is pursued by Johnston and Wright, and byanother component of Blackburn’s suggestion. In the debate about




dispositions, Lewis’s (1997) revised conditional analysis is the mostprominent instance of this strategy.

Finally, the core ideas behind response-dependence theories may survive the discovery that no traditional response-dependence bicondi-tional – or indeed any simple formula at all – can capture them com-pletely, provided that the counterexamples can’t be rephrased in a waythat strikes directly at the intuitive content. There may be better waysto capture response-dependence theses than the traditional bicondi-tionals, and response-dependence theses so understood might avoidconditional fallacy problems. Personally, I am attracted to this option,

as I think the biconditionals may be problematic for other reasonsthan conditional fallacy problems (see Gundersen 2006). But in thispaper, we shall take a conservative line and defend the biconditionalsagainst the present challenge.

3. Johnston on Dispositions and Response-dependence

Mark Johnston believes that conditional fallacy problems are bestavoided by formulating response-dependence claims in explicitly dis-positional terms. He takes conditional fallacy problems to refute bothsimple conditional accounts of dispositions and response-dependence claims formulated in terms of subjunctive conditionals. An account of dispositions is therefore needed that avoids the prob-lems. Johnston’s hope is that once we have such an account, we canuse it to formulate fink-free response-dependence claims.

This approach to conditional fallacy problems can only be properly

assessed in combination with an account of dispositions that fits thejob description. What could such an account look like? A simpleconditional analysis like (2) obviously won’t do for the purpose. Gi v-en such a view, dispositional formulations of response-dependencetheses and formulations in terms of subjunctive conditionals aresimply equivalent. Perhaps a simple conditional account of disposi-tions can be defended against conditional fallacy problems. But if so,the successful defence is likely to be applicable to response-dependence theses formulated in terms of subjunctive conditionals,and so choosing dispositional formulations will not make the differ-ence Johnston thinks it makes.



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An eliminativist view of dispositions would not serve the purposeeither, unless we wanted to concede that there are no response-

dependent qualities, in which case it would be hard to see why weshould bother with an account of response-dependence at all. Thiscertainly isn’t what Johnston is after. An account that identifies dispo-sitions with their causal bases would be an equally strange bedfellowfor response-dependence claims. This would make a response-dependence thesis formulated in dispositional terms nearly indistin-guishable from a primary quality account, e.g. a theory that identifiescolours with surface structures. But these views are supposed to be

opponents in the debate on colours; if they were nearly identical,most discussions on the topic would be seriously misguided.

A primitivist view that construes dispositions as sui generis proper-ties, and dispositional terms as unanalysable in other terms, wouldappear to be a more suitable companion for Johnston’s strategy. (In-deed, Johnston is said to be inclined towards such a view.) This view would provide dispositions with an ontology of their own that couldbe appealed to in an account of response-dependence. However, the

view might not allow a whole lot of explanation of anything ex-plained in dispositional terms, and so the resulting account might berather uninformative. Some may feel that, unless more can be saidabout dispositions than that they are primitive, sui generis properties,the view sounds more like a problem formulation than like a solution.

Johnston surely has views about the proper theory of dispositions toground response-dependence claims. Unfortunately, the paper in which he presents his work on dispositions is unpublished,5 so we

only have two brief passages in Johnston 1993 and 1992 to judgefrom. Johnston (1992, 234) offers a very brief account, construing a(constituted) disposition as ‘a higher-order property of having someintrinsic properties which, oddities aside, would cause the manifesta-tion of the disposition in the circumstances of manifestation’. Justhow the oddities are to be put aside is not explained.6 So as it stands,

5 ‘Dispositions: Predication with a Grain of Salt’, mentioned e.g. in John-

ston 1993, 129n44.6 Johnston (1993) offers a preliminary suggestion, designed to rule outmasking counterexamples. But his remarks on the subject are disowned in afootnote (1993, 129n44). The suggestion appears to rule out some intuitively




the account does not provide a full solution to the problems. Howev-er, quantification over bases (as supposed to identification with them)

is a strategy worthy of further consideration, and it is compatible with (at least some forms of) response-dependence theories as usuallyunderstood. We shall briefly consider such a view in section 7. Finalassessment of Johnston’s strategy will have to await an account ofdispositions that avoids the counterexamples. Unless supported bysuch an account, the strategy comes across as an expression of hoperather than a full solution to the problems.7

4. Blackburn’s Elasticity Approach Simon Blackburn’s (1993, 263f) approach to the problems combinesan element of revision with an element of explaining away the coun-terexamples. Blackburn suggests the following revised biconditional:

(5) x is F iff x (is naturally such as to) tend to elicit response R fromsubjects S under conditions C . (1993, 267)

Replacing ‘would’ with ‘is naturally such as to’ is meant to rule out

counterexamples based on supernatural manipulations, e.g. Johnston’sfragile vase protected by an angel.8

Next, Blackburn argues that the remaining alleged counterexamples,including the chameleon case, are to be resolved by recognising ‘theelasticity of being such as to do something’ (1993, 265). If conceivedof in one way – hold fixed the chameleon’s surface structure and im-agine looking at it in daylight – the chameleon is such as to lookgreen. If conceived of in another way – hold fixed its entire nature,

including its tendency to blush, and imagine looking at it in daylight – it is such as to look red. Both are legitimate ways of thinking aboutthe situation. When faced with a problematic case, ‘all we need to dois weight our selection of the feature dominating the ‘is naturally such

unproblematic dispositions, and to fail to rule out (a large subclass of) coun-terexamples based on finks and finkish lacks; perhaps that is why Johnstonrejects it.7 This section is based on material from Gundersen 2010.8 Johnston (1993, 120). Though Blackburn doesn’t mention this, the sug-gested revision may also help to rule out counterexamples based on externalmaskers or mimickers.



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as to’ clause’ (Blackburn 1993, 267). I.e. whatever your intuition re-garding the left-hand-side, the biconditional will come out true if you

choose the corresponding respect in which the object ‘is such as to’on the right-hand-side. If you think of the chameleon as green (as isnatural), you hold fixed the chameleon’s surface structure as the fea-ture dominating the ‘is such as to’ clause. Then the right-hand-side of(5) for green will come out true, even if the chameleon would in factchange colour on coming into C -conditions. There may be other ex-amples where the natural choice is, instead, to let the ‘is naturally suchas to’ clause concern the entire object, fink and all. One such case is

Blackburn’s finkish pig, whose meat tastes frightfully until finked intodeliciousness by death or dismemberment. This pig is naturallythought of as delicious, even if it takes a fink to make it so. Either way, we can get the results we want by choosing the respect of being‘naturally such as to’ appropriately. For some cases, there are intui-tions both ways. This is unproblematic, as both ways of thinking areboth legitimate and consistent with the truth of the biconditional ifconsistently applied on both sides. It is tempting to construe Black-burn’s remarks as suggesting the following diagnosis (c.f. Gundersen2002): In the problem cases, one way of thinking is applied on theleft-hand-side of the biconditional, while another is applied to the ‘isnaturally such as to’ clause. It is this illicit mixture that drives thecounterexamples.

This is a neat explanation of the counterexamples and how to resistthem. But as usual, there are objections; I shall briefly discuss two.

A first problem is that intuitions seem unevenly distributed across the

biconditionals. If the above diagnosis is correct, intuitions shouldhave it that to the extent that the photo paper is white, it is naturallysuch as to appear so in C -conditions, and to the extent that it is not, itis not. But this is not the result we get. There is a lot of intuitive pulltowards thinking of the photo paper as white. Its appearance in thelab and its uselessness for photo production once exposed to daylightsupport this verdict. Furthermore, the paper actually changes colouron coming into C -conditions. Such changes are not just stipulation;

you can watch the photo paper in various conditions, and when thelight becomes too strong, you can watch it change. Any acceptable



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another respect) naturally such as to look red, then do we not get theresult (by the right-to-left reading of the biconditional) that the cha-

meleon is both green and red (simultaneously, uniformly, all over)? While it seems perfectly acceptable to admit that the creature is inone respect such as to look red, and in another such as to look green,there is no innocent-sounding analogue in terms of all-out colourascriptions. Admitting that the chameleon is red in one respect, and(simultaneously, uniformly, all-over) green in another sounds decided-ly weird.

One response to this problem is to bite the bullet. We might try to

explain away the weirdness by pointing out that colours are bestthought of as relative anyway, and that a similar story is needed aboute.g. the colours of the pixels on the TV screen and the colours of thepicture they allow us to see. But these cases are importantly different;in the chameleon case, the weirdness is a result of advanced amend-ments in order to defend particular theories of colour, while the simi-lar conclusion about the pixel case is much more basic and unavoida-ble. Worse, in many cases, one of the colour alternatives seems simp-

ly unpalatable. The photo paper just isn’t black until placed in day-light, though on a very reasonable interpretation it is such as to ap-pear black in C -conditions.

An alternative response would be to require of our favourite theoryof colour that it must not only (i ) provide an understanding of ‘isnaturally such as to’ that yields the desired result for the theory, butalso (ii ) show that the opponent’s understanding of that clause is infact illegitimate, so the right-to-left-reading that yields the undesired

colour ascription becomes irrelevant. However, that would be a verydifferent suggestion from Blackburn’s, as the latter is very tolerant ofdifferent ways of thinking. This tolerance (or elasticity) is at the coreof Blackburn’s suggestion.

To conclude, then, Blackburn’s approach seems attractive, but there isfurther work to do in defending it, and any forthcoming solutions tothe problems may be such that only a friend of response-dependence will see their merit.




5. Wright on Provisional Equations

Crispin Wright (1992, 117f) proposes to solve the problems by adjust-ing the equations. Because of their vulnerability to conditional fallacyproblems, he rejects ‘basic equations’ (his version of what is essential-ly the traditional response-dependence biconditionals) of the form

(6) For all S , P : P iff (if CS then RS ). (1992, 108)

(‘S ’ is any subject, ‘P ’ ranges over a class of disputed judgements(colour judgements, value judgements, etc.), ‘CS ’ says that S is in C -conditions, and ‘RS ’ says that S gives a certain characteristic re-

sponse.) Basic equations are replaced with provisional equations where the C -conditions are placed in a proviso (hence the alternativelabel provisoed biconditionals):

(7) If CS , then (it would be the case that P ↔ S would judge that P ).(1992, 119)

Basic equations are vulnerable to conditional fallacy problems be-cause the C -conditions’ coming to obtain could alter the truth-value

of P . But provisional equations make predictions only about cases where the C -conditions are already met. Any changes in x induced byentering into C-conditions will already have taken place in these circumstances ,and so will not give rise to counterexamples. This move makes theequations immune to finks triggered by x coming into C -conditions.

This is an elegant solution to the problems. However, it generates worries of its own. One is that provisoed biconditionals seem vulner-able to finks triggered by the response rather than by the C -

conditions.9 Consider Camelia, a very shy and perceptive young lady whose skin is pale when no one is looking, but who would immedi-ately notice whenever an appropriate observer was in the process ofmaking a judgement on her complexion, and blush bright red as aresult. Suppose C -conditions obtain and Camelia is in the companyof an appropriate observer (true antecedent of (7)). If the observer were to make a judgement on her skin colour, that colour would im-mediately change, which means that the two sides of the embedded

biconditional will have different truth-values. If you are uneasy aboutCamelia’s telepathic powers, consider instead an object equipped with

9 This challenge is stated and discussed in Gundersen 2011.



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a sensor that registers judgements by means of science-fiction tech-nology – perhaps by measuring electrical impulses in S ’s brain – and a

mechanism that changes the object’s colour so it is always out of step with the judgements made on it. These counterexamples are of a verysimilar kind to those that motivated the shift to provisional equations;if such counterexamples can be constructed against provisional equa-tions too, the motivation for using the latter becomes questionable.Counterexamples based on finks triggered by the responses consti-tute a challenge, not a knockdow n objection, to Wright’s strategy. Butthe challenge must be addressed if provisional equations are to stand

their ground.10

A second worry is this: we want to be able to say – straightforwardlyand with no reservations – that the unexposed photo paper is white.Provisional equations do not give us that (nor do they deny it), asthey are silent on what happens outside C -conditions. With basicequations replaced with provisional equations, best opinions get todetermine the extensions of the disputed concepts in C-conditions , butif the concepts are to be applicable outside C -conditions, they need

to be extended to those cases by other means. This may be done, as Wright suggests (1992, 126f), by appealing to the physical characteris-tics on which colours presumably supervene (where the relevantphysical characteristics get picked out by being correlated withjudgements in C -conditions). But this is hardly sufficient on its own,as we don’t check an object’s surface structure in order to judge on itscolour. The reason we want to be able to say that the paper is whitein the lab is not that it has a particular surface structure, but that it

looks in a certain way (similar to the mug, not the coffee), correctedfor known perturbing circumstances (the pink appearance caused bythe red lab light). Appeals to appearances outside C -conditions, cor-rected for known perturbers, may be built into the proposal besidethe appeal to physical characteristics, which would presumably makethe proposal stronger. But it would still seem desirable if an accountcould be found that allowed us to say, for more straightforward rea-sons, that the paper is white. We shall return to this point below.

10 In my manuscript ‘In Defence of Provisional Equations’, I argue that thechallenge can be met by a further adjustment of the equations.




Wright’s strategy deserves more discussion than we can attempthere.11 Instead, we shall devote most of the remainder of the paper

to an alternative that, to my knowledge, has not been explored in theliterature.

6. Relativised C -conditions

The photo paper is intuitively white in the lab, but it would blacken ifexposed to daylight. This constitutes a counterexample to response-dependence biconditionals if, but only if, C -conditions for judgingthe colour of the paper must include daylight. Could this be the as-

sumption we should challenge in order to solve the problem? If C -conditions for determining the colour of unexposed photo paperinvolve lab light rather than daylight, we avoid the conclusion that theunexposed paper would look black in C -conditions, and the counter-example does not get off the ground.

In discussions about response-dependence, it is often assumed with-out argument that C -conditions are relative to classes of disputedconcepts, but uniform for all concepts and all cases within such aclass; one set of C -conditions for colours, another for values, etc. Butthis is too crude. The optimal conditions for judging the colours ofe.g. fireworks, starlight, and northern lights clearly do not include day-light, even though daylight forms part of the C -conditions for mostcolour determination tasks. So the assumption of domain-wide C -conditions is dubious in any case. For the photo paper, there is a casefor saying that the optimal conditions for determining its colour in-clude lab light, not daylight. The case is admittedly less clear than for

the other examples. The special C -conditions would apply only forsome colours the paper might have, not others, and would no longerapply when the photo-making process is completed or the paper has

11 For further discussion, see my manuscript ‘In Defence of ProvisionalEquations’, where I discuss three objections: the Camelia objection, (a rela-tive of) Wright’s univocity objection (1992, 124f), and the possibility ofmasking and mimicking counterexamples to provisional equations. I argue

that provisional equations can be defended against all three objections (witha small further adjustment in response to the first objection). However, forreasons that will emerge, the strategy may need to be supplemented with therelativisation strategy discussed below in order to yield optimal results.



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been ruined by exposure to daylight. But the case is sufficientlystrong for the suggestion to be worthy of serious consideration.

Let us start by addressing some worries that a ‘relativist’ view of C -conditions might raise. First, if C -conditions should be treated asrelative rather than uniform across entire domains, how come this hasbeen missed so far? A likely answer is that since response-dependenceaccounts are of relatively recent origin and raise lots of issues, it isunsurprising if some of the complexities have gone unnoticed. Theconsensus about domain-wide C -conditions is not based on argu-ments; it is just the way things have been done this far. If we have

good reasons to reconsider the matter, consensus alone is not enoughof a reason to resist further relativisation.

Next, are relativised C -conditions compatible with the substantialityrequirement that rules out trivialising whatever-it-takes-clauses? Theanswer is yes. We can’t say whatever we like about relativised C -conditions, any more than we can about the details of any domain- wide C -conditions. Relativisation raises no new problems in this re-spect.

Thirdly, is it an ad hoc move to invoke relativised C -conditions inorder to avoid conditional fallacy problems? Arguably, the answer isno. For if we look at the best candidates we have for general accountsof the C -conditions, they all seem to recommend relativisation tocases. In order to assess the relativisation strategy, we need somebackground about how C -conditions could and could not be speci-fied. One approach would be to provide a fully specified list, filling in

the ‘etc.’ until every possible trick scenario has been ruled out. Giventhis approach, relativisation to (smaller classes of) concepts and cases would pose a problem, as it would make an already daunting taskmuch larger. But the approach is doomed in any case; even for do-main-wide C -conditions, there is no hope of generating a list a priorithat deals with all anomalies (including e.g. unusual colour appearanc-es on spinning discs, the influence of not-yet-invented drugs, etc.). Infact, the idea of relativised C -conditions suggests an explanation of why the requirement of a fully specified list is unjustified as well as




unnecessary: concept users can be relied upon to contextualise aptly,even if they may not be able to articulate the rationales in each case.12

The only type of account of C -conditions that seems likely to be ableto accommodate (the reasoning behind) both the substantiality condi-tion and the a priority condition is a two-part approach like the onesuggested by Pettit (1999). This approach combines a role-level speci-fication of C -conditions that is fully knowable a priori with a realiser-level specification that provides the substantiality and is partly, butnot fully, knowable a priori (in the sense of being accessible to usersjust in virtue of their competence with the concepts). Elsewhere

(Gundersen 2006), I have discussed three candidates for role-level,general recipes of C -conditions. One is Pettit’s account of C -conditions as the conditions that minimise discrepancies – i.e. yieldmaximal constancy – in verdicts across times and persons. (Thisshould perhaps be supplemented with a clause about maximising dis-criminability in order to avoid a problem discussed in Gundersen2006.) A second approach construes C -conditions as the conditionsin which several kinds of features connected to the disputed concepts

are co-instantiated. For example, the colour red is connected with acharacteristic range of surface structures and reflectance spectra be-side a characteristic kind of visual experience and the disposition toelicit such experiences in suitable observers. C -conditions can be un-derstood as the conditions in which all those characteristic featurescoincide, whereas outside C -conditions they might diverge. A thirdapproach to C -conditions understands them as the conditions accept-ed as favourable by competent language users in everyday practice

with the concepts (perhaps with certain suitably specified idealisa-tions). All three suggestions raise difficult questions. But for currentpurposes, what we need to notice is this: all prima facie plausible can-didate accounts are not only compatible with relativisation of C -conditions; they seem to actually recommend it. Maximal constancyand discriminability in judgements on e.g. northern lights would bereachable in the dark, not in daylight. The overlap between visual im-pressions and the complex physical bases of the phenomenon wouldalso be found in such conditions. Finally, people generally accept thatthe night is the time to look for northern lights; no-one waits for day-

12 Thanks to Sarah Broadie for suggesting this.



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light in order to see them better. Thus, all the likely candidates for ageneral recipe of C -conditions would entail that the C -conditions for

appreciation of e.g. fireworks and ordinary surface colours are differ-ent. Not only is relativisation of C -conditions not an ad hoc move; itseems mandatory given the best ways we have of understanding C -conditions.

6.1 Further Relativisation and an Independence Worry

How fine-grained should the relativisations be? It is not enough torelativise to objects or similar systems. This would give us the correct

results with e.g. northern lights, where a uniform set of C -conditionsinvolving darkness will probably suffice. But in the case of the cha-meleon, things are more complicated. It is easier to judge its colour when the light is on. And so if we insist on one set of C -conditions,that set is likely to include daylight, and we will still get counterexam-ples.

A way out is further relativisation. The suggestion would be thatwhenever there is a colour change, the C- conditions can’t be assumed to be the

same . If the chameleon is such as to change colour on coming intodaylight, a different set of C -conditions is relevant to judging its col-our in the dark. This squares well with common sense and ordinarypractice: if you want to know the colour of the photo paper in thelab or the chameleon in the dark, you had better find a way of inves-tigating that does not cause colour changes. So you look for the bestconditions for determining the colour compatibly with not changingit.

This suggestion invites a worry similar to that which motivates Wright’s independence condition. The independence condition re-quires that C -conditions be specifiable without presupposing exten-sions of concepts of the disputed class as independently determined(Wright 1992, 120f). The motivation is simple; if extensions of theseconcepts are needed in order to specify what opinions are best, it ishard to see how best opinions could be what determines those exten-sions. The appeal to colour changes in picking out the C -conditions

looks like a serious case of presupposing extensions of the disputedconcepts as already given. If we need to presuppose that much aboutthe extensions of colour concepts in order to find the relevant C -




conditions, how can those extensions be determined by responses inC -conditions?

There are two ways to respond to this worry. One response would beto argue that C -conditions work in a more complex and holistic waythan usually assumed, and that C -conditions and extensions are de-termined together , rather than one being prior to the other. The chang-es exploited by the counterexamples can be described in different ways. If we describe them as changes in the distribution of colourproperties, invoking them in the specification of the C -conditionssounds suspect indeed. But if we describe them as sudden changes in

appearance in a certain familiar respect as conditions are varied, and where this change is unexpected in the light of the normal patternsof changes as a function of changing conditions, the story begins tosound less problematic. Something like this may be sufficiently differ-ent from explicit presuppositions about extensions to work. If thecorrect story about C -conditions is that they settle where the rightamount of constancy occurs, and/ or where different types of relevant features are co-instantiated, then either such changes in appear-

ances are permissible determinants of the C -conditions, or nothing is. Another response to the independence worry would be to appeal tochanges in the bases of the relevant response-dispositions. (Or better:intuitions about changes of bases , as we don’t want to require exactknowledge of the bases.) If the change that makes a different set ofC -conditions relevant is described as a change in base properties ra-ther than as a change in colours, illicit presuppositions about colourconcepts are avoided, and the independence worry can be put to rest.

This suggestion may sound heretical in the context of defending re-sponse-dependence theses. However, appeals to bases are arguablycompatible with response-dependence – certainly with Pettit-styleresponse-dependence, but also with the stronger kinds advocated by Wright and Johnston – as long as no identification with bases is made.No such identification is in question here. So appealing to basesmight allow us to describe the C -conditions – and their changes – in a way that does not undermine the extension-determining potential of

judgements in C -conditions.



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6.2 Multiple Colours?

The ‘further relativisations’ proposed above invite another objectionthat we considered for Blackburn’s approach: Things that we wouldnormally describe as having one colour come out as having two. Thechameleon is green relative to the C -conditions relevant to apprecia-tion of its greenness, and red relative to the (daylit) C -conditions rel-evant for judging its redness. If both sets of C -conditions are legiti-mate, does it not follow, by the right-to-left direction of the bicondi-tional, that the chameleon has both colours at once?

A straightforward solution to this problem would be to replace thetraditional biconditionals with Wright-style provisional equations. Ifthe C -conditions are placed in a proviso, the equation says only whatis true if those conditions are fulfilled . If, for the same object, there aretwo legitimate but mutually exclusive sets of C -conditions that wouldyield different colour ascriptions, this is no problem; only one set ofC -conditions is fulfilled at any given time, and hence only one provi-soed biconditional gets to make any pronouncement about the colourof the object.13

Against this response, it might be objected that Wright’s move on itsown is sufficient to solve any conditional fallacy problems for re-sponse-dependence theses, assuming that the Camelia objection canbe addressed. Why bother with relativised C -conditions if we candefend the relativisation strategy only by invoking another strategythat could have done the job alone? This would be a fair point if rela-tivised C -conditions had been invented just for the purpose of ad-

dressing conditional fallacy problems. But relativisation is needed inany case, cf. the northern lights, and an advocate of provisional equa-tions should accept it for independent reasons. Also, for what it’s worth, relativised C -conditions have the advantage that they allow us

13 Would that mean that there could be colour change without change inintrinsic properties (if different C -conditions come to obtain)? No, for dif-ferent sets of C -conditions come into play only when some finkish mecha-nism would change x ’s colour when it enters into what we would usually

think of as the C -conditions for judging x ’s colour. A shift from one set ofC -conditions to another will thus coincide with a change in x ’s colour, andaccompanying changes in intrinsic properties. Thanks to Alex Steinberg forpressing me on this point.




to call the unexposed photo paper white for more straightforwardreasons than if we opt for provisional equations with domain-wide

C -conditions. The photo paper is white because that is what it wouldlook like in the appropriate set of C -conditions, and there is no needto appeal to any other features in order to extend the colour conceptto this case.

C -conditions are a confusing and under-defined lot. The complex way they seem to work in ordinary linguistic practice gives reason foroptimism about the relativisation strategy, as does the vagueness with which they are defined. For example, it is often left open how broad

the range of C -conditions is: Should we defer on matters of taste tothose select few with a very sensitive palate? Or should we includethe judgements of most of us, only discounting those with a very weird taste or under influence of circumstances known to distorttaste experiences? In real life, we clearly do both. Recognising thecomplexities involved in real-life practice with C -conditions may bean important part of the solution to conditional fallacy problems forresponse-dependence theses.

The relativisation strategy will probably be most attractive to friendsof response-dependence; a sceptic may see only epicycles. But it is astrategy that deserves consideration. Apart from its potential againstconditional fallacy problems, it offers the added benefit of correctinga common but over-simplified way of thinking about C -conditionsand response-dependence in general.

7. A Base-based Solution?

Appeals to the bases of response-dispositions have come up severaltimes in our discussion. Perhaps the problems could be solved in asimpler way by invoking changes of bases? One possibility would beto adopt Lewis’s strategy from ‘Finkish Dispositions’. Lewis proposesa revised conditional analysis of dispositions, designed to avoid fink-ish counterexamples by introducing (quantification over) base-properties into the equations. Roughly, the simple conditional analy-sans, ‘x would give response r to stimulus s ’, is replaced with ‘x has aproperty B – the base – which, assuming it stayed around longenough, would join with s to cause r ’. This is true even for finkishdispositions, because even if x loses the disposition and its base as a



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result of s , and so fails to give response r , it is still true that had x re- tained B long enough, x would have given response r . The problem with fink-

ish lacks of dispositions is solved by requiring that B is a property that xalready has at t , i.e. not one it gains as a result of the stimulus. (Thissummary is simplified, but captures the essence of the proposal.)Lewis’s suggestion is generally recognised as a solution to the prob-lems with finkish dispositions and finkish lacks of dispositions. Iftransposed to response-dependence biconditionals, it would presum-ably render them immune to finkish counterexamples.

Again, appeals to bases might sound heretical in the context of re-

sponse-dependence. But the suggestion would be, not to identify theresponse-dependent features with their bases, but only to require thatthere is a base property doing a certain job. The account would be neu-tral on what sort of properties do the work, whether they are sub-stantial, natural properties or highly complex combinations of fac-tors, and whether the base property is the same for different instanc-es of a given response-disposition. The appeal to bases would entailthat the relevant response-dependent features supervene on physical

properties (probably in a fairly strong sense), but nothing strongerthan that.

This strategy would be particularly well suited for Pettit’s brand ofresponse-dependence. A Pettit-style response-dependence thesis ismainly a thesis about how concepts are acquired, and it is compatible with reference to response-independent properties. The bicondition-als are supposed to be a priori true solely in virtue of the reference-fixing role of responses in C -conditions. The base-based strategy

against conditional fallacy problems is a natural choice for this kindof response-dependence theory. But even for response-dependencetheses of Wright’s and Johnston’s kinds, it should be legitimate toappeal to bases, as long as no identification is made.

The strategy may not be suitable for all response-dependent con-cepts. It makes good sense for colours. But for a domain like humour – another likely candidate for response-dependence – an appeal tobases is more controversial. Here, the bases would be extremely het-

erogeneous and unruly; perhaps too unruly for Lewis’s strategy to beapplicable. (But then, it may be that finkish counterexamples makesense exactly to the extent that there are intuitions about bases doing




work, and changing because of the fink.) We might speculate (and Ihope to argue in a different paper) that different accounts might be

suitable for different kinds of response-dependent concepts: that aLewis-type account might work for some concepts – those closelyconnected to (manageable disjunctions of) base properties – and thatdifferent accounts may be needed for other domains, e.g. values, where the connection to bases is less straightforward.

The base-based proposal invites a range of questions and objections.Unfortunately, this discussion is too large for the present context, so we shall simply list some of the issues that need further considera-

tion, and leave the discussion for later.One question concerns the class of B-properties quantified over. What requirements must be placed on candidate properties, e.g. withrespect to unity and objectivity? Depending on the answer, the strate-gy may be applicable to few, many, none, or all response-dependentconcepts.

Another question is whether and how we can avoid concluding that

the chameleon has two colours at once, since it might have suitable B-properties for both a finked disposition to look green and a non-finked disposition to look red. Lewis endorses the analogous conclu-sion for dispositions in general, but for colours it is very unattractive.

A third question is whether the move leaves a class of conditionalfallacy problems unaddressed. It has been objected to Lewis’s analysisthat while it is efficient against finkish counterexamples, it is vulnera-ble to counterexamples where external influences mask or mimic dis-

positions.14 Do masking and mimicking cases pose problems for re-sponse-dependence theses too?15

Thus, there is a lengthy discussion to be had about the base-basedstrategy. We shall have to leave that discussion for later. But the strat-egy deserves closer investigation, as does the relation between re-sponse-dependent features and their physical correlates in general.

14 See Bird (1998) on masking and Choi (2003) on mimicking.15 I think there is a good response to this problem, which is why I have notpaid special attention to masking and mimicking cases in this paper. But thatresponse belongs in a different paper.



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8. Concluding Remarks

While finkish cases like the photosensitive paper and Johnston’s cha-meleon pose prima facie problems for response-dependence theses,the response strategies considered offer sufficient resources to solvethe problems. The appropriate conclusion of our discussion is notthat one of them is the correct approach, but that several promisingapproaches are available. Quite possibly, components from more thanone approach would enter into a final solution. Also, different solu-tions may be appropriate for different response-dependence theses. ALewis-style account with appeals to bases may be the most suitable

match for response-dependent concepts that are thought of as close-ly connected to underlying physical properties in relatively simple andstraightforward ways. It would certainly be a natural choice for Pettit-style response-dependent concepts with response-independent refer-ents. For other domains, where the connection to bases is more com-plex or dubious, the best option may be provisoed biconditionals,supplemented with the recognition – which is needed anyway – ofthe relative nature of C -conditions. Or the combination of provisoed

biconditionals with relativised C -conditions may be the best choiceacross the board. It is also possible – though to my mind less likely – that a new account of dispositions, fink-free and appropriate forserving as a basis for response-dependence theses, will make John-ston’s strategy an attractive response to the problems. Insights fromBlackburn’s proposal may also contribute to a solution. There may beother useful strategies that have not yet been considered in the con-text of response-dependence theses; a good place to look for inspira-

tion would be discussions of conditional fallacy problems in otherareas, e.g. for conditional analyses of dispositions. Whichever strategyturns out to be the optimal choice, there is reason for optimism. Sev-eral promising approaches to addressing conditional fallacy problemsare available, and there is reason to expect that one or more of themcan do the job.16

16 Thanks to Lars Gundersen and Crispin Wright for many inspiring dis-cussions on response-dependence and conditional fallacy problems. Thanksto Sarah Broadie and Katherine Hawley for comments on an early versionof this material, and to Benjamin Schnieder and Alex Steinberg for helpful




References

Bird, A. 1998: ‘Dispositional Antidotes’. Philosophical Quarterly 48, pp.227 –34.

Blackburn, S. 1993: ‘Circles, Finks, Smells and Biconditionals’. Philo- sophical Perspectives 7, pp. 259 –80.

Choi, S. 2003: ‘Improving Bird’s Antidotes’. Australasian Journal ofPhilosophy 81, pp. 573 –80.

— 2008: ‘Dispositional Properties and Counterfactual Conditionals’. Mind 117, pp. 795 –841.

Gundersen, E. B. 2006: Making Sense of Response-dependence . Ph.D. the-sis published online at http://hdl.handle.net/10023/211.

–– 2010: ‘Dispositions and Response-dependence Theories’. In Poliand Seibt 2010, pp. 119 –34.

–– 2011: ‘The Chameleon’s Revenge’. Philosophical Studies 153, pp.435 –41.

Gundersen, L. 2000: ‘Bird on Dispositional Antidotes’. Philosophical

Quarterly 50, pp. 227 –9. –– 2002: ‘In Defence of the Conditional Account of Dispositions’.

Synthese 130, pp. 389 –411.

Haldane and Wright (eds.) 1993: Reality, Representation and Projection .Oxford: Oxford University Press.

Johnston, M. 1992: ‘How to Speak of the Colours’. Philosophical Studies 68, pp. 221 –63.

–– 1993: ‘Objectivity Refigured: Pragmatism Without Verification-ism’. Haldane and Wright 1993, pp. 85 –133.

Lewis, D. 1997. ‘Finkish Dispositions’. Philosophical Quarterly 47, pp.143 –58.

Martin, C. B. 1994. ‘Dispositions and Conditionals’. The Philosophical Quarterly 44, pp. 1 –8.

Poli, R. and J. Seibt (eds.) 2010: Theories and Applications of Ontology 1:

Philosophical Perspectives . New York: Springer.

feedback on a nearly final draft. Thanks to Sigrid and Steen Busck forbabysitting while the paper was revised.

http://hdl.handle.net/10023/211

http://hdl.handle.net/10023/211



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Shope, R. K. 1978. ‘The Conditional Fallacy in Contemporary Phi-losophy’. Journal of Philosophy 75, pp. 397 –414.

Wright, C. 1992. Truth and Objectivity . Cambridge, Massachusetts: Har- vard University Press.



Rigid vs. Flexible Response-DependentProperties

Dan López de Sa

There is a longstanding attempt to make dispositional theo-ries of value and of colour run in parallel. But the analogy isnone too good, and I doubt that it improves our understand-ing either of colour or of value.

David Lewis (1989)

According to a more or less traditional view of secondary qualities,they are – or would be – real though not fully objective features of

external objects. Roughly speaking, they are real not only by being thesignifications of natural simple predicates which can be used to makepredications that are, for the most part, truth-evaluable and some-times true, but also by being exemplified independently of those rep-resentations. Roughly speaking, they are less than fully objective in that itis essential for something having them that it bears a certain relationto subjective responses of ours, at least as we actually are.

Response-dependence was intended to generalize the notion of a

secondary quality in that respect, by applying also to values in a waysuch that – at least a qualified form of – realism was vindicated. My view is that response-dependence, by itself, fails with respect to thisproject. There is, I agree, a general notion of a response-dependentproperty, corresponding more or less to that usually used in the litera-ture, under which both secondary qualities and evaluative properties – but not all properties – fall. But the claim that a property is response-dependent in this general sense falls short of constituting a vindica-tion of realism concerning the property in question. This is so be-cause response-dependent properties, in this general sense, compriseboth what I will call rigid response-dependent properties and flexible response-dependent properties. My main aim in this paper is to pre-



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sent this distinction between response-dependent properties, and toclaim that only response-dependence of the rigid variety supports

realism. The structure of this paper is as follows. In the first section I willprovide a brief background by explaining Johnston’s original charac-terization of a response-dependent concept and offering an argument,due to a number of philosophers, to the effect that it fails with re-spect to the original project and that a metaphysical notion is requiredif this is to be pursued. In the second section I will present a generalnotion of a response-dependent property that is not affected by the

given consideration. As I said, however, this notion also ultimatelyfails with respect to the original project. In the third section I willpresent the distinction between rigid and flexible response-dependentproperties. I will then illustrate respectively the notion of a rigid re-sponse-dependence property with the case of colours (section 4), andthat of a flexible response-dependence property with the case of val-ues (section 5). Although both cases will contain controversial ele-ments, their mere defensibility should suffice, I hope, for supporting

my claim about the exclusivity of the connection between rigid re-sponse-dependence and at least a qualified form of realism. I willclose with some considerations regarding the many response-dependencies.

1. Response-Dependent Concepts

The phrase ‘response-dependence’ appeared in the literature for thefirst time in Mark Johnston’s ‘Dispositional Theories of Value’

(1989). By analogy with secondary qualities, and colour in particular,some philosophers, including McDowell and Wiggins, had attemptedto defend realism about value against those who claim that value isnot a genuine feature. Here is the idea: Consider a view according to which (say) redness is the disposition to produce in (say) perceptuallynormal humans an experience as of red in normal viewing condi-tions. Now statements predicating redness would clearly be, vague-ness aside, truth-evaluable, and some of them true. Furthermore,

something could be red independently of actually eliciting the re-sponses from the subjects (if, for instance, the conditions are not thenormal viewing ones) and, to the extent that we consider the relevant



RESPONSE-DEPENDENT PROPERTIES 371

subjects, responses and conditions as they actually are, even inde-pendently of what the relevant subjects might be like or whether they

exist at all. It seems that if values were analogous to colours, at leastconceived as such, then certain anti-realist positions concerning theevaluative could be rejected. Something like this line of argument is what, according to Johnston, the ‘analogists’ pursue for defendingrealism about value. As he puts it, ‘the leading idea of the analogisthas been to show that by the same standards of genuineness it wouldfollow that colour is not a genuine feature of surfaces’ (Johnston1989, 139).

There are obvious and less obvious disanalogies between colours and values, but these, according to Johnston, do not preclude there beinga further analogy capable of doing the work in defending realism theanalogists wanted it to:

The most plausible, if highly generalizing, way of taking theanalogy is this: evaluational concepts, like secondary qualityconcepts as understood by the analogists, are ‘response-dependent’ concepts. (Johnston 1989, 144)

His original characterization of the notion of a response-dependentconcept was:

If C , the concept associated with a predicate ‘is C ’, is a conceptinterdependent with or dependent upon concepts of certainsubjects’ responses under certain conditions then somethingof the following form will hold a priori

x is C iff In K , S s are disposed to produce x -directed responseR

(or x is such as to produce R in S s under conditions K )]

[W]hen for a given C we have substantial or non-trivializingspecifications of K , R , and the S s, and the resultant bicondi-tional holds a priori, then we have a concept interdependent with or dependent upon a concept of subject’s reactions underspecified conditions. Such will be a response-dependent con-

cept. (Johnston 1989, 145 –6) Two features of the characterization are worth noting, which prima facie contrast with each other. The first is that the project for which



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the notion of response-dependence is introduced is straightforwardlymetaphysical : to provide a way of explicating the (possible) analogy

between secondary qualities and values by means of which ‘a realismabout value’ (Johnston 1989, 139) could be defended, and thus expli-cating the

qualified realism [which philosophers have urged about manyareas of discourse], asserting both that the discourse in ques-tion serves up genuine candidates for truth and falsity, andthat, nonetheless, the subject matter which makes statementstrue or false is not wholly independent of the cognitive or af-

fective responses of the speakers in the discourse. (Johnston1989, 144)

The second is that, all this notwithstanding, ‘response-dependent’ asused here by Johnston qualifies concepts for properties like secondaryqualities and values, and not those very properties themselves. As willbe apparent in a moment, I have been convinced by the argumentpresented below that this is more than a prima facie contrast, and thusthat his original characterization of response-dependence should bemodified if his original project for it is to be pursued. But before go-ing on to this, let me rephrase the proposal slightly, in a way that willbe useful for the discussion to come.

Let me say then that if F is a (predicative) concept, a response- dependence-related (or rd , for short) biconditional for F is a substantialbiconditional of the form:

x is F iff x has the disposition to produce in subjects S the

mental response R under conditions C or the form

x is F iff subjects S have the disposition to issue the x -directedmental response R under conditions C

where ‘is F ’ is a predicate expressing F , and ‘substantial’ is there toavoid ‘whatever-it-takes’ specifications of either S , R or C . No furtherrestrictions on the relevant specifications are imposed. In particular

the relevant subjects could be more or less the very same possessorsof the concept, or a subset of them, or an idealized subset of them,or some other disjoint set; the relevant mental responses could be




cognitive (a certain belief or judgment), or experiential (the enjoy-ment of experiences instantiating a certain quale), or desiderative

(valuing). And those specifications could contain rigidifying devices. This last element will be crucial for the distinction among response-dependent properties I am interested in.

Now,

rd0 A (predicative) concept is response-dependent iff there is anrd biconditional for it which holds a priori.

Several philosophers1 have provided compelling arguments which in

my view show that this original characterization of response-dependent concepts by Johnston does not succeed with respect to hisoriginal, metaphysical, project – i.e. the project of appropriately gen-eralizing the notion of a secondary quality.

The main element can be put straightforwardly: there are also rd bi-conditionals for concepts for – what we reasonably take to be – primary qualities which hold a priori. Or more generally, there are con-cepts that are response-dependent, in the sense of (rd0 ), independent-ly of whether they signify primary, fully objective, properties. If thatis so, then the notion of a response-dependent concept of (rd0 ), in-teresting as it could be for other reasons, fails with respect to the pro-ject for which it was introduced.2

Why is this? Take a predicate signifying – what we reasonably take tobe – a primary quality, like ‘is cubic’. It arguably does so in virtue ofbeing associated with some reference-fixing material that, it seems,

would crucially involve the relevant mental responses of subjects likeus in question. But then there will be rd bidconditionals for the con-cept expressed by the predicate in question such that their left-hand-side expresses that reference-fixing material, along the lines of:

1 Including Brynjarsdóttir (2008), García-Carpintero (2007), Gundersen(2010), Haukioja (2000), Jackson and Pettit (2002 inter alia ), and Wedgwood(1998).2 For alternative purposes that the original characterization, or a closely

related one, might help pursuing see Jackson and Pettit 2002 and Hauikioja2000. Sveinsdóttir (2008) argues that a response-dependence account of aconcept can yield metaphysical results, but only on a conception of proper-ties on which they are ‘mere shadows’ of concepts.



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x is cubic iff x has the disposition to produce in perceptuallynormal humans an experience instantiating a cubic-quale in

normal viewing and tactile conditions.But now, for reasons familiar since Kripke’s Naming and Necessity (1980), the fact that the relevant material plays at least a reference-fixing role suffices for those biconditionals to hold a priori , analogous-ly as ‘the standard Paris meter is one meter’ holds a priori (assumingthat the length of the standard Paris meter plays a reference-fixingrole with respect to ‘meter’). But then, although ‘is cubic’ signifies – what we reasonably take to be – a primary quality, it expresses a con-

cept that is response-dependent, in the sense of (rd0 ). Another way of putting the point is as follows. Red clearly seems aresponse-dependent concept in the sense of (rd0 ). Suppose that it isbecause the following holds a priori :

x is red iff x has the disposition to produce in perceptuallynormal humans an experience instantiating a red-quale innormal viewing conditions.

Will the acknowledging of this suffice for rejecting the so-called pri-mary view on colours, according to which red is a primary, fully ob-jective, property? It doesn’t seem so. On the contrary, defenders ofthe primary view may be quite willing to accept that something likethis holds a priori. And the reason could be put as before: even if‘red’ signifies a primary quality, it arguably does so in virtue of beingassociated with some reference-fixing material that involves the relevant mental responses of subjects like us in question. That being so,

there will be rd biconditionals for red expressing that material andthus holding a priori . Given this, then, we can conclude that (rd0 )should be modified at least insofar as the original project for whichresponse-dependence was introduced is pursued.3

3 Wasn’t it apparent to Johnston himself ? I think it was. Just after his orig-inal characterization of the notion, he adds in a footnote: ‘At least this holds with one proviso having to do with concepts introduced by reference-fixing

descriptions. [...] Everyday terms for shapes might provide some examples’(Johnston 1989, 146n8). (And in all his subsequent contributions to the de-bate, he explicitly characterizes response-dependence by means of identities ,among concepts or properties, and no longer in terms of the apriority of




2. Response-Dependent Properties

I said at the beginning that according to a more or less traditional view, secondary qualities are – or would be – not fully objective fea-tures of external objects in that it is essential for something havingthem that it bears a certain relation to responses of ours, at least as we actually are. It seems as if, for response-dependence to pursue theaim of appropriately generalizing that notion, it should better distin-guish between different sorts of properties themselves, rather thanbetween different sorts of concepts of properties, and hence requirethe relevant rd biconditionals to have certain metaphysical status, cap-

turing the ‘essentialist’ component alluded to. One first thought in that direction will not do.

A property P is response-dependent iff there is an rd bicondi-tional for a concept signifying it which holds necessarily .

The reason is parallel to that just considered above, in that the pro-posal would fail by covering primary qualities as well. Let ‘is F ’ be apredicate signifying a primary, fully objective property which express-es a response-dependent concept in the former sense of (rd0 ). Thentake any particular true response-dependence-giving biconditional forthem, and add to the specifications of the subjects, the responses andthe conditions the rigidification device ‘as they actually are’ as to havesomething with the form:

x is F iff x is disposed to produce in subjects S as they actuallyare the responses R as they actually are in conditions C as they

actually are.Due to the semantics of ‘actually’, this biconditional will be necessarily true, and hence the property in question, primary by assumption, would count as response-dependent.4 The failure to capture those

the relevant biconditionals.) But of course, the proviso would make (rd0 )useless, at least with respect to the original project.4 Indeed, this was my reason for not including, when characterizing (rd0 )

the requirement that the relevant rd biconditionals should hold not only apriori but necessarily (a requirement which, although absent in Johnston’s(1989) characterization, is commonly added). That requirement, when rigidi-fied specifications are allowed, is not a further requirement: whenever there



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particular essentialist claims alluded to in terms of the modal notionof necessity is nothing but a special case of the general failure to cap-

ture essentialist claims in terms of necessity, a general failure which was diagnosed by Fine (1994), see García-Carpintero 2007 and Wedgwood 1998.

The main idea behind Fine’s view is delicate and subtle. But, for mypresent purposes, it can be sufficiently illustrated (I hope) with thehelp of the following examples. It is a necessary property of Socratesthat he belongs to the set whose sole member is Socrates. That is aproperty which is impossible for Socrates to fail to have. But this

property hardly is, it seems, an essential property of his: there seemsto be nothing in the essence or the nature of Socrates which involveshis belonging to any set whatsoever. As Fine puts it, ‘[s]trange as theliterature on personal identity may be, it has never been suggestedthat in order to understand the nature of a person one must know which sets he belongs to’ (Fine 1994, 5). Another example could help.It is a necessary property of Plato that he is not identical to Aristotle. That is again a property which is impossible for Plato not to have.

But again it hardly seems to be an essential property of Plato. Other- wise Aristotle (and, for that matter, any object not identical with Pla-to) would be involved in explicating the nature of Plato.

The moral drawn by Fine from these and related considerations isthis: essence is a more fine-grained notion than necessity , in that it is sen-siti ve to the ‘source’ of the latter, as it were. Even if it is necessarilythe case that Socrates belongs to his singleton, this is not somethingthat holds in virtue of the nature of Socrates (but arguably in virtue

of the nature of the singleton). And again, even if it is necessarily thecase that Plato is not identical to Aristotle, this is not something thatholds in virtue of the nature of Plato (but arguably in virtue of both the nature of Plato and the nature of Aristotle).

Coming back to response-dependence: the proposal is then that inthe case of response-dependent properties, the necessity of the rele-

is a relevant a priori rd biconditional there is also a necessary and a priori(suitably rigidified) rd biconditional. Conversely, when rigidified specifica-tions are allowed, nothing changes if an existing necessity requirement isremoved, pace Haukioja 2001.




vant rd biconditional has its source in the very nature of the propertyin question, whereas nothing like this is true of the (also necessary)

rd biconditionals corresponding to primary, fully objective, proper-ties.

rd A property P is response-dependent iff there is an rd bicondi-tional for a concept signifying it which holds in virtue of thenature of P .

As I said above, I think this is indeed a general notion of a response-dependent property under which plausibly both secondary qualities

and evaluative properties – but not all properties – fall. But this no-tion also fails with respect to the original project, in that the claimthat a property is response-dependent in this general sense falls shortof constituting a vindication of realism concerning the property inquestion. The reason is, as I advanced, that response-dependentproperties, in this general sense, comprise both what I will call rigid response-dependent properties and flexible response-dependent prop-erties.

3. Rigid vs. Flexible Response-Dependent Properties

Let me say that a specification of the subjects in an rd biconditionalis rigid iff the relevant predicate involved in the specification is rigid.5 So for instance ‘normal human perceivers as they actually are’ is rigid, whereas ‘those disposed to value as I am, however I was’ is flexible.

5 I am assuming, with Kripke (1980), and a lot of people in discussions inthe philosophy of mind, the philosophy of science and metaethics, that thenotion of rigidity might be extended to be applicable to predicates, roughlyalong the lines of: a predicate is rigid iff it signifies the same property in allrelevant worlds. On that (controversial, although I think plausible and defen-sible) view, simple predicates like ‘is red,’ ‘is funny,’ ‘is good’ and the like are(arguably) rigid. Given this I will speak of them as signifying properties , withoutrelativizing such talk to worlds. Lebar (2005) contends that a response-dependent property need not be rigidly signified but, if I understand it right,

the considerations are in effect compatible with there being (flexible) prop-erties rigidly signified by the relevant predicates. As to his other alleged‘dogmas’ of response-dependence – that the relevant biconditionals be nec-essary and a priori – see my discussion in footnotes 4 and 10.




respect to w , the relevant response under certain conditions, as speci-fied with respect to w .7

Admittedly, the possibility of drawing some distinction along theselines is not terribly original, as allusions to the possibility of rigidify-ing devices figuring in the relevant biconditionals are customarilymade. This notwithstanding, I take it that the common opinion is thatthe distinction, even if it can be drawn, lacks real sinificant import, atleast insofar as the issue of realism is concerned. A paradigmatic ex-ample of someone who holds this opinion is Pettit:

[The relevant biconditionals can be interpreted] in rigid ornon-rigid mode. Rigid mode: something is red at a world ifand only if in the actual world it looks or would look red to therelevant observers. Non-rigid mode: something is red at a world if and only if at that world it looks red to the relevant ob-servers […]. [T]he difference generated by the rigid and non-rigid readings may not be very intimately connected with therealist problematic. (Pettit 1991, 612 –3)8

The main point of this paper is indeed to vindicate the significanceof the distinction precisely vis-à-vis the issue of whether response-dependence succeeds in sustaining realism.

As a first step in this direction, notice that the question of what kindof consideration could lead one to defend that a given response-dependent property is of the rigid or the flexible variety turns out to

7 Could one alternatively characterize the distinction directly in terms of

the notion of a disposition? As García-Carpintero (manuscript) emphasizes,the issue of distinguishing dispositional from categorical properties parallelsexactly that of distinguishing secondary from primary qualities, and familiarproposals, dwelling upon the apriority and/or necessity of the suitable con-necting biconditionals, fail for structurally the same reason we have alreadyconsidered: they over-generalize by covering categorical properties as well.8 A notable exception is Valentyne. He says, however: ‘On rigid response-dependent accounts [the attributes in question] are entirely objective andtheir satisfaction conditions have no essential connection with the respon-

sive dispositions that are used to pick them out’ (Valentyne 1996, 103). Buthe is explicitly operating with a notion of properties or attributes with modal individuating conditions, and thus incapable of distinguishing between fullyobjective properties and, precisely, rigid response-dependent properties.



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be far more complex than it appears. As it stands, a complete re-sponse would involve highly heterogeneous kinds of considerations.

Let me, somewhat stipulatively at this stage, call both primary, fullyobjective, properties and rigid response-dependent properties ‘realist properties ’. The issue as to whether or not a given realist property inthis sense is a rigid response-dependent property (and in particularthe issue as to whether colours are secondary qualities) is not some-thing to be settled only on a priori grounds. Suppose that F-ness is arealist property. Now, for considerations related to those alluded toabove, there will be a rigid rd biconditional for it holding a priori and

necessarily. That will be so independently of whether the property inquestion is response-dependent (of the rigid variety) or a primary,fully objective, property. Now, the issue as to whether it is a response-dependent property (of the rigid variety) will depend on whether ornot it holds in virtue of the nature of F-ness. But even if there couldbe (and in all probability there are) essentialist claims like those allud-ed to, i.e., statements which hold in virtue of the nature of a givenentity, which are knowable a priori , this doesn’t entail by itself that thestatement concerning its essentialist status is itself something knowa-ble a priori . And, as we have seen, the latter would be required for a view according to which one could settle on a priori grounds the issueas to whether one realist property is a rigid response-dependentproperty.

I want to suggest that what can be settled on a priori grounds is whether a given property is a realist property, in the present sense, ora response-dependent property of the flexible variety. Or rather, and

more precisely, whether a given everyday ordinary predicate or con-cept signifies a property of one or the other sort.

Suppose that S and C are relevant flexible specifications of subjectsand conditions, and S @ and C @ their relevant rigidifications. Suppose,for simplicity, that the following is the only pair of relevant rd bicon-ditionals:

(R) x is F iff x is disposed to produce in S @ the response R underconditions C @.

(F) x is F iff x is disposed to produce in S the response R underconditions C .



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Conversely, if ‘is F ’ signifies a realist property then (R) will be neces-sary. Now consider something, b , which actually doesn’t fall under ‘is

F ’ but is nonetheless disposed to produce R in the subjects under theconditions as S and C specify them with respect to the (counterfactu-al) target situation w , which, as before, concurs otherwise with the way the world actually is. The fact that this is a possibility is again ofcourse independent of the nature of the property signified by ‘is F ’.But the crucial question is now: how would we evaluate the statement‘b is F ’ with respect to this target situation w ? If we evaluate it as true with respect to w then, of course, (R) is false with respect to w , given

that b is F in the target situation even though b is not disposed toproduce R in the subjects S specifies with respect to the actual worldunder the conditions C specifies with respect to it (otherwise b wouldactually fall under ‘is F ’). But then (R) is only contingently true in theactual world, and hence ‘is F ’ does not signify a realist property butrather a flexible response-dependent property.

Let me stress once again that most of the facts that hold both in theactual world and in the target situation w do so independently of the

nature of the property signified by ‘is F ’. In particular it is neutral onthat score to suppose, as we have done, that a has, whereas b lacks,both in the actual world and in the relevant target situation, the dis-position to produce in certain (rigidly specified) subjects certain re-sponses under certain (rigidly specified) conditions; and that a lacks, whereas b has, both in the actual world and in the relevant target situ-ation, the disposition to produce in certain subjects (as the specifica-tion specifies them with respect to the target situation) certain re-

sponses under the conditions (as the specification specifies them withrespect to it). Acknowledging this is neutral in that it doesn’t by itselfprovide a way of settling the issue of the nature of the property sig-nified by ‘is F ’. That is settled, I have suggested, by means of that which would be the proper description of those target situations interms of ‘is F ’. But let us go on now to some illustrations of theseconsiderations and thus of the distinction.

4. Rigid Response-Dependent Properties: Colours

As I announced at the beginning, the case of colours and that of val-ues to be considered in the next section, even if containing contro-




versial assumptions, should serve to illustrate both the distinctionbetween realist and flexible response-dependent properties, and the

kind of relevant considerations involving the proper description of(counterfactual) target situations we have been concerned with in thepreceding section.

Concerning the colours, Wright says the following:

We are […] obliged to pay attention to the following intuitionabout colour: that had the typical visual equipment of humanbeings been very different, or had the lighting (by day) on the

earth typically been of a quite different character —perhaps re-sembling the illumination generated by sodium street light-ing —that need have made no difference to the colours thingsactually are. The extensions of ‘red’ and ‘green’ would not havebeen different if all human beings had been colour blind, and would not change if they were to become so. (Wright 1992,113)

Now I take it that Wright is here submitting what seems to be an in-

stance of the relevant considerations to the effect that ‘is red’ doesnot signify a flexible response-dependent property.

For take for instance a certain rock which is actually a deep red, andcall it Mahá . Consider the target situation, resembling the actual worldas much as possible – and thus in particular Mahá is similarly dis-posed to produce the relevant response in certain (rigidly) specifiedsubjects under (rigidly) specified conditions – in which the flexiblerelevant specification of the subjects specify, say, humans with per-

ceptual apparatus which would make them count as colour blind inthe actual world; or in which the flexible relevant specification of theconditions specifies, say, the illumination actually generated by sodi-um street lighting. So, Mahá does not have the disposition to producethe relevant response in the subjects as specified with respect to thetarget situation under the conditions as specified with respect to it.

The fact that this is a possibility is of course independent of the na-ture of the property signified by ‘is red’. But the crucial question isnow: How would we evaluate the statement ‘Mahá is red’ with respectto this target situation? Wright’s intuitions, and I take it that mostpeople’s intuitions would concur with them here, have it that it



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should be evaluated as true . But if this is so then the relevant flexiblerd biconditional for red will be false with respect to the target situa-

tion, and hence only contingently true in the actual world, and hence‘is red’ will not signify a flexible response-dependent property butrather a realist property.

Many philosophers dealing with this issue, I believe, do agree withour intuitions concerning the applicability of ‘is red’ with respect tocounterfactual worlds having such a consequence. Maybe evenmost —but not all . Consider for instance Averill:

[T]he human eye could change, in certain physically possible ways, so that after the change a few objects would appear to bedifferent in colour to normal observers (i.e., observers who arenormal after the change) […] For the sake of definiteness,suppose that after the change lumps of the metal gold (puregold) look red to normal observers under optimal viewingconditions. (Averill 1992, 552 –3)

Now this certainly seems to be the (suitably uncommitted) descrip-

tion of a target situation to assess the issue concerning the nature ofthe signification of ‘is red’. And, as just alluded to, most people would say that our intuitions regarding this case are just those sup-porting the previous claim that ‘is red’ signifies a realist property.However, Averill says precisely the opposite:

Surely the identification of objects by their colour is so im-portant to us that it would be preserved; so that after thechange we would say that gold is red . … [W]e ought to say (now in

the actual world) that in the possible world imagined … gold isred . (Averill 1992, 553 –4)

As I said, my purpose here is illustrative, and not to defend the viewof colours as realist properties.9

Suppose, then, that our relevant intuitions are such that colour termsand concepts signify realist properties. Now the notion of a realist property, as I am using it here, comprises both primary, fully objec-

9 Let me notice, however, that the view of colours as flexible properties is,I think, much more popular nowadays than it was when this material wasfirst written, partly due to Cohen’s recent work, see, inter alia , Cohen 2009.




tive, properties, as well as secondary, rigid response-dependent, prop-erties. One obvious question is: are colours of one or the other sort?

As I said above, I want to claim that the answer to this question willcrucially involve a posteriori considerations only accessible to the scien-tist. I think that most participants in the debate about the colours would agree in holding that it is not a priori true that colours are sec-ondary qualities: as a matter of fact, our terms and concepts for col-ours are such that they don’t reveal by themselves the secondariness,or rigid response-dependence, of the properties they signify, if anysuch exists. Although different people offer slightly different ration-

ales for this, the core of them is, I take it, the point that has been al-ready exploited above: our concepts for primary and secondary quali-ties are on a par, and thus, there is nothing in the concept of rednessthat entails that it signifies a secondary quality. Given the nature ofthe present perceptual case, this point can also be put thus: there isno relevant phenomenological difference between the way experiencerepresents shapes and colours (assuming the latter are secondaryproperties), or again, there would be no relevant phenomenologicaldifference in the way experience represents colours on the assump-tions that they were primary or secondary qualities.10

5. Flexible Response-Dependent Properties: Values

Let me consider now the case of values. As we saw, the issue of whether a given predicate or concept signifies a realist property orrather a flexible response-dependent one is to be settled by assessingthe modal status that intuitively should be attached to the appropriate

flexible relevant rd biconditional for them, of the form(F) x is F iff x is disposed to produce in S the response R under

conditions C .

10 Notice that the a posteriority component I am presently concerned withconcerns whether a given (a priori) true biconditionals holds in virtue of thenature of a property. Miscevic (1998) claims that the relevant rd bicondi-tionals for red should not be required to be a priori , but if I understand his

consideration right, his considerations actually supports the view that it neednot be a priori that colours are secondary, compatibly with the a priority ofthe involved biconditionals, see for further discussion López de Sa forth-coming.



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or its suitable rigidification, of the form

(R) x is F iff x is disposed to produce in S @ the response R underconditions C @.

These, in turn, crucially involve intuitions about which would be theappropriate intuitive description, concerning them, of certain suitablyuncommittedly described counterfactual target situations.

Consider the case of ‘is funny’. Something along the lines of the fol-lowing seems to be an a priori (flexible) truth:

x is funny iff x is disposed to amuse those like me under ap-propriately attentive conditions.

Now take something funny, even something, I am ready and willingto grant, really really funny, like The Simpsons . Lang suggests that we would not take very seriously the suggestion that it ‘would continueto be funny even if a comprehensive alteration in our comic sensibili-ties took place’ (Lang 2001, 201). And it certainly seems to be so:consider the possible world in which such a comprehensive alteration

in our comic sensibilities takes place, but which agrees, in so far as itis compatible with this, with the actual world, and in which in particu-lar The Simpsons are exactly the same. Suppose further, for the sake of vividness, that the disposition of something to amuse us as we actuallyare , exhibited by The Simpsons , is somehow constituted by expectationof ours (say). Then, in our envisaged world, The Simpsons do exhibitthis feature all the same; it is just that, unlike what we may supposeactually happens, doing so fails to make something disposed to amuse

us once the alteration is in place. So far, this is the description of arelevant target situation, for it is uncommittedly described, in that it isnot assumed that the relevant disposition to produce amusement inus as we actually are is being funny – nor is it assumed, of course,that they are distinct either. The fact that this is a possibility is inde-pendent of the nature of the property that ‘is funny’ signifies. But what does it signify? Well, consider the statement ‘The Simpsons arefunny’. How are we to evaluate it with respect to this target situation?Lang’s suggestion, with which, I take it, most of us will agree, is thatit should turn out to be false . But then ‘is funny’ does not signify arealist property but rather a flexible response-dependent one.




At this point one could try to resist this conclusion by something like:‘We do say, at least sometimes, that The Simpsons are funny, in the ob-

jective mood, as it were, rather than that I find them funny . Further-more, we say those things even acknowledging that they could notamuse some people, for after all some days, even if they’re funny,they don’t amuse us. Why couldn’t we say then that The Simpsons arereally funny even in the target situation, only that those unlucky peo-ple fail to be disposed to be amused by them?’ I will say somethingmore about the worry concerning relativism below. But the straightanswer now is that we could definitely say so: it’s only that intuitively

we, or at least most of us, don’t want to. Remember that the crucialissue is how a given target situation should be intuitively described . Butas I have stressed, the situation should be characterized uncommit-tedly, so that in the appropriate sense, it could be described in the wayincompatible with what seems to be intuitively required.

In the submitted consideration, there is also another important ele-ment which is worth stressing in order to avoid possible misunder-standings. The fact that we have simple predicates like ‘is funny’ signi-

fying the property of being funny does arguably entail that thereshould be a real/appearance distinction concerning what is funny,that being funny should be distinct from seeming funny or actuallyamusing. But that of course is also the case even if being funny is a flexible response-dependent property , and hence in particular does not entailanything about what the proper intuitive description of target situa-tions should be. There are things which seem funny although they arenot fun at all,11 and conversely, as submitted, The Simpsons are funny

even if they sometimes fail to seem so. But that is indeed entailed bythe use of the dispositional idiom in the rd biconditionals. Dispositionscan be possessed without issuing their characteristic manifestations. And conversely, their manifestation could occur without being themanifestation of a possessed disposition. Flexible response-dependent properties are not dispositions, true enough. But with re-spect to each world, the things that have a given flexible response-dependent property in this world are those that are disposed to pro-duce the relevant response in the subjects as they are in that worldunder the conditions as they are in that world. Hence, in each world,

11 See Wright 1992, 101, for a dozen examples of this.



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having the property of being funny is not the same as issuing the rel-evant response, seeming funny.

This seems to hold for a number of similar evaluative predicates: ‘istasty’, ‘is disgusting’, ‘is comfortable’, let alone ‘is sexy’, ‘is fashiona-ble’, or ‘is cool’. With respect to any of these, it seems, hardly anyone would claim to have the intuitions supporting their signifying realistproperties. But if that is so, and realism concerning their significa-tions is rejected, then we do have the required support for the claimthat response-dependence fails to vindicate even a qualified realismconcerning the properties in question, contrary to the purpose for

which it was introduced. For those flexible response-dependentproperties are response-dependent properties.

But thinking about these particular cases of what can be called softevaluative predicates might make one wonder whether the situation will generalize to encompass all evaluative predicates. And indeedsome initial plausibility could be given to the view even in the sketchyterms we have been dealing with so far. For consider the predicate ‘isgood’ and suppose something like the following is the relevant flex i-ble rd biconditional, see Lewis 1989:

x is good iff we are disposed to value x in appropriate reflec-tive conditions,

where valuing is the favourable attitude of desiring to desire, and ‘we’refers to a population consisting of the speaker and those relevantlylike her and to be relevantly like a given subject is to be disposed, withrespect to valuing the relevant thing in question in the relevant conditions,

exactly how the subject is. It is important to stress that, so understood,‘we’ turns out to be a flexible characterization of a group of subjects. The predicate ‘is relevantly like me’ actually picks out the property ofbeing relevantly the way I am actually. But I could be otherwise, and inparticular my disposition to value could be very different from what itactually is. But then, with respect to those worlds in which I am suit-ably different, ‘is relevantly like me’ will signify the property of beingrelevantly the way I would be in those situations.

What are we going to say about its modal status? What is good surelyis not what we happen to value: we easily fail to value some things which really are good and value some things which really are not.



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of its signification contains the materials for a suitably irremovabledivergence.13

It is important to notice that, independently of the contention aboutthe values, this entailment by itself makes the notion of flexible re-sponse-dependence illuminatingly connected with the problem ofdelineating the realism/antirealism debate, which in turn could vindi-cate my use of the label realist for the properties signified by simplenatural predicates which aren’t flexible response-dependent.

6. The Many Response-Dependencies

Response-dependence was introduced in order to generalize the no-tion of a secondary quality by applying also to values in a way suchthat – at least a qualified form of – realism was vindicated. The origi-nal characterization of a response-dependent concept fails with re-spect to this original project, as it arguably overgeneralizes, coveringconcepts independently of whether they signify primary, fully objec-tive, properties. The amended general characterization of a response-dependent property does not suffer from this difficulty, as it covers

13 A relativism of this sort, it is often said, would contradict a basic plati-tude regarding conversations concerning the evaluative: ordinary participantsare committed to regard utterances of ‘that is good’ and ‘that is not good’ as(literally) contradicting each other. Here is Wright: ‘If it were right, there would be an analogy between disputes of inclinations and the ‘dispute’ be-tween one who says ‘I am tired’ and her companion who replies, ‘Well, I amnot’ (when what is at issue is one more museum visit). There are the mater i-

als here, perhaps, for a (further) disagreement but no disagreement has yetbeen expressed. But ordinary understanding already hears a disagreementbetween one who asserts that hurt-free infidelity is acceptable and one whoasserts that it is not’ (Wright 2001, 51). I agree with the datum : in any ordi-nary non-defective conversation it is common knowledge among the partic-ipants that utterances of (say) ‘that is good’ and ‘that is not good’ wouldcontradict each other. But I resist the idea that a Lewisian proposal, with therelativism concerning the evaluative it entails, is incompatible with it. Thisresistance can be substantiated by making explicit a presuppositional com-

ponent it has, along the lines of: ‘is good’ triggers the presupposition thatthe addressees are relevantly like the speaker both in actual and counterfac-tual situations. That element is anticipated by Lewis himself, see Lewis 1989,84; see for elaboration López de Sa 2008.




both secondary qualities and evaluative properties, but not all proper-ties – and thus constitute a prima facie candidate for the original pro-

ject for which response-dependence was introduced. I have arguedthat it ultimately fails however, as the claim that a property is re-sponse-dependent in this general sense falls short of constituting a vindication of realism concerning the property in question. As I said,this is so because response-dependent properties, in this generalsense, comprise both rigid response-dependent properties and flexi-ble response-dependent properties. Flexible response-dependentproperties very plausibly include soft evaluative properties like being

tasty, disgusting, comfortable, sexy, fashionable or cool, and in anycase entail the sort of relativism traditionally contrasted with realism. Yet flexible response-dependence properties are response-dependentproperties.

To conclude I want to make explicit that the way all this is expresseddepends on having decided to use ‘response-dependent property’ toexpress a notion that at least constitutes a prima facie candidate forthe original project for which response-dependence was introduced.

This contrasts with at least two possible alternatives, present in theliterature.

García-Carpintero (2007) characterizes ‘response-dependent proper-ty’ stipulating that the specifications figuring in the relevant bicondi-tionals are rigidified, that is, so that ‘response-dependent properties’in his sense just are rigid response-dependent properties. ‘Response-dependence’ in his sense would indeed serve to support realism. Butthat values are ‘response-dependent properties’ in his sense would

require the kind of a posteriori considerations illustrated with thecase of the colours, and in any case would be at odds with what mostthink is plausible to hold with respect to being tasty, disgusting, com-fortable, sexy, fashionable and cool.14

Johnston (1998) characterizes ‘response-dependent property’ stipulat-ing that the necessity of the relevant biconditionals is not the result

14 If I understand him right, at the time that paper was written he seemedto hold that it was impossible for a predicate to signify (what I am calling)flexible response-dependence properties. He may have changed his mindsince.



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of the specifications figuring in them being rigidified, that is, so that‘response-dependent properties’ in his sense just are flexible response-

dependent properties. That values are ‘response-dependent proper-ties’ in his sense would be certainly congenial with what most think isplausible to hold with respect to being tasty, disgusting, comfortable,sexy, fashionable and cool. But for that reason, and for the considera-tions involving relativism I alluded to, ‘response-dependence’ in hissense does not seem a prima facie candidate to serve to support real-ism.

Response-dependence as applied to properties, as I have been using

the notion, does indeed constitute a prima facie candidate for theoriginal project for which response-dependence was introduced. Italso ultimately fails, though.15

References

Averill, E. 1992: ‘The Relational Nature of Colours’. The PhilosophicalReview 101, pp. 551 –88.

Brynjarsdóttir, E. M. 2008: ‘Response-Dependence of Concepts isNot for Properties’. American Philosophical Quarterly 45, pp. 378 –86.

Cohen, J. 2009: The Red and The Real: An Essay on Colour Ontology . Ox-ford: Oxford University Press.


15 This paper elaborates on the core distinction of López de Sa 2003. Thanks to audiences at the Australian National University, Euskal HerrikoUnibertsitatea, Stockholms Universitet, Turun Yliopisto, Universidad deBuenos Aires, Universidad de Granada, Universitat de Barcelona, and Uni- versity of St Andrews, and in particular to Agustín Arrieta, Eline Busck, Josep Corbí, Fabrice Correia, Martin Davies, Esa Díaz-León, José A. Díez, Andy Egan, Manuel García-Carpintero, José Gil, Andrea Iacona, JussiHaukioja, Frank Jackson, Philipp Keller, Kevin Mulligan, Philip Pettit, Sven

Rosenkranz, Armin Tatzel, Ekai Tzapartegi, Agustín Vicente, Crispin Wright, Elia Zardini, and the editors of this volume. Research has been par-tially funded by FFI2008-06153 and CSD2009-0056 (MICINN), 2009SGR-1077 (AGAUR), and ITN FP7-238128 (European Community).




García-Carpintero, M. 2007: ‘A Non-modal Conception of SecondaryProperties’. Philosophical Papers 36, pp. 1 –36.

— manuscript: ‘A Non-modal Conception of the Categori-cal/Dispositional Distinction’.

García-Carpintero, M. and M. Kölbel (eds.) 2008: Relative Truth . Ox-ford: Oxford University Press.

Gundersen, E. B. 2010: ‘Dispositions and Response-Dependence Theories’. Poli and Seibt 2010, pp. 119 –34.

Hales, S. (ed.) 2011: A Companion to Relativism . Oxford: Blackwell.

Haukioja, J. 2001: ‘The Modal Status of Basic Equations’. PhilosophicalStudies 104, pp. 115 –22.

Jackson, F. and P. Pettit 2002: ‘Response-dependence Without Tears’.Philosophical Issues 12, pp. 97 –117.

Johnston, M. 1989: ‘Dispositional Theories of Value.’ Proceedings of the Aristotelian Society (suppl. vol.) 63, pp. 139 –74.

— 1998: ‘Are Manifest Properties Response-Dependent Properties?’.

The Monist 81, pp. 3 –43.Kripke, S. 1980: Naming and Necessity . Cambridge, MA: Harvard Uni-

versity Press.

Lebar, M. 2005: ‘Three Dogmas of Response-Dependence’. Philosoph- ical Studies 123, pp. 175 –211.

Lewis, D. 1989: ‘Dispositional Theories of Value’. Proceedings of the Aristotelian Society (suppl. vol.) 63, pp. 113 –38.

López de Sa, D. 2003: Response-Dependencies: Colours and Values . Univer-sitat de Barcelona. URL:http://webspace.utexas.edu/deverj/personal/test/response.pdf

— 2006: ‘The Case against Evaluative Realism’. Theoria 21, pp. 277 –94.

— 2008: ‘Presuppositions of Commonality’. In García-Carpintero

http://webspace.utexas.edu/deverj/personal/test/response.pdf

http://webspace.utexas.edu/deverj/personal/test/response.pdf

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