studies in wilfrid sellars' philosophy || sellars' ontology of categories

Sellars' Ontology of CategoriesAuthor(s): Murray KiteleySource: Noûs, Vol. 7, No. 2, Studies in Wilfrid Sellars' Philosophy (May, 1973), pp. 103-120Published by: WileyStable URL: http://www.jstor.org/stable/2214486 .

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SELLARS ONTOLOGY OF CATEGORIES 103

14 The defense is given in my "Belief and Error," forthcoming in a volume edited by E. Klemke and M. Gram to be published by Northwestern University Press. (Available from the author.)

15 Such definitions are given in my "Induction: A Consistent Gamble," THIS JOURNAL, 3 (1969): 285-97, and in "Induction, Rational Acceptance, and Minimally Inconsistent Sets." Compare also the definitions of utility in Carl G. Hempel, "Deductive-Nomological vs. Statistical Explanation," in H. Feigl and G. Maxwell (eds.), Minnesota Studies in the Philosophy of Science, Vol. III (Minneapolis: University of Minnesota Press, 1962): 98-169; Jaakko Hintikka and J. Pietarinen, "Semantic Information and Inductive Logic," in Aspects of Inductive Logic, J. Hintikka and P. Suppes (eds.) (Amsterdam: North-Holland, 1966): 96-112; Risto Hilpinen, Rules of Acceptance and Inductive Logic, Acta Philosophica Fennica, Vol. 22 (Amsterdam: North Holland, 1968); and Isaac Levi, Gambling with Truth (New York: Knopf, 1967).

16 Science, Perception, and Reality, p. 356. 17 I defend this thesis in "Scepticism and Conceptual Change," forthcoming

in a volume edited by R. Chisholm and R. Swartz. (Available from the author.) 18 Science, Perception, and Reality, p. 334, and in conversation. 19 Cf. Keith Lehrer, "Induction and Conceptual Change," Synthese 23 (1971):

206-225. 20 I show this in "Evidence and Conceptual Change," forthcoming in Phi-

losophia and in "Evidence, Meaning and Conceptual Change," forthcoming in a volume edited by G. Pearce to be published by Reidel. (Available from the author.)

21 "Non-Deductive Logics," pp. 102-3. Sellars discusses categorical rea- sonableness in Science andMetaphysics (NewYork: Humanities Press, 1968): 213-222.

22 "Non-Deductive Logics," p. 103. 23 Soren Kierkegaard, A Kierkegaard Anthology, Robert Bretall, ed. (New

York: Modern Library, 1936), "The Task of Becoming Subjective," pp. 207-208. 24 N. 0. Brown, Life Against Death (New York: Vintage Books, 1959): 307-322.

Sellars' Ontology of Categories MURRAY KITELEY

SMITH COLLEGE

"Category," said H. W. Fowler, "should be used by no-one who is not prepared to state 1) that he does not mean class, and 2) that he knows the difference between the two." (Modern English Usage.) I am sure that Fowler did not intend to rob philosophers of this word, that his animus was directed rather at those who use it as an elegant variant of 'class'. Nonetheless, conscientious ob- servance of the rule of his prohibition would eliminate this old technicality from the professional vocabulary of the most confident



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category-theorist. If Fowler's phrase "know the difference between the two" entails "be able to state correctly and with confidence the difference between the two," then I reckon a great silence would descend over large tracts of ontology.

I shall refer to this problem, the problem of distinguishing categories from extremely general classes, for convenience of designation, as Fowler's challenge.

Wilfrid Sellars has taken up Fowler's challenge in two papers that I shall examine in the first part of this essay: "Grammar and Existence: a Preface to Ontology," and "A Theory of Categories."' At the end, I shall set out a putatively different account of categories, one that defines them as classes whose conditions of membership are syncategorematic in a particular and peculiar way. Whether 'putative' will give way to 'merely apparent' will be my closing note.

Although Fowler's challenge concerns the word 'category' and not category-words, it is with the latter that we must begin, and begin somewhat lamely by setting out a sample list. The category-words 'property', 'class', 'relation', and 'thing', whatever other candidates philosophers in their ingenuity have proposed, represent an honorable tradition in the subject. If their categoricity can be accounted for, other less obviously paradigmatic examples such as Sartre's 'being-for-itself' may plausibly be hoped to succumb to a like handling.

These at any rate are the category-concepts that are among Sellars' quarries in the two papers just mentioned.

The first part of "Grammar and Existence" is directed at the proposition that such formulae of second-order quantificational logic as '(3f)fx' commit their user to the existence of abstract entities. This Sellars denies. That they appear to assert the existence of properties, and therefore abstract entities, is an illusion.

The illusion is induced by medium and association. In the case of '(3f)fx' the distorting medium is the corresponding English sentences used either to read off the formula, or to describe it in a meta-language. The two usual readings of '(3f)fx' may take one of two forms differing in degree of categorial explicitness. The less explicit pair, 'there is an f such that x is f', and 'some f is such that x is f', assume a prior understanding of the categorial difference between the variables 'f' and 'x', viz., that 'f' is a property- variable and that 'x' is an individual variable. The second pair make this difference explicit: 'there is a property x is' and 'x is




some property'. The greater explicitness, however, leads to incoherence, for the formula does not say, as these readings of it say, that there is a property identical to x. If anything, it says that there is a property that x has, not that x is identical to; but it cannot be read to say this either, since 'fx' says that x is f, not that x has f.

The non-explicit readings are equally, if less patently, incoherent. The two occurrences of the variable 'f' in 'there is an f such that x is f' are asymmetrical as to context. The indefinite article preceding the first occurrence of 'f' requires a count noun; the copulative 'is' preceding its second occurrence requires an adjective. In fact the difficulty with the categorially explicit readings also arises from asymmetry of context. The phrase 'is some property' determines an internal position controlled by conflicting contexts. One context, 'is ', calls for an adjective, the other, 'a property, namely, ', calls for an abstract singular term. The reading is, therefore, a zeugma in precisely the same way as is 'the pineapple was eaten and the apples neglected'-'pineapple' calls for 'was' and 'apples' for 'were'. The quality of zeugma appears with much greater force if some other copula is substituted for 'is', e.g., 'x sounds some property' or 'x becomes some property'.

The straightforward solution to these problems of conflicting context is to impose consistency. This can be done by removing from second order formulae open sentences of the form 'fI', 'fxy', etc., and replacing them with their platonic counterparts, 'x has y', 'x bears y to z', etc. '(3f)fx' now will run '(3y)x has y', a formula that can be both read off smoothly as 'there is a property that x has,' and instantiated coherently by, e.g., 'redness is such that x has it'.

The problem for which this is a solution is one of conflicting mixed idioms, one platonic, '(3f)', insofar as its 'f' is understood to be replaceable by abstract singular terms, the other non-platonic, 'fx', insofar as its 'f' is understood to represent the adjectival part of a predicate applicable to x. The solution indicated in the last paragraph rewrites the formula to make it uniformly platonic. At this there are those who would wince, or smile wanly.

Sellars' demurral from a platonizing solution like this is solider than a wince: he argues no need to move this far towards a platonic ontology, with one's variables ranging over properties and relations, as well as individuals, unless the problem which the notational revision solves is real. It is not real. '(1f)fx' does not need to be rewritten, only resaid. Not that this is simply a matter



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of phonetic contrivance, like spelling the formula rather than pronouncing it so as not to commit oneself to the substitution- range of 'f'. The reading Sellars suggests entails a re-appraisal of second-order quantifiers as, in Quine's phrase, non-objectual, or even more aptly for Sellars' account, as non-categorial, since to speak of the range of quantified variables, whether a substitution- range of expressions or a range of objects, is to speak of a class. Talk of membership in classes, however, is the platonic counterpart, the categorizing counterpart, of sentences that assert something to be of a certain kind. To substitute class-names for kind- words (common nouns) and the two-place predicate 'E' for 'is a' is as unnecessary as putting property-names for adjectives and 'instantiates' for 'is'. The first position of the kind-variable 'k' in '(3k)x is a k' no more needs to be thought of as a position for a singular term than does the first 'f' in '(3f)fx'.

Sellars' how-quantification is then a form of non-objectual quantification distinct from substitutional quantification. What is it?

My account, I should warn, is partial or metonymic. I tell only what Sellars says about quantifiers that bind adjective- variables, although he says similar things about quantifiers that bind sortal or kind-variables and sentential variables.

Category-words, being the chief objectifying villains, must be exorcized wherever they appear. The incantation effective for their appearance in general sentences is, Sellars suggests, to review the effect of replacing them with those pre-categorial place-holders, interrogative pronouns. The conceptually liberating reading of '(3f)fx' is, then, 'x is somehow', or to use Sellars' own word, a word that revives the memory of the relation of category- words and interrogatives, 'x is some quale' (not, note, qualitas.) The phrase chosen for the reading is not in itself important. What is important is that it, like the phrase 'is somehow', not impose a conflicting internal environment that inconsistently demands an adjective after 'is' and an abstract singular term like 'redness' in specification of the 'some'-phrase. 'Somehow' is thus preferable to 'some property'.

One apparently awkward consequence of Sellars' account is that the variable 'f' in the formula '(3f)fx' ranges over (one cannot say properties without being besieged by all the old troubles) shows.

Can sense be made of this? Can Sellars coherently talk about the range of the variables at all without reifying their values and




nounizing their substituends? Ordinarily a range is thought of as a class; thus, to assign triangular to the range of 'f' is to assert its membership in a certain class, and thus tantamount to saying that the object triangularity belongs to that class. It is not clear to me how eschewing talk of classes in favor of talk of kinds or sorts avoids this problem: the position of 'x' in both the following open-sentences, 'x is such and such a kind' and 'x belongs to such and such a class' calls for a singular term, whether abstract or concrete.

This is an instance of a more general difficulty. Even if '(3f)fx' can be read so as not to require that 'f' be both an adjective and an abstract singular term, there is no assurance that we will not wish to say things in which the initial quantifier binds predicate variables that occur in open sentences whose context demands that the substituends of the variable be singular terms, and in particular, abstract singular terms.

Suppose, to take a case, one has good reason to say that some properties are identical, for instance the properties of being a prime number and of being divisible only by itself and one. Surely there is a general statement of which the latter is an instance, in point of fact '(3f) (3g)f = g'. But the places governed by the relation of identity are for singular terms; thus the substitution- range of 'f' and 'g' cannot be adjectives.

Put generally the problem is this. Let '(Qf)b' represent any sentence, general or singular, in which 'O' is an open sentence containing 'f' and in which '(Qf)' represents the closure of 'O' either through quantificational binding of 'f', as in '(3f)', or by way of substitution of a constant for 'f'. If 'f' is to be an adjective- variable, then the grammatical structure of 'f' must not require a singular term at the position occupied by 'f'. I have mentioned three 'O's where just this seems to happen: the first was where 'f' (or 'y'-variable style makes no difference) appears as the second term of the relational predicate 'has' or 'instantiates'; the second was where it appears as the first term of the relational predicate 'is a member of' or 'is of such a kind'; and the third was where it occurs on either side of the relational predicate 'is identical to'. Where the predicate of 'O' is any one of these three relational predicates, '(Qf)o' introduces abstract singular terms at the position of 'f'. My complaint, then, is that Sellars' how-quantification shows only the first of these forms to be eliminable.

Sellars is alive to this problem. He gives, on page 268 of "Grammar and Existence," several examples of ineliminable



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platonic idioms, idioms formed of such categorial predicates as 'is a quality', 'is a class', and 'is a proposition'. When predicates such as these govern the position of 'f' in 's', its substituends cannot but be abstract singular terms.

Categorial predicates like these are in a sense fundamental to all other platonic idioms, for even if one's language lacked both abstract names and an apparatus by which such names could be constructed from other parts of speech, one would still be able to assert the existence of properties. Having the category- word 'property' would be enough, and although the speaker of such a poor language would be unable to meet the challenge, "Give me an instance!", except by constructing a definite description around the very predicate in question, he would perfectly well be able to describe the domain of his property-naming variables.

Category-words are the nub. Even if they be eliminated, in the Sellars way, from the bad mixed-idiom readings of such sentences as '(3f)fx', they will still appear in pure platonic sentences like 'redness is a property'.

Sellars begins his discussion of such words as these last by observing that the truth of what they say is not determined by appeal to empirical criteria (p. 268). However it is that we find out whether or not redness is a property, we do not follow methods like those used to determine whether a particular insect is a tiger beetle. What we do do, Sellars says, is to reflect "on the role in discourse of the corresponding expression," i.e., 'redness' in the example I have given (p. 269).

'Redness is a property', then, seems to express an a priori, or at least a non-empirical, truth. It also seems to express an eternal truth, since the present tense 'is' does not admit of contrast with such other tenses as past and future, e.g., the queer 'redness once was but is no longer a property'. Yet, unless there is some hidden logical complexity, either in the word 'redness' or in the word 'property', it cannot be a truth of logic, lacking as it does any expressions for logical operations. Its truth then, on the above suppositions, could not be explained by showing it to be, when unravelled, an instance of an assertible proposition of logic.

The word 'property', however, may well have a logically complex criterion of application; but it seems less plausible to think this of the abstract singular term 'redness'. If this word is simply a proper name for the property of redness, it is difficult to see how it could resolve into logically connected parts, the way,



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say, 'two' does when defined as the class of all pairs. Yet if the sentence is to express a logical necessity, the abstract singular term 'redness' must behave like a common noun whose criterion of application entails that of 'property'.

To understand why this is so is, I think, a condition for appreciating Sellars' two doctrines regarding the words of the sentence 'redness is a property', the first being that 'redness' is, in spite of appearances, a general term, and the second being that the logical form of the sentence is, in spite of appearances, the same as that of 'lions are animals'.

It may be said, however, in opposition to the argument of the preceding paragraph, that although 'redness' is a singular term which, for that reason, lacks a criterion of general application, still it has a sense as well as a referent, a sense moreover that is our only guide in discovering what and what sort of thing it singles out. This sense, further, is a property that entails the criterion for the application of the word 'property'.

A Fregean explanation like this of the joint singularity of 'redness' and the logical necessity of 'redness is a property' would have to take the next step of identifying the sense of 'redness' and displaying its relationship to property-hood. If its sense is the property of being identical to redness (in symbols, 'I(redness)'), and if the criterion of 'property' is understood to be the disjunctive property of being identical to redness, or being identical to triangularity, or being identical to salinity, or ..., then clearly I(redness) will entail property-hood. The underlying logical structure of 'redness is a property' would then be of the form 'p D p V q V r V ... '. Although this account explains the way in which the target sentence is true, it would seem to make the categorization of a newly discovered property a pretty arbitrary matter. 'Blankness is a property' would be false until one added to the disjunctive list that tells us when the word 'property' is applicable the new alternative 'or is identical to blankness', and one could still not be sure, assuming blankness to be a simple, unanalyzable property, that such an addition would not be a category-mistake.

I turn then to Sellars' theory.2 What 'redness is a property' says is that the role played by the word 'red' is a predicate- role.

This paraphrase of Sellars' paraphrase is as it stands misleading. It makes, e.g., an explicit reference to the English word 'red', and by doing this implies the existence of this particular



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word, which existence is a merely contingent matter of fact. Further, by referring to the role that 'red' does now play, the paraphrase makes explicit reference to time and the putative abstract entity, 'red's role. Yet the target sentence seems to express a timeless, a priori truth that carries no implications to contingent matters of fact. One may wish to argue that these properties of the sentence are merely apparent, but the way to do it is not simply to paraphrase them away.

The ingenuity and the difficulty of Sellars' account consists in its explanation of how this sentence says this which it does not appear to say at all. It seeks not only to unmask the sentence's appearances but to save them.

Consider, first, 'redness'. It is an abstract noun formed from the adjective 'red' by the addition of the nounizing suffix 'ness'. What the suffix 'ness' does is analogous to what the mentioning quotation marks around it do: it changes one part of speech to another. The quotes around 'ness' allow me to mention the suffix rather than using it; the 'ness' added to 'red' allows me to mention the property rather than to ascribe it.

Suppose now that I want to say something about the suffix 'ness' for which mere quotation is inadequate. Suppose I want to single out, not the class of morphemes similar in sound or look to what lies between the quotes in 'ness', but rather the grammatical operation indicated by the italicized suffix on each of the following words: 'redness', 'serfdom', 'governance', and 'triangularity'. If I were hard pressed to know how to say this, if I lacked such technicalities as 'the grammatical operation of abstract nominalization', I might simply speak of ness-dom and leave it to my audience to calculate the import of this outlandish word. In so doing, I would be doing something very much like what Socrates did to an unprepared Theodorus by springing on him his neologism 'votorqg%' a word whose literal equivalent is 'howness', later translated by the Latin 'qualitas'.3 Thus the etymological origins of the category-word 'quality' are hardly less outlandish than my imagined invention of 'ness-dom'.

That the import of 'ness-dom' would be understood to be linguistic in some very general way, that it would not be thought to refer to a queer property common to all properties, seems more plausible than the similar doctrine about 'redness'. But if the import of 'ness-dom' is linguistic, why not 'redness'?

For Sellars ness-dom is quote-dom. The quotation function he has in mind, however, is an extension of the ordinary one. To




indicate that it is an extension, he uses dots rather than inverted commas for its expression.

For 'redness' then substitute '-red-'. This five-letter word, unlike the abstract singular term it replaces, is a common noun, is general rather than singular. So, to do the same job as 'redness', it must be singularized, which Sellars does in the singular way of prefixing it with 'the'. 'Redness' gives way to 'the *red.'.4

Since the use of many quotation marks is something of a strain, I shall make use of italics to mention dot-quoted expressions; they are to be understood to have greater scope than dots, i.e., when the letters between the dots are in italics so are the dots.

*Red- is a common noun uncommonly formed. Its three middle letters illustrate, give an instance of, the elements of the class to which it applies. Unlike mentioning quotation, however, the elements of the covered class do not belong to the class simply in virtue of their shape or sound; they belong to it in virtue of playing a role like that played by 'red' in English. Since the conception of a role is a rule-fraught or prescriptive conception, the criteria by which *red- selects that to which it applies will at best be only partly phonological/graphological. Let me quote:

... dot quotation corresponds to ordinary quotation where the latter practice has been modified in such a way that the descriptive component of the criteria for the application of the common noun formed by quoting has been reduced to that which is implied by the prescriptive component, and the latter has been given its most generic formulation.5

What now does the singular term, the -red-, refer to ? It does not refer, as one might imagine, to the common role played by 'red', 'rot', and 'rouge' in their various languages. If it were to do this, then the nominalist advantage might seem to have been lost, a role being about as general and abstract an entity as a property. The phrase is not a definite description at all, 'the' being used in that institutional manner whereby it forms a distributive singular term like 'the lion' in 'the lion is an animal'. It picks out a particular lion only as a rhetorical representation of all lions, as does Lepidus' possessive pronouns in his speech on Pompey's galley: "Your serpent of Egypt is bred now of your mud by the operation of your sun. So is your crocodile." Although drunk, Lepidus is no more referring to a single serpent or crocodile than he is giving Antony title to it. 'Your serpent', like the -red-, is a distributive singular term.



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One last point in this exiguous exposition of Sellars on 'redness is a property'. The reconstruction of this sentence cannot go half way; it cannot stop with the first word; it must be applied simultaneously to both subject and predicate. The reason for this is that the predicate that is to replace 'is a property', namely, 'is a one-place predicate', carries with it dot quotes around its subject position, thus: '__- is a one-place predicate'. So, if one performed the analysis incrementally, first changing 'redness' to the -red-, and then changing 'is a property' to 'is a one-place predicate', the result would be 'the *the -red- - is a one-place predicate', a sentence that wrongly calls the distributive singular term the *red- a predicate. Categorial contexts require contextual analyses.

The apparent singularity but the real generality of the reference of 'redness' is deducible, then, as a consequence of its being a distributive singular term, as the *red- is by contrivance, and Lepidus' 'your serpent' is by nature, or by force of circumstance. There are things that are *red-s, just as there are things that are serpents; nothing similar can be said about the common noun embedded in 'redness', since it cannot be extracted, as were 'serpent' and *red- from their distributive singular phrases.

Does Sellars' theory save or explain features of the whole sentence as well as its first word ? 'Redness is a property' seems a) to express a timeless, a priori truth, b) about a single object named 'redness', c) which truth makes no reference to contingent matters of fact, nor, d) via quotation, to a particular word in a particular language, thereby and to that extent resisting word by word translation into another language.

'The -red- is a one-place predicate' is an explanatory substitute for the categorizing target sentence in that it either has or apes each of the properties listed above. It is timeless and a priori in exactly the same way that 'all lions are animals' is timeless and a priori: just as the criteria for being a lion number among themselves the criteria for being an animal, so the criteria for being a -red-, e.g., having the same co-occurrence restrictions, number among themselves the criteria for being a one-place predicate. The -red-, like 'redness', appears to make singular reference; the appearance in both cases is a rhetorical illusion owing to a single sample of the term's extension being selected to represent the whole lot. Nor does the expression -red-, even though a special form of quotation, make reference to contingent matters of linguistic fact, such as the existence of the word 'red'. Using




the word 'red' to evoke its compatriots does not imply its existence in the way, say, that saying it is being so used would. The sentence does itself, as distinct from what it says, give evidence of the reality of the word 'red', a contingent fact, but then so does the sentence 'redness is a property'. The logical form of the sentence is anyway universal, not singular, its formula being '(x)(if x is a -red, then x is a one-place predicate)', a formula that does not imply the existence of *red s. Finally, the dot quotes do not introduce a context opaque to translation into another language (nor are they, says Sellars, opaque to quantification); they do not operate like the mentioning quotes in the following German setence, " 'red' ist ein englisch Adjectiv." In similar circumstances the 'red' in Credo would translate, and do so without introducing misleading information, since the German word 'rot' can just as well represent the class to which it and the English 'red' belong as 'red' itself.

The artifice of dot quotation lifts the spell of Platonism thus from the abstract-singular-term-introducing (AST-introducing) contexts determined by such categorial predicates as 'is a property'. What about the other AST-introducing contexts mentioned at the beginning of the paper, namely, identity, membership, and instantiation? The discussion of this last I shall defer to the next section in which I set out an alternative account of categories, but identity and membership will get a word now.

A singular statement of property identity, e.g., 'redness -rotheit', causes no difficulty for Sellars' theory: it becomes on analysis the general statement '(x)(x is a -red- = x is a -rot )'. Clearly, then, the generalization of such a putatively singular assertion of identity is going to be a little complicated. It would have to be, not '(3f)(3g) f g', but, using 'o' and 'p' as variables whose substituends are dot-quoted adjectives, '(x) (3ao) (3p) (x is an o - x is a P)'.

Similarly, to assign redness to the range of the how-variable, 'f', is to say that one-place predicates substitute for 'f', and -red- is a one-place predicate.

Do categories classify reality, or do they rather classify the language and thought that we use to classify reality? That they appear to do the former but in fact do the latter is a proposition that Sellars has defended by the invention of sentences that bear a point by point comparison to category-sentences, yet which draw

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together into classes, not extra-linguistic entities, but inter- and intra-linguistic role-determined expressions.

Sellars' short response to Fowler's challenge is that categories are not classes at all but kinds of role-defined linguistic, and mental-linguistic, entities. The distinction between kinds and classes is of the same sort as the distinction between properties and hows: to move from 'x is an animal' to 'x is a member of the class of animals' is the same as to move from 'x is red' to 'x has redness'.

A prima facie different response to Fowler's challenge would be to conceive categories as classes with peculiar conditions of membership, conditions that are such as to set off all categorial from non-categorial classes, and that are such that when generalized to assign all categorial classes to the class Category. (I shall below, as with this last word, distinguish kind-words from class-names by capitalizing the latter, e.g., 'redness is a property' but 'redness belongs to Property'.)

How then does the class Property differ from the class Uncle? They differ in condition of membership. Although the members of both these classes merit their position by standing in a certain relation, the relations are very different. Excluding for the moment null properties, to belong to Property it is necessary and sufficient to be instantiated; to belong to Uncle it is necessary and sufficient to be the brother of a parent. The difference between the relation of instantiation and the relation of being the brother of a parent is clearly not one of degree of generality: kinship is the genus of avuncularity, and relatedness the summum genus of them both. Instantiation may indeed not be thought to be a proper relation at all, since it is a sort of platonic shadow of the copula 'is'. The truth-conditions of the two sentences 'this is red' and 'this has (or instantiates) redness' seem to be exactly the same, yet the first is clearly not relational. In consequence of this, the asymmetry of the relation of instantiation is eccentric; reversing the terms of the relation result in nonsense rather than falsity, e.g., 'this balloon has redness' which with terms reversed becomes the unacceptable 'redness has this balloon'. This latter, I suggest, if it could be given an interpretation at all, would be read as the original sentence in oddly inverted word-order, not as a new sentence got by inverting the word-order of the original.

The oddities of the relational predicate 'instantiates', including the one complained about in the early pages of this paper, viz., that it requires abstract singular terms on its right flank, are for



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present purposes advantageous. Its relational character allows it to be used to determine the membership of the category Property; the eccentricity of its relational character accounts for the oddness of this categorial class.

I suggest, then, that categories are classes determined by such relations as instantiation. Can the 'such' of this last sentence be explained ? A category-forming relation can perhaps be explained this way: it is expressed by a relational predicate which forms sentences that are true under the same conditions as a sentence like the original except that in place of the relational predicate it has a simple copula or other sentence formative. This condition is sufficient to select instantiation, membership, and implication as category-forming or apparent relations. The three relational sentences 'this instantiates redness' (A), 'this is a member of the class of red things' (B), and 'that A implies that B' all are true under the same conditions that make true the three non-relational sentences 'this is red', 'this is a red thing', and 'if A, then B'. The three categories formed from these apparent relations are Property, Class, and Condition (or Cause if the implication is causal.). There is a marked difference between the first two relations and the last. Instantiation and membership shadow the copulative 'is' used with either an adjective or noun-complement to form a simple sentence, whereas implication shadows the compound- sentence forming conjuntion, 'if-then'. This is part of the difference between Kant's and Aristotle's categories. In what follows, however, I shall stick to the basic and Aristotelian categories, and ignore the compound and Kantian categories.

Although I think this condition is sufficient for meriting a relation category-forming, I am not at all sure that it is necessary. There are other technical difficulties as well, only two of which I shall attempt to meet. The first is how to frame the definitions so as not to exclude null elements from the appropriate category: if Class, e.g., is defined as that which has members, then the null class is not a class. The second is how to square the definitions with a non-platonistic account of categories like Sellars'.

The definitions can be stated quite simply if the problem of nullity is ignored. It is convenient to begin then with their simple and defective forms and delay the complications until the end of the paper. The definitions of 'class' and 'property' are as follows:

w is a class Df W E X ( (3y)y E x),



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i.e., w belongs to the class of all membered elements;

w is a property -Df W E X ( (3y)y instantiates x),

i.e., w belongs to the class of all instantiated elements.

These definitions collapse three steps into two. The missing step transforms the definienda into what Sellars calls their categorizing counterparts; thus, 'w is a class' becomes 'w E Class'. Definitions of the correlatives of 'Class' and 'Property', viz., 'Member' and 'Instance'; can be stated by reversing the variables of the open sentences in the class abstracts. The sets Class and Member, like the sets Father and Son, are not disjoint, although if there are Adam-members, i.e., members that lack members, the set of such members would not overlap Class.

These definitions determine an array of concepts derived from the terminal positions of apparent relations. Let 'R' be a variable for all those apparent relations that shadow simple- sentence forming copulae. Category, then, is the union of the converse domains of all relations R, whereas Individual, as it might be called, is the union of the domains of all relations R. The lists of converse domains (categories) and domains (individuals) will be as uncertain as the range of R; however, the following examples seem fairly certain: Class and Member (R - E), Property and Instance (R - instantiates), Relation and Term (R bears), Event-kind and Event-instance (R = the instantiation of occurrences, i.e., the instantiation image of occurrence).

Each of the categories is a class of elements to which R is borne, and each of the classes of individuals is a class of elements that bear R.

How does this account differ from Sellars'? Does it, for instance, entail the existence of such abstract entities as properties or classes ? The answer is no to properties, but a provisional yes to classes. There is nothing in the definition of 'Property' that suggests that this class is non-null, but the existence of the class is entailed by its being named. The moment something like redness is assigned to the class, however, platonism of a more extravagant sort is afoot. According to the definition, to say that redness is a property is to say that redness is the sort of thing that is instantiated, but since this can be construed as saying no more than that something is red, it seems to me moot whether saying redness E Property entails that something E Property. The existence of properties is entailed by the ascription of properties to proper-



SELLARS' ONTOLOGY OF CATEGORIES 117

ties. The property of being a property, however, on this account, reduces to the property of being instantiated, but this can be eliminated in favor of the property simply of something's being, in the copulative sense-'redness is instantiated' yields to 'something is red'.

It is not so easy when the property is not named by an abstract like 'redness' which can be reduced to its adjectival component by eliminating the suffix. If it is said, e.g., that Revson's delight is a property, and, ex hypothesi, instantiated, it is less easy to eliminate 'instantiates' for 'is', but not impossible. The singular term, 'Revson's delight', can be turned into an adjective by the simple if somewhat brutal expedient of affixing to it the adjective-maker 'ish'. The addition of the denominalizing suffix 'ish' may then be thought of as a summary representation of some procedure like the following for turning a semantically opaque property-name into its corresponding property-predicate. First, standardize the opaque term by giving it the form of a definite description, as e.g., 'the x such that x delights Revson'. This, then, can be formed into the opaque predicate 'is such as to delight Revson'.

These particular worries about platonism may, however, be put to rest by the general consideration that the definitions introduce no platonic locutions other than those discussed in the first part of the paper. Thus, if Sellars' strategies for restoring ontolog- ical innocence to such platonic or AST-introducing idioms as predicate quantification and categorization are successful, they will successfully restore innocence to such definitions of categories as those above.

A point at which the two accounts come very close is this. The core of the notion of property, according to Sellars, is that of one-place predicate, and, according to the definition above, that of being instantiated. But since the verb 'instantiates' selects its accusatives in virtue of their being, like 'redness', names made of adjectives (or other predicate constituents), instantiation is as predicate-selective as is 'predicate'. Instancing and predicating are correlative speech acts.

The semantics of category assignments like 'redness is a property' is, as noted above, queer: such statements when true seem very true, but when false something less than false. Alice Ambrose has made this point strikingly by noting that open sentences of the categorial sort, 'x is a property', appear to lack a dimension in their ranges, namely that dimension got when



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substituends for 'x' make the sentence (what it says) false. The usual three choices, true, false, nonsense, collapse into the first and last.6 To say, e.g., that Socrates is a class, is not a simple case of misclassification on a footing with confusing a mastodon with a wooly mammoth; its semantic defect is much more serious. But is the statement nonsense? It may be nonsense in the sense of being outrageously false, but not it seems to me in the sense of being neither true nor false. It is false to say that Socrates is a class (so long as unit classes are not identified with their elements) because it is false to say of anything that it belongs to Socrates, is a member of Socrates.

At this point, however, I have a problem. Socrates and the null class are alike in lacking members, a fact that calls for a correction of the definition of 'class' given above; yet they seem not to lack their members in the same way. Socrates, the null class, and the class of unicorns all lack members, but each it seems for a decreasingly strong reason. For something to belong to the null class it would have to meet a self-contradictory condition of membership, being non-self-identical. Thus it is necessarily false that something belongs to the null class; that something belongs to Socrates cannot be more false than that. If therefore a distinction in degree of semantic failure between sentences of the form 'x E Socrates' and 'x E A' is to be drawn, one way to do it would be to call sentences of the first form nonsensical, and of the second necessarily false.

The way in which the definitions must be complicated so as not to exclude null elements bears on this problem, so I now offer the following null-inclusive definitions of the categories Class and Property:

w is a class =Df W e X (((3y)y e x y 0 x) V w A,

i.e., something is a class just in case it has members distinct from itself or it is the null class;

w is a property =Df W E X ( (3y)y instantiates x * y # x) V x (x instantiates w) A,

i.e., something is a property just in case it is instantiated by something other than itself, or it determines the null class.

The complexity of these two definitions results from the difficulty of distinguishing formally between something that lacks members but is a class, like the null class, and something that lacks members but is not a class, like Socrates.




That Socrates is not a class according to this definition is shown as follows. For Socrates to fail to be a class, he must either fail to be identical to the null class, or fail to have members distinct from himself.

There are several different ways, perhaps, to show that Socrates is not the null class, e.g., that he unlike the null class is a famous philosopher. I think the longer but more interesting method to show this, however, is to argue that for the identity to hold statements of the form "-'a (x E Socrates)' must be true and, if true, well-formed, but that none of them can be well-formed because Socrates lacks a condition of membership. This rests on the supposition that any sentence of the form 'x E y' is well-formed only if it has a truth-condition, in particular the truth-condition that x E y iff x satisfies y's condition of membership. 'x E Socrates' and its negation would be well-formed, therefore, only if Socrates' condition of membership were such were x to satisfy it, x would belong to Socrates.

There are two possibilities. First, Socrates has a condition of membership; second, he doesn't. If the latter, then 'x E Socrates' is ill-formed, as is its negation and generalization, and as is also 'Socrates A'. This last being ill-formed, Socrates fails to meet the second alternative of the condition for being a class. Does he meet the first alternative? Clearly not, since to do so he would have a member distinct from himself, and therefore a member, which has been ruled out by assuming the second possibility above.

Suppose, however, that Socrates does have a condition of membership. Now it would seem possible that Socrates might meet either disjunct of the definition of 'class'. If, however, his condition of membership is that x E Socrates iff x Socrates, then only Socrates belongs to Socrates, as is proper. Thus Socrates will fail to be a class by failing to have a member distinct from himself. Finally, if it were supposed that Socrates had some other condition of membership than being identical with Socrates, the counter-example would lose all force, for on such a supposition Socrates would be a paradigm case of a class.

An analogous argument distinguishes a null property like square circularity from Socrates.

NOTES

1 The first of these two papers appeared in Mind 69(1960), and has been reprinted in Sellars' Science, Perception, and Reality, pp. 247-281. The second



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appears in Experience and Theory, edited by Lawrence Foster and J. W. Swanson, pp. 55-78.

For efforts not wholly misspent to decrassify this essay, I thank Wilfrid Sellars, M. B. E. Smith, and H. Heidelberger.

2 See as well as the two papers mentioned, "Abstract Entities," in his Philosophical Perspectives, pp. 229-269.

3 Theatetus, 182a: see Cornford's footnote on page 97 of his Plato's Theory of Knowledge.

4 Op. cit., "Abstract Entities," pp. 246 ff. 5lbid., p. 245. 6 "Factual, Mathematical, and Metaphysical Inventories," ch. 14 of her

Essays in Analysis, in particular p. 246.

Theoretical Phenomenalism JAMES W. CORNMAN

UNIVERSITY OF PENNSYLVANIA

One of the problems that faces a phenomenalist who claims that there is nothing over and above ideas, or sense-data and, perhaps, perceiving minds, is how to account for the seemingly evident truth that there are physical objects. The solution to this problem I shall defend is Berkeley's, or at least Berkeleyan, for I shall attempt to defend one particular explication of the relationship Berkeley expresses when he says that "a certain color, taste, smell, figure and consistence having been observed to go together, are accounted one distinct thing signified by the name 'apple'; other collections of ideas constitute a stone, a tree, a book and the like sensible things" ([2]: 22). The principal objection to the view I shall defend has been raised by Wilfrid Sellars. Thus, my defense is primarily to examine and, Iltimately, to reject his objection. By so doing, I hope to explicate and make plausible this Berkeleyan thesis.

The problem is to find a defensible explication of the thesis that a physical object, such as an apple or, using Philonous' example, a cherry, is nothing but a collection of ideas, sense-data, or percepts, that is, what I shall call "sensa." It is clear that it is of no help to interpret the thesis as would an analytical phenomenalist, such as the early A. J. Ayer, who claims that physical



studies in wilfrid sellars' philosophy || sellars' ontology of categories

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