bell, ian -- demonstration in aristotle's metaphysics

Demonstration in Aristotle'sMetaphysicsIan Bell

In recent years scholarship in Aristotle has focused extensively on therole of the Posterior Analytics in understanding the structure and meth-odology of other parts of the Aristotelian corpus. In particular, a sub-stantial amount of work has been done on the relevance of the PosteriorAnalytics to Aristotle's biology, and it is now widely acknowledged thatattempts to understand the biological works must take the Analytics intoaccount.1 However, most recent scholarship implicitly assumes that theinvestigation undertaken in the Metaphysics follows a methodology dif-ferent from that developed in the Analytics. In so doing scholars arefollowing a tradition that goes back at least to Owen's influential Τιθέναιτα φαινόμενα', which argued that much of what goes on in Aristotle'smajor works is not the kind of empirical investigation described in theAnalytics but rather conceptual or 'philosophical' investigation using adialectical methodology.2 Walter Leszl and T.H. Irwin have applied thisconclusion specifically to the Metaphysics, arguing that it contains asecond-order investigation into the presuppositions of the empiricalsciences.3

1 See, for instance, Gotthelf and Lennox (1987), chs. 5-7. For considerations of the roleof the Posterior Analytics outside biology proper see particularly Bolton (1991) andAnagnostopoulos (1994).

2 See Owen (1961), 83-92. The 'empirical' vs. 'conceptual' distinction is Owen's; hecalls the Analytics methodology 'empirical' because of its insistence that principlesbe arrived at through εμπειρία (83-4).

3 See Leszl (1975), Irwin (1988); cf. Witt (1989), 25-31.

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76 Ian Bell

The most significant way in which the Posterior Analytics could berelevant for understanding Aristotle's methodology in the Metaphysicsis through its account of scientific knowledge (επιστήμη) based on dem-onstration (άπόδειξις). A strong claim for the influence of the formerupon the latter would thus involve the claim that the science (επιστήμη)of being undertaken in the Metaphysics, or at least a part thereof, is ademonstrative science. There are at least three reasons to think that thiscannot be true. First, metaphysics is thought to be a science of principles,and it is a commonplace that principles are undemonstrable. Aristotle isquite explicit, for instance, that the principles of demonstration cannotthemselves be demonstrated. Some scholars — Irwin, for instance — takethis to indicate that metaphysics as a whole is prior to demonstration.Second, it is difficult to see how the Metaphysics position that being is aπρος εν equivocal can be reconciled with the Posterior Analytics require-ment that the terms used in definitions and demonstrations be univocal.Finally, there is no explicit statement anywhere in the Metaphysics thatits investigations follow a demonstrative proof-structure, nor do thereseem to be any arguments in the Metaphysics that strictly conform to themodel of syllogistic demonstration that emerges from the two Analytics.4

In what follows I shall argue that these objections can be met, and thatthe proof-structure for at least one significant task undertaken in theMetaphysics is sufficiently close to that presented in Analytics to justifycalling it 'demonstration'. The first objection, I shall argue, is based on amistaken conception of what the tasks that Aristotle assigns to meta-physics have in common: this commonality results not from their proof-structures but from the ή αυτό relation of their objects to being andsubstance. In Metaph IV 2, it becomes clear that one of these tasks is theinvestigation of the per se attributes of being and unity. The secondobjection can be met by recognizing that the nature of a προς εν equivocalis found in its primary instance, which is not itself equivocal. Finally, weshall point to texts in the Metaphysics and De Anima that state or implythat demonstration is the appropriate proof-structure for the treatmentof per se attributes, and examine what characteristics of demonstrationsare emphasized in these texts. We shall see that one of the proofs that

4 I use 'proof-structure' specifically to refer to the part of a discipline's methodologythat indicates how the principles or premises of an investigation are related to itsconclusions. Brought to you by | St. Petersburg State University

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Demonstration in Aristotle's Metaphysics 77

Metaph IV 2 would lead us to expect to be demonstrative — the proofthat each contrary has only one contrary — has the characteristicsemphasized in these texts. The absence of demonstrations that conformstrictly to the Analytics model is not peculiar to the Metaphysics: it is notclear that there is any such proof anywhere in the corpus. Together thesefacts suggest that Aristotle intends demonstration as the proof-structurefor the treatment of per se attributes in the Metaphysics, even if he is tacitlyabandoning some of the constraints imposed on the form of demonstra-tions by the Posterior and particularly the Prior Analytics.

I

We shall begin with an outline of the demonstrative methodology de-veloped in the Prior and Posterior Analytics. Although the relation be-tween these two books is controversial, Aristotle's characterization ofdemonstrations as 'scientific syllogisms' (APo I 2, 71bl8) creates theprima facie expectation that demonstrations will be species of the syllo-gism described in the Prior Analytics.5 A proof that clearly conformed tothe Analytics conception of demonstration would thus be a Pnor Analyticssyllogism that possessed certain additional characteristics peculiar todemonstrations.

In its basic outline the model of the syllogism developed in the PriorAnalytics is well known. A syllogism contains two premises and aconclusion; the conclusion states a relationship between two termswhich is proved using a third term as a middle term. The general formof the universal affirmative syllogism (Barbara), for instance, is as fol-lows:

C belongs to all B.ß belongs to all A.

C belongs to all A.

One of the extreme terms (C) is shown to belong to the other (A) usingthe middle term (ß). It is this form of syllogism that is most 'scientific'(APo 114) and most useful for demonstration.

5 For recent discussion of the relation between the two Analytics see Barnes (1981),which summarizes the earlier Solmsen-Ross debate, and Smith (1982a and 1982b).Brought to you by | St. Petersburg State University


78 Ian Bell

Broadly speaking, demonstrations prove the existence of effectsthrough their causes, ultimately from first causes (APo I 2, 71bl9-72a7,110,76a37-bll). Just by itself this leaves open a wide range of possibilitiesfor the structure of demonstrations. In effect, however, the PosteriorAnalytics is much stricter about what kinds of principles can appear indemonstrations and what kinds of effects demonstrations prove to exist.First, there is the subject genus (το ύποκείμενον γένος, cf. 75a42-bl), whichis posited to exist and whose per se attributes (75bl, 76bl3) the scienceinvestigates. Each science is one by having one subject genus (I 28,87a38-9), whose signification and existence it assumes (76b5; cf. I 1,71al5-17). Second, there are the attributes that are demonstrated tobelong per se to a subject genus. The signification or whatness (τί εστί)of a per se attribute is assumed as a premise, but its existence (το ότι) —that is, the fact that it belongs to the subject genus — is the conclusion ofa demonstration (75a40; 76a31-6, b6-ll; cf. 11, 71all-17). Finally, thereare the common axioms (αξιώματα), such as the principle of contradic-tion, which are used by all the sciences to the extent that they are usefulin each (75a41-2; 76a37-b2, b!4-15; cf. 111, 77alO-35). A demonstrationproves that a per se attribute belongs to a subject genus, using theexistence of the subject genus and the definitions of the genus andattributes as premises. The common axioms do not appear as premisesin individual demonstrations (APo 111). Thus the subject genus wouldmap onto term A of our Prior Analytics syllogism, the attribute itself ontoterm C, and some definition which expresses the cause of the attribute'sbelonging onto term B (cf. Aristotle's example, II8,93bl4).

What kinds of thing are demonstrable attributes? This is a matter ofdispute, and there are at least three different accounts in the recentliterature.6 All scientific truths are necessary truths, and a predicate mustbelong per se (καθ' αυτό) to its subject in order to belong to it necessarily(APo 16,74b5-8). The demonstrable attributes will thus be the predicatesthat belong to their subject καθ' αυτό. In APo 17 and 110 Aristotle refersto these attributes generically as καθ' αυτά υπάρχοντα (75a40-l, 76b4),but also as καθ' αυτά συμβεβηκότα (75bl), πάθη (75bl, 76bl5), andπαθήματα (76bl3). In APo 16 (74b6-10), Aristotle implies that of the fourkinds of καθ' αυτό described in APo 14, two are relevant for demonstra-tion and καθ' αυτά υπάρχοντα. In the first sense the attribute will be part

6 Ferejohn (1991), chs. 3-6, McKirahan (1992), ch. 7, Goldin (1996), ch. 6Brought to you by | St. Petersburg State UniversityAuthenticated | 93.180.53.211



of the definition of the subject (type [1] καθ' αυτό); in the second, it willbe defined in terms of the subject without being part of its definition(type [2] καθ' αυτό). Examples of the latter are oddness and evennesswith respect to number (14,73a39-40); according to Metaph IV 2 these areπάθη of number (1004blO-12).

The relation between the various words used for these attributes is notentirely clear. In APo I 6 Aristotle uses υπάρχοντα to refer generically toboth kinds of predication. This reflects its etymological origin in υπάρχει,which may be used to refer to the fact of almost any state of affairs.Likewise, πάθος and παθήματα are used generically at 76bl3-15. On theother hand, Aristotle's usual use of συμβεβηκός is to refer to somethingnonessential; the notion of a καθ' αυτό συμβεβηκός ('essential accident')is almost an oxymoron. It is thus possible that the word refers primarilyto type (2) καθ' αυτό predications, i.e., to those where the predicate is notpart of the definition of the subject. This is suggested, for instance, byAristotle's brief treatment of καθ' αυτά συμβεβηκότα at Metaph V 30,1025a30-4. On the other hand, although there is no instance in the PosteriorAnalytics where καθ' αυτό συμβεβηκός alone is used generically to referto all καθ' αυτό predications, Aristotle does appear to be using the phraseto refer to all demonstrable predications in his discussions of the thirdand fifth aporias in Metaph III (997al5-34). Thus, although we shallreserve 'per se accidents' to translate καθ' αυτά συμβεβηκότα, there is nosharp distinction in Aristotle's use of the terminology.7

Finally, APo 14 demands that attributes that are strictly καθ' αυτό toa subject also belong to it universally (καθόλου) and 'qua itself (η αυτό)(73b26-32). Otherwise put, the attribute must belong to all instances ofthe subject, and to that subject primarily (πρώτον, 73b39; cf. b33). This isbest illustrated with an example. The attribute of having angles equal totwo right angles belongs η αυτό to triangles. It is not καθ' αυτό or ή αυτόto the genus above triangle, i.e., plane figure, because there are planefigures to which the attribute does not belong. Nor is it η αυτό to isoscelestriangles, even though it does necessarily belong to isosceles triangles.Rather, the attribute of having angles equal to two right angles is η αυτόto the widest subject genus of which it is true that the attribute belongsto all of its members (73b32-74a3). The attribute belongs primarily to thatgenus, and is 'in a sense not καθ' αυτό' to lower species of the genus to

7 Pace Ross (1924), 1.224 Brought to you by | St. Petersburg State UniversityAuthenticated | 93.180.53.211


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which it belongs (74a2). As Aristotle emphasizes at greater length in APoI 24, the subject to which the attribute belongs ή αυτό is the cause of theattribute's belonging to it and its species (85b23-86a3). From this Aris-totle concludes that the best demonstration of the existence of an attrib-ute is a universal demonstration, that is, a demonstration that shows itto belong to the subject to which it is ή αυτό. More generally, theinvestigation of an attribute should demonstrate it to belong to thesubject to which it belongs ή αυτό.

We shall see that the investigation into the per se attributes of beingdescribed in Metaph IV 2 shares many of the features of the proof-struc-ture described here. At the same time, the foregoing should make it clearwhy it is so difficult to find any proof that strictly conforms to theAnalytics conception of demonstration. It is difficult to see how demon-stration as described in the Analytics could be flexible enough to describeand explain any wide range of phenomena, if Aristotle's reference toscientific syllogisms in APo 12 does refer specifically to the syllogism asdescribed in the Prior Analytics. We shall see that there is evidence boththat Aristotle wishes to retain the term 'demonstration' with the basicelements recognizable from APo 17 and 110, and that he tacitly abandonsthe requirement that such demonstrations be presented in the form of aPrior Analytics syllogism.

II

Aristotle introduces metaphysics in Metaph TV 1 with the statement thatthere is a science (επιστήμη) that studies being qua being and whateverbelongs to it per se (το δν ή δν και τα τούτω υπάρχοντα καθ' αυτό,1003a21-2). This science is distinguished from those that do not investi-gate 'universally about being qua being' (καθόλου περί του οντος ή v,a24) but only about a part of being. If we are to read this declaration inlight of the methodology described in the Posterior Analytics, we shouldexpect Aristotle to be indicating two things. First, the science will studybeing universally (καθόλου) and qua itself (ή αυτό). The phrase 'beingqua being' indicates the level of generality at which the science of beingstudies beings: there are scientific truths applicable to beings not quasome kind of being but precisely because they are beings.8 Second,

8 Cf. Stevenson (1975). Brought to you by | St. Petersburg State UniversityAuthenticated | 93.180.53.211



Aristotle's references to the υπάρχοντα καθ' αυτό (a22) should refer tothe per se attributes (καθ' αυτά υπάρχοντα) that are the Posterior Analyticsobjects of demonstration.9

The difficulty, of course, is to show that the passage should be read inthis light in the first place. If Irwin is right that Aristotle is introducing awholly new kind of investigation in the Metaphysics, then probably theapparent references to the Posterior Analytics are only apparent. In sup-port of this view, Irwin appeals to Aristotle's characterization of theMetaphysics as a science of principles and the prominent place that thetreatment of the principles of demonstration (or common axioms) playsin Metaph IV. Since the axioms are principles of demonstration, it isimpossible to demonstrate them without circularity. Moreover, part ofAristotle's treatment of the axioms is dialectical, and this dialecticaltreatment appears to serve as a justification for the axioms.10 Irwin takesthe treatment of the axioms to be indicative of the character of metaphys-ics as a whole: it serves as 'a test for the method of first philosophy.'11

Metaphysics will constitute a second-order dialectical justification ofprinciples assumed by the first-order demonstrative sciences.

We shall argue, against views such as Irwin's, that what Aristotletakes to be distinctive to metaphysics is not a second-order, dialecticalmethodology but the ή αυτό relation that the objects of metaphysics allhave to being and substance. There are three kinds of thing that possessthis ή αυτό relation to being: the principles and causes of being, the perse attributes of being, and the common axioms or principles of demon-stration. Metaphysics thus has three tasks, each of which has a proof-structure appropriate to it.

The clearest evidence for our account of the tasks of metaphysics isfound in the first five aporias concerning the scope of metaphysics, and

9 This is the interpretation adopted by the Greek commentators on Book IV; Alexan-der assumes a demonstrative methodology in commenting on IV 1,1003a21-2 (inMetaph 239.6-9), IV 2, 1004bl-8 (258.8-10), and IV 2, 1004bl7-26 (260.2-5, cf. 25-6).See also Syrianus in Metaph 63.6-8,24-6; Asclepius in Metaph 246.6-9.

10 So Irwin (1988), 187-8; against this view see Code (1986) and Bolton (1994).

11 Irwin (1988), 179-80, see also 172-3, 196-8. Irwin recognizes in a footnote that 'toclaim that first philosophy is to [some] extent non-demonstrative is not to claim thatit is wholly non-demonstrative' (547 n. 2), but this does not seem to affect hisapproach in the main text. Brought to you by | St. Petersburg State University


82 Ian Bell

in Aristotle's answers in Metaph IV and VI.12 It is clear from whatAristotle assumes in the first aporia that metaphysics is somehow ascience of causes, and from what he assumes in the second through fifthaporias that it is somehow a science of substance. Taking for granted thatmetaphysics is a science of the principles of substance, the second aporiagoes on to ask whether it is also a science of the principles of demonstra-tion (995b6-8, 996b31-2). Likewise, the fifth aporia asks whether thescience of substance is also the science of its per se attributes (995bl8-25,997a25-6). In Metaph IV, 1-3 and VI1, Aristotle both confirms his initialassumption that metaphysics is a study of principles of substance, andargues for affirmative answers to the second and fifth aporias.

In Metaph IV 1, Aristotle maintains that there are certain principlesand causes that are καθ' αυτό to being and belong to it qua being, thatis, qua itself (η αυτό).13 It belongs to the science of being qua being toinvestigate these principles and causes (1003a26-32). In Metaph IV 2Aristotle isolates the primary instance of being in substance, and somaintains that the science of the causes of being will investigate theprinciples and causes of substance (1003bl6-19). The relation of theinvestigation of the causes of being to the methodology of the PosteriorAnalytics is complex. In APo Π 1-2 Aristotle recognizes the existence ofscientific investigations into the τί εστί and ει εστί of substances, and atone point even goes as far as to imply the cause of either a substance oran attribute will be the middle term of a demonstration.14 When it comestime to give detailed examples of such explanation in APo II8, however,Aristotle restricts himself to the explanation of attributes. Moreover, wehave seen that demonstration in the strict sense explains the existence ofattributes by proving that they belong to subjects whose own existence,as we have seen, must be assumed. If substances cannot be attributes ofsome other subject, it is difficult to see how there can be a demonstrativetreatment of the ει εστί of substances. The Posterior Analytics recognizes

12 I follow the enumeration of the aporias in Ross (1924) and Apostle (1966).

13 On this passage see especially Dhondt (1961). Cf. Metaph IV 2, 1003bl6-19, VI 1,1025b3-18.

14 For the explanation of the ει εστί of the subject see APo Π 1, 89b31-5, Π 2 passim(Aristotle alternates between the explanation of substances and attributes). At90a9-ll Aristotle writes that the cause for both substances and attributes is foundin the middle term. Brought to you by | St. Petersburg State University



that there must be a science that explains the ει εστί of substances, but itappears that the methodology for this treatment is not demonstration.

This much is implied by Aristotle's methodological remarks about theinvestigation into the principles and causes of being in Metaph VI1:

All [the other sciences], marking off some being or some genus, conducttheir investigations into this part of being, although not into beingαπλώς nor into their part of being qua being, and they do not give anaccount of τί εστί; but starting from the τί εστί, which in some sciencesis made clear by sensation but in others is laid down by hypothesis,they thus proceed to demonstrate more or less rigorously the per seattributes [καθ' αυτά υπάρχοντα] of their genus. Consequently, it isevident that there is no demonstration of ουσία or of τί εστί from suchan induction but that these are made known in some other way.Similarly, they say nothing as to the existence or nonexistence of thegenus they investigate, and this is because it belongs to the same powerof thought to make known both τί εστί and ει εστί. (1025b7-18)15

Without attempting to address the many difficult interpretative prob-lems posed by this passage, it is possible to see that in investigating theει εστί of the subject genus to which attributes belong, one of the tasksof metaphysics will be concerned with things that must be assumed bythe demonstrative sciences and hence are not themselves objects ofdemonstration according to the paradigms developed in the Analytics.While the investigation into the principles and causes of substances doesnot constitute a simple repudiation of the Posterior Analytics, the meth-odology for such an investigation will likely go beyond anything es-poused there.16

What is of greater interest for our purposes is one of the passage'sother implications. We have suggested that one of the tasks of metaphys-ics is a demonstrative investigation into the per se attributes (καθ' αυτάυπάρχοντα) of being. While the Metaph VI 1 passage seems to confirm

15 Translations from the Metaphysics are based on Apostle (1966). I have noted onlysignificant departures. I take 'from such an induction' to modify the clause 'there isno demonstration ...'; cf. Ross (1924), i.352, Kirwan (19932), 184, Owens (19783), 288,and Bolton (1991), 16; this reading is not crucial for my argument.

16 Metaph ΥΠ 17, 1041a21-b9 suggests that the explanatory structure for substantialexplanation is analogous to demonstration. See Bolton (1995), 452-8.Brought to you by | St. Petersburg State University


84 Ian Bell

that Aristotle regards the treatment of these attributes as demonstrative,it also implies that it is sciences other than metaphysics that undertakethis treatment. Metaphysics, our passage suggests, is concerned with τίεστί and the εϊ εστί of the subject; it is contrasted with the sciences thatassume these in order to demonstrate υπάρχοντα.

On the other hand, if there are attributes that belong καθ' αυτό and ήαυτό to being, it is difficult to see to what science they would belong ifnot to metaphysics. It is precisely this difficulty that gives rise to the fifthaporia, whether metaphysics is 'concerned only with substances or alsowith the per se accidents of substances [τα συμβεβηκότα καθ' αυτά ταΐςούσίαις]' (995bl8-20). The reason for doubting that metaphysics willstudy the attributes of substances is that if it does, there will be ademonstrative science of substance, but there is no demonstration of τίεστί hence (it is implied) neither of substance (997a30-2). If metaphysicsdoes not study the attributes of substance, however, it is difficult to seewhat science will do so (a32-4). The implication is that substance hasσυμβεβηκότα that are καθ' αυτό to it, and that the science that studiesthem must be demonstrative. The aporia does not doubt the existence ofa demonstrative science of the attributes of substance: it doubts only theidentification of this science with the science of substance.

Aristotle concludes Metaph TV 2 with the statement that 'it belongs toone science to investigate being qua being and the attributes that belongto it qua being [τα υπάρχοντα αΰτω ή δν], and that the same scienceinvestigates not only substances but also their υπάρχοντα' (1005al3-16).We shall argue that this is the conclusion of Aristotle's solution to thefifth aporia: there is a single science of being and its attributes, and thescience that studies substance also studies the attributes of substance. Thepassage thus retrospectively indicates how we should read Aristotle'sreference at the beginning of Metaph IV 1 to a science of being qua beingand its υπάρχοντα καθ' αυτό (a21-2). These should be understood notsimply as 'all the things that a science of being would study', but asobjects requiring a specifically demonstrative treatment and whose in-clusion in a science of being and substance is controversial. We shall alsoattempt to see how this position may be reconciled with Metaph VI1 andthe arguments contra in the fifth aporia.

The last task of metaphysics is that proposed in the second aporia, thestudy of the principles of demonstration. The second aporia raises twoobstacles to assigning the study of the common axioms to the science ofsubstance: it is not clear why it is the science of substance that shouldstudy the axioms (996b33-997a2), and it seems that the science of theaxioms cannot be a demonstrative science (997a2-ll). In Metaph IV 3Brought to you by | St. Petersburg State University



Aristotle attempts to solve the first problem with the identification of thescience of being qua being and the science of substance. The axiomsbelong to being at that level of generality: they belong (υπάρχει) to allbeings and not peculiarly to one genus apart from the others, and so theybelong to beings qua being (η v) (1005a22-7). Therefore, since the scienceof substance is the science of being qua being, it belongs to the philoso-pher to study both substance and the principles of demonstration(1005b5-8). The fact that the axioms cannot be demonstrated does notprevent them from being included among the principles studied in thescience (1005bll-1006all). Notice, however, that although the axiomsυπάρχει to beings qua being, Aristotle does not call them καθ' αυτάυπάρχοντα, or even just υπάρχοντα. This may be merely coincidental, butit is also what one would expect if Aristotle is reserving καθ' αυτάυπάρχοντα for the demonstrable attributes of being and substance. Theprinciples of demonstration themselves would be known by some non-demonstrative means, perhaps dialectically, perhaps by νους. In thelatter case, the Metaphysics will follow the Posterior Analytics account ofthe knowledge of the principles of a science.17

What common feature of these tasks requires that they all be assignedto metaphysics? What they have in common is that their objects belongto being qua itself (η αυτό), to being qua being. There are causes (1003a28-32,1025b3-4) and attributes (1005bl3-14) that belong to things qua being,and the ή αυτό relation to being is true of all the principles of demonstra-tion (1005a21-9). As we have seen, the Posterior Analytics requires thatobjects of investigation be investigated at the appropriate level of gener-ality. If horses and oak trees have certain causes and attributes notbecause they are horses and oak trees but because they are living things,the study of these causes and attributes will belong not to zoology orbotany but to universal biology. If they have causes and attributes thatbelong to them not qua living things but qua substances, the study ofthese causes and attributes will belong not to physics or biology but tothe science of being and substance.

If it is a η αυτό relation to being and substance that makes somethingan object of metaphysics, then it becomes unnecessary to suppose thatmetaphysics is distinguished from the special sciences by its proof-struc-ture or methodology. Metaphysics may itself be a first-order science of

17 With Code (1986), 344,1 incline to the latter alternative; see Bell (1998), 115-23.Brought to you by | St. Petersburg State UniversityAuthenticated | 93.180.53.211


86 Ian Bell

a certain nature, and be distinguished from the other sciences by study-ing only causes, attributes, and so forth that are ή αυτό to that nature.Because everything is in some sense a being, metaphysics will be in asense a universal science. However, it does not attempt to be a universalscience in the vicious sense ruled out in APo I 9: it does not attempt todemonstrate the principles proper to the special sciences (76al6-25). Thecauses expressed in the definitions proper to biology, for instance, are ήαυτό to the explanation of biological substance qua biological, not quasubstance. Metaphysics may take an interest in explaining why giraffesare giraffes, but it is not interested in explaining why they are giraffes.™Likewise, it will be interested in explaining why giraffes have the attrib-utes that belong ή αυτό to being and substance, but will leave theexplanation of the attributes that belong to giraffes qua living being oranimal to biology and zoology respectively. One may take issue withAristotle's claim that studying the being and substantiality of a giraffe issomehow different from studying the giraffe-ness of a giraffe, but theclaim is nevertheless Aristotle's.19

One may wonder why Aristotle makes no mention of metaphysics inthe Posterior Analytics, if metaphysics does not violate the PosteriorAnalytics restrictions on a universal science. The short answer, as Owen(1960) recognized, is that the Posterior Analytics does not recognize anysort of commonality between the various things that may be called'beings'. In the absence of any such commonality, there would be nonature to which the objects of a science of being would be ή αυτό, and sothere could be no genuine science of these things. Any attempt at ascience of being would constitute the kind of science that Aristotle seeksto rule out: a master science capable of proving all truths about all things.

18 Cf. Bolton (1995), 454-5.

19 See esp. Metaph IV1 and VI1,1025b3-18. At VI1,1025b 10-14 Aristotle suggests thatmetaphysics explains τί εστί. Whatever this means, it does not mean that metaphys-ics explains why a certain definition has a certain content: as Aristotle emphasizesat Metaph VII17,1041314-04, there is no explanation of why, e.g., humanity itself ishumanity. A broader investigation into the reasonableness of Aristotle's claimswould require a lengthy treatment of the nature and causes of being; see Bell (1998),chs. 3,6-9. Brought to you by | St. Petersburg State University



III

If Aristotle's account of the tasks of metaphysics does not rule out ademonstrative account of some of these tasks, does his προς εν accountof metaphysics' universality? According to the Posterior Analytics, whatmakes scientific knowledge possible is the universal (καθόλου), andwhat this in turn requires is the possibility of predicating the same thingin the same sense of all of its instances (APo 111,77a5-9,1 24,85b4-22, II13, 97b26-39). Although προς εν equivocity generates a kind of univer-sality, it is not clear whether and how this universality can be sufficientfor demonstration.

Aristotle's account of the προς εν relation is extremely familiar inoutline, desperately obscure in its details and implications. Nevertheless,two things seem to emerge clearly from Aristotle's descriptions of thisrelation in Metaph IV 2 and EE VII 2. First, any προς εν equivocal willhave a primary instance: souls, bodies, instruments, and actions can allreceive the predicate 'medical', but the name belongs properly (κυρίως)to its primary instance, that is, to the art in virtue of which a man can becalled a medical man (EE VII 2, 1236al9-23; cf. Metaph IV 2, 1003bl6).Second, what makes for a προς εν equivocal is the fact that the derivativeinstances must be defined in terms of the primary instance, that is, thepriority in λόγος (or 'logical' priority) of the primary sense to the deriva-tive senses. This is clearly stated in the EE passage (1236a21-3) andimplied by Aristotle's examples of προς εν equivocals in both passages.20

To use an example common to the two passages, a medical tool is definedas one used by someone possessing the medical art, and not vice-versa(1236al9-23,1003bl-4).

The model of προς εν equivocity presented in these passages thussuggests that there is one instance where the nature under considerationis found, and other instances that deserve to receive the name of thisnature owing to their definitional connections with it. Hence the openinglines of Metaph IV 2:

The term "being" is used in many senses, yet not equivocally, but all ofthese are related to something which is one and a single nature [προς

20 Cf. Owen (I960), 171-2 For Aristotle's definition of logical priority and posterioritysee Metaph ΧΙΠ 3,1077a36-b4. Brought to you by | St. Petersburg State University


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εν και μίαν τινά φύσιν]. It is like everything that is called "healthy",which is related to health by preserving health, or by producing health,or by being a sign of health, or by being recep live of heal th. (1003a33-b 1)

Many things are called healthy, always because of some relation to healthunderstood as a state of an organism. It is not the case that healthy foodhas the state of health in some derivative, attenuated sense: rather, it iscalled 'healthy' precisely for its capacity to cause this state in its primarysense. Likewise, a science of health will study tools precisely in theircapacity to be of use in bringing about health.

The same language appears in Aristotle's account of the derivativeinstances of being. Of the derivative instances some are called beings

by being attributes [πάθη] of substances, others by being on their wayto becoming substances, or else by being destructions or privations orqualities of substances, or productive or generative either of substancesor of whatever is related to substances, or negations of any of those orof substances. On account of this, we say that even nonbeing is nonbe-ing. (1003b7-10)21

If we are to follow the model of the other examples of προς εν, we shouldexpect the nature of being to be found in substance, and the derivativeinstances of being to be so called only in virtue of their definitionalrelations to substance. Nonsubstantial beings are so called not becausethey are beings and substances in some lesser sense but because they aredefinitionally related to substance.22 To this one may want to respondthat if only substances share in the nature of being, then presumablynothing apart from substances would exist. Aristotle's point seems to bethat this is to assume the wrong conception of being in the first place:being is not the sort of nature that everything in the world must share.If one assumes that it is, differentiation becomes impossible and Par-menidean conclusions must follow (III 4,1001a29-bl, cf. 998b22-7).

21 As Owen (1960), 173 n 23 points out, echoes of this list of derivative instances arefound in Aristotle's Metaph V treatments of unity (1016b6-9), contraries (1018b31-8),potency (1019b35-1020a6), quantity (1020al4-32), perfection (1022al-3), and falsity(V 29, passim).

22 Cf. Owens (19783), 264-75. Brought to you by | St. Petersburg State UniversityAuthenticated | 93.180.53.211



If the nature of being is found only in substance, then the primaryinstance of being is something that is itself univocal, at least vis- -vis thenonsubstantial instances of being.23 If the per se attributes of being andsubstance are also univocal or at least have univocal primary instances,then the univocity requirements of Posterior Analytics demonstrations aremet. In what follows we shall argue that Aristotle sets up his investiga-tion of the per se attributes of being and unity in such a way as to meetthese requirements.

IV

The treatment of the per se attributes of being in Metaph IV 2 followsimmediately upon Aristotle's account of προς εν equivocity. The first part(1003bl6-1004a2 and 1004a9-31) introduces sameness, difference, and soforth as 'forms' (εί'δη) of being and unity. Aristotle then explicitly raisesthe fifth aporia and argues that its solution is to regard these εϊδη as perse attributes of being qua being and unity qua unity (1004a31-b26). Thescientific approach to this study is contrasted with dialectical and sophis-tic attempts to deal with the same material. Finally, Aristotle attempts toshow how his approach is continuous with his predecessors' accountsof the contraries as principles of all things: all things are reduced tocontraries and these ultimately to the one and the many (1004b27-1005al3). The chapter ends with the conclusion we have alluded to: itbelongs to the same science to study both being qua being and its per seattributes (1005al3-18).

Our discussion begins abruptly with the statement that it belongs togenerically one science to investigate all the 'forms' of being (εϊδη τουδντος):

23 To this extent I follow Bolton (1995), 423-9, though I do not follow his identificationof the per se attributes with the secondary instances. Although the question whethersubstance itself is univocal between sensible and suprasensible substance is impor-tant to a final evaluation of whether metaphysics can be a science, it is impossibleto address it within the scope of this article. If substance is not univocal, thenpresumably another προς εν reduction to the primary kind of substance will benecessary. For the present it is sufficient to point out that Metaph IV 1-2 is not itselfconcerned with any sort of equivocity within substance.Brought to you by | St. Petersburg State University


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For each genus of things there is both one power of sensation and onescience; grammar, for instance, which is one science, investigates allspoken sounds [πάσας θεωπεΐ τάς φωνάς]. Accordingly, it belongs togenerically one science to investigate all the forms [εϊδη] of being, andthe forms of the forms. (1003bl9-22)24

The role of this text is initially unclear. We shall argue that it is Aristotle'sintroduction to his treatment of sameness, otherness and so forth, whichare the εϊδη and per se attributes of being.25 The passage has been givenat least two other interpretations, however, as referring either to thevarious kinds of substance or to the various categories. These difficultiesarise partly because of uncertainties about the interpretation of certainkey words and phrases. The notion of εϊδη of being is unusual and hasno parallel outside this text and its immediate context (cf. 1003b33-4). Itis unclear whether εϊδη should be translated as 'species' or 'forms'; sincethe translation 'species' has certain definite and problematic connota-tions, let us tentatively use the less interpretive 'forms'. Furthermore, thecryptic phrase τα τε εϊδη των ειδών has two possible translations: eitherthe one we have given or a more expansive reading like Apostle's ' ...and it belongs to one specific science to investigate each εϊ'δος of being.'26

Of these issues the one that can be resolved with the most confidenceis that of the intended referents of εϊδη. At 1003b33-6 Aristotle refers tosameness and likeness as εϊδη of unity and hence of being. This in turnlinks 1003bl9-22 to the treatment of these things in the texts that imme-

24 Our translation differs significantly from Apostle's, on the difficulties of translationsee this paragraph and the next in the main text. The Greek text from 'Accordingly...' is: διό και του οντος ή 6ν όσα εϊδη θεωρήσαι μιας εστίν επιστήμης τω γένει, τα τεεϊδη των ειδών.

25 Cf. Metaph ΠΙ 1,995b23-4. This interpretation is supported by, among others, Ross(1924), i.256-7, Owens (19783), 275-9 and n. 55; and Mansion (1958). However, Jaeger(1957), apparatus ad 1004a2, and Kirwan (19932), 82 follow Alexander (in Metaph250.32-251.6) in associating 1003bl9-22 with 1004a2-9 rather than with 1003b22-1004al. All are agreed that 1004a2-9 is out of place in its current position; thedisagreement is rather whether 1004a2-9 interrupts 1003al9-4al and 1004a9ff., or1003a22-4al interrupts 1003bl94a9ff. For references to the various other interpre-tations see Leszl (1975), 241 nn. 25-7.

26 Owens (19783), 275 and n. 55, and Kirwan favour the translation we adopt; inaddition to Apostle, Ross (1924) marginally favours the expansive translation, asdoes the ROT. Kirwan believes both are possible; see his note ad loc.Brought to you by | St. Petersburg State University



diately follow it (1003b22-1004al and 1004a9-b32). We shall have a betteridea of what kinds of things are είδη of being after having examined thesepassages.

Aristotle makes his way into an investigation of the forms of being viaa limited identification of being and unity. The motivation for makingthis identification is that many of the forms of being are strictly speakingforms of unity. 'Being' and One', while not having the same connotation,correspond to each other just as 'principle' (αρχή) and 'cause' (αίτιον) do(1003b22-9). If something is a being, it is also one (and vice-versa); andthe ουσία of each thing is both essentially a being and essentially one(b32-3; cf. VIII6,1045a36-b7). Hence there will be as many forms of beingas there are of unity (b33-4). The investigation of the forms of being andunity will thus belong to the same science as the science that investigatesbeing and unity (1003b33-1004al). In particular, the science of being willalso study sameness, likeness, and equality.

Aristotle moves on to show that the science of being will also studythe opposites of sameness, likeness, and equality:

Since it belongs to one science to investigate opposites [αντικείμενα],and plurality is opposed [αντίκειται] to unity, and since it belongs toone science to investigate also denial and privation because unity isinvestigated in both ways, with respect to its denial as well as to itsprivation ...; it belongs to the same science to know also the oppositesof the kind of unity we mentioned, for example otherness [to έτερον]and unlikeness [το άνόμοιον] and inequality [to άνισον] and all theothers which are named either according to these or according toplurality and unity [κατά ταΰτα η κατά πλήθος και το εν]. (1004a9-20)

Additionally, contrariety itself is investigated by this science, being aninstance of difference and so of otherness (a20-2). These things are eithernamed 'according to' (κατά) plurality or unity or, as in the case of con-trariety, are named according to something else that is in turn namedaccording to plurality or unity (in the case of contrariety, according todifference). Aristotle explains further in Metaph V 15 that quantity,quality, and so forth are named κατά το εν because they are defined interms of unity (1021alO-12).

Since 'unity', like 'being', has many senses, and sameness, otherness,and so forth are ultimately reducible to unity, these too will have manysenses. Nevertheless it belongs to one science to know all of them, sincethey are προς εν equivocals (1004a22-5). Brought to you by | St. Petersburg State University


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Now since all things are referred to that which is primary, as forexample all things which are called "one" are referred to what isprimarily one, we must say that the case is similar with sameness andotherness and the contraries; so that after distinguishing the varioussense of each, we must give a similar account of how all the others arerelated to that which is primary in the case of each predicate [εν εκάστηκατηγορία] ... (1004325-30)27

The univocity required for a science of the forms of being and unity isgenerated by the fact that unity and its forms are studied in their primaryinstances.

The προς εν relation between the primary and secondary instances ofunity and its forms is analogous to the προς εν relation in the case of being.What is one in the highest degree is that thing whose ουσία is one; otherunities are so called for their relations to things that are primarily one:

Most things are called "one" in view of the fact that they act on, or areaffected by, or have, or are related to, some other thing which is one,but things which are primarily called "one" are those whose ουσία isone, either by continuity, or in kind, or in formula; for we count as manyeither things which are not continuous, or things which are not one inkind, or things whose formula is not one. (V 6,1016b6-ll)

Similar relations hold for sameness, likeness, and equality: 'since "one"and "being" have many meanings, all the other objects which are calledaccording to these must also follow, so sameness and otherness andcontrariety must be distinct in each category' (V 10, 1018a35-8). AtMetaph V 10,1018a31-5 and X 4,1055a35-8 Aristotle explains the προς ενrelation for contrariety in the same terms as he does for unity. A primaryinstance is identified (and in this case, defined), and the derivativeinstances are defined in terms of the primary instance. Just as thesecondary instances of being are intelligible only in relation to thesubstance to which they are related, the secondary instances of contrari-ety are intelligible as contraries only in light of the contraries that theyhave, produce, or are acquiring or losing.

Having introduced the forms of beings and shown how they arethemselves προς εν equivocals, Aristotle is now in a position to make the

27 I follow Ross (1924), 1.206, on the translation of κατηγορία.Brought to you by | St. Petersburg State UniversityAuthenticated | 93.180.53.211



connection between the forms of being and the issues raised in the fifthaporia. We saw that the aporia asks whether it belongs to the samescience to investigate both substance and its per se attributes, but thequestion is not raised only in these terms. Taken as a whole, the aporiaasks

whether our Investigation is concerned only with substances or alsowith the per se attributes of substances [τα συμβεβηκότα καθ' αυτά ταΐςούσίαις]; and in addition, concerning sameness and otherness andlikeness and unlikeness and contrariety, and with regard to priority andposteriority and all other such, about which the dialecticians are tryingto inquire, conducting their inquiry from reputable opinions [ένδοξα]only, to what science does it belong to investigate all these? To these wemust add their own per se attributes, for we must inquire not only intowhat each of these is, but also whether there is only one contrary to acontrary, (ffl 1,995bl9-27)

It is necessary to investigate both whether metaphysics studies καθ'αυτά συμβεβηκότα of substance and whether it studies the things that the'dialecticians' attempted to inquire into. In Metaph TV 2 Aristotle makesit clear that in inquiring into the 'forms' of being, metaphysics is con-cerned with the objects discussed in the second half of the aporia:

It is evident, then, that it belongs to one science to discuss [sameness,otherness, etc.] as well as substance (this was one of the problems welisted); and so, it is the philosopher's task to be able to investigate all ofthem. For if it is not the philosopher, then who will examine whetherSocrates and sitting Socrates are the same, or if a given contrary hasonly one contrary to it, or what is a contrary, or the various senses ofthe term "contrary"? And similarly with all other such questions.(1004a31-b4)

The study of these objects belongs to the science of being and morespecifically, to the science of substance. More precisely, they are investi-gated as per se attributes (καθ' αυτά πάθη) of substance in its capacity asthe nature and primary instance of being.

Since, then, these are the per se attributes [καθ1 αυτά ... πάθη] of unityqua unity and of being qua being, but not qua numbers or qua lines orqua fire, clearly it belongs to this science also to know both the whatnessof these and their accidents [συμβεβηκότα]. And those who inquire intothese matters err not in the sense that they do not philosophize, but inBrought to you by | St. Petersburg State University


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not considering ουσία, of which they comprehend nothing, as prior. Forjust as there are Ί'δια πάθη of number qua number (e.g., oddness andevenness, commensurability and equality, excess and deficiency), andthese belong to numbers per se and in relation to one another (andlikewise other ί'δια belonging to solids ... ), so there are certain thingsϊδια to being qua being, and it is the task of the philosopher to examinethe truth about these. (1004b5-17)a

In the first passage, Aristotle gives two examples of the sorts of questionthat the philosopher will ask: it is the philosopher's job to investigatewhether Socrates is the same as Socrates sitting, and whether any givencontrary has only one contrary. We know from the fifth aporia (995b25-7)that Aristotle considers the investigation into whether a contrary hasonly one contrary to be an investigation into a per se attribute, presum-ably an attribute of contrariety. The beginning of the second passageindicates how we should take the other example: to ask whether Socratesand sitting Socrates are the same or different is to inquire into a per seattribute of Socrates qua being and one, that is, qua substance.

The science of substance will thus be able to establish truths about twokinds of things. First, it will be able to establish that certain attributes —for instance, sameness or lack of sameness — belong to substances quasubstances (1004b5-6). Second, it will know the τί εστί of these attributesand be able to establish that certain other attributes belong to theseattributes, for instance, that each contrary has only one contrary (b6-8).29

Aristotle emphasizes the parallelism between this investigation and hisparadigm demonstrative sciences of arithmetic and geometry: just asthere are attributes that belong ή αυτό to number and solid, so there areη αυτό attributes of being and unity in their primary instance, substance.Metaphysics studies the same objects studied by the Academic dialecti-cians, but as per se attributes of being qua being and unity qua unity, andhence of substance qua substance.

28 In the context 'accidents' should be read as shorthand for 'per se accidents'; cf. ΠΙ2,997a25-34

29 I take αύτοϊς (b8) to refer to the πάθη of being and unity rather than to being andunity themselves, although this does not significantly affect the overall interpreta-tion. Brought to you by | St. Petersburg State University



Aristotle distinguishes his treatment of these objects from that ofdialecticians in two ways. First, the dialecticians do not recognize thepriority of substance (1004b8-10). It is easy to see the significance of theirfailure to recognize this priority if, as we have suggested, substance is toserve as the subject genus to which these attributes are καθ' αυτό and ήαυτό. The dialecticians were arguing merely from 'reputable opinions'(ένδοξα, 995b23-5). As Topics 11 puts it, dialectic argues from reputableopinions, demonstration from premises that are 'primary and true'(100a26-30). If substance is prior to these attributes as their subject genus,it should be possible to reach conclusions about the ways in whichSocrates is the same and not the same as Socrates sitting by relying notonly on reputable opinions but on the sorts of premises required in ascientific demonstration.

Aristotle goes on to draw a different contrast between metaphysicsand dialectic, this time emphasizing the difference in their powers:

Dialecticians and sophists put on the same appearance as the philoso-pher. Sophistry only appears to be wisdom. Dialecticians discuss allthings, and being is common to everything; but clearly dialectic em-braces these things because they are proper to philosophy. Sophistryand dialectic busy themselves with the same genus of things as philoso-phy, but philosophy differs from dialectic in the manner of its capacity,and from sophistry in the kind of life chosen. Dialectic is such as toprobe [πειροστική] concerning things that philosophy knows [γνωρισ-τική], sophistry makes the appearing of knowing without knowing.(WQ4bl7-26)x

Aristotle is clearly attributing to philosophy the capacity of knowingtruths in a way that dialectic does not: philosophy is γνωριστική. Whatdoes Aristotle mean by calling dialectic πειραστική?

On one account, Aristotle is referring to Platonic dialectic: Platonicdialectic is 'peirastic' and subscientific whereas Aristotelian dialectic canbe properly scientific.31 This interpretation seems unlikely. As Bolton hasemphasized, the label 'peirastic' is not intended as a pejorative but rather

30 Kirwan makes the most sense of the obscure sentence at b!7-22, and my translationreflects his.

31 Berti (1996,125-7) Brought to you by | St. Petersburg State UniversityAuthenticated | 93.180.53.211


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to indicate both the limits and the philosophical uses of dialectic. Dialec-tic does have a genuine function within philosophy in the examinationand refutation of alternative philosophical positions. In particular, it ispossible to use dialectic to refute an opponent's position by showingeither that it is self-contradictory or that it is incompatible with what iscommonly accepted as scientifically true.32 Clear examples of such argu-ments may be found in Aristotle's criticisms of his predecessors' viewsin Metaph I and III. These arguments do not, however, establish anythingexcept in relation to the views they are criticizing; they do not have thecapacity (δύναμις, 1004b24) for establishing philosophical truths.33

What kind of arguments do have this capacity? Irwin suggests thatAristotle is using the passage to introduce a distinction between 'pure'and 'strong' dialectic. The former relies on generally-accepted beliefs forits premises, whereas the latter operates from a more restricted, moreepistemologically reliable set of premises.34 In particular, strong dialectictakes its starting point from the conditions for the possibility of scientificknowledge. The possibility of scientific knowledge is not just any com-mon belief; it is a belief that all scientific investigation presupposes.Therefore, it counts among the restricted set of premises appropriate forarguments in strong dialectic.

As we have seen, Irwin uses Aristotle's treatment of the commonaxioms, particularly the principle of noncontradiction (PNC), as a modelfor strong dialectic. Although it is prima facie plausible to regard Aris-totle's argument in Metaph IV 4 as an example of strong dialectic, it isdifficult to see how 1004b25-6 could be pointing to strong dialectic in thecontext of the Metaph IV 2 texts we have considered.35 Irwin suggests thatwe should read Aristotle's insistence on the priority of ουσία (b8-10) asa statement that metaphysics should study the 'presuppositions of the

32 See SE 8,11; Bolton (1990), 212-19, (1994), 327-30.

33 For passages contrasting dialectic and philosophy see Irwin (1988), 528nl. On therelation between dialectic and philosophy see further Bolton (1987), 146-51, Smith(1993), Lennox (1994), 58-64.

34 Irwin (1988), 174-5,185-7

35 I have argued in Bell (1998), 113-28, that Metaph IV 3-8 is not attempting a justifica-tion of the common axioms using strong dialectic, and that there too Aristotle's useof dialectic is peirastic. But there is at least a pnma facie case for construing thesearguments as Irwin does. Brought to you by | St. Petersburg State University



special sciences' (176), but it is hard to see why Aristotle should be mak-ing this point in this context. There is no suggestion in Metaph IV 2 thatAristotle is considering sameness, difference and so forth because theyare presupposed by the other sciences. Aristotle's stated reason is ratherwhat we should expect from our account of the tasks of metaphysics:sameness, difference, and so forth are ή αυτό to being and unity and sobelong to the science of being and unity.

Metaph IV 2 and Metaph IV 3-8 are responses to different aporias thatintroduce what appear to be two different tasks. The second aporiamakes it clear that the methodology for the treatment of the commonaxioms is nondemonstrative. However, it is equally clear from the fifthaporia that Aristotle expects a treatment of per se attributes to be demon-strative, and the Metaph IV 2 passages we have examined show that heexpects metaphysics to undertake an investigation of certain per seattributes. Aristotle has already contrasted the epistemic reliability ofdialectic and demonstration in the Posterior Analytics (16,74b21-6 with I19, 8lbl8-23).36 In its context, then, the Metaphysics contrast betweenπενραστική and γνωριστική is most naturally taken not as distinguishingbetween pure and strong dialectic, but between dialectic and demonstra-tion. We shall provide additional evidence to support the view that thisis the contrast Aristotle intends in the next section.

Aristotle finishes Metaph IV 2 with a brief discussion of the relation ofthe contraries to the science of being qua being. The principles of allthings are contraries, and the principles of the contraries are unity andplurality (1004b27-5a5). Hence, since the science of being qua being isalso the science of unity, this science will also be the science of thecontraries (1005a2-5). The passage seems to be developed mainly out ofa Platonic and pre-Socratic background (cf. 1004b31-3). Aristotle's em-phasis on the contraries as principles is somewhat worrying, since in afew places he seems to be on the verge of suggesting that the contrariesare principles even of (and thus are prior to) ουσία. At one point Aristotleattributes the view that all beings and ούσίαι are composed of contrariesto 'nearly all thinkers' (1004b28-9); at another point he himself writes that'all things' are either contraries or composed of contraries (εξ εναντίων,1005a3-4). Aristotle is clearly concerned to express the continuity of his

36 As Irwin seems to recognize (1988), 470, there is no clear evidence for a distinctionbetween pure and strong dialectic anywhere in the corpus.Brought to you by | St. Petersburg State University


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science of being with the investigations of his predecessors, which mayaccount for the appearance of being willing to reduce even substance tothe contraries.37 His indication that being and one are probably not καθ'εν (1005a5-ll), however, suggests that here too Aristotle ultimatelyintends a προς εν reduction of the basic contraries (being and not-being,unity and plurality) to substance (cf. Metaph XII7,1072a30-2). Being andnot-being are not treated as equals, nor are they principles of ουσία: inthe προς εν reduction being in its primary instance simply is ουσία, andnot-being is nothing more than a privation of ουσία, called a 'being' onlyderivatively and in the weakest possible sense (IV 2,1003blO).

The chapter concludes with an unqualifiedly affirmative answer tothe fifth aporia. The science of being is a science both of substance andits per se attributes.

It is clear, then, that it belongs to one science to investigate being quabeing and whatever belongs to it qua being, and that the same scienceinvestigates not only substances, but also whatever belongs to sub-stances [ου μόνον των ούσίων άλλο και των υπαρχόντων], both the[attributes] mentioned and also priority and posteriority, genus andspecies, whole and part, and the others of this sort. (1005bl3-18)

The introduction of priority, posteriority, and so forth in addition to thetopics already mentioned is unexpected, though Aristotle has alreadymentioned priority and posteriority 'and all other such' in the firstexposition of the fifth aporia at Metaph III 1, 995b22-3. Although it isprima facie plausible that such things are also considered per se attrib-utes of being qua being, it is impossible to determine this just from thetext.

37 Apostle (1969), commentary 38 ad loc., suggests that this passage is dialectical.Likewise, Kirvvan (19932), 85, suggests that the argument is ad hominem against hispredecessors. Brought to you by | St. Petersburg State University



In examining Metaph IV 2 we have shown that Aristotle aims to introducescientific rigour to the treatment of certain traditional objects of Aca-demic dialectic by including them in the science of being qua being. Inparticular, Aristotle insists that these things be treated as attributes thatare καθ' αυτό and ή αυτό to being and unity, and so as per se attributesof ουσία, which is prior to them as their subject genus. It is possible toshed further light on the methodology proposed for this investigationby considering the proof in Metaph X 4 that each contrary has only onecontrary. When Aristotle raises the fifth aporia (III 1, 995b25-7), thequestion whether each contrary has only one contrary is his example ofthe problems involving καθ' απτά συμβεβηκότα whose treatment mightbe supposed to belong to metaphysics; the example reappears in Aris-totle's solution to the aporia at Metaph IV 2,1004b3. Aristotle's proof forthis example is thus our best indication of what he intends the method-ology introduced in Metaph TV 2 to look like in practice.

The proof begins with a statement of the ότι and τί εστί of contrariety:Since things which differ from one another may do so to a greater orlesser degree, there exists also a greatest difference, and this I call"contrariety". That contrariety is the greatest difference is clear byinduction [έκτης επαγωγής]. (105533-6)38

Aristotle goes on to show this by appeal to the extremes from whichgenerations take place. From his discussion he also concludes that con-trariety is 'complete difference' (1055al6). Aristotle thus establishes boththe existence and definition of subject genus, making use of the PosteriorAnalytics methodology of induction to establish the definition.39 Havingset down the εί εστί and τί εστί of the subject genus, Aristotle goes on toprove a fact (δτι) that is true of it:

This being so, it is evident that each contrary cannot have more thanone contrary; for (1) neither can there be anything more extreme thanthe extreme, nor can there be more than two extremes for one interval.

38 With the ROT I take im δ' ή μεγίστη εστί διαφορά to mean 'that <contrariety> is thegreatest difference' rather than 'that there is a greatest difference' (Apostle). Forother mentions of induction in book X see 1054b33,1055bl7, and 1058a9.

39 Cf APo 110,76a31-6, b3-22, and APo Π 19 generally.Brought to you by | St. Petersburg State UniversityAuthenticated | 93.180.53.211


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And (2) in general, if contrariety is a difference, and difference isbetween two things, then complete difference will also be between twothings. (1055al9-23)

Both proofs start from an element of the definition of contrariety toestablish a conclusion about it. Moreover, the definition is the cause ofthe fact that is proved to hold of it. The fact that there can be only onecontrary to a contrary follows from the definitions of 'extreme' (whichcarries the implication of superlativeness and thus singularity) and 'dif-ference' (which carries the implication of duality rather than plurality).40

How closely does the proof follow the model of demonstration pre-sented in the Analytics? The requirements of APo I 7 and 110 appear tobe met: the proof explicitly uses the definition of contrariety and implic-itly assumes the existence of contrariety to prove the ότι of an attributeof contrariety. An appeal to the definition of unity is implicit in thestatements that there cannot be more than two extremes and that differ-ence is between two things. In this respect the proof may usefully becontrasted with Plato's dialectical treatment of the same question in theProtagoras (332a ff.), which does not start from a τί εστί but uses dialec-tical induction.

What is more difficult to see is how this proof could be formalizedinto a Prior Analytics syllogism. A version of the first argument might bequasi-formalized as follows:

The relation between contraries is (by definition) one ofcomplete difference.

All relations of complete difference are such that the relataare extremes.

Therefore, all contraries are extremes.But, all extremes are such that there cannot be more than

two for an interval.

Therefore, all contraries are such that there cannot be more thantwo for an interval (which is to say that every contrary hasonly one contrary).

40 The καθ' αυτό relations seem to be type (1) rather than type (2): the conclusion iswholly implicit in the definition of contrariety.Brought to you by | St. Petersburg State University



Whatever this is, it is not a chain of idiomatic Prior Analytics syllogisms,nor is it clear that it could be further formalized to give this result. EitherAristotle is recommending a methodology that is very close to demon-stration yet ultimately not demonstration, or the Metaphysics is workingwith a conception of demonstration less rigid than that implied by thetwo Analytics. The available texts do not allow us to answer the questionwith certainty. I think, however, that the balance of evidence is in favourof the latter conclusion.

The most significant pieces of evidence are texts in the Metaphysicsand de Anima — that is, in works thought to be mature — that recom-mend or assume demonstration as the proof-structure for per se attrib-utes.41 An important short text is Aristotle's remark, made in the courseof inquiring whether there is a single method for the study of ουσία, thatthere is a single method, demonstration, for the study of its per seattributes (τα κατά συμβεβηκός ίδια, 402al5). Two more extended textsemphasize the APo I 7/110 criteria for demonstrations: demonstrationsshow per se attributes to belong to a subject using τί εστί as a principle.As we have seen, Aristotle writes in Metaph VI1 that 'starting from theτί εστί,... [sciences]42 proceed to demonstrate more or less rigorously theκαθ' αυτά υπάρχοντα of their genus' (1025bl2-13). The same connectionbetween demonstration, definition, and the per se attributes of a sub-stance is drawn in Aristotle's preliminary remarks on the definition ofthe soul at DA 11,402bl6-3a2.

There is no suggestion in any of the texts we have considered thatAristotle means to introduce some methodology distinct from demon-stration as described in the Posterior Analytics. Aristotle is not hesitant todistinguish his methodology from demonstration when he thinks thelatter to be inappropriate for the task at hand. We have already seen thatAristotle does something of the sort for the principles of being in MetaphVI1. Likewise, in PA 11 and Metaph IV 4 Aristotle introduces demon-stration through hypothetical necessity (639b30-40a6) and elenctic dem-

41 See Metaph 992b30-3, 997al7-22, a30-6, 1025012-13, 1039b31^0a2, 1077020-2,1086b34,1087a23; DA 402al5,402bl6-3a2.

42 As we mentioned, the passage is problematic in appearing to suggest a contrastbetween metaphysics and the other sciences on this count. We shall consider thisproblem in the next section. Brought to you by | St. Petersburg State University


102 Ian Bell

onstration (1006a5-12), and explicitly distinguishes them from Analytics-style demonstration.

What Metaph IV 2 and X 4 rather appear to attempt is to set up anduse a proof-structure that is as close as possible to Posterior Analytics-styledemonstration, and that possesses at least the characteristics associatedwith demonstrations in our Metaph VI 1 and DA I 1 passages. Theexample in Metaph X 4 is as close to a demonstration as anything else inthe corpus: examples of demonstrations in strict syllogistic form are notmore easily found outside the Metaphysics than within.*3 Thus if there isanything in the corpus that Aristotle would regard as a demonstration —as his remarks imply there should be — this argument should be aninstance of a demonstration.

If so, Aristotle's criteria for demonstration in practice are less rigidthan those imposed by the two Analytics. In particular, Aristotle is notscrupulous about presenting demonstrations in the form of a syllogism.Perhaps Aristotle thought (rightly or wrongly) that arguments presentedrelatively informally in his scientific writings could be formalized as PriorAnalytics syllogisms. William Wians, for instance, argues that the Poste-rior Analytics 'gives a formal description of scientific practices which maythemselves remain informal in their patterns of argument.'44 It is alsocontroversial whether Aristotle always regarded the Prior Analytics ac-count of the syllogism as describing the only valid form of inference thatcould serve as the 'infrastructure' for demonstrations. Although the wordσυλλογισμός appears in various places in the Metaphysics, none of Aris-totle's mentions of demonstration in the Metaphysics and de Anima (note41 above) imply that demonstrations must take the form set out in thePrior Analytics. Another possible sign of increasing distance from thePrior Analytics is Aristotle's remark in Metaph VI1 that one may demon-strate per se attributes more or less rigorously (ή άναγκαιότερον ή μαλακ-ώτερον, 1025bl3).

The other evidence in Metaph X is not as clear as our Metaph X 4 proof,although Aristotle appears to be attempting similar kinds of proofs inMetaph X 5 in his treatment of the relations between being greater than,being less than, and being equal, and with the argument that intermedi-

43 In his 1969 Barnes claimed to be unable to find a single example anywhere in thecorpus; to my knowledge no one has convincingly identified one since.

44 See Wians (1989), 251; cf. Lear (1980), 10-11, Gotthelf (1987), 195-6.Brought to you by | St. Petersburg State UniversityAuthenticated | 93.180.53.211



ates are composed of contraries in chapter 7. Much of book X is con-cerned with establishing the definitions and hypotheses that are precon-ditions for demonstration. Thus chapters 1-2 define unity and chapters3-4 those things that are defined in terms of unity. Chapter 8 definesdifference in species. Wians points to texts that suggest that once theexplanatory structure for a science has been determined and the princi-ples of demonstrations established, the business of constructing demon-strations on the basis of these principles is relatively straightforward.45

If so, the absence of many written out proofs may not be surprising.

VI

It is now possible to clarify some details of Aristotle's argument inMetaph IV 2 in light of our account of its project as a whole. Let us returnto the difficult passage at the beginning of the text.

For each genus of things there is both one power of sensation and onescience; grammar, for instance, which is one science, investigates allspoken sounds [πάσας θεωρεί τάς φωνάς]. Accordingly, it belongs to onegeneric science to investigate all the forms [είδη] of being, and the formsof the forms. (1003bl9-22)

One of the issues raised by the text was the translation of εί'δη του δντος.Many translators render this as 'species' of being. Given Aristotle'sultimate identification of the εί'δη with the per se attributes of being andunity, it seems clear that these cannot be 'species' in any traditionalAristotelian sense. This suggests that Owens and Kirwan are right totranslate ενδη as 'forms' rather than as 'species'. For the same reason, itseems best to follow Owens and Kirwan on their reading of τα τε εί'δητων ειδών, rather than the expansive reading that attributes to Aristotlethe view that being and metaphysics have species.46 The phrase is betterread as referring to things such as contrariety, which are denned not

45 Wians (1989), 249-50, citing APo 130,46a22-7, and NE17,1098a20-6.

46 See note 26 above. For additional textual arguments for this interpretation seeMansion (1958), 185-9. Brought to you by | St. Petersburg State University


104 Ian Bell

directly in terms of being and unity but rather in terms of something itselfdefined in terms of being and unity, in this case difference.47

Why would Aristotle introduce the per se attributes as 'forms' ofbeing and unity? Owens and Berti see a reference to the Forms discussedin Plato's Parmenides and Sophist.*8 Although this is dependent on con-troversial interpretations of these dialogues, these scholars must be rightin seeing some sort of reference to Platonic dialectic. As we have seen,the fifth aporia is introduced in Metaph III 1 as raising two differentquestions: Does the science of substance also shady the per se attributesof substance? and, Does the science of substance study certain topics nowaddressed by the dialecticians using arguments from ένδοξα? The objectsof investigation introduced in Metaph IV 2 are not new: they are alreadyobjects for dialectical study in the Academy. The Analytics makes it clearthat Aristotle believes that no merely dialectical treatment of a problemcan be scientific (APo 16,74b21-6 with 119,81bl8-23). Aristotle's positionagainst the dialecticians is greatly strengthened if he can show that atreatment of these traditional objects of dialectic is possible using hismethodology. If such a treatment is possible, these objects must them-selves be subjects with demonstrable attributes or demonstrable attrib-utes of some other subject. Aristotle makes them directly or indirectlyattributes of substance as the primary instance of being, thereby alsounderlining the priority of substance in his metaphysics.

Aristotle nowhere explains how the confident conclusion to MetaphTV 2 is possible in light of the objections to a demonstrative science ofsubstance raised in the fifth aporia and in Metaph VI1. It is possible tosuggest a solution along the following lines. Metaph VI 1 is concernedwith the principles and causes of beings qua beings (1025b3-4). The προςεν reduction of being to substance requires that this be an investigationinto the principles and causes of substances qua substances (IV 2,1003bl6-19). Every substance has causes that are studied in metaphysics,just by virtue of the fact that it is a substance. At Metaph VI1,1025blO-18this characterization is given further precision: metaphysics inquires intothe τί εστί and ei εστί of substances. This investigation is to be distin-guished from the special sciences, in which the ει εστί of the subject is

47 See p. 91 above.

48 Owens (19783), 275-7 and notes, Berti (1996), 124-8; cf. de Strycker (1979), 53-7. Thiswould explain the absence of any other Aristotelian uses of the phrase ε'ίδη του οντος.Brought to you by | St. Petersburg State University



assumed and only the οτι of the per se attributes is demonstrated andthus explained (1025blO-14). The mere fact that an attribute exists (thatis, that it belongs to a subject) does not require explanation in the scienceof being: it is explained in the science of its subject.49 The moral of MetaphIV 2, however, is that there are certain attributes whose subject is beingand substance. These attributes will therefore be studied in the scienceof being and substance. As an inquiry into substance, metaphysics isdistinguished from the other sciences by the fact that it provides anexplanation of the subject, whereas other sciences must assume theexistence of the subject to demonstrate its attributes. If substantiality it selfhas attributes per se to it, however, metaphysics should also undertakethe investigation of these attributes. Otherwise put, the aim of Metaph VI1 is to show not that metaphysics cannot have tasks whose proof-struc-ture is demonstrative, but rather that it can undertake a task that theother sciences cannot: an inquiry into subjecthood and substantiality.

VII

We have argued that Metaphysics TV 2 is intended to establish one of thetasks of the science of being as a demonstrative treatment of the per seattributes of being qua being. If this conclusion is correct, then one maymake a strong claim for the influence of the Posterior Analytics on theMetaphysics. It is worth pointing out that this is not the only way in whichthe Analytics can be seen to influence the Metaphysics. In particular, theη αυτό relation Aristotle uses to connect the tasks of metaphysics is itselfdue to the Posterior Analytics. Even if one does not accept our conclusionthat Aristotle intends a precisely demonstrative proof structure for theper se attributes of being and substance, the influence of the PosteriorAnalytics is nevertheless in evidence in a proof-structure that resemblesdemonstration in crucial respects. We have also suggested along the waythat the methodologies of the nondemonstrative tasks of metaphysics,while going beyond anything presented in the Posterior Analytics, never-theless do not represent a simple repudiation of the Analytics.

If we are right about Aristotle's project in Metaph IV 2, then it seemsthat certain influential views about the character of the Metaphysics are

49 APo 124,85b23-7, Metaph VI1,1025b7-14 Brought to you by | St. Petersburg State UniversityAuthenticated | 93.180.53.211


106 Ian Bell

incorrect. In particular, it is wrong to distinguish metaphysics from theother sciences as a nondemonstrative science of principles as opposed toa demonstrative science of per se attributes. The distinguishing characterof metaphysics is not a nondemonstrative proof-structure, still less arepudiation of the Analytics generally, but the ή αυτό relation of its objectsto being and substance. While metaphysics' investigations into the prin-ciples of substance and the principles of demonstration will not beamenable to a demonstrative methodology, the lesson of Aristotle'ssolution to the fifth aporia is that the science of being must also includea demonstrative treatment of whatever attributes belong per se and ήαυτό to being, unity, and their primary instance in substance.50

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50 I am grateful to Lloyd Gerson, Stephen Dumont, Brad Inwood, Michael Ferejohn,and several anonymous reviewers for helpful comments and criticisms. The mate-rial in this article was originally researched and written while I was the recipient ofa Social Sciences and Humanities Research Council Doctoral Fellowship.Brought to you by | St. Petersburg State University


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