The Foundations of Aristotle's Categorial Scheme

PAUL STUDTMANN

THE FOUNDATIONS OF ARISTOTLE'S CATEGORIAL SCHEME

..

MARQUEITE l "'I\ I ~ln

PRI ~-.

MARQUETTE STUDIES IN PHILOSOPHY

N0.63 ANDREW TALLON, SERIES EDITOR

LIBRARY OF CONGRESS

CATALOGING~IN~PUBLICATION

CONTENTS

DATA

Studtmann, Paul, 1969The foundations of Aristotle's categorial scheme I Paul Studtmann. p. em.- (Marquette studies in philosophy; no. 63) Includes bibliographical references and index. ISBN-13: 978-0-87462-761-9 (pbk.: alk. paper) ISBN-10: 0-87462-761-3 (pbk.: alk. paper) 1. Aristotle. Categoriae. 2. Categories (Philosophy) I. Title. B438.S78 2008 160-dc22

h Categories~ ................................... .................. 7 Chapter 1 ~Whence t e 25

d Problem in Aristotle ....................................... .

Chapter 2~ The Bo y 2008018257

49

Chapter 3~Form.......................................... ·········································· 79 Chapter 4~Prime Matter.......................................... ····························101

COVER DESIGNER & ILLUSTRATOR COCO CONNOLLY

Chapter 5~Quality .............................................................................. 125 Chapter 6~Quantity ............................................................ ............... 141

© 2008 Marquette University Press Milwaukee, Wisconsin 53201-3141 All rights reserved. www.marquette.edut mupress/ FOUNDBD 1916

§The paper used in this publication meets the minimum requirern f th American National Standard for Information Sciences- ents 0 e . Permanence of Paper for Printed Library Materials, ANSI Z39.481992 MARQUETTE UNIVERSITY PREsS ~ltW,o\l)l(ff'

Chapter

7 Substance..........................................................................

~

Index ......................................................................................................

173

CHAPTER I WHENCE THE CATEGORIES: SECTION I THE CATEGORIES: TWO QUESTIONS ristotle's categorial scheme had an unparalleled effect not only on his own philosophical system but also on the systems of many of the greatest philosophers in the western tradition. The set of doctrines in the Categories, what I will henceforth call categorialism, play, for instance, a central role in Aristotle's discussion of change in the Physics, in the science of being qua being in the Metaphysics and in the rejection of Platonic ethics in the Nicomachean Ethics. And commentators and philosophers ranging from Plotinus, Porphyry, Aquinas, Descartes, Spinoza, Leibniz, Locke, Berkeley, Hume, Kant, Hegel, Brentano and Heidegger (to mention just a few) have explicitly defended, criticized, modified, rejected or in some other way commented on some aspect if not the whole of Aristotle's categorial

A

scheme. Despite its influence, however, categorialism raises two fundamental questions that to this day remain open. The first concerns Aristotle's list of highest kinds. At Categories lb25-2a4, Aristotle provides a tenfold division of the things that are said, 'tcOV AEYOIJ.EVCOV, which are naturally interpreted as words (De Interpretatione 16al-10). According to Aristotle, words signify the following basic types: ( 1) a substance, like a man; (2) a quantity, like a line two cubits long; (3) a quality, like the white; (4) a relation, like the double; (5) somewhere, like in the Lyceum; (6) at some time, like yesterday; (7) being in a position, like

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

8

lies; (8) having, like is shod; (9) acting, like cuts; or (10) being acted upon, like is cut (Catg.lb25-2a4). :Mthough impressive for its philosophical insight, Aristode's list raises the following very natural question: why think that it contains all and only the highest kinds in the world? Indeed, Aristotle gives some reason to suspect the correctness of his list, for even he seems ~nsetded about it. Only in one other place, at Topics 103b22, does he li~t ten categories, though in that list he replaces substance, oucria, Wl~h what it is, ti ecrn. In Posterior Analytics I, 22, on the other hand, .-:nstode_ only lists eight categories: substance, quantity, quality, relatives, action, passion, where and when (PA 83b15). In Metaphysics V, 7, he repeats the list from the Posterior Analytics, though he again repla~es substance with what it is. And less directly, one might interpret Anstotle at Metaphysics 1089b18-25 as claiming that there are only four categories: substance, quality, relatives, and being acted upon. The_lack of any justification for his list of highest kinds has not gone unnoticed by critics and in fact has been the source of some famous criticisms. Kant, for instance, just prior to the articulation of his own categorial scheme, says: It w~ an enterprise worthy of an acute thinker like Aristotle to try to -~cover these fundamental concepts; but as he had no guiding pnncrple he merely picked them up as they occurred to him, and at first gathered up ten of them, which he called categories or predicaments. Afterwards he thought he had discovered live more of them which he added under the name of post-predicaments. But his tabl; remained imperfect for all that ••• I According to Kant, Aristode's list of categories was the result of an un~ystematic, albeit brilliant, bit of philosophical brainstorming. Hence, lt cannot stand firm as a correct set of categories. Moreover, the troubles for Aristode's scheme do not end with this list of highest kinds - Kants ' cntiasm · · · · d es ' mtra· extends to Aristo categorial divisions of quantity and quality as well. Aristode divides ~h of ~ese categories into several distinct species: quantity divides ~nto ~onnn~ous and discrete quantities, the former of which divides mto ody, lme, surface, time and place, the latter of which divides into

~~PressuelKant, CritUjuc of Pure Reason, tr. N. Kemp Smith (London: St. artms

1965), p.114.

.

1 fi6l Whence the Categories?

9

speech and number; and quality divides into habits and dispositions, natural capacities, affective qualities and affections and shape. Aristode, however, never gives any justification for these divisions and as a result they appear just as arbitrary as his list of highest kinds. J.L. Ackrill, for instance, says about the category of quality: When Aristotle says that quality is 'spoken of in a number of ways' he does not mean that the word quality' is ambiguous but only that there are different kinds of quality. He proceeds to list and discuss four kinds. He does not 'deduce' them or connect them on any principle 2

And no doubt the lack of such a deduction lies behind Ackrill's criticisms of Aristotle a little later in his commentaries: He [AristotleJ gives no special argument to show that [habits and dispositions] are qualities. Nor does he give any criterion for deciding that a given quality is or is not a [habit-or-disposition]; why, for example, should affective qualities be treated as a class quite distinct from [habits and dispositions] ?3 The first great question concerning Aristotle's categorial scheme, then, is this: is there some philosophically cogent way to justify both the highest kinds and the intra-categorial kinds in Aristotle's categorical scheme. Unlike the first question, the second concerns the way in which categorialism relates to doctrines Aristotle articulates in other works. The question arises as a result of a rather common story that is told about 4 the categories and its apparent deep tensions with hylomorphism. 2 Aristotle, Categories and De Interpretatione, trans. J.L. Ackrill, (Oxford: Clarendon Press,1963), p.104.

3 Ibid. p.104. Ackrill translates the words ESt~ and 3ui9eot~ as 'states' and conditions' respectively. I have interpolated 'habits' and 'dispositions' to provide continuity with my translations.

4 I should say that the view I am presenting is only one among several views about Aristotle's development that have been proposed in the twentieth century. Starting with Jaeger, Aristotle: Fundamentals of the History of his Development, trans. Richard Robinson, (Oxford: Clarendon Press, 1925), scholars have proposed theories of Aristotle's development in terms of his gradual acceptance or rejection of Plato's philosophical positions. Jaeger argued that Aristotle originally accepted a Platonic framework and broke from

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

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According to the story, Aristode wrote the Categories during a phase ofh!s thought characterized by logical concerns. The Organon, the col~ lection of works to which the Categories is generally thought to belong, contains an articulation of Aristode's logic along with the semantic an~ ontological foundations of a philosophy motivated by logical in~ ~wry. The Categories presents this ontological foundation; and one of Its central tenets is that the metaphysically basic entities are primary 5 substances, which, if we are to judge by Aristode's examples in the Categories, include living members of natural kinds as well as parts of substances, e.g. heads and hands (Catg. 3a29~32,8a13~28), bodies (2b1~2), bits of matter, e.g. logs (8a23), and stuffs, e.g. honey (9a33). All o~er entities bear some sort of asymmetric ontological relation to pnmary substances. For example, all accidents inhere in primary substances while primary substances do not inhere in anything (Catg. the ~ework ~~r in his career. David Ross, "The Development of Aris~ toties Thought,_ In Aris~otle and Plato, ed. During (Goteborg, 1960):1~17, ac~ted a modified version of such a theory. Ingemar During, "Aristotle on Uln~te Principles From 'Nature and Reality;' in Aristotle and Plato, ed. ~rrng (Gote.borg, 1960): 35~55, strongly disagreed with Jaeger's view, argurng that Anstotle was too strong a spirit ever to be so taken with Plato's ~heo~es. c£ also, CJ. De Vogel, "The Legend of the Platonizing Aristotle," !;' A~tstotle and Plato, ed. During (Goteborg, 1960): 248~256. G.E.L. Owen, Logic and Metaphysics in some early works of Aristotle" in Aristotle and :lato, ~· D_uring (Gotenborg, 1960):163~190, "The Plato~ism of Aristotle;' In LoK!c • Sc~~ce and Dialectic, ed. During (London, 1960): 200~220, reversed 5 Jaeger position, arguing that Aristotle started out rejecting Plato's views and gradually came to accept them. Daniel Graham, op cit., on the other hand, stro~gly argues that Aristotle's development should be viewed in reference to e Internal dvn,...,; fh' · ,--·~cs o 1S own VIew rather than in reference to his attitudes towards Plato's view. G ah th · · d betw · r am en argues th at an InconsiStency can be foun . ~ hylomorphism and the categorial scheme. On the basis of such an InconsiStency, Graham th A · d then develo ' ar~es at nstotle wrote the Organon early an ibili ped hylomorphiSm, an ontology designed to accommodate the 1 0 r:s. ~~ge. As opposed to these developmentalist views, cf. Mary ~~ ~ ~. rtstotle on Substance, (Princeron: Princeron University Press,

th

19

d-

3

5 That Aristotle's eat-..:~t sch . -'---:.c .. . venial claim. we~•-.. eme IS a UilllliUIQltlon of entities is a contro~ 1988) Bvangeliou, Aristotle$ CAtegories and Porphyry (Leiden: Brill ·• pp.17-33 presents an --"-t ..a:. ___ -• f-L. L: .•. •..... n.. · • • ~ II.UKUSII10no UJC wawn....., prom~~ Dent lntet'ptetatiou of the subject matter of the categorial scheme.

1 ~ Whence the Categoriesf

II

la20~1b8). Furthermore, within the categorial scheme primary sub~ stances appear to be ontological primitives and hence do not appear to admit of ontological analysis into further constituents.6 Aristode's attention, according to this common interpretation, even~ tually turned to the physical world. And though Aristode never lost sight of the categorial scheme, his attempts at physical explanation forced him to a different view about the metaphysically basic entities. In his physical and metaphysical treatises, Aristode claims that physi~ cal entities are composites of form and matter. According to this view, called hylomorphism, not only are physical entities ontologically com~ plex but they depend for their existence on form (Meta. 1041b29). Thus, while categorialism treats physical entities as ontological bed~ rock, explaining the existence of all other entities in terms of them, hylomorphism finds a layer of reality below this bedrock. Form, not the composite of form and matter, is ontologically basic. This apparent disparity between categorialism and hylomorphism is all the more striking in view of Aristode's development of the categori~ al scheme without the central concepts he employs in his development of hylomorphism. The Greek word for matter (uA.n) does not appear in the Categories or anywhere else in the Organon. Furthermore, al~ though Aristode uses the concept of form ( Eiooc;) in the Categories, his use of it in his physical/ metaphysical treatises is far more varied and extensive and is not obviously commensurate with his use of it in the Categories/ Thus, categorialism and hylomorphism, far from

6 The ontological simplicity of primary substances in the Categories is a controversial claim. In support of such a claim, one can point to the fact that Aristotle says of primary substances that they are indivisible (atOJlOV), uni· tary (ev apt8J.Lc!l), and hence a this (to&: tt) (3b10~13). C£ Daniel Graham Aristotle's Two Systems (Oxford: Oxford University Press 1987), pp.25-27, for a defense of this view. 7 The extent to which form and matter and the closely related concepts of aCtllality and potentiality are present in the Organon is debatable. Although matter is not mentioned in the Organon, there is evidence at Posterior Analytics 94a20-95a10 that Aristotle had developed his four~cause scheme of explanation by the time he wrote the Posterior Analytics. Such a scheme obviously includes both form and matter. Scholars have questioned the ex· tent to which Aristode's use of four causes in the Posterior Analytics is evidence that he had a fully developed four-cause scheme of explanation when

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

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representing two obviously complementary ontologies that permit an easy synthesxs · mto · · g1e coh erent system, instead seem to manifest a sm deep tensions both. with respect to thexr · fu n d amental presupposinons .. and the very terminology used in their construction. I Not

s~rprisingly, the discrepancies between categorialism and hy~

~morphxsm have been the

source of considerable scholarly specula~ non about the relationshiP b etween th e two systems. The resolunon . of these discrepancies and the arn'culanon · o fth e reIanonship . . between

the two systems have promised to provide acute insights into the con~ tours of Aristotle's thou ght. v~et the wrrerence .l!Lr . . o f scholarly opmxon ab out the relation between th b · f · · . e two systems, as a ne exarmnanon o f : ; e prormnent scholars' views will reveal, is almost as drastic as the e~ence between the two systems themselves. Mxchael . tle d eveloped hylomor~ his . Frede argues that the 1ater A nsto

P

m m response to perceived inadequacies of categorialism.

· t h e Categortes . as 1f . the claim . that While Aristotle has spoken m substances underlie p . . Meta h . h b . ropemes IS totally unproblematic, in the 1' ystcs . e egms to draw consequences from this claim as to · of substance. As one can see in Met Z 3 wh at really . 1s the ob~ect h e considers whether t 0 h b everyth. Is . say t at su stance, that which underlies ekene, IS matter or form; by contrast in the Categories he had stillmg . spo bl asifsubstances were t h e concrete thmgs · of our ex~ penence ~ ta es, horses tr · h H ' ees, men~ JUSt as we are acquainted with t em. ow does it com bo longer satisfied with e a ut, we must ask, that Aristotle is no the answer of the Categories rs According to Frede A · tl • th transform . & ' thnsto es eory of substance underwent a anon om e Cat · th h egones to e Metaphysics. In the Catego~ e wrote the Organon Some . the Postert'or A al t. • Ia mterpret the discussion of the four causes in n !)'tcsasa ter' Ia' unsatisfactory ace f th mterpo non; some, as a rudimentary and physical~meta h s~:;rtro . e four~ca~e scheme that Aristotle uses in his & Co. LTD ~~) e_;tiSes. Cf. Dav1d Ross Aristotle (London: Methuen 5 2 Anarytics (Oxford:' d Jo~th:m Barnes, tr. and ed., Aristotle: Posterior p. 157. lhe distin . mversity Press 1975), p.215, Graham, op. cit., 0rgCJnon though itcnon ~ acttiality and potentiality is clearly in the necessity and .seems restncred to contexts in which Aristotle discusses connngency· C£ fo 22b30~23a25) andP . A' al.,. r example, De Intepretatione (19a30~19b4, rtor n !)'ttcs (25a37) 8 Michael Frede, 'Individuals . . . p.24. m Aristotle; Antike und Abendland 24, (1978),

1

rJ::ro

b

1 Pal Whence the Categories?

13

ries, Aristotle thought it unproblematic to view the concrete things of our experience as substances; while in the Metaphysics, Aristotle carefully considers whether the fonn and matter of concrete things are substances. Thus, Frede sees Aristotle addressing the same prob~ lems in the Categories and Metaphysics but developing different and incompatible theories. According to Frede, the discrepancies between categorialism and hylomorphism point to Aristotle's dissatisfaction with the former ontology: Aristotle developed hylomorphism as a response to his own criticisms of categorialism. In Aristotle's Two Systems, Daniel Graham proposes an interpreta~ tion that, like Frede's, finds a deep tension between categorialism and hylomorphism. In fact, Graham argues for the radical conclusion that categorialism and hylomorphism contradict each other. Unlike Frede, however, Graham thinks that Aristotle was never critical of categorialism; indeed, Graham thinks that Aristotle, unaware of the contradiction in his own thought, attempted an ill~fated synthesis of the two systems: What emerges is an Aristotle that is bifurcated into a young philosopher with brilliant logical insights and the energy and organization to work out their implications while astutely applying them to design a priori a programme of scientific research; and a mature philosopher with a powerful and flexible theory which better adapts itself to the more practicable scientific projects which he engages in carrying out. Aristotle's early system (categorialism] was elaborated on a linguistic model that rendered it particularly suitable for generating a logical system of discrete terms in which strict connections could be established. Dependent from the start on the craft model, the later system [hylomorphism] was less rigorous in its articulation but more flexible in application, pluralistic in its outlook but more powerful in scope, less perspicuous in dealing with phenomena but more penetrating in analysis .•. The late Aristotle wished to integrate his early principles with his later ones ... (but] he never succeeded, and he could not have, for the gulf between the two systems was a logical one. But in the process of developing his theories he gave us two of the greatest philosophies the world has known. 9 Graham thus agrees with Frede that Aristotle's hylomorphism is in tension with categorialism. Unlike Frede, however, Graham does not think Aristotle was ever dissatisfied with categorialism. Instead, the 9 Daniel Graham, op.cit. p. 332.

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

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mature Aristotle tried to synthesize his two systems, an attempt that was in vain since, unbeknownst to Aristotle, the two systems contra· diet each other. Although both Graham and Frede find a tension between Aristot· le's two systems, not all scholars think an irreconcilable tension exists. Montgomery Furth advances an interpretation according to which Ar· istotle's two systems, despite appearances, do not conflict; instead, the Categories is a work of limited scope • it does not address the problems hylomorphism does. Hence, it is a self-consciously simpler ontology than hylomorphism, yet one that properly and consistently supplies the basis for a richer hylomorphic ontology. ••• the Categories is a carefully limited work • possibly an intro· ductory one • which seems determined to contain the discussion at a metaphysical level that is, though in some ways sophisticated, still simple, and especially to block any descent from its own cur· tailed universe into the much deeper as well as wider universe of the Metaphysics. There is also evidence of a notable concern not to get involved in Causes'· to set out some ontological phenomena .••with· o~t delving • here • into the underlying structure of the nature of things from which these phenomena eventuate. And a critical factor ~n ~taining that simplicity is the designation of the substantial lildividuals as ultimate objects, as the 'floor of the world' ••• 10 Furth thus agrees with Graham as against Frede that Aristotle did not see any tension between categorialism and hylomorphism. Unlike Graham, however, Furth thinks that the discrepancies between the two systems are due to a difference in subject matter. Aristotle developed hylomorphism in response to Cleeper' and 'wider' questions than those that were the source of the categorial scheme. Thus, hylomorphism, ~ough more sophisticated than categorialism, is not in tension with It. The difference between the two systems is one of degree, not kind: hylomorphism was not an abandonment or even an implicit criticism of categorialism; rather it was a natural extension of categorialism. 11 1

~ Montgomery Furth, 'Trans-temporal Stability in Aristotelian Substanc· es.]ournal ofPhilosophy 75 (1978), pp. 627-32.

~ 1 ~ notable exception to the dominant trend in contemporary scholarship ~Michael Wedin, Ari.ttotks Theory ofSubstance (New York: OxfOrd Univer·

Sity Preu, 2000). Much of what I say in thia book ia compatible with Wedin's

1 ;., Whence the Categories?

IS

The second great question concerning the categorial scheme, the~, is twofold: (1) how is categorialism related to Aristotle's hylomorphis~; and (2) are there irreconcilable differences between the two ontologt· cal schemes~

SECTION II THE DERIVATIONAL THESIS This book contains a series of interrelated chapters that collectively support an interpretation that provides answers _to the two ~reat ques· tions concerning Aristotle's categories. According to ~e mterpret~­ tion, Aristotle's categorial scheme is derivable from his hylomorphic ontology, which itself is derivable from very general theses about the . 12 nature ofb emg. general line of interpretation, though I will not try to be explicit about spe· cific points of agreement or disagreement. . . 12 It should be noted that there have been other attempts to explam _the on· gin of Aristotle's categorial scheme. J.L. Ackrill, op.cit PP· 78-79, proVI~es ~e most well known, and perhaps the most well supported textually-t e evi· • 103b20-104a1-contemporary gen· . fr om 'T' d ence cormng .LOptcs -'',..attempt at ethods . I • li f . Ackrill proposes two wrrerent m . . f . erating Anstot es st o categories. of generation According to the first, Aristotle amved at the list o c~tegories by discoverin~ the different types of questions that can be asked ~ ~u~ one subject. Of Callias, we can ask: 'What is het, 'Where is het, 'When IS the. ; we at an can answer, 'A substance,"In th e Agora,• and 'Today'.' and we can see h 'Wh .., . ·11 t rve as an answer to t e eref . answer to the 'What is he:' question Wl no se . Th · ing the different types is he?' and 'When is he?' quesnons. us, recogniZ foo . b k d A · totle introduced a category . Ar irreducible questions that can e as e ' ns r· . A din t Ackrill's other suggesnon, 0 each type of distinct quesnon. ccor g diffi istotle arrived at his categorial scheme by recognizing dthef -'';rent anbs·w~rs . It . " question . that is, aske .o wrrerentm~. o ~eand s. that can be given to a "What 1s n r k 'Wh · Calli ~'What is a square?; What 1s the Lyceu · , vve can as : at Is as., . ill be irreduc· we can see that the most general answers to these questions w . · . ible to each other. For example, Callias is a subst~blce; square ~ a 1U:t:J'; but a quantity is not a substance. For every irreducl e answer,ftCen, . , . m introduced a category. Julius M oravscik' 'Aristotle's Theory oh ategones, d Aristotle, (Garden City: U 1967), pp.125-148, on.th~~~er: K~;:::.. an alternative account, one that he tra.c:es to Bonltz,. ~O er( ; ) 1-645 18 . 3 : 59 des Aristoteles: Sitzungsberichte der Wiener A~demJe a list of (repr. Darmstadt, 1967). According to Moravsok, the categones 15

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

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Although such an interpretation is rather heterodoxical from a contemporary perspective, at least the first part of the thesis, namely that the categorial scheme admits of a derivation from hylomorphism, has a long lineage. There is a rich tradition of commentators includ~ ing Radulphus Brito, Albert the Great, Thomas Aquinas, and most recently Franz Brentano, who provide derivations of Aristotle's cat~ egorial scheme. 13 According to the commentators in this tradition, Ar~ istotle's highest kinds are capable of a systematic and arguably entirely a priori derivation. The following quotation from Brentano captures nicely the philosophical import of such derivations. On the contrary, it seems to me that there is no doubt that Aristotle could have arrived at a certain a priori proof, a deductive argument for the completeness of the distinction of categories ... 14 Although Brentano does not note in this passage the connection be~ tween the categorial scheme and hylomorphism, an inspection of the various derivations in this tradition reveals that they generally contain hylomorphic terminology. Consider, for instance, the following part of the types of entities to which any sensible particular must be related. One final attempt at articulating some principles of derivation occur in Michael Baumer's 'Chasing Aristotle's Categorial Scheme Down the Tree of Gram~ mar: Journal of Philosophical Research XVIII (1993), pp. 341-449. Inspired by an interpretation that can be found in Trendelenburg, Geschichte der Kategorienlehre (Berlin: Verlag von G. Bethge 1846), PP· 23-24, Baumer provides a far less ontological and a far more grammatical method of derivation than Moravscik by attempting to show that Aristotle's list of categories reflect the fundamental types of grammatical expressions. Needless to say, the interpretation I defend in the book stands in marked contrast to all these interpretations. 13 For excellent discussions of Medieval derivations of the categories,

cf.

W~iam Mcmahon 'Radulphus Brito on the Sufficiency of the Catergo~es' ~ahter~ de l'Institut du Moyen-Age Grec et Latin 39 (1987), PP·~1-96; 'Ar-

l~t~tehan Categorial Theory Viewed as a Theory of Componential Semantics, Studies in the History of the Language Sciences vol. XXXVIII, ed. H~s A~sleff, Louis G. Kelly and HansJosefNiederhe (Amster~: John ~enJa· rnms 1987) pp. 53-64. 'Some Medieval Ideas about Relations Proceedmgs of the Conference on the Ontology and epistemology of Relations (forthcoming). 14 F~ Brentano On the Several Senses of Being in Aristotle, tr. and ed. George, R., (Berkeley: University of California Press 1975), P· 96.

1 e61 Whence the Categories?

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Aquinas's derivation of the categorial scheme in his commentaries on Aristotle's Metaphysics. A predicate is referred to a subject in a second way when the predicate is taken as being in the subject, and this predicate is in the subject either essentially and absolutely and as something flowing from its matter, and then it is quantity; or as something flowing from its form, and then it is quality; or it is not present in the subject absolutely but with reference to something else, and then it is relation. 15 Aquinas claims that the category of qualiry flows from form and that the category of quantity flows from matter. Furthermore, although Aquinas does not use the word 'motion' in his derivation in the Metaphysics commentaries, it is dear from the following passage that he is talking about motion as Aristotle in Physics III, 2, characterizes it In another way, that from which a predicate is taken, though outside the subject, is nevertheless from a certain point of view in the subject of which it is predicated. And if it is from the viewpoint of the principle, then it is predicated as an action; for the principle of action is in the subject. But if it is from the viewpoint of a terminus, then it will be predicated as a passion; for a passion is terminated in the subject which is being acted upon ... 16 It is dear, then, that Aquinas not only thinks that the highest kinds in Aristotle's categorial scheme can be derived from hylomorphism but also that the derivation he gives posits connections between vari~ ous aspects of Aristotle's hylomorphic ontology and certain highest kinds. If this Medieval thesis is correct, then, we can provide the following answers to the two great questions about Aristotle's categorial scheme. First, if Aristotle's categorial scheme is systematically and a priori de~ rivable, then the justification for the list of highest kinds lies in the derivation of them. Second, we could conclude not only that catego~ rialism and hylomorphism are not in tension with each other but that categorialism is derivable, at least in part, from hylomorphism. Now, in this book, I do not examine the tradition to which Brentano and Aquinas belong. My focus is entirely on Aristotle-the interpre15 Aquinas, Commentary on Aristotle's Metaphysics, tr. Rowan, J.P., (Notre Dame: Dumb Ox Press 1961), pp. 321-322. 16 Ibid.

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tati I · · o~s giVe are meant to be Independently defensible. Moreover, I admit up front that I do not plan to provide an exhaustive defense of the thes~s that the categorial scheme is completely derivable from hylomorphism. Indeed, unlike Brentano, I am skeptical that an a priori proof of the correctness of the categorial scheme is possible. Moreover, as shall become clear, I focus entirely on form matter substance quan· . d ' ' ' ~ty an quality. Hence, much of the categorial scheme is left unexam· ~ned. Nonetheless, each chapter in this book is directed at a topic that In some way or another crucially implicates either Aristotle's categorial sch.erne, hihl s Y omorphism or the relation between the two. And the unifri.ng theme of each of the chapters is the idea that a deep and in· teresnng derivational connection exists between Aristotle's categories and his hylomorphism. Thus, although I do not try to exhaustively defen~ the philosophical thesis that underlies the interpretation in ~uesnon, I do hope to do enough to make the interpretation in ques· ~on plausible and indeed to make it plausible that someone could have ou~t that the interpretation in question was a reasonable philo· sophical thesis.

SECTION III META-INTERPRETIVE STANCE ?ne might understandably ask why this sort of interpretation is of Interest. My answer to this question is three-fold. First, although con· tern~~ scholarship has moved far away from the synthetic inter· prenve Impulses of the Medieval commentators I have found those co~ ' . ~ntators to be remarkably insightful. Although they can perhaps be JUStifiably . ·_.: __ .J c . · cnn...~ ror their attempts to synthesize parts of Ans· , totles system I main . th th d th ' tam at eir attempts to do so force em to find conceptual connectlons . that are invisible to those who are content take : a much more historical approach to Aristotle's work. Indeed, e v~ fact that such commentators tried so hard to derive Aristotle's ~tego~ scheme from his hylomorphism points to their conceptual vennhveness. So, in some sense, this book is aimed at those scholars w· o. share something o f the Medieval spirit: if you are a scho1ar that IS Interested · fl shin · tles' In e g out conceptual connections in Ansto

1 et; Whence the Categories?

19

thought that are not at first sight obvious, this book might be of interest to you. Second, the chapters in this book are meant to belong to the tradition of interpretation that provides interesting answers to the two great questions concerning Aristotle's categorial scheme. Now, I have already indicated a certain amount of skepticism that such an a priori derivation is possible. Moreover, I do not even address seven of the categories. Nonetheless, I maintain that the general line of interpreta· tion is of interest. The fact that an a priori derivation of a list of cat· egories cannot in the end be successfully carried out can hardly suffice in removing the interest in attempts to do so. Much of the interest in logicism, for instance, is its failure; and surely a work investigating the extent to which something like Frege's original plan for logicism could be made to work is worth studying, even if in the end one must admit that the mathematical doctrine cannot succeed. The chapters in this book are thus to be understood as attempts to articulate and defend interpretive doctrines that are part of a larger interpretation, one that aims to provide philosophically and interpretively compelling theses concerning some of the most basic metaphysical questions. Finally, the interpretation I am offering acts as a kind of interpretive paradigm-it not only places constraints on some of the other fundamental concepts in Aristotle's system but does so in a way that has a satisfying interpretive and philosophical payof£ Supposing, for the moment, that Aristotle's categorial scheme admits of a systematic derivation from hylomorphism which itself follows from theses about the plenitude of being, one can ask: what would Aristotle's metaphysi· cal views end up looking like:' For instance, what view of form and its relation to the category of quality would be needed in order to carry out such a derivation? Likewise, what view of matter and its relation to the category of quantity would be needed? As I hope to show, there are interpretations of the main aspects of hylomorphism and the catego· rial scheme, namely interpretations about the natures of form, matter, quantity, quality and substance that not only facilitate the larger thesis about the relation between the two systems but can also be defended independently of any such larger considerations. Hence, the interpre· tations of the various aspects of Aristotle's system, if correct, not only stand on their own, but also cohere so as to provide a coordinated

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

zo

answer to the two great questions concerning Aristode's categorial scheme.

~timately, I intend my interpretation to be what might be called a rattonal reconstruction of Aristode's philosophy. What I mean by this can be understood by way of an analogy. Aristode's texts are incom· ~lete and imperfect in well-known ways. They can thus be likened to 1 ~P~rfect and incomplete archaeological evidence of an ancient civi· lizanon Such ·..:1: __ • . • a Civ~tton, we can imagine, must have been rather 'd f · . . . . . Impressive - th e eVI ence o vanous forms of soph1sttcanon 1s underuable. But' let us suppose that th e eVI.dence underdetermmes . the extent to which th ·..:1: __ • h d . . e Civ~tton a vanous desirable institutions. Did it have a JUSt legal system~ Did it have the full range of science and the arts? Al~ough various arguments can be made in favor of one hypothesis or e other, let us suppose that the facts as we know them cannot settle the matter. one rm'ght content onese1f w1'th a ;::re i:ntement of. the ~s about which we can be certain. On the . er d, one might begin to speculate about the civilization. One m:gh~ speculate, for instance, that the civilization had such and such ~Zn system; and that if it did have such a legal system, then the ce we now possess should be interpreted in a certain light. Of coursed, such speculation, if it were to be satisfying, would have to be groun ed in th c.. -- . . e .lactS as we know them; but such facts would also be Interpreted 10 · ligh 0 f inevitabl . t the speculation. Indeed, such a project would Y Involve a give and take between a faithfulness to the facts as we know them d · ligh f . ~ an attempt to understand such facts m to the s fro ~~ns being made. In this way, one might try to reconstrUct ;: e. available evidence the nature of the ancient civilization. .10 th~ne Is to go beyond mere biography, Aristode must be approached 18 way. Although we have a great deal of evidence concerning his system, the eviden · · ell d · feet. In this ce IS, In w ·known ways, incomplete an .Im~book, therefore, I attempt a reconstrUction of Aristotles system that ia 6,.,..:L.J b eraJ1 th reco . ~ Ya certain Set of principles. Most gen Y,. e ays~on 18 gwded by the view that Aristode's twO metaphystcal a sin '~e. ca~m and hylomorphism, can be integrated into h~ . ghly uni6ed system. More specifically, it is guided by the e&1S that the categorial scheme admits of a systematic deriva-

In the face of such a

'tuanon, ·

SI

1 PI; Whence the Categories?

ZI

tion &om the various structures latent in Aristotle's hylomorphism and that the latter system is the result of certain general principles concerning the nature of being. And why are these good reconstructive principles? Well, to repeat what I've already said, they provide a kind of interesting paradigm that has significant interpretive and philosophical payoffs; and given the greatness of Aristotle, it is reasonable to suppose that Aristode deserves to be treated in such a manner. In the case of the civilization, it is not obvious what advantages there would be to reconstructing the civilization so that it ended up looking like a highly unified one operating in accordance with fully coherent and just principles. But, my aim in this book is to show that in the case of Aristotle the reconstructive principles guiding my interpretation lead to a significant increase in our understanding of the structures in his metaphysical system.

SECTION IV THE CHAPTERS Briefly, the contents of the remaining chapters in the book are as follows. In chapter 2, I discuss a problem that at first seems to concern only Aristode's categorial scheme but that in the end has significant implications for the relation between it and hylomorphism. What I call the body problem in Aristode arises as a result of Aristotle's apparent commitment to the following three inconsistent claims: (1) Body is a genus in the category of substance; (2) Body is a genus in the category of quantity; and (3) No genus can be in both the category of substance and the category of quantity. I shall argue that the correct resolution of this problem requires a certain understanding of Aristotle's views about both the nature of mobile substances and the nature of mathematics. As shall become apparent, these views implicate Aristotle's hylomorphic ontology. Hence, this problem, which at first seems re· stricted to the categorial scheme, has a resolution that extends beyond the categorial scheme. By the end of the chapter, not only will I have articulated and defended substantive accounts of Aristotle's philosophy of mathematics and his theory of mobile substance but I will also have gone some way toward showing that there are deep conceptual connections between hylomorphism and the categorial scheme.

THE FOUNDATIONS OP ARISTOTLE's CATEGORIAL SCHEME

Each subsequent chapter, then, focuses on the nature of one of the key concepts involved in the larger thesis, namely form, matter, qual~ ity, quantity and substance. In chapter 3, I examine the nature of fonn. I do so by arguing for the following theses: (1) 'form' in Aristotle has over twenty distinct meanings; (2) there are two central meanings of'form' that correspond to two distinct types of entity; (3) the two types of form, what I shall call Jorm~m andJorm~c, are respectively (a) a capacity like entity that is the source of the dynamical activities of a material substance and (b) a species. I also argue that Aristotle accepts a functional detennination thesis, which provides a conceptual bridge between the two types of form. Finally, as shall become apparent, the first type of form, form~m, is precisely the sort of entity that I invoke in chapter 2 so as to resolve the body problem. By the end of chapter 3, I will have not only gone a considerable way to clarifying what Ar~ istotle means by 'form' but I will also have laid the groundwork for a derivation of the category of quality from the nature of form. In chapter 4, I address the nature of matter by addressing the dif~ ficult question of prime matter in Aristotle. I do so by discussing and criticizing the interpretation according to which prime matter is ex~ tension. Such an interpretation is an old one - it goes back at least to Simplicius - and has been defended in recent times by Robert Sokolowski and Richard Sorabji. Although I think that such an in# terpretation is incorrect, I argue that prime matter nonerhe.less bean a very intimate relation to extension. By providing a mathematicaUy rich characterization of the nature of extension, I show how one is naturally led to the concept of prime matter. I also thereby show hoW prime matter so characterized. avoids the objections that are typically raised against it. Finally, I show how such an interpretation of prime matter not only can be integrated into Aristotle's philosophy of math# ematics but also coheres with the solution of the body problem I give in chapter 2. Hence, by the end of chapter 4, I will have given robust characterizations of form and matter that augment conceptual links I will have already drawn between hylomorphism and the categorial scheme as a result of my resolution of the body problem. In chapter 5, I argue that the category of quality can be systemati~ cally derived from form. According to what I call the canonical inter~ prttation, the category of quality divides into four main species. I argue

1 ~ Whence the Categories?

23

to the contrary that quality in fact first divides into two main species under which fall the four species Aristotle lists. Furthermore, I argue that such a regimented differentiation unfolds systematically from the very nature of form as I have characterized it in chapter 2. As a result, not only can one give an explanation as to why quality is a highest kind -it is in essence a basic type ofhylomorphic entity- but one can also show that its species admit of a principled derivation. In chapter 6, I argue that the species in the category of quantity admit of a derivation from the nature of matter. I do this by noting and then explaining a discrepancy between the species in quantity that Aristotle lists in Categories V and the species he lists in Metaphysics V, 7. I argue that the discrepancy can be the source of a derivation of the list in the Categories as long as one accepts the thesis that the category of quantity is derivable from matter as I have characterized it in chap~ ter 4. Hence, as in the case of quality, there is both an explanation as to why quantity is a highest kind and a principled way of deriving the species that fall under it. In chapter 7, I address three issues: (1) the category of substance; (2) the system of Aristotelian sciences; and (3) the plenitude of being. I argue that attributing to Aristotle a certain version of the plenitude of being allows for a systematic derivation of the Aristotelian sciences, which in tum provides a derivation of the main species in the category of substance. In addition, I shall argue that Aristotle's hylomorphism, as I have characterized it in chapters 3 and 4, is derivable from the plenitude of being. In fact, as shall emerge, the main species in the category of substance can be traced to features of form and matter as I have characterized them in chapters 3 and 4. Hence, by the end of chapter 7, I will have shown that general considerations about the na~ ture of being generate the structures inherent in hylomorphism, which in tum generate the main structures in Aristotle's categorial scheme.

CHAPTBR2: THE BODY PROBLEM IN ARISTOTLE n this chapter, I discuss a problem that at first seems confined to Aristotle's categorial scheme. As shall become apparent, how~ ever, what I take to be the correct resolution to the problem has several implications for the relationship between hylomorphism and the categories. Moreover, coming to grips with the problem requires substantive views about Aristotle's philosophies of mathematics, mo~ cion, substance, form and matter. So this particular issue provides a convenient place to begin the treatment of the topics that will be the focus of the rest of the book. The problem arises as a result of Aristotle's treatment of body in the Categories. Aristotle, it would seem, commits himself to the following three inconsistent theses.

I

1. Body (OIDJ.la) is a genus in the category of substance. 2. Body is a genus in the category of quantity.

3. No genus can be in both the category of substance and the cat· egory of quantity. A less precise, but perhaps also less artificial statement of the problem presented by these three theses, what I will call the body problem, is simply this: where in the categorial scheme does the genus, body, lid For, Aristotle at times talks as if body is in the category of quantity, and at times as if it is in the category of substance. But according to the orthodox reading of the Categories, a genus cannot be in both the category of substance and the category of quantity. In this chapter, I shall be primarily focused on resolving the incon~ sistency in theses {1H3). Before turning directly to a resolution of the body problem, however, I first want to indicate briefly why Aristotle

THEPOUNDAnONSOP

' AJUSTOTLE S CATEGORIAL SCHEME

26

seems co 'tted th really do mnu ~ ~ (1)-(3) in the hope of showing that tbey that the~ ~t ~of Aristotle's thought and benet 'cal Y problem 15 a senous and deep one for Aristotle's metapb}'Sl System.

2 P., The Body Problem in Aristotle

marcated dimensions, the three dimensions demarcated being bodyas-quantity? That Aristotle accepted (1), however, does not rest entirely on the interpretive insights of Medieval commentators and the one passage from the Topics. Two further passages in particular provide strong support. At De Anima 434bl2, as part of an attempt to argue that every animal must have the faculty of touch, Aristotle says that an animal is an ensouled body. The surrounding context makes it dear that Aristotle is providing a definition-the claim occurs within a scientific syllogism, which is something that, according to Aristotle, must proceed from a definition. To define animal as an ensouled body, however, is to provide a differentia, ensouled, and a genus, body. And because an animal is a substance, body must be a genus in the category of substance. The evidence from the De Anima passage finds corroboration in Aristotle's division of substance in Metaphysics XII,l. Aristotle divides substances into immovable and sensible substances the latter of which is divided into eternal substances and destructible substances 'like plants and animals' (Meta. 1069a31). Aristotle does not in this passage say that sensible substances are bodies. But it is hard to see what else they could be. Indeed, his mention of animals as a kind of destructible substance immediately calls to mind his definition of animal in the De Anima according to which an animal is an ensouled body, a definition which could in light of the Metaphysics passage be expanded to ensouled sensible destructible substance. Furthermore, at 1069b38, shortly after his division of substances, Aristotle says that sensible substances are the subject of physics. And at De Caelo 268al-3, he says that physics concerns itself for the most part with bodies, magnitudes and their properties and movements. Because the only item on this list that is a candidate for substancehood is body, it is straightforward to take Aristotle as asserting that sensible substances are bodies.3

2 Thomas Aquinas, On Being and Essence in Tunothy McDermott (trans.), Aquinas: Selected Philosophical Writings, (New Yorlc press 1993), 95. 3 The 'fOr the most part' quali6cation is moat plausibly read as a reference to the fact that physics also studies the unmoved mover. But, because the un. tnoved nuwer is not sensible, this does not detract from the cridence for the that body is a substance.

p

THE FOUNDATIONS OF • • ARISTOTLE S CATEGORIAL SCHEME

28

That body is a genu · h f · ·h A · tl , sIn t e category o substance also dovetails wrt nsto es repeated in . h . di . F . . srstence t at rn vrdual bodies are substances. or Instance, In Physics II 1, Aristotle says: · b Animals and their p arts exrst y nature as do plants and the simples among the bodies fc · h th .h h ' or rnstance ean , fire, air and water ... And all ose wrt sue a P · · I h nncrp e ave a nature; and they are all substances, fcor each of them i b' d b Ph ( ys. 192 9-34). 4 s a su ~ect, an nature is always in a subject Aristotle here clai h . I ms t at srmp e bodies are among those things with a h h. . nature, and he goes on t 0 (Ph 193 b say t at t mgs With a nature are substances 32 3 c di'Y~· - 3). It would follow, then, that at least some bodies, acor ng to Aristotle ar b . . . . D C I I ' e su stances. In a similar vern, Anstotle says at e ae 0 II 1, 298a26-31: al Now things that w call and 'b e natur are either substances or functions A b attn Utes of sub t i fi s ances. s su stances I class the simple bodes- re, eanh, and the other terms of the series-and all things that are composed of th fc pan . al em; or example, the heaven as a whole and its s, anrm s again, and plants and their parts (DC 298a26-31). According to A · I from th . I nstot e, not only simple bodies but also those that are e Simp e bodies 1 d II And h . ' e.g. P ants an animals, are substances as we . e rerterates such a claim in Metaphysics VII 2. bI Substance is though say th t b h . t to e ong most obviously to bodies; and so we so area ot alanbrmals and plants and their pans are substances, and natur odies h fi thing f h sue as re and water and eanh and everyo t e son ... (Met. l028b9-12) Aristotle does ex h . . b press t e need to question whether all the Items m the li H~mn~ (M bodi es eta. l028bl3); but he nowhere argues t hat es are not subst d b ances; an his claim that form is primary su stance (M 1041 Hen . eta. b7) does not imply that bodies are not substances. ce, grven the ex I. . P ICit acceptance of such a thesis in the passages cited · . _r ' It Is sare to s h . substances. uppose t at Aristotle thinks individual bodies are From the thesis th t . di 'd . . a short a In VI ual bodies are substances, however, It IS step to the concl · h b f substan If b . Usion t at ody is a genus in the category o ce. odies are In · diVI'dual substances, to infer that b o d Y IS · a _

4AII

-

the translations of Aristotle are mine.

2 Pal The Body Problem in Aristotle

29

genus in the category of substance, one need only suppose that 'body' is part of the answer to the question 'what is it{ asked of some individual body. And though I do not know of a passage in which Aristotle makes this claim, it is extremely plausible to suppose that 'body' is part of the answer to such a question. After all, body is what an individual body such as a fire element or a plant is. Unlike his acceptance of the first thesis, Aristotle's acceptance of the second thesis is directly and incontrovertibly supported by textual evidence. In two different places Aristotle says that body is a kind of quantity. In Categories VI, Aristotle says that body is in the genus of continuous quantities: 'Among continuous quantity are line, surface and body: (Catg. 6a23-4) And in Metaphysics V 13, within a discussion of the various senses of quantity, Aristotle says that body is a kind of magnitude and that magnitude falls under the genus quantity. Hence, body, according to the text of the Metaphysics is a genus that falls under quantity. 5 The third thesis, like the first, doesn't have the support of a quotation in Aristotle; but Aristotle's acceptance of (3) follows straightforwardly from features inherent in his classification of entities in the Categories. Any genus in an accidental category is said of and present in a subject; while any genus in the category of substance is said of but not present in a subject ( Catg. la20-lb5). Hence, any genus that is in both the category of substance and the category of quantity must be both present in and not present in a subject. In order to avoid such a contradiction, therefore, one must suppose that there is no genus that is in both the category of substance and the category of quantity. Aristotle, then, is committed to theses (1)-(3). In this chapter, however, I show that, far from revealing a deep contradiction in Aristotle's thought, the body problem admits of a resolution that throws considerable light on several aspects of his metaphysical system. The resolution begins with a thesis concerning Aristotle's philosophy of mathematics and its relation to the conception of science Aristotle articulates in the Posterior Analytics. In order to resolve completely the body problem, though, such a thesis must be combined with theses about the relationship between substance, form, motion and quantity. 5 I will discuss Aristotle's definition of quantity in greater detail in section II.

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

30

What . an Interpret . . h . eventually emerges Is Anstotle's conception fb di b anon t at not only illuminates 0 o es oth b "al . ' su stantr and non-substantial, b ut also shows this co ncepnon to be . Aristotle's most fundamental a.n :oos around which some of metaphysical views turn.

.

SECTION 11 MATHEMATIC S, SCIENCE AND BODY

Anstotle characterizes math . . ferent places. Nonetheles .emanchs m slightly different ways in difthe I"dea that mathemati .s, m eac charactenzatron, . . he emphasizes h h . crans somehow i t e P ysrcal aspect of mat "al b gnore or abstract away from tl en su stan I M e says that a mathematicr"an tudi h~es. n etaphysics XI, Aristo. "bl s es Is b. aft Is sen~r. e, such as heaviness and ligh o ~ect er leaving out what quantities and qua continuous . ~ness, and instead studies, qua two or three dimensions. ' quanttttes that are continuous in one, d Now just as the mathematician by abstraction (for he theorizes :n ret~ his investigation of these :h" and ~eeping only continuous qu:t~av~gbout. all that is sensible) ~enstons, he investigates the attr"b ty, ett er In one, two or three an qua continuous and not wi 1 utes of these qua quantities (Meta.l06la28-36) th respect to something eIse ... In Metaphysics XIII 3 A . tl "bl ' nsto e says th SI ~ material substances but in their sat ma~ematicians study sentheir physical aspect· tudy rgnore or abstract away For if the. objects of math ematics . are am th qua sensible, then mathematical . ong e sensibles but n sciences ar 0 f th ot not t here fcore concerned Wit · h somethi e e senst"bles and ng separate from thesens1"bles (Meta. l078al-5) · Later, he says: On the other hand, the geometer investi ates man nor qua indivisible, but qua as 0 l"d (Mg a man neither qua a 1 . eta. 1078a25-6) Anstode makes similar remark . Ph . . · . s m 'JSICS II 2 wh h tmgmsh between the mathematician and th h' . ~re e tries to dise P ysicist: The mathematician is concerned with th ese as well but . r:_ h· . as eac IS a 1Imit of a physical bod . d h : not Inso,ar y, nor oes e Investigate attri-

2 P11 The Body Problem in Aristotle

31

butes qua existing in such substances. Consequently he separates them, for in thought they are separable from motion ... (Phys. 193b31-4) Two different characterizations of mathematics plausibly emerge from these passages. In the first Metaphysics passage, Aristotle says that mathematics is the study of quantities qua F, where F is some quantitative notion. It is, for instance, the study of quantities qua quantity, or qua continuous, or qua solid, etc. According to such a characterization, quantity is the subject matter of mathematics. The latter passages above, though, suggest that mathematicians study sensible substances in abstraction from motion and sensibility. In the third passage from the Metaphysics, Aristotle says that geometers study men; and in the second Metaphysics passage and the Physics passage, Aristotle argues that mathematicians abstract from sensibility and mobility. The latter three passages thus suggest that mathematics, according to Aristotle, is the study of sensible substances, i.e. the study of bodies. It is not, however, any sort of study of bodies but rather the study of bodies not qua sensible, or given the convertibility of sensibility and mobility, not

qua mobile. The first characterization of mathematics, unlike the second, is entirely affirmative and so, in virtue of the positive content it contains, is to be preferred. To say in accordance with the second characterization that mathematicians study bodies but not qua mobile is to say in what respect mathematicians do not study bodies, namely not qua mobile. But to say that mathematicians study quantities qua F is to say both what mathematicians study, namely quantities, and how they do it, namely qua F. Nonetheless, for the moment I want to focus on the second characterization. For reasons that will become apparent, the resolution of the body problem I propose is facilitated by a discussion of the second characterization. Furthermore, there is a sense in which the difference between the two characterizations is a manifestation of the body problem; and so, by the end of this paper, an explanation of the first characterization will come into view. So what does it mean to say that mathematicians study bodies but not qua mobile~ One could answer this question by putting a psychologistic spin on Aristotle's philosophy of mathematics. According to some interpreters, Aristotle thinks that mathematicians mentally

~ ~--------------I!!!!!!L_I!I!I!I_~_~~-!~!~!!!~!!!-~--~-~~---::21

THE FOUNDATIONS OF ARISTOTLE'S CATEGORIAL SCHEME

2

abstract th . 3 rna emancal objects and/ or £ and then go on to investi th eatures from mobile substances sensible substances but gate ese ~bjects and/or features. To study · not qua mobile din tanon, requires one to b , accor g to such an interpre· sens1"ble substances anda £stract mentally from th e mo bile features of . Ab ocus on the math "cal c mam. straction thus be ki eman reatures that recomes a "nd of el . rnathematicians to focu th s ecnve attention allowing ld.6 Such an interpretati s on e mathe · al wor h mane aspects of the material tracted fromAnstode's . . 1 . remaon, ks dowever:' though not 1mp aus1bly exIan_guage that Aristode . r • oes not pay gh . uses to ch . enou attennon to the ~ It should, view Aristode's hil ar:actenze mathematics. It does not, discussion in the Posterior A~alot"sophfythof mathematics in light of his I th n . ytcso e'q '1 . n e rostertor Analytics A . d ua ocunon. metrical hi chi , nsto e uses amo 0 th th erar "es in order to elucidate h . ng er examples geoat some entity has a feature qua wthiat It means to demonstrate · the followinggenus/species hierarchsome ng• Bor Instance, consider

y.

1i. nangle-three-sided closed plan ,; __ 1. Equilateral-three equal len e ~..re 2. Isosceles-two equal length~ sides 3. Scalene-no equal length sicksdes In this hierarchy, triangle is th of the number of equallengthe ~deenus, and it is differentiated . s1 s a tri, ......1~ h m terms A s was known to Aristod all . ---"&""" as. . al e, triangles ha mtem angles whose sum is 180o· and all ve two right angles •. scalene · gl h ' so equila .e. . tnan es ave two right angles N ter:al, isosceles 'and t1on to ask of the having of tw "gh • ow, one very natural o n t angles is: in . ques6 Julia Annas, Aristotle's Metaphvsics· B L M V1l'tue of what fea•29-30 though h th J • OOK,J and N c~.r-rd: r ' s e accepts e psychologisti · .'-'Ql • }Jreaal976) rorward an apt criticism of Arist tl . c mterpretation ofAriat--ttions [of mathematics] ar o he so mterpreted. 'Both th-a r~....::" ~uts e somew at vagu d h ...... -::--~ that the nature of mathematics is el .dat~an ~ ile they make th . • subject-matter, they are not very inro:ative method and ..•· The theory of abstraction is charact... ....;~ __ .J more by e nature what· of the ..-......L-.J tq;Qvu mi~ent ~o abstract objects) than by any positive PrnaP!I--~t Ill'~ ((USn. not gtven It the thorough dialecticall ed --o--......... Ariatotie nu t.._I d , y argu treatment that h . p ace, etc., an incoherencies are latent in its li . bothe gwea to tift-. and to arithmetic.' app Cation to SCOmetry

as~:~

0.0:

c;:

2 Pel The Body Problem in Aristotle

33

ture does an instance of one of the species of triangle, for instance an equilateral triangle, have two right angles? And the correct answer, according to Aristotle, is that an equilateral triangle has two right angles in virtue of its being a triangle (PA. 73b31-38). Why? Because there is nothing peculiar to equilateral triangles as opposed to isosceles or scalene triangles that makes it the case that they have two right angles. Were one to examine the proof that all triangles have two right angles, one would notice that nothing in the proof requires the figure in question to be equilateral, isosceles or scalene, but it does require the figure in question to have three sides, i.e. to be a triangle. In other words, the highest genus whose complete definition is used in a demonstration that any triangle, whether it be equilateral isoscdes or scalene, has two right angles is the genus triangle (PA. 74a4-74b4). So it is possible to say that all equilateral triangles have two right angles, not qua equilat· eral triangle, but rather qua triangle. Aristode ties his use of the qua' locution to his view that a science consists of categorical syllogisms. Consider the following two syllogisms, the first of which is a demonstration of the fact that triangles have two right angles, the second of which is a demonstration of the fact that equilateral triangles have two right angles. #l

All triangles are three-sided closed plane figures. All three-sided closed plane figures have two right angles. Therefore, all triangles have two right angles. #2 All equilateral triangles are three-sided closed plane figures. All three-sided closed plane figures have two right angles . Therefore, all equilateral triangles have two right angles.

In both syllogisms, having two right angles is demonstrated of the subject of the syllogism via a middle term that is the definition of a triangle. Hence, in both syllogisms the demonstration is qua triangle. But, in syllogism #1, the subject is triangles and so is a demonstration concerning triangles qua triangles, while in syllogism #2, the subject is equilateral triangles and so is a demonstration concerning equilateral

triangles qua triangles.

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

34

According to Aristotle, only the first syllogism can be part of an ideal scientific demonstration. The second syllogism, because it shows that equilateral triangles have an attribute qua triangle and not qua equilateral, is not, in Aristotle's terminology, universal (PA. 74a4-74b4). Nonetheless, the second syllogism illustrates the fact that a syllogism can be a demonstration (or perhaps it is better to call it a quasi-demonstration') of an attribute that something has not qua that thing but only qua part of that thing. In syllogism #2, because the middle term is not the complete definition of an equilateral triangle but only the definition of a triangle, it is a demonstration not qua equilateral but qua triangle. Although there may be some problems of detail, Aristotle's general use of the locution in the Posterior Anarytics, especially when illustrated with mathematical examples, makes a reasonable amount of intuitive sense. An attribute, P, is demonstrated of subject S qua M just in case (1) S, M and Pare the subject, middle and predicate terms respectively of a valid categorical syllogism; (2) the premises of the syllogism are true; and (3) M is the reason for S's having P. Furthermore, if M is the full definition of S, then the demonstration is a demonstration qua S, since M is what S is. If, on the other hand, a demonstration uses a middle term, M, that excludes part of the definition of the subject term-call such a part 'Q -then the demonstration can be said to be not qua Q For instance, because the middle tenn of the demonstration in syllogism #2 excludes part of the definition of equilateral triangles, it can be said to be a demonstration not qua equilateral, or alternatively not qua equal length sides.

qua'

Now, in the Posterior Analytics, Aristotle's mathematical examples all concern some particular genus a mathematician may study and not mathematics itsel£ Nonethdess, the terminology Aristotle USes when he characterizes mathematics itself is the same as his tenninology in the Posterior Anarytics. According to such a ~on. math. ematicians study bodies but not qua mobile. So, if AristotJis USe of the qua locution is consistent in both cases, he must haw: thot.a.ght there are syllogisms of the following form. ·

#3 All bodies are M

2 ~ The Body Problem in Aristotle

35

AllM are P. Therefore, all bodies are P. . al attribute that bodies b th p ould be a geometnc ll . In such a sy ogtsm, w d . middle term, M, that is o uld b demonstrate vta a hili d. e b al somehow excludes mo ty. have. An lt wo a part of the definition of bod! utf so 'b te that bodies have but o an attn u In this way, it wo uld b easylloO'tsm b" not qua mobile. . . f which bodies have their uld M th feature m vtrtue o d fini . So what co , e Wh . ther words, would a e non geometrical attributes, be~ at, =o~ili be~ In Metaphysics V 13, of body that somehow excludes . tr. ·n his discussion of the Aristotle provid es an answer to thts quesnon 1 • category of quantity. At Metaphysics 1020a 10-15, he says. . . all d . . . uous in one dimensiOn 1S c e Of magnitudes, ~~t whtch .ls ~~~~d if in three, 'depth: Of ~es~, ~ 'lengcll, if in two lt lS calle.d Wl tb, , 1' ited length is called a line, . . alled anum er, a 1m • b d , limited plural tty lS c , fa , d a limited depth, a o Y· a limited width is called a sur ce, an £ ll . In this passage, Anstotle defines line, surface and body as o ows. line =elf a limited length. surface = elf a lirm'ted breadth. body =elf a limited depth? He also defines length, bread th and depth as follows. . ' e8o<; in one dimension. length =elf (that which is) connnu~us J.l.E'Y~ye8o<; in two dimenbreadth =elf (that which is) connnuous

. SIOns. .h .) tinuous J.l.E'' YE eor~ in three dimendepth =elf (that whtc 1S s con sions. (Meta.l020all-12) . ,_~ th; though 'volume' might be . AAOor 7 1 am trans1anng ~"-' ~ as is usual, t.e. by uep better. ed t avoid an ambiguity in the Eng, ' otranslat so as 0 'cal and 8 I am leaving J.l.EYEuu<; un , . • but extension has a numen lish. It is naturally tr~ted as ext:sa:.nie of its numerical use is: the ext~n­ a technical non-numencal use. An p 'cal use extension refers to a kind feet In its non-numen ' • . . th meaning I intend in the paper. sion of the rope is ten of extended continuum. This 18 e

:~FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

36

lth the latter three defini . . tions of line surface db nons In hand, one can expand the definiin them with the de:U o~y bthy replacing 'length: 'breadth' and aepth' d epth·The resulting defini ens .In e definitions o f 1ength, breadth and nons are as follows. line =df (that which is) limited ' . surface =df (that which is) limi:ye~oc; m ~ne dimension. body =df (that which is) limited fl£YE9o.c; m two dimensions. J.I.EYE9oc; m three dimensions.

And if'J.I.EYe9oc;' . is replaced .th , definition Aristotle provides ~easurable quantity' which is the these definitions become: o to JJ.£ye9oc;just a few lines prior, then

7,

li.ne =df (that which is) limited ston. measurable quantt'ty m · one di men· surf.u;e =df (that which is) limit menstons. ed measurable quann'ty mtwo · di • bod _ Y -df (that which is) limi mensions. ted measurable quann'ty m · th ree di-. It must be admitted, I think tha th.ey treat lines, surfaces and Lt_~~ese definitions are slightly odd r wrth q ·· I uuw.es as q .. , ror u:mnnes. t is far more natural uannues rather than thin s thing wtth a measurabl to underst d lin g than something tha . e quantity, i.e. with som ~ a e as someThis odditv h t Is a measurable quantitv e su:e or other, rather .,, owever,canbeunderst ·r not completely rectified 'th ood, though perh . crucial ' WI a certain undera aps lil the end 1h .conc~ts Aristotle uses in these defini .tanding of one of the ere IS an Interpretation of Ari telian tiona, namely J.1i cently defended by Robert Sokol:ski J.l,tye8oc; that haa .,:eeoc;. traces back at least as far . . . and Richard g..._L.. n reis a kind f as S•mphaus acco..-1:-......iiOJl but that 0 matter. 9 According t S rab' --.~to which J,Lt An~ is not so much a property, o o !Ji and Sokolowalci J.Ltye,"":' continuum simil h , not an amount, but rather • yeOoc; ar to w at Descartes call , . an underl.~._ s extensto.L In~~ 9 Rob~ Sokolowski, 'Matter, Elements and Subst . . of th~ Hutory of Philosophy 8 (1970),263-288. Richanardce m ~]..,_, den nal Address: Analyses of M~-- An . Sorabj~, -nte --~· :tt....._. · t· ......., aent and~-· D....••• J. A rutote ran Society 86 (1986} 1-22 ~ .. ·~~~of the

2 ~ The Body Problem in Aristotle

37

suggestive terminology, j.lEyE9oc; is continuous, extended space-filling

stuff. If j.lEye9oc; is interpreted in this way; Aristotle's definitions of body; line and surface take on an intelligible hue. If j.l£ye9oc; is a kind of indeterminate three dimensional stuff, then a body, according to Aris· totle, is such stuff in three dimensions in so far as it has been limited. And what would the limit of such a body be? A surface, which itself is limited j.lEyEOoc; in two dimensions. And the limit of a surface is a line which itself is limited by a point. And here the progression ends, since a point, because it is unextended, is not limited j.l£ye9oc; in any dimensions. 10 Because Aristotle's definition of body can be illuminated by focussing on the nature of lleyeOoc;, in the remainder of this chapter, I will leave 'j.lEyE9oc;' in the definition of body rather than what could in principle replace it, namely 'measurable quantity'. Hence, the definition of a body that emerges from book V of the Metaphysics is: body =df (that which is) limited ~yeeoc; in three dimensions. And hence we have our middle term in syllogism #3, which now looks like the following. #4 All body is (that which is} limited JlE"YE9oc; in three dimensions. All limited JlEye9oc; in three dimensions has P. Therefore, all body has P. But, if this is to be a demonstration of an attribute that bodies in the category of substance have but not qua mobile, the middle term here cannot be the full definition of a body in the category of substance. Indeed, this is clear enough from the fact that the definition occurs in Aristotle's treatment of the category of quantity. So what, then, is the definition of body in the category of substance? The answer to this question is quite simple and has been foreshadowed by the discussion of Aristode's use of the locution. If a demonstration

qua'

10 This understanding of Aristode's views about geometrical objects is similar to Ian Mueller 1\ristode on Geomettical Objects: Archiv Fur Geschichte Der Philosophie 52 (1970} 156-171.

THEFOUN

ofbodies .DATIONS OF ARISTOTLE's CATEGORIAL SCHEME

38

lS not qua mobile, then 'mobile' . . tenn. If so, the full definition f bod . must be nussmg &om the middle 0 'the category of quanti al m .yJSthdefini' e non of body as it occurs the category of substancelo:i1=th the word 'mobile Hence, a body in defined as follows:

body =df (that which is) b' . sions. mo ile !united J.tEyeeo~ in three dimenThe difference berween a bod . stance and a body as it appe: ~s thit appears in the category of subcurrence ofthe word ,mobile' insthIn r e category 0 f quannty . IS . the oc. m the latter. e rormer defin'Inon · and its exclusion remarks concerning Aristode's . . precise Interpretation. Abstrac . g~merry now admit of a clear and th non Is a logical meth d f . parts of the definiti but u ons at are used . o o removmg fr es. To study bodies geometricall m the demonstrations of attriom the definition of bod . y requires the removal of' bil , y as It appears in th mo e Geometers th beilcat~gory of substance. three di ' . en, study those features of be d mo e limited ' e . mensions that ited megeqoV in three candi . emonstrated via the middl!lEYE oli~ m (" th mensions In th e term mm e category of substance) but • o er words, they study bodi not qua mobile. es

SECTION III A DIFFICULTY The solution to the bod bl . 1i ..l!nY pro em ts in wo uurerent conceptions of bod some ways alread them 'body-s' and 'b d ' r y have been loca d y at hand. b o y-q ror bod . th te - I will call · y m e category of sub ody in the catego of ited J.LEYE8oc; in thrryee di q~nty respectively. Body-a . stance and th mensions whil bod 18 mobile lim ree dimensions. The body probi e. y-qialinutedJJ.£ eo . that body is in both th em ansea because Aristottye S m e category of subatan e acr,._a . e c atm that body · · th ce and quann.... ----y.... th I Is m e category 0 f 8 ubs - --:-r· But as the claim that body-s Is · In · the category of substan tance can be :--IKOOCl uftA.........~~ ce, while tbe ...t...=~11, I thus agree with Cleary 'On the Te . ......UU,. de, Phronesis 30 19S5 1345 h rmmology of A.batraction . ally means a method of Iogi~ o argu~ that by Q+aipecn~ ~Ariato.. than an act of al b . Separation of terms from deJini , Jener• ment a stractton &om pam·--'--tloba rather '-WMB to universaJa,

2 fial The Body Problem in Aristotle

39

that body is in the category of quantity can be understood as the claim that body-q is in the category of quantity. So, strictly speaking, no contradiction arises. A difficulty, however, remains. According to the interpretation I have proposed, body in the category of quantity is (that which is) limited JlEYE8oc; in three dimensions; and the definition ofbody-s results from adding 'mobile' to this definition. But adding 'mobile' to '(that which is) limited JlEYE8oc; in three dimensions' looks like the adding of a differentia to a definition. But adding a differentia to a genus, like adding 'rational' to 'animal: results in the definition of a species that falls under the genus. So it would seem that mobile limited JlEYE8oc; in three dimensions should be a species under limited JlEYE8oc; in three dimensions. But, because limited !!Eyt::Soc; in three dimensions falls under the genus quantity, mobile limited !!Eyt::Soc; in three dimensions, if it really were just a species that results from adding the differentia 'mobile: would likewise fall under the genus quantity. But, mobile limited JlEYE8oc; in three dimensions is supposed to be the definition of body in the category of substance and so should not fall under the genus quantity. This difficulty can be given the following pictorial representation. It would seem that the following genus/ species structure is naturally suggested by the definitions I have proposed. Quantity J,tEyeeo~-measurable quantity

body-q-limited p.Eyeeo~ in three dimensions body-s-mobile limited p.EyeSo~ in three dimensions

In this diagram, body-s falls under the genus quantity. But what is wanted is the following: Substance body-s-mobile limited p.Eyeeo~ Quantity p.Eye6o~-continuous quantity body-q-limited ~ye9o~ in three dimensions In the latter hierarchy, body-s falls, as it should, under the genus substance, while body-q falls, as it should, under the genus quantity. If the

I

!

THE FOUND • ATIONS OF ARISTOTLE's CATEGORIAL SCHEME

Interpretation ro d 40 th P pose so far is correct th · 1 . e way that Aristotle should h b , Is atter diagram represents . mvolving . reIanons quanti bave een thinking of the genus/species "tled ty, su stance and b0 d S h enn to accept the latt hi hi Y· o, ow is Aristotle er erarc ·cal merr How is it that addin , bil , structure rather than the for, to speak, create, a genus/ ~pm~ e to the definition of body·q can, so the genus under which b d eoesfallstructure that is not subordinate to 0 y·q sr

SBC1'ION IV 1'HB SOLUTION The answer to this difficul the source of mobility and ~s r:r~es first an interpretation about

~:ten;:on and precisification of:; ~sub~tantiality and second

ms Involved in Aristotle's sop .Y of mathematics. According to Arist tl . in . o e, a mobile hod . g a nature, I.e. a Principle of motion y IS mobile in virtue of its hav· Each of these things [ . . • motion and of rest ·:Snng by nature] has in it If . . alteration Con Wt respect to place, in se a pnncrple of ciple and ;~us seqfL~~dy the substance ofcrease decrease and eo UCUlgm _.J nature ts t b . ovcu or of rest in th . o e a pnn· bdongs pritnaril and Y according to itself ( e thtng to which it Aristotle locates th Pbys.l92bl3·3)

o:

e source of mo . . • substances have-con non m the world in is effected by the intr~y, the move from imrnob~e natures that h cnon of natures. Furtherrn ility to mobility are form and one wav,,then ~:tuaps~.-:nd"stotle wavers about the ~re, these natures ,, • re Is sat to be th c._~ ISSue, things which have in th el e urat underlvin... matter. In ems ves a p · · '' --& matter in th . nnaplefoof rnotion or of chanose but m, another it is said to be the JLOnM mula (Phys. 193a28-2I).'But th t"l''l ~r rrn~ ge, (Phys. 193Ib6-7).12'1h .. 'r e form IS nature rather ..L~ the forus, It Is rorm that is nature' ( "'.tan matter' Pbys.I93bt8). 12 I am taking J.uiUov to mean rath f her, nhot more. So taken, A..:~--• • at Physics193b18 is a reiteran· ·. on 0 W at e has "d - · L • uuwae-a daian ~osttlon. If one insists that J.UiUov should be sat •-.ncr than a~ . tstode can be seen as strength . . translated aa ·~theft Ul which the disCllSSion takes p~mg hiS position at the end of the~~

I

2 N The Body Problem in Aristotle

41

Suppose, then, that substances are mobile in virtue of having form. Because a body·s is mobile, it must have a form, or, to speak adjecti· vally, be enformed. Form, however, plays a crucial role in Aristotle's theory of substance. In fact, in Metaphysics VII, 17, after a long search for substance, Aristotle argues that form is the principle of substance. Crucially, Aristotle claims that form is that which causes matter to be something: Thus, we are seeking the cause of matter (and this is the form) by means of which it is something; and this is substance' (Meta. 1041b7·8). Now, the interpretive difficulties surrounding book VII of the Metaphysics are immense; and I do not intend to enter into the details of scholarly disagreement about it. Instead, I shall simply assert what could in the end be defended by a thorough examination of book VII, namely that Aristotle accepted the following thesis: form is the principle of substance of composites of form and matter. These two claims-(1) body·s must be enformed; and (2) form is the principle of substance of composites of form and matter-end up having an interesting effect. But to see this requires some precisifica· cion of Aristotle's theory of abstraction. Aristotle claims that it is possible to demonstrate some feature of X's but not qua F. For instance, geometers demonstrate features of bodies but not qua mobile. To capture this idea formally, let X be some con· cept that contains as a part the predicate F. Let X_not_qua_F be the concept that results from abstracting F from X. Now, X's_not_qua_F can have properties; but because F has been abstracted from them, they cannot have the property F. Nor can they have any property that entails that they are F. For if they could, then F would not have really been abstracted from them but would be implicitly contained in some property they have. Hence, a necessary condition for X's_not_ qua_ F having some property G is the following: it is not the case that Xs hav· ing G entails that X's are F. This can be stated formally as the following abstraction schema (AS). 13 (AS) If G (X_ not_ qua_ F), then~ ( G(X) f- F(X) ) 13 I am in general agreement with Jonathan Lear, ~ristode's Philosophy of MathematiCS: Philosophical Review, XCI, No.2 (1982) 161·192, about the correct way to understand the qua locution. Lear does not discuss how to interpret Aristode's claim that one can demonstrate a feature of something not qua F; but he does provide the following schema with which I agree for

I I

I

I Ii I I

THEFOUNDA TIONS OF ARISTOTLE's CATEGORIAL SCHEME

Now, I have argued that b 0 d . 42. away. In other words bod .y-q IS body-s with 'mobile' abstracted following is an instan~e of C~~)s body-s not qua mobile. Hence, the (1) If Substance (bod ) th (body-s)] y-q ' en ..... [Substance (body-s) 1- Mobile lnformall · to be read as· ifb0 d . y, this IS . • . y-q Is a substance, then body-s's b emg a substance do t (1), three further pri es not . mobile. In addition . l entail body-ss, bemg 0 terpreting him. Aristodncrp es are attributable to Aristode as I am ine accepts th £ . and so accepts the followin h at orm IS the principle of mobility gsc ema, (2) Has form (X) 1- mobile (X)14

2 fll; The Body Problem in Aristotle

43

(5) Substance (body-s) f- mobile (body-s). And (5) and (1) entail that body-q is not a substance. And so the difficulty vanishes. Because form is both a principle of substance and of mobility, the removal of mobility from body as it appears in the category of substance does not push one up the genus/ species hierarchy; rather, it tears one away from the category of substance, leaving one in the category of quantity. In the other direction, adding'mobile' to body-q does not, like the mere addition of a differentia would, simply create another species in the category of quantity. Rather, it is tantamount to the addition of a metaphysical principle sufficient to create another genus-species hierarchy not subordinate to the category of quantity; it is tantamount to the creation of the 15

Furthermore, Aristode · · 1e of substance. accepts is the p rmcrp H that amo h ng composite substances form ence, e accept th c II (3) Co . s e ro owing schema, mpos1te substance (X) 1- h asform(X)

category of substance. The principles in (1) - (5) thus show that the underlying picture about the relationship between substance, form and body can be made precise. But it is really the underlying picture that is of interest. The picture is of a metaphysical principle, namdy form, which is connected to two fundamental aspects of the world: substance and motion. The presence of form confers both substantiality and the capacity for motion on a physical body. And its abstraction from body leaves something of a metaphysical shadow, a genus in the category of quantity,

which has as an ins

which can only have only accidental being.

which has as an inst ance the following principle.

(2a) Has fo rm (body-s) 1- mobile (body-s)

tance the following p rmcrp . . 1e.

(3a) Composite substance (bod ) F'nall y-s 1- has form (body-s) 1 . Y, Aristode accepts that bod . . . pos1te substance. He h y-s, if It IS a substan nee, e accepts the foU . ce at all, is a comOWing prin ' 1 (4) Substance (body-s) 1. crp e. (2a), (3a) and (4), then, entailCompOSite aubstance (body-s) what it is for something t o havea kature 1- G(x)].

14 1h fo

F

qua : G(b qua F) 1- F(b)

·. · & [F(w\ . at rm is a principle of moti . , . "1:: " tlonal sch has fo on m fact a u - .L_ ·.. · · is n ema: rm (X) 1- mobile (X). But rr-·- we~~-

eeded for the above argument. Similar

only the conditioaal ac:hetna remarb apply to (3) u •ell.

SECTION V THE BODY PROBLEM SOLVED The solution to the body problem is now at hand. The problem arose because body appeared to be a genus in both the category of substance and the category of quantity. But this appearance results from a subde equivocation. Body-s is in the category of substance; body-q is not. Body-q is in the category of quantity; body-sis not. And how is it that, 15 This view requires interpreting Aristode as not thinking that being a subject of predication is sufficient for being a substance. Hence, when Aristode says at Metaphysics 1020al7, 'Of things that are quantities by their own nature some are such as substances, e.g. the line is a quantity ... and others are modifications and states of this kind of substance.' he must be taken as speaking of substance analogically to the primary sense of substance.

"' THE FOUNDATIONS • OF ARISTOTLE S CATEGORIAL SCHEME •

44

gtven the way I claim Aristode w0 uld d be in a aenus/ . efine these terms, body~s can eo spectes structure th . b in which bod at IS not su ordinate to the structure y~q occurs? The answer be c d · th connection Aristod dra be can roun m e conceptual e ws twee . c body~s is mobile and h h ~ monon, rorm and substance. A . c ence as a pnmary · . 1 f . hich Is a rorm. Form how . al pnnop e o monon, w , ever,ts soap . . I f b nnop e o su stance, and so body~ s is a substance. Wh en one removes hili" fr y~s, the havina of . mo ty om the definition of bod ---eo a pnmary prin · I f · no longer be entailed b th . ~P e o monon, namely form, can however, is a principl y f eubremauung part of the definition. Form, eos stance d . wh at remains after th an so Its removal entails that e removal cann b cannot be in the cat~o f ub ot e a substance. Hence, body~q . . . th -eo ry o s Stance. Rath . . . er It Is, as Aristode claims It Is, m e category of quannty. 1his so1ution to the bod bl actenzanons · · of math.-..- Y. prothaem also explains h ow the two char~ ~.....ncs t can b th texts are not at odds with h e ga ered from Aristode's stud~ ~odies but not qua mo~ isother. To say that mathematicians ~anoan~ study limited Jliye9o '~ 1 have ~gued, to say that math~ JJ,eye9oc; In three dimenst· . c; m three dimensions. But limited · onsxsa . ' oans study quantities. Of cours thquannty. And hence, mathemati~ old fashion. Rather: th e, ey do not study quann·n· . .. ' ey attempt to dem es m any quannnes that belong to them vi onstrate those attributes of the essence of quantities. For instanrtu~~~-one or another aspect of ous quantirv ce, UC\:aUSe ,_..yeuuc; uo a_ is continu~ .,, a rnathetnatician may demo b~o~g to limited ~ye9oc; in three di ~te those attributes that thts Is precisely the alternative char m~tons qua continuous And tode provides. actetUation of mathe--n· . ..... cs ·Ans~

in

SECTION VI A FINAL AMENDMENT ~e proposed solution to the body problem, tho

It stands, admits of a final amendment that willup.~ ~uate mg result concerning the relationshi betw lead to a rather •triltstance ~d quantity. The opportuniri.'or een cateaoriec of~ _. ment anses from certain· d . _perhap need,fOrfhe,....;...;.;...s< ·.· . . ma equaaes m the definition ._._..... (that which Is) mobile continuous limited Jliye~ in;_~

:U

-;se

2 ~ The Body Problem in Aristotle

45

sions. Although such a definition makes perspicuous the relationship between body in the category of substance and body in the category of quantity, it does not accord well with Aristode's preferred method of defining kinds in terms of a genus and a differentia. For it is not clear what in the definition serves as the genus and what serves as the differ~ entia. Furthermore, it is at odds with the definition most naturally ex~ tracted from the passage in Metaphysics XII, 1, a passage that provides crucial evidence for body's location in the category of substance in the first place. In that passage, Aristotle divides substances into immobile and sensible substances. Hence, if mobility and sensibility are convert~ ible, and if sensible substances are bodies, the definition of body as it appears in the category of substance should be: mobile substance. Suppose then that the definition of body~s is in fact mobile sub~ stance. It is nonetheless possible to construct a syllogism which, when supplemented by a subsidiary principle, entails that body-sis enformed limited jl.Eye9oc; in three dimensions. The syllogism is as follows. I. Body-s is mobile substance. II. Mobile substance is a composite of form and a first underlying matter. III. Therefore, body-s is a composite of form and a first underlying matter.

The first premise is, of course, the proposed definition of body,s. The second premise finds strong support from passages in the Physics. At Physics 193a28~31, Aristotle says, 'In one way, then, nature is said to be the first underlying matter in things which have in themselves a principle of motion or of change, but in another it is said to be the jl.Op~n or form according to a formula' (Phys. 193a28,31). Shortly af~ ter this passage Aristode speaks of that which is from both form and matter, i.e. a composite of form and matter, and he says that it exists by nature (Phys. 193b6). But at the beginning of Physics II 2, Aris~ tode says that those things existing by nature are substances (Phys. 192b32~33). Hence, Aristode is committed to the claim that mobile substances have form and a first underlying matter. Now, a question arises as to the nature of the first underlying mat, ter Aristode mentions. And I have already alluded to two contempo~ rary scholars, Sokolowski and Sorabji, who have discussed at length

jP

THE FOUNDATIO , NS OF ARISTOTLE's CATEGORIAL SCHEME

46

Jl£YE9o~ According to both S k 1 . only a kind of matter but . . o co owski and Sorabji, JlEYE8o~ is not . IS In ract pri If a bout this, the first under! . me ~atter. they are correct above passage from th Ph~g matter to which Aristotle refers in the e ')'SICs can b · e Interpreted as JJ.EyESo~ • And h ence, the first unde l . • _ r ymg matter in th b 0 Jl£YEuv~ So interpreted th d . e a ove syllogism would be 0 f th bodY Is · a composite of fo' e con · d USion , e s yllog~sm asserts that such Jl£yE9o~ is both th!.' ~an ~yESoc;. But if it is assumed that enforms it, then the condee . menfsional and limited by the form that th usxon o th ll . e category of substance i b d e sy og~sm asserts that body in ited JJ.EyEOoc; in three di ' .e.. o y-s, is (that which is) enformed limof bod mensxons. And th. . . y-s that I have argued . ts ts precxsely the conception 18 body problem.I6 needed in order to fully reso1ve the A fai . rly remarkable result has th attons. The emerged firom th ese constder. • . . a bove syllogism is 1' us . P ectsely the sort that b I . Anstotelian science.1h s· th . emmorpl' . . e ongs man ' 'ddl e tna.Jor premise contaxns . te emtse contaxns a d efi rutton · · o f b o d ymx .e term; and the conclusion~ nchecessarily convertible with the contaxns within . th ts a aract . . . It e source of at leas ertzatton of body-s that quanttty. Being limtt · ed enformed • t one speexes · m · the category of a property, in the Aristotelian sense Jl£YE0oc; in three dimen . . thus fbod sxons xs ryof substanceand '0 yasita · 11 F can be shown to be 80 b ppears m the categosyllnai -b"'sm.· urthermore, if!-:-Y an Aristotelian scxentt · 'fic act · f """"'IS ...... t:.._ - • . enzatton o body-s obtained by-•u.ul:llleQ ts l'emoved fro th ch because it lacks . the syllogi bod m e arsubstance. Rath a ~~ciple of substance, ~m, fall r-q results which, er, tt ts a species · ot tn the f tn the category of uan . category o least one genus in the ca First, an Aristotelian sci ~ory of quantity is deri~I ~ty. Hence, at entific syllogism conce . e In two stages. ~6 As shall become apparent in cha rtUng the hylomorphic ls extension. Nonetheless th pter 4, I do not ..._._, th . ' e connecti bet. ..UDJt at prim ter ts sufficiently intimate to justify this 1 . ~extension and -::~er 17 It is worth no . . o Utlon to the S......t.._ r .... ..., matfbod nng that m the Topics Aristotle -vv.y ptobletn. 0 Y and soul is a correct " derin says that bein ics 13la8-ll) This is con6rrn:' . gof a Propertyofliving I•CO!nposire posite of form and prim g ~ce for the claim thar..a.~ (Tope matter IS a pro~ fL-.J,_. o;uar ~- . . . o uuuiea.Portbc"d::.a~. livmgcreatureswouldbeaspeci6 . the fact that living ........ .......... tup.e IS . a s,..,es ~onun.J of __ theththesis about L- ..JL a ; .....a aboUt • one would expect. r-ucr e genua~ dUa ia~:

0:

r---,

2 Pal The Body Problem in Aristotle

47

principles required for the possibility of change is constructed; and second, one of those principles, i.e. form, is abstracted away.

CONCLUSION In one sense the body problem is not a genuine problem at all for Aristotle; but in another it is perhaps the deepest problem in Aristotle's metaphysical system. It fails to be a problem because it admits of a completely seamless resolution that draws from familiar aspects of Aristotle's views about science, substance, quantity, form and motion. In fact, the resolution is so seamless and flows so gracefully from theses central to Aristotle's thinking that it provides an explanation of his reticence concerning the issue-there is no reason to comment on the perfect convergence of the pieces of a puzzle that one has constructed oneself The problem is extremely deep, however, precisely because its resolution does depend on as well as draw together theses that are so central to Aristotle's thinking. In addition to being centrally located in Aristotelian metaphysics, the body problem also illuminates the possibility of deriving the cat· egories from hylomorphism. Though a contemporary heterodoxy, and though underdeveloped in the Medieval derivations, the view that the categories are at least in part derived from hylomorphism is at least somewhat vindicated by the ease with which a very deep connection between the two systems has emerged. For the interpretive theses needed to bridge the gap between hylomorphism and the categories are, especially when viewed in relation to the boldness of the Medieval thesis, reasonable and certainly within the confines of plausible scholarship. lhe theses are as follows. I. Body in the category of substance is mobile substance. II. Body in the category of quantity is limited ~yeeo~ in three dimensions. Ill. Any mobile substance is a composite of form and a first underlying matter.

THEFOUNDATI

ONS OF ARISTOTLE's CATEGORIAL SCHBMB

IV. If body has a form, then body is mobile.

v.• If body IS. a substance, then bod

Y h asa fo nn.

VI.Prime ........ .... ~-er IS · Jl£Y£0os. , VII. For any predicate G if G I- F(X) ] ' ' (X_ not_ qua_ F), then "" [ G(X)

. Aris tl , Thesis I finds support m the Metaphysics. Thesis IT to es di~sion of substance in book XII s1on of the comes directl fr . , di ctl category of quantity. th Y om A nstotles discus· re Y from Aristotle's discus . m f e Metaphysics. Thesis III comes comes fro m Aristotle's claim tha s1on . the Physics. Thesis IV foo chan . ge m t rm 1s a princi 1 f . V comes from Aristotle' and that bodi . s views that com . P e o motton. Thesis . fall es m the category of ubs poslte substances have forms Is, o the th th s tance ar . chapter 4 N eses, e most controversial. I e composites. Thesis VI . be • onetheless, as shall bee n fact, I shall reiect it in on tween · orne ap""" tl the bo p~e matter and exten • • r-ent there, the"J connec· a ve solutton to the bod Sion IS sufficiently . . th to accommodate wha . Y problem can easil mttmate at Finall th . t 18 the correct: d Y be altered in order y, esiS vn em- fro un erstanding 0 f . ~----o-s man examinati pnme matter. standing of th on of Aristotle's under· From th e qua ocution. ese seven theses it is not only satisfies the . . possible to construct also demonstrates for an Aristotelian sci .a syllogism that namely body, is derivai,ttf::t one genua in the entific syllogism but 0 of change. e m theses that belong~ ~ of quantity, Aristotle's theory

CHAPTER

o:

:terta

3

FORM

A

defense of the thesis that the categorial scheme is derivable from hylomorphism clearly requires some account of the na· tures of form and matter. Hence, in this chapter I address the

nature of form; and in the next, the nature of matter. What Aristotle says about form presents an initial, and in some ways deep, interpretive difficulty.1 Simply put, Aristotle seems to con· tradict himsel£ Perhaps the most striking such contradiction concerns form's substantiality. In the Categories, Aristotle says that form is sec· ondary substance (Catg.2b7 -30); while in the Metaphysics, he says that it is primary substance (Meta. 104lh8). Another such contradiction concerns form's universality. Aristotle says at Metaphysics 1036a29 that form is universal; and at Metaphysics 1049a35-6 he says that it is particular.2 Not surprisingly, Aristotle's apparently divergent views about form's nature have not gone unnoticed by scholars. Consider, for instance, Geach's lament: 'there is hardly a statement about form

1 Aristode uses three words - elSo~ ~opc1rfl, and ax,fu.l.a - that are com· monly translated as 'form: Often enough. he uses - elSoc; and ~op#\ inter· changeably, though he tends to use el&c; when he means species. Further· more, he tends to use when he speaks of the figures, i.e. forms, of predication. In this chapter I shall be focusing on his use of the word; but because of the proximity in meaning betWeen-el&c; and ~opc1rfl, much of what I say is ap· plicable to Aristote's use of ~opctn\. 2 Interpreting Aristode as calling form in these respective passages universal and particular requires treating the Kai in each passage as epexegetical. A close examination of each passage would support such a reading.

~HB FOUNDATIONS OF ARISTOTLE's CATBGORIAL SCHBMB

SO

m the Metaphysics that is not (at lea st verbally) contradicted by some other statement.'3 Clearly, Aristotle's apparent! .

.

make interpreting his me Y. InCO~SIStent statements about form part of this chaptet h taphysical vxews a difficult affair. In the first

, owever, I shall th A . , k argue at nstodes statements about form present an even star er difficul th largely unnoticed by h lar b ty at has not only gone sco s uttha bl . . endY Inconsistent statem A . t argua Y underlies the apparchapter, I shall argue thentsA .nstode makes. In the first part of this · at nstode attach mearungs to the word 'form: es over twenty different It should be obvious tha ch to make interpretin..- A · tds'u a plethota of meanings threatens F . --"6 nsto es metaph ·ca1 or Instance, the apparent! ysx system a hopeless task b c a out rorm are not "'en .Y conttadictory statements Aristotle makes· diffi c ume conttadi . erent by 'form' in the .J!lr cnons if he means something uurerent statem B may .. . seem a positive result · . . ents. ut even though this tton· ha doe ' It Immediate! · . •. w t s Aristode mean h y talses the following quesIS pnmary substance~ Well · A--w en he says' ror c . Instance, that form mearung· h h ' It "'"'}'Qlds on hich . ~ e as in mind. Indeed w of the twenty or so Aristodes use of'forni und , unless there is some way ofb . . the nature of form beco eralcontrol, the statements he mak nnbogmg wo me most i "b es a ut tse, as I hope to show. the~ lllpOssi le to interpret. Wh t the WOrd 'fo I _ _ L_ • I ergent meanm Ari a S . As rm "..UU: It very difficult to kn · gs stode attaches to Is. I hope shall become apparen . . ow what the nature of form could possibly subsume all th . t, It IS difficult to see wh h e vanous m · at genus to kn0 ' ; w. at a form, according to A..:--.~gs. And so it is difficult My axm m this chapter h ......a.uuc. IS. fi ul R ' owever, IS not · 1y c ty. ather, I ultimately want to . sunp to point out this diEnature of form. Hence, in sections ~hat I take to be the ~me way toward resolving the difficui of this chapter, I try to non of form to be complete! exh ~·I do not intend mv • go an · book Y austtve-such .... _L ---, examina.en~re • Nonethdess, my goal in this a .....: is a Pl'oject fOr pomnng out the plethora of meanings f th cbapte.., in a.dditi is to bring these mean in... de o e word 'lOnr{ in A..J.•.... on...-.~to . ----e- un r some ~-~ IS as follows. I pick twdveof the

r:7vculate

meanin;:::~~~

SI

3 fill Form

fundamental notions of form in Aristotle. I then attempt to taxonomize them in a systematic manner. In the end, I shall propose that all the meanings in some way or another fall under the genus - principle of order. Now, the taxonomy by itself should be of interest; for it shows that Aristotle's use of the word 'form' is not as haphazard as it might at first seem. But, in providing the taxonomy, I make use of several substantive theses about Aristotle's metaphysical system. The theses help provide the contours for the taxonomy; and the taxonomy in tum help justify the theses. So the process of coming to grips with Aristotle's use of the word 'form' should, in addition to creating some order out of an apparent chaos, provide a means for addressing some of the more fundamental aspects of Aristotle's metaphysical system. Furthermore, the taxonomy, because it is a genus/ species strUcture provides a specification of the nature of form. So, by the end of this chapter, we shall be one step closer to a defense of the claim that Aristotle's categorial scheme is derivable from his hylomorphic ontology - we shall know the nature of one of the entities from which the categorial scheme is derivable.

SECTION I I

I

THE MEANINGS OF FORM Because of the centrality of form in Aristotle's philosophy, and because it is a technical notion, one might think that determining what a form is would be a relativdy straightforward task. For surdy, one might think, Aristotle would not repeatedly use a technical notion without defining it. So, determining what a form is should only require an inspection of Aristotle's definition. In keeping with this optimistic line of thought, one might tum to Aristotle's definition of form in his lexicon of terms. In Metaphysics V, 2, Aristotle says: . Also, the form, i.e. the paradigm. is the formula of the essence, ~d the genera of this; (for example, in the case of the octave, the rat1o 2:1, and in general, number) and the parts in the formula (Meta. 1013a27-9).

3 P.T. Geach, 1\quinaa' in Three Philosophers (Ithaca: . . ......- 196l),p.75. Corneu~Presa

This passage does provide some insight into the nature of form; but at the same time it also falsifies the bdief that Aristotle's views about

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

con~

the nature of form can be discovered by a mere inspection of his sidered definition. In this passage Aristotle disconcertingly identifies form with three different and not obviously commensurate types of entity. In the first instance, Aristotle says that form, which by way of an epexigetical leaf-i.e. an 'i.e.'-he takes to be equivalent to a para~ digm, is the (formula) of an essence. Except for the fact that Aristotle identifies form with the M>yoc; of an essence rather than with essence itself, Aristotle's claim here is straightforward enough; and it forges a crucial link between form and essence. Aristotle also says, however, that the genera of essence are forms. But if he thinks, as it is plausible to suppose he does, that the formula of an essence fies a species, Aristotle in this passage is asserting that a form can be both a species and the genus of a species. Finally, in the last part of the passage, Aristotle identifies form with any of the parts of a formula. lhe Parts of a formula, however, include a genus and a differentia the combination of which determines a species; and so Aristotle appears commit himself to the view that a form can be a species, a genus or atodifferentia.

Myo~

signi~

reformu~

A bit later in the chapter, Aristotle complicates matters by lating his definition of form in a way that brings into view two other notiona. An.. 6nt identify;.g- with that of 1¥hich something consists, Aristotle identifies form with SOinething's essence (Meta.

1013b20-5). In saying du. he i.o m..dy '"P
My~

es~

fum{ (Mota. 1013b23). He.. ArWode ~""' aew notions whole andcompo.;tion, 1¥hich are neUber u in the ptev;oua definition nor inde.d ""-'-.,...,..,..ofeach <>the. A whole, one might think. i.o IOntetbing that lo a . . _ of li>nn wd mattno with a .................

obrioaaiyt~.o- ~

like the odd jf not~ identllication ~'-with.~ that has form as a consntuent. And something's cotnpoation •'Would seem to be something akin to the structure a whole baa tat:het than the

wholeitsd£

53

3 N Form . din Aristotle's explicit · of'form'e contame The plurality of meanmgs difficulty, but the difficultydoes . definition in his lexic~n pres~~ts s~:ultiplicity is a manifestanon ~fs~ d there For thts defiruoon d'~" rm' For in thexhMetap·vdy 'Y not en • , f the wor ro • general trend in Aristotles use o different meanings to it. E . ausn uld ics alone he attaches over twenty .ngs though insrrucnve, wo li . and ' documenong · all these mearu ' rt alread y b een •nng affiri,, whlch ha• fu, the wd "' I provide only the be a lengthy . . h. Index Aristoteltcum, . d . gly many uses ly done by Borut:~ m ls . c d for the bewil enn to gtve are following citations so as of'form' in Aristotle.

adequate~

~" ~

FORM AS ART

1032b13-' ···for themedical• art and t he building art are the forms of health and of the house •..

b from thought h" hcometo e . in things w IC fo the causes are m 1070b31~33-' while the contrary of the rm, dical art is in the mover is the r~ or ther sense four. For the me the form of one sense three but m =of building is in some sense some sense health, the the house···'

·r;,

HICH, THOUGH N OT GENERATED, FORM AS THAT W A CHANGE IS THB BND OF

the first matt~ . ·.~or 1015a7~11-'Nature, then, is .either h end of generation. Kat substance, an

d this latter IS t e

al to substance one

the form

that our ar~

~ 10-'I~:::e~:;:~:~generated; ~~::n;tquan~

· alike

1034b7 :e gument reveals all forms, su ·th respect to P . • common WI f h ther categones. tity, of quality, and o t e o nmary·

could mean 'and; · g reason. Itassages, -------:-, slated for the followm especi.ally 4 I am leaving Kat un~tran eaning is stark. In many p f form I think Th m o so as ' not to 'or' or 'i.e.' e diffi.erence. inmaking claims about.the nature anslated those in which Anstotle~ "t as 'i.e.' But, I leave It ~~0: ues concerning its it is appropriate to trans e I genuine interpretive ISS glosaover the f.tct that there are translation.

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

S4

55

3 fJtl Form

1069b35-6-'Nen, neither the matter nor the form is generated, and I mean the ultimate matter and form: 1070al-2-That by which it is changed is the first mover, that which form: changes is matter, and that to which it is changed is the

FORM AS ESSENCE

1032bl-2-'bY•crorm' I mean the essence of each thing x:al. the first substance:

h. · the sub-

.mal (for t IS IS an ant 1035b14-6-'And since t he soul ofdin to A.Oyoc; is the substance

FORM AS THAT FROM WHICH GENERATION PROCEEDS

1055bll-3-'If, then, generations in matter take place &om contraries, and if they proceed either (a) &om the form or the possession of form, or (b) &om some privation of the form •.. '

ensouled body) accor g , stance ence o f such a body · •· ' of an , x:at form Kat ess

rna be a part of the fo~ 1035b31-3-'A part, then, ~ fformandmatter. mean essence) or 0 f the compostte o FORM AS THAT T

FORM AS SPECIES

m.-c..

1he of thi. are so nwnerou. that it;. not wotth quoting passages in which it occurs.

(b 'form' I y

0 WHICH ESSENCE BELONGS

th

"b something to ano er ute to the mqut;y . . intoality.' sen1043a37-1043b2-'But, these "b contn te nothing h · inquiry, but t ey do not contn senceubelongs to th e fo rm 1cat actu sible substances; for the es

FOR.M AS A.6yo~s FORM AS DIFFERENTIA

1044bl2-3-The caUSe as form is the M>yo;, but this is not made clear unless it includes the cause 1069b31-4-'lhe causes and plinciples, then, are three; two of them are the contraries, of which one is the My<><; Kai the form and the other is the J>rivation, and the third is the

. of the differentia were taken, ' h the differentia , 1038a25-6- If t en £ al. substance ••· the last one would be the orm K

matter:

FOR.M AS THAT WHICH IS SIGNiplBI> BY THB

AOyO~

1084b9-13-'As matter, then, the acute angle and the dements and to •ubatanc:e accordthe unit are prior, but with respect to furrn ing to A.Oyo;, the right angle and the whole as~ of matter and form are prior; for the COmposite is l1earer to JCQi. to what is signified by the fOrmula, but it ia FOaterior in sen~

~eat.

the~

5 I am leaving A.Oyo~ un-tranalated due to the di6iculaea in ......"\'"'1ifetbe . ~ ~,,?;,.~~. ,,·,~*"·~ word throughout Greek philosophy. That being said, I do think dale &y,fhat Aristode almost always uses it to mean linguistic account.

FORM As SUBSTANCE

. either the first matt~ •·; orthe form 1015a7-11-'Nature,.then, IS. the end of generanon. d this latter IS Kat substance, an . . .th the ultimate Ways . 1t 1s e1 er h t W h"ch "d. twO • I 1017b26-'Substance is :at~ of something .else ,o~:; of each subject which is not pbrel ch being the JiOpq,it Kat . a thiS. and is separa e, su IS . .d . many ways. In one "' . ·rrue ofwhI·ch" 1S sat . m, 1022al4- that m "! of each thmg; Kat substance th £ way, it is e orm . from both would seem th form or what 1S 1029a29-'Accordingly, th.: matter: to be a substance rather

thing:6

- ----:---:-;.

6 I have left Ji0 '*i un·tranSlated so

that it is not confused with etoo~

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

s6

3 iJ11 Form

.

FORM AS WHOLE

Form as the cause by

which matter is a thtng

. . h £ m) by

l013b21-3-'but the other in each case is a cause in the sense of essence, and this is the whole Kat the composition Kat the form:

Se (and thts ts t e or th 1041b7-8-'Thus we are seekin g. ecau . and this is substance.• . h matter is somethmg, f h means o w tc · orne

1023b19-20-i\Iso, it means those into which a whole is divided of which it is composed, whether this is a form or that which has or a form:

· potentt"ally because tt can . c· 5 6 -'F rther, matter extsts. 1050al - a form, u . and when it extsts actually, then it extsts m a to possess form.

FORM AS THAT WITHOUT WHICH A THING IS NOT A WHOLE

1016b11-l3-i\gain, in one sense we say that anything is one··· but in another sense we do not say so unless the object is a whole of some kind, that is, unless it has one form:

S THE FIRST CAUSE OF A THING's EXISTENCE ( d this is the ki the cause an 'Thus we are see ng d h. cause is the 1041b8/1041b29h-h the matter is a thing; an t ts f each thing; And this is the subs~ance o form) through w ~~ substance of the thmg .•. f he thing's existence. for this is the first cause o t FORM A

FORM AS THE CAUSE OF A WHOLE's BEING ONE

1016b11-l3-i\gain, in one sense we say that anything is one ..• but in another sense we do not say so unless the object is a whole of some kind, that is, unless it has one form: l052a23-i\s in the previous case, if the thing is a whole and has some 1.10pq,TJ or form, it is said to be one to a higher degree; and most of all, if it is by nature of this sort and has something in itself which is the cause of its being continuous, and not by force as in things which are glued together or nailed together or tied together: FORM AS THAT WHICH MAKES SOMETHING CONTINUOUS

l052a20-5-i\s in the previous case, if the thing is a whole and has some 1.10pq,TJ or form, it is said to be one to a higher degree; and most of all, if it is by nature of this sort and has something in itself which is the cause of its being continuous, and not by force as in things which are glued together or nailed together or tied together: 1075b28-30-l\gain, how can magnitude or what is continuous come from things which have no magnitude!' For number cannot make what is continuous, either as a mover or as a form:

FORM As ACTUALITY

h ombine both, speak of £the third (for of matte_r ant"sdth:::fthe 1043a18-21-'Bthut thothsee:n: ese, ul by means o f t h e differentiae substancehfrom . IS. rather that t c it seems t at he rorm tha fo mula o f t h e constttuents . but e r form Kat actualtty,

c~mposed

of the matter)'

th etimes we are h fact atsom hould not ignore t e site substance, or 1043a29-35-Whes ame signifies the e' signifies the f het er a n h ther ous h w 1. op¥1, for example, e and stones laid in sue unaware the actuality ' form that ,·s• a covering. . hICO·s !la coverm·g made ofbncks compostte, t at t ' h actuality Kat , and whether d t e . 1ength or two-ness, an sueh a manner , . ifi or, s two-ness m ' whether 'line stgn e 1. a body or a soul. , imal' signifies a sou m , ali ,

~

~

com~oh

an an

the form Kat actu ty. 'fo the essence belongs to 1043bl-2- r , the form is actual. 1050b2 -'It is evtdent t hat the substance Kat

ity:

. the form, if separable, and

exists actually IS 1071a8-9-' For what ' · from both. what IS

THE FOUND

FOR

ATIONS OF ARISTOTL , E S CATEGORIAL SCHEME

8

59

3 fill Form

M AS THAT WITHOUT WHICH

5 A THING DOES NOT HAVE A NATURE

1015a3-5 '1h . alth us m things wh "ch . ough there is already a con; . exist. or are generated by nature, ture they are generated or exist tltuent In them &om which by nan ature unless th ey have a form , we say th at th ey d o not yet have a 0 r a IJ.Op<jnl. FORM AS THELIMI

f

1022a ' . T lOF MAGNITUDE) 4-6-Limit which has magnitu~ans .•• the form of a magnitude or of that

FORM AS T

l022a14-5- "'TL ~nat

HAT INVIRT UE OF WHICH

•

Ill

·

sense it means the fo VI~e of which' has man . rm Kat the subst f y meanmgs. In one l022a17-9-"That in . ance o each thing' means the form and . VIrtue of which: then . first underlying sub. Ill a secondary sense th , In the primary sense ~ect of each: e matter of each or the FORMA

S THAT IN VIRTUE

OFWHICHTHI

1054b7-9-'lhin . NGS ARE SIMILAR and admi · ~ are sa~d to be similar . ttmg a difference of degr th , If having the same fo ee, ey do not diffi . rm er In degree: FORM AS PAn~

~DIGM

l013a24-7-J\ caus the fo ul f e means ••• the fo rm a o the essence: rm Kai paradigrn, thiS . being 1034a2-'Consequendy it is d up a form as a paradigm , ear that there is no ~..1 ••• no;Ql of setting · FORM AS SHAPE/FIGURE

l023all-3-'for exam I h and the body has the dip e t ,e bronze has the form of th sease. e statue.

SECTION II FORM: ITS FUNDAMENTAL MEANINGS Of the meanings ofform' in the above list, I shall focus on the following. l.Art. 2. That which, though not generated, is the end of a change. 3. Species. 4. A.Oyoc;. 5. That which is signified by the A.oyoc;. 6. The cause of a whole's being one. 7. That which makes something continuous. 8. The cause by which matter is a thing. 9. The first cause of a thing's existence. 10. That without which a thing does not have a nature. ll.Shape. 12. Essence

Already the items on this list, though diverse, contain some obvious family resemblances by which some sense can be made of their being named by a single word. To a contemporary reader familiar with the distinction between use and mention, (4) and (5), i.e. A.Oyo~ and that which is signified by A.Oyo~ appear radically different. But Aristotle was not always scrupulous in maintaining the distinction, and so (4) and (5) need not appear at odds with each other. A /..Oyo~ when used, signifies something, i.e. form, whose name, i.e. 'fo~ is used by Aristotle to mention the A.Oyo~. Furthermore, a A.Oyo~ if it is a true Aristotelian definition in terms of a genus and a differentia, signifies a species. So an obvious connection exists between (3), (4) and (5). And one might contend, though I shall argue that this issue is in fact a difficult one, that an essence is a species. If so, a direct connection exists between (3), (4), (5) and (14). Making sense of the meanings in this list by noticing family resemblances, however, can only go so far. For some very deep dissimilarities exist as well. (7), that which makes something continuous, does not easily fit into a nest of terms that center around the concept of a species. Nor do (1), art, and {2) that which is the end of a change. And though. (6), the cause of a whole's being one, {8), the cause by which

jill

THE FOUNDATIONS OF ARISTOTLE'

matter is a thin 9 S CATEGORIAL SCHEME 60 th ·h g, ( ), the first caus e o f a th.mg's existence, and (10) . at Wit out which a th. d Into h mg oes not h ' . sue a nest, they do not fit . . ave a nature, might be pressed Into Aristocles• use of the w d 'fc Into It · · · more order . , easil Y. S 0 Hl)ectmg Into his m etaph ys1cal . system.or orm requires a d eeper mvesnganon . . .

SECTION III TWO TYPES OF FO The taxonomy I shall RM one f · propose has tw · Its absolutely funda a1 mam starting points. First in o n1 y r a1 .d ment sen 'fc , ' ber o; . evi ence needed for such a d ~es, . orm means species. The times Aristotle uses 'fc ' aim Is the overwhelming num. orm to mean species. . But the fact that several of th e meanmgs in th b . cept of a s . e a ove 1Ist all I di to est bli ~:es provides whatever fu h re. ate reedy to the conform af s e claim. Second, a cruci·alrtdi~r ~vidence might be needed o a .compos1te · of form and Stiner·Ion eXIsts · between the matter and the form ofth f a composite of form and fc matter. e matter o Evide . nee or this latter dai tion between tw m can be derived & . says: o types of subject. In M o.m Aristotle's distincetaphystcs VII' 13, Ansto . cle

°

°

~or we h~ve discussed two of xng a subJect is two-fc I . . . ~em: essence and . attributes, or (b) as o d. It .Is either (a) a this, as a subJ~ct. ~nd be. matter Is to actuali ( an animal Is to its And In Metaphysics IX ty Meta. l038b4-7). '7, he says: !he universal and the . Ject is a this and th ~nderlyxng subject diHi . to his affections e umversal is not; for ex er Insofar as the subbeing pale are affieascti~e the body and the so~anpde, ba ~an is a subject ' exng · ons Ad each subject is a b . . . n whenever su h eli musical and (Kat) a this, eachs:u~~anc~, but if a predicat: isp~e :es are used, 1049a27-36). ~ect IS matter and a maten"al su stebstance a form, i.e. (M

futh

~

ese passaaes . cle ake · c ' A nsto Jeers-a subject can be a m . s a dear distinction b th composite of form and etween submatter. I will supp . ose, en th matter, or · su ~ect are two f'vh.>., f r ' at corresponding to th It can be h b -,r~ o ronn h ese two IVh orm of matter, and'£ ' , w at I shall henceforth '-,res of onn-c, form of th . call form-m,' e compoSite. fu fact,In . the sec-

3 fit! Form

61

ond passage, Aristotle provides a clue as to the resolution of the difficulty that results from his calling a form both a universal and a particular. If the \:at' in the last sentence is epexegetical, then Aristotle holds that when the subject is matter, the form predicated of it is a particular. (This reading is supported by the fact that in the first sentence in the above passage, Aristotle uses the soul, which he elsewhere explicitly identifies as a form (DA 412a21, Meta.1035b16), as an example of a this). Furthermore, by setting up a contrast between the two types of subject and by explicitly saying that the form predicated of one type of subject is a this, Aristotle makes it very natural to suppose that the form predicated of the other type of subject is universal. Hence, I shall suppose that form-e is a universal and form-m is a particular.? 7 The question as to the ontological status of form is no doubt one of the most hotly debated issues in Aristotelian scholarship. Among those who think that there are particular forms are Wilfrid Sellars, "Substance and Form in Aristotle:' journal of Philosophy 54 ( 1957) 688-699; E. Harter, "Aristotle on Primary ousia:' Archiv fur Geschichte der Philosophie 57 (1975) 1-20; Edwin Hartman Substance, Body, and Soul: Aristotelian Investigations. (Princeton: Princeton University Press 1977); T. H. Irwin Aristotle's First Principles. (Oxford: Clarendon Press 1988); Charlotte Witt Substance and Essence in Aristotle: an Interpretation of Metaphysics VII-IX. (Ithaca, NY: Cornell Uni~ersity Press 1989). Among those who do not are: M. J. Woods, "Problems m Metaphysics Z, Chapter 13:' lnJ. Moravcsik (ed.), Aristotle: A Collection of Critical Essays. (New York: Anchor 1967) 215-238. I am not entering directly into this debate, though I obviously think that there are particular forms. One reason that I am not directly engaging in the debate is that the various factions seem oblivious to the possibility that there is a systematic ambiguity in Aristotle's use of the word 'form' of the sort I am suggesting. As a result, many of the arguments given are, in my opinion, inadequate. Consider, for instance, a common argument that fOrm cannot be universal. Aristotle says (1) Substance is form; (2) Form is universal; (3) No universal is substance. Or consider what S. Marc Cohen says against the particularity of form: "In my opinion, the indefinability of particulars makes it impossible for substantial forms to be particulars. If there were a substantial form that is unique to some sensible particular, say Callias, then the definition corresponding to that form, or essence, would apply uniquely to Callias-it would define him, which is precisely what Aristotle says cannot be done." S. Marc Cohen "Aristotle's Metaphysics': The Stanford Encyclopedia of Philosophy (Winter 2003 Edition), Edward N. Zalta (ed.), URL = . Both arguments, in my

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

62

SECTION IliA FORM~M

With the distinction between for tum to their respect' m-m and form-e in place, we can tve natures I shall b . . h r: form-mr What is th f. egm Wit rorm-m. What is a e nature o that entity th . di d f . f r: at Is pre cate o matter as opposed to the composite o rorm and ~ Th. . . turns out can be an d b r: matter· IS question, as tt ' swere y roc · h the pairs of contra . h h usmg on t e natures of the soul and nes t at c aracte . th 1 soul and the pai f . nze e e ements-for both the A rs o contranes are predicated of matter. mong contemporary scholars th . it is the standard ch . . ' ere Is a common, indeed perhaps 1' , aractenzation of an A . to the characterization A . 1' nstote Ian soul. According , an nstote Ian soul . f d pendi·ng on subtle nuan f . Is a set o powers or, e. ces o mearung, f f ul . . ties. Which capacities~ Th h a set o ac ties or capaci· . ose c aracter. . n· . souls contain at least th . fc IStic o IVmg things. Hence, all e capacity or nutriti d 1' . . two di rections; animal ul . . on an Irmted growth m . . so s contam m ddi . d' .. ceptual activities· and h l a tion Isposltlons for perthought . ' uman sou s contain dispositions for rational

Jon~than Barnes provides a dear state an Anstotelian soul. ment of a capacity account of Thus Aristotle's souls are not . b· f pieces f I' · h Its o spiritual stuff placed inside tho I' I:mg t ings; they are not sets.of powers, capacities or fa I . e Ivmg ~ody; rather, they are sessmg a skill.s cu ties. Possessmg a soul is like pasLikewise, Richard So b" fc count. ra ~I pro esses alleaiance t 0 th e capacity aco· Aristotle sometimes thinks f h the capacity for nutrition t~ t e s~ul as a set of capacities, such as capacity for thought. Th:se :acap~.Ity of sense perception and the tion, but are related to each oJ:aci.tie~ a~e not a mere conglomeraer tn mttmate ways, so as to fo . . rma opmion, are no good, since th I ous. In one sense of'fo , foey o~er o~k the possibility that'form' is b' . nn, rm IS UniVersal• . th . . am IguCOUrse, one might want to establish a syst , m Of · ano 1aer,· It ts parti~·'-~· '"UJar. senses. I do just that in section lllb. emattc corre tton between the two 8 Jonathan Barnes i\ristod , . Gr totle, (Oxford: Oxfurd Uni·ve, ~ Preek Philosophers: Socrates, Plato, and Ar· ersity ess 2001), p.275. ts-

3 fit; Form

unity. The lowest capacity (nutrition) can exist without the higher ones, but not vice versa ... I shall follow Aristotle below, by thinking of the soul as a set of capacities. 9 The capacity account is reasonably well supported by Aristotle' texts. Aristotle often talks of the soul as if it were a set of capacities. He begins the discussion of his views about the soul in the De Anima with a discussion of powers and even appears to identify the soul with certain kinds of powers. He says, for instance, that plants are living because they have an originative power through which they increase or decrease in all spatial directions (DA 413a25-30). He then goes on to say: This is the originative power the possession of which leads us to speak of things as living at all' (DA 413bl-2). And a bit later he says: 'At present we must confine ourselves to saying that the soul is the source of these phenomena and is characterized by them, viz. by the powers of self-nutrition, sensation, thinking, and movement' (DA 413b10-3). Aristotle's analogy between soul and sight just prior to these passages also recommends an identification of the soul with capacities. At 412b17-413al3, Aristotle says that the relation of soul to body is analogous to the relation of sight to eye. Because sight is the capacity to take on the forms of objects without their matter, by analogy the soul is the capacity or unified set of capacities to engage in living activities. Finally, at De Anima 412a22-8, Aristotle after defining the soul as the first actuality of a natural organic body potentially possessing life, goes on to say at 417a21-b2 that a first actuality is a second potentiality. Aristotle then illustrates the distinction between first and second potentialities by appealing to kinds of knowledge, an example that would, again by analogy, recommend thinking of a soul in terms of capacities. For the present purposes, two points about a capacity account must be made. First, the notion of a capacity will have to remain unanalyzed. This conforms to Aristotle's own practice, for he is not concerned to analyze the notion. In fact, it is in this instance reasonable simply to follow Aristotle's lead and consider a capacity an apxiJ that is a principle or source-it is the source of the dynamical interactions with the world an object has. This, at any rate, is precisely what Aristotle says about the soul: 'At present we must confine ourselves to saying 9 Richard Sorabji, 'Body and Soul in Aristotle; Philosophy 49 (1974) 64-5.

THE FOUNDATIONS OF ARISTOTLE's C

that SOU} . h ATEGORIAL SCHEME 64 . ts t e source (ci .) tlon, thinking and move!~~ of th~se phenomena [sensation, nutrithe powers of self-nutr't' ] an~ Is characterized by them, viz. by 413bl0-2) · I Ion, sensation, thinking, and movement'(D'A:n

al Second, A· nsto d e dead th 'nk

so the form of some marty I s that a soul is not only a form but . d e says: er, namely th e b 0 d Y. At De Anima 414a152 0' A nsto For, as we h al read matter, an d tave h at whichy issatfr'd' •substance' . sat'd m . three ways-form, b h IS orm actual' om ot Of th bfc d . tty. Since then that h ..h . ese matter is potentiality, o y IS not the actuality of th w Ic IS from both is ensouled, the . not a b ed soul, . the actuality bof dsome bod y ••• I t Is b but th e souI IS 0 Y ut someth mg · of (relative to) a 0 Y· The soul, accordin to A . matter I d g nstode sta ds £ ers for. n eed, ~ust after this pa:sag nA ~s orm to the body, which is ·· · to A · not d specrfyi , ng t h e sort of b de, thrtstod e crtttciZes earlier thinknsto e, each th. ' o y at a s0 ul n£ the pote 'al· mgs actuality b . e orms. According nn tty wh. h b y Its natur . matter' (D• A tc elongs to th h. e can extst [only] with n 414a26 7) at t mg 0 · h · de defines th - · And in keepin . h r Wit Its appropriate . e soul a th fi g Wit the · . tlally possessin lifi s e rst actuality of se strictures, Anstoa natural organic body potenTwo oth ~ I e. er Important fa confirm its statu cers of Aristocle' where he di . s ~s a form-m. In the s treatment of the soul snngwsh b passage fr AK that matter in es etween two typ f om ~VLetaphysics VII, , contrast t h es o sub' A . o t e composite d . !Ject, nstode says that is an actuality. ' stan s m I . to a form F re anon . or we have d'lscussed tw f mg a subject is two-£ ?~ them: essence d . attributes, or (b) old: It Is either (a) h' an a subJect. And beas matt . a t Is, as an . Aristode, howeve,. . er Is to actuality (Meta. 103~~) is to its . H ., says m th D . tty. ence, the soul t' s correcd e e Anima that th e soul · passage from Metat"h . y seen as a form-m F rth Is an actualtw r ys1cs IX · • u e o types of subject h m which he distingui h rmore, in the form-m, in contrast t' r e says that a form that enfos es between the o rorm-c · . rms matt . P assages recommends tr . ' ts a Particular. But each f th er, t.e. a Met. 1037 6-10 Furth eanng the soul as a partt' ulao e followina th • ermor 111 c r: DA 412a ---o at no universal is a sub e, at ~vJ.etaphysics 1039al Ari 7-8, Stance; and at 1037a6 he sa' stode says ys that the sou}

3 Pti Form

is the first substance. The inference to the soul's particularity, then, is straightforward enough. The soul is thus a form-m par excellence. And as such, it is the source of the dynamical activities, in this case the living activities, of a material substance. Likewise, the pairs of elemental contraries are both forms of the ~atter of a composite and the source of dynamical interactions. ArIStotle introduces the elemental contraries into his system in De Gen· eratione et Corruptione II 2 and 3. In chapter 2, Aristotle searches for the fundamental tangible properties. He considers different pairs of properties-hot/ cold, dry-moist, heavy /light, hard/ soft, viscous/ brittle, rough/smooth, coarse/fine (GC 329b20-1)-and concludes that the two fundamental pairs hot/ cold and wet/ dry can explain the presence of all the others ( GC 330a25). For instance, something is fine because it is suitably wet-fine matter, like moist objects, conforms to the shape of a containing body (GC 330b30). Then in chapter 3, Aristotle reasons that the fundamental contraries occur in four different pairings-cold/ dry, hot/wet, hot/ dry and cold/wet-that account for the forms of the four fundamental elements, earth, air fire and water respectively (GC 33la3-5). Now, the connection between temperature, dessicative dispositions and the elemental contraries is obvious enough. Fire, for instance, as a result of having the hot as part of its form, is hot and so has the capacity to heat objects that are cooler than it. But in addition to being connected in obvious ways to temperature and dessicative dispositions, the elemental contraries are connected to the full range of tangible dispositions. Aristotle describes very briefly these connections in De Generatione et Corruptione II, 2 but presents them in painstaking detail in Meteorology IV. He traces all the following dispositions to the four fundamental contraries: unqualified becoming (378b27 ff.), natural change and destruction (379al0 ff.), concoction and its species boiling, parboiling and broiling (379all ff.), ripening, rawness {379all ff.), hardness, softness (38lb23 ff.), liquefaction, condensation (382b29 ff.), solidification, melting, thickening, softening (383b17 ff.), the capacity to bend, combustibility, and inflammability (385b6 ff). Furthermore, Aristotle thinks that the elements, due to their forms, have natural places in the world toward which they tend. Earth naturally tends downwards; fire, upwards; and air and water,

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

66

to intermediate positions (Phys. 205al0-2, 205a25-9, DC 276~1.f£). Hence, the elemental contraries are, according to Aristotle, an ongmal source of the dynamical activities of tangible bodies. al In addition to being the source of d ynamic · al activities, · · · th e element contraries, like the soul, enform matter. At least, such a view, thou~ it has been challenged in the twentieth century, is to be sure the his10 torically dominant one. For the moment, however, I won't defend the view but merely assert it, since I discuss this very issue in the next

chapte<.

d

The natures of the soul and the elemental contraries thus proVI e the basis for a characterization of fonn-m: a fonn-m enforms matter; it is a particular; and it is a capacity-like entity in that it is the source of the dynamical activities of the composite of it and the matter it enforms. This characterization will be very fecund; for I shall eventually argue that many of the meanings of'form' that do not easily relate to the notion of a species do relate naturally to the notion of a form-m. For the moment, however, consider just one of these senses, namely the sense according to which a form is that without which something does not have a nature. In the Physics, Aristotle says that nature is a principle of motion (193b7). Now, one might argue that a species is a principle of motion. But, such an identification is surely strained. On the other hand, as I have characterized a fonn-m, it just is a principle of motion - it is, in other words, the source of the dynamical capacities of a material substance. Hence, on the assumption that a nature is a form-m, it is trivially the case that without a form-m something would not have a nature. One last comment about form-m is in order before I tum to form-c. In chapter II, I argued that the resolution of the body problem re10 To deny that the elemental contraries enfonn matter is to deny the existence of prime matter. Among those who have denied that Aristotle thinks there is prime matter are H.R. King, i\ristotle Without Prime Matter;'journal of the History of Ideas 17 (1956): 370-89; W. Charlton, Aristotle's Physics Books I-II (Oxford, 1970); Barrington Jones, "Aristotles Introduction of Matter,n Philosophical Review 83 (1974): 474-500; M. Schofield, "Met4ph. Z 3: Some Suggestions,n Phronesis 17 (1972) 97-101; D. Stahl, "Stripped Away: Some Contemporary Obscurities Surrounding Met4physics Z 3 (1029a10-26);' Phronesis 26 (1979): 177-80; and M.L.Gill,Aristotle On Substance, (Princeron, 1989).

. al interactions with dynamiC al quires form to be a body,s source of the h tt' Ml The resolution so . JUS . t sue. an en· -r the world. Clearly, form-m IS s with the world to be required the source ofth e d ynamical mteraction d the body's substanti·al . fr om a body remove __ a: . such that its abstraction h rce needs to be swucient h · nofsuc asou · To ity· or conversely, t e possessiO . also such an entity. ' b Form-m IS fi for something to be a su stance. . first an examination of orm-c. argue for this claim, however, reqmres 3 Pal Form

SECTION IIIB FORM~C

. o fcrorm andmatof a composite . . sy to characterize. In I~s Unlike a form-m, a form-e is the form IS eawords, the paradigmatiC ter. Furthermore, u nl'k I e fro m-m,. form-e I other f · a speCies.f n terial composite · IS · that o a primary sense, a rrorm-c IS · predicated o a rna'al particular. I shall offer an case of a forms, b emg di . ply asspecies being pre cated 0 f some maten B t for now, I shall sim · m · a moment. u . cl atm argument for t h IS .

sert it. . . de was operating . WI'th two disNow, it would be surprising if Anhsto being some intimate conn~cdfr 'thout t ere · rene tinct conceptions o rorm WI . s out the two conceptions ;h. ld tion between the two. And as ,It turn. ce'to what Christopher . Ie s together in virtue of Aristotlesalalldegtanmination thesis:u Accordifng to . a member o some has aptly termed the 'function h .etern entity, x, IS . . the functional determination t esis, a a aci to engage in the actiVIal ki d F if and only if x has the c p Ary de articulates such a natur n f kind F. nsto full near ties characteristic of members o the matter most force y view at Politics 1253a19- 25 but states the end of the Meteorology.

. fu . n· for each thing e . d b their nctlO . All these things are determl~e ~ function, for instance an ey truly is itself when it can per ~~m ~~nnot do so it is only homon;when it can see. And when a t mg e e or one made of stone. o . for instance a deadbutr.lS rather a likeness of a saw.f mously wh at lt. lS, too a wooden saw is not really~ sa~nction is less clear than tha~ o The same is true of flesh. But;; but its function is even less c ea~ th gu o ~e, true of the parts of plants an e ton e. The same is. true . likewise in the Philosophy than that of flesh. This lS . Order it• Multiplicity: Homonymy 11 Christopher Shields, p 1999) P· 33. ' of Aristotle (Oxfo rd : C iarendon ress

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

inorganic bodies like bronze and silver. Everything is what it is in virtue of some power of action or passion (Met. 390a10-9). The extent of Aristotle's allegiance to the functional deter~nation thesis is quite striking. Even a kind like fire, according to Anstotle, a kind which one might think would resist determination in terms of function, is subject to it. . Because of his acceptance of the functional determination thesis, one can attribute to Aristotle the following bi-conditional schema concerning kind membership.

I. For all x, x is a member of species F if and only if x is capable of performing those activities characteristic ofF's. This schema already brings the connection between form-m and forme into view. According to I, something is in a species just in case it has the capacities for engaging in activities characteristic of that species. But, because a form-m is the capacity-like entity that is the source of the dynamical interactions of a composite of form and matter, something can only be a member of a species if it has an appropriate formm. A fire element, for instance, is in the species, fire, if and only if it has the form-m, in this instance the pair of contraries hot and dry, that is the source of those activities characteristic of fire. This fact about the relation between form-m and kind membership is captured by the following bi-conditional schema, II. For all x, x is capable of Performing those activities characteristic of Fs iff x has matter enformed by a form-m, i.e. a source of dynamical activities, that is ordered toward F-ness. Theses I and II, then, combine to entail the following bi-conditional schema. III. For all x, x is a member of a species F if and only if x has matter enformed by a form-m, i.e. a source of dynamical activities, that is ordered toward F-ness. Now, thesis III does not specify the domain of the variable x. But Aristotle dearly thinks that composite substances are those entities that are members of species, at least if those species are natural kinds. This is such a basic presupposition of Aristotle's physical-metaphysical treatises that it hardly needs corroboration. But whatever evidence

69

68

3 Pt; Form . blZ. There, Aristo434 . occurs ~tDe is needed for such a chum d b Antma d Hence it is not the £orm of de says that an animal is an e~sou e i : J nor is ~t the matter, i.e. the the animal, i.e. the soul, that IS an an d ' atter is the animal. Hence, body. Rather, the composite of form an : over composites of form . blem . III should be seen as rangt g f t hevana and matter. . . ubstances that are m embers . od With the view that it IS composi~e s b een form-m, speCies ~n . · h an d ' th e connections · natural kinds m f .etware composites, a spec1es, If hers o species h form-c become clear. mem . c _ Hence, we ave an argu. ' form IS rorm c.Moreover, accordin g to III because it is the composites f

d ·

ment for the identity of form-cillanh spe~I;;;m-c, i.e. be a memberth o a any composite ave enformed b y a £orm-m at . sub stance, x' w matter species F, if and o nlY if x has some . th two notions of £orm coalesce F d In th1s way, . the form ofth e matter of a comorders x towar s -ness. . 1 · ·form-m1s e · g a meminto the followmg re anons. d ufficient for c•s b em posite, c, and as such is necess~ry ~ s -c. Furthermore, the_forml-~ . cror c's havmg a rormfor instance S ocratess sou IS, her of its species, I.e. . ul partie ar. Socratess , · that enforms cs matter IS a . ·versal-for mstance , form-e lS a um a this-soul-while cs . 1.e. . h uman, is universal. spec1es,

SECTION IV TAXONOMY A c -c and character£ rm-m and rorm tl , By making the distinction betwee~ .oct some order into Aristo f~: ap-, · 1y, one can d'form: mJe izing them appropriate So far, the mean ings o rorm d 1 use of the wor di parently sor er Y . th following way. from the above list cluster m e Form-e 3. Species

4. A.Oyo~ . h. . Hied by the A.Oyo~ 5. That whic IS sign Form-m h. h a thing does not h avea nature 10. That without w IC . meanings to be explained. Th. leaves the followmg

ed is the end of a change. 2. Art. That which, though not generat '

lS1

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

71

70

6. The cause of a whole's being one. 7.1hat which makes something continuous. 8. The cause by which matter is a thing. 9. lhe first cause of (something's) being. 11. Shape. 12. Essence I noted above that (6), the cause of a whole's being one, (7), th:t which makes something continuous, (8), the cause by which matter IS a thing, and (9), the first cause of a thing's existence, do not obviously or easily fit into a duster of terms associated with species. By now it should be clear, however, that this does not present an intractable problem, for they may (and I shall now argue they do) fit easily into a duster of terms associated with form-m. This will then leave (1), art. (2), that which, though not generated, is the end of change, (11), shape, and (12) essence.

(B) and (9) come from Aristotle's discussion of substance in Metaphysics VII, 17. At 1041b7-8, Aristotle says: 'Thus we are seeking the cause (and this is the form) by means of which matter is something; and this is substance' (Meta.1041b7-8). And near the end of the chapter, he says: J\nd this is the substance of each thing; for this is the first cause of being' (Meta.1041b26-7). Now, Metaphysics VII has been the source of so much scholarly controversy that any conclusions made about it must be accompanied with some reservation. Nonetheless, there are reasons for supposing that the form Aristotle mentions here is form-m. In the first instance, Aristotle denies at 1039a1 that anything that belongs universally can be a substance. Form-e, however, is universal. Furthermore, just prior to the quotation at 1041b7-8, Aristotle says that the question he is pursuing in the chapter is: why is the matter some one thing~ And he then says that the answer is: 'because it has that which is the essence of a house; and because a man is this, or, a body has this' (1041b5-6). Hence, in one stroke Aristotle brings into view both matter and the fact that what explains matter's being something is some particular, i.e. a this. He then immediatdy identifies the this in question with form. Form-m, however, is precisdy a particular form that, in enforming matter, makes matter something. There is one final piece of evidence supporting the identification of the cause by which matter is a thing and the first cause of a thing's

3 PI! Form f the Metaphysics existence with form-m. In the penultimate sentence o

VII, 17, Aristotle says:

h that are subf h. s but t ose Since some are not substances o t mg 'by nature, it would seem . to nature or which is not an e1ement stances are formed accor dmg . · this nature, ) that the substance 0 f t h ese IS . · 1 (M t 1041b28-31 · c d but a prmCip e e a. b nee are rorme b" hat are su sta h Aristotle here says that those o ~ects tb tance of such substances, e c mte · rpreaccording to nature or by nature. The. su. s mind the need ror h 1 concludes, is this nature. Now, keep1 ~g ~ that Aristotle identifies t .~ tive caution, one can none theless mamtam . h a substances' nature· But, 1 1 . m · t h e chapter W. t the identification · f form-m obiect he is pursumg 1•p le of monon, J • 'nature' here means a pnnc . . di ectly supported • Of course, . q uest1on 1S ranings; an d so t his passage with the senses o f •crorm' m . . · qu est1on 1s 'nature' might, like 'form,• h ave many me f that the form m eredoes not provide incontrove rtible proo d . ht of the ev1.dence oives cr fi h b"ne we1g . d the rst form-m. Nonetheless, t e com 1 f tter's being a thmg an 1 . h the cause o rna deuce to the c atm t' at . is form-m. . • what does cause of somethings ex1stence . does raise the quest1on. . thing Of course, this line of reaso~mt~e cause by which matter 1S t:aighth . however, aCs nsider it mean to say t at a form-m . ' 1S . tencd There 1S, 0f thmgs exts d and the first cause a fr theses alrea Y 1at"d down. F · 0stance, h £ llows om · c. or m forward answer t at .o h tter of some compos1.te, Aristotle, in that 1s t e rna A ording to some matter, m, f 1. ·ng organism. cc . this case a h form-m, m . h body o a 1Vt suppose m 1s t e f it must ave a gl ggested b th matter o c, . stron y su order for m to e e . This at any rate, 1S 3 2 There he ' A . a 412b20-5, 412b27 -41 al . a body.' In soul, that orders c to cs' spec1es. by his discussion at De e:~:ody is only ho~o~ymous y s the following prmc1ple. . seems to accept that a d other words, Aristotle accept . d 1 if there exists a species If an(2)on y a fo rm -m that orders IV. m is matter for composite, has Fc,and m has (form-c),F,suchthat(l)c f

°

c toward F-ness. mething is the matter o_ a . . . le insofar as so f that compos1te, According to thi~ pnnhc1pt i; is namely the matter o · "ts bemg w a ' compostte, 1 ed b a form-m. y requires it to be enform

• THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

72

Because something can count as the matter of a composite substance only if it is enformed by a form~m, insofar as some matter just is the matter of a composite, form~m is the cause of that matter's being some~ thing. For instance, a soul is the cause of some body's being the matter of a living organism - for without the soul, the body is no longer the matter of a living substance. Hence, form~m can be described as the cause (explanation) of some matter's being what it is, namely the matter of a composite. And in addition to its being the cause of matter's being a thing, form-m, as was made clear previously, is necessary and sufficient for some composite substance's being a substance. Hence, it 12 is also legitimately described as the first cause of a substance's being. This result provides a way to reconcile Aristode's apparendy different attitudes toward kind membership in his biological works and his metaphysical works. According to the functional determination thesis, kind membership is determined by capacities. In his biological works, however, Aristode distinguishes species in virtue of the parts that they have. He says explicidy that this is an appropriate mode of division (PA 644b7~10); and he goes on to make divisions according to ani~ 12 This line of interpretation provides an interesting possibility concerning Aristotle's claim at De Anima 412b 20-5, 412b27-413a2 that a dead body is only homonymously a body. Aristotle's claim there has been the source of considerable scholarly speculation and criticism. In an influential article, J.L. Ackrill, ~ristotle's Definitions of 'I'UXft, Proceedings of the Aristotelian Society 73 (1972-3), pp.119-33; reprinted inJ.Bames, M. Schofield, and R. Sorabji, eds., ~rticles o~ Aris~otle, vol. iv (London, 1978), pp. 65~75, argues that this doctnne of Anstotles threatens the intelligibility of his hylomorphic framework. Bernard Williams, 'Hylomorphism Oxford Studies in Ancient Philosophy 4 (1~86).' ~P· 186~99, argues that the doctrine is intelligible though has counter:mtutnv~ results. Christopher Shields, Order in Multiplicity: Homonymy m the Phtlosophy of Aristotle (Oxford: Clarendon Press 1999), ch. 5, presents a sustained examination of the doctrine within a larger treatment of homonymy in Aristotle. Within the present framework Aristotle's claims might. be interpreted as follows. If the second occurrence ~f'body' in 'a dead bo~~ IS only ~omonymously a body' is understood as meaning the matter of a hvmg organ1sm, ,then it is true that a dead body is not a body. Hence, the first occurrence of body: i.e. the occurrence that follows 'dead' could not have the same meaning as the second occurrence. Again, if'body: literally means ~tter of a living organism, then 'body' in
3~

73

Form , f h" b · di · · is between those mals parts. For instance, one o ts aslC vtstons .h p · · 1 IV: however resolves animals with blood and those wtt out. nnctp e ' ' any tension. For, the parts of an animal, which collectively make up th)e , . 1 · tter (GA 715a7~10 · animals body, are, according to Anstot e, tts rna . . . f. · h t it ts m vtrtue o tts According to principle IV, however, matter ts w a . · · of its having certam being enformed by a form~m an d h ence m vtrtue . . · n1 · ·rrue of its havtng cer~ capacities. Hence, a part is what 1t ts o Y m Vl . . b th" • . . . . tl · 1 t ly explicit a out ts. tam capacities. And mdeed, Ansto e ts comp e e (DA . . . n1 h monymously an eye an eye wtthout the capacity to see ts o Y 0 f . al · h the parts o antm s . 412b20-5). Hence a division in accord ance wtt . ' .th h pacities that an ant~ Is ultimadey a division in accordance Wl t e ca ~~ "th "d ·fi cion ofform~m Wl It is worth noting at this point that t h e 1 entl ca th" • . th" d th first cause of some mgs the cause of matters, bemg a mg an e I M t physics . . . u1 ing essence. n e a eXIstence has an mterestmg res t concern . ·fi d b tance c h h tdentl e as su s VII, 17, Aristode says that the rorm e as . This runs . th th £ m-m 1s essence. Is an essence. It would follow en at or . · Such th ssence ts a speoes. thing's es~ counter to the natural view, however, at an e . ·fi 'I • .., , s1ant es some a view is supported by the facts th at a !I.O 1 0 ~ o-- f d dif~ . . '\ ' sists o a genus an sence, and typically an Anstotelian !l.oyo; con 1h t ondusion . · e correc c ferentia that combine to determme a spectes. d, • is ambigu~ , f the wor essence . c rm-m. Given to draw, I think, is that Aristo tl es use 0 c . ther lt means ro ous. In one sense it means rorm-c; m ano findi ambiguity in •c '• any ways ng an . hi s willmgness to use rorm m so m ' his use of'essence' can hardly be objectionabledi.. ht"ch form is the '£ , ccor ngtow f What, then, about the senses o orm a f thing's being con~ , . d th cause o some cause of a wholes bemg one an e . s requires some · these nooon tinuous? The complete story concemmg . hI hall give in the next account of Aristotle's theory of matter, whtc th"s oint that they can · · · nough at lS P ch apter•• But it should be mtu1nve e . hunk of matter, a form-m be identified with form-m. By enformmg ~.~belongs to a species and 1 creates a unified composite, i.e. a whole, w f th nformed matter. For . th . uityo ee f) In so doing accounts for e connn ( lains the being o a . . _c · bodv: causes exp · Instance, a soul, m enrormtng a ''. th h as matter a cononu. . . · mpostte at as composite hvmg organtsm, a co ous chunk of living material.

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THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

74

Three meanings remain-art, the end of generation and sha~e. The first two of these meanings can be accommodated by appe~ng to one of Aristotle's distinctions in Metaphysics V, 1. Aristotle thinks that there are three types of pnncip · · 1es: prmcip · · 1es of knowing, becoming and being: 'It is common to all principles, then, to be ~e first from which a thing either exists or is generated or is known (Meta. 1013al7). Hence, because form is a principle, it can be expected to have three aspects. The senses ofform' so far discussed have been f~rm under the aspect of a principle of being. As a principle of_knowmg, however, form is art. And as a principle of becoming, form IS the end of a change. d Form as a principle of becoming and its relation to form-m an form-e deserves some comment. First, it is not dear that as the end of a change a form must be either form-m or form-c. C onsi'der, for instance, a generation. Not only is the having of a soul the end of a generation but so too is belonging to a species. Hence, I will suppose that both form-m and form-e can be an end of a change. Furthermore, Aristotle thinks that in every change there is some matter that acquires a form. Hence, there must be forms for each of the types of change, namely substantial, quantitative, qualitative and local. So far, however, form has been related only to substance-form-e is a species in the category of substance and form-m is a source of dynamical interactions that order a composite toward a species in the category of substance. Despite their obvious relation to substance, however, the categorial features of both form-e and form-m lend themselves to a conceptual extension to accidental categories. A form-e is, categorially speaking, a shareable feature of a composite, while a form-m is a particular feature of some matter of a composite. These categorial features, however, can apply to features in the other categories. A universal quality, for instance roundness, is a shareable feature of round spheres, while a particular quality, for instance this roundness, can be thought of as a particular feature of the matter of the sphere. 13 So, in a relaxed sense, 13 There is of course a substantial literature on non-substantial particulars in Aristotle's categories. Some of the more important contributions include: Gareth B. Matthews and S. Marc Cohen, "The One and the Many" Review of Metaphysics 21 (1968) 630-655; R. E. Allen "Individual Properties in Aristotle's Categories" Phronesis 14 (1969) 31-39;]. Duerlinger, "Predication and

75

3 etl Form · which change m in any category m . h d£ there are both forms-c an orn:s- f . st this sort from form m ~ e · 1y, a progression o JU . a progression occurs. Interesnng . the other categones, . of substance to form m . f change occurs m category h . al requirements o t substance alone that ~ur that is fuelled by the metap Y~IC Metaphysics VII,9: 'It is not with respect oted· the argument is alike c · tgenera' . such as those of quannry, argument reveals that rorm IS. no c all pnmary rorms ) common with respect to . , (Meta 1034b9-10 • f of quality and of the other categones 1 • of the twelve senses o c h even The argument so rar as sh o_wn. that eou s that center around two •c , c_n rurally into two distmct gr P . that of shape. It rorm rau na nl aining sense IS f main notions of form. The o yh reml 'fication of shape has so ar is not surprising, h owever, that .t e 1c assibsumed by the two senses so eluded us, since shape is not obvious y s~ nor is it obviously a source far discussed. Shape is dearly not a sp.~I::bstance. In fact, quite apa~ of the dynamical activities of a matef~ hape is difficult to conten . h nature o rorm, s from issues concernmg t e all . quality (Catg. 10a11)·' but ·nk · · ht to c a relation to quantity than with. Aristotle, I thi ' ts ng . t'Itmate I b nit would seem to ear a much more ali m likI whiteness and sweemess. . 0 f qu ty 1 e nlik whtteness other standard examp es all sidered shape, u e b

deed, later philosophe~s gener Ji co~ong with features l~e n~~a e: and sweetness, as a pnmar~ q~ ~ghtly considers quannnes. Pg and place, features that Ansto e _.!: fi d its appropriate placedamon n simply p1aong . it un er one is thus something o f an anomaly.· .10 . not c h fore reqwres f ( ) 179-203; B· Jones' the senses o rorm, t ere ' . 1970 5 J. AnInherence in Aristotles, Categaries". Phronests .. Phronesis1 17 (1972) 107-123; . 19 (1974) · 1 • Categones, · "Phronests "Individuals in Anstot es · . Two Quenes, I' Investiganas, "Individuals in Aristotle's Categorl~~dy, and Soul: Aristote ta~A Defense . H artman Substance, 146-152; Edwm . · Press 1977); H Granger, ·a1 Particup . Umverstty tions. (Princeton: rmceton in Aristotles, non -substantl R Heinaman. 6 6 of the Traditional Position ~~re~y (19800) 59~- ~ (19S1) 295-307; lars:· Canadian Journ~l. of!:::~ Categories:' Phrones;s; Aristotle's Catego"Non-substantial Indivtdu d Primary Substanc h "The Enigma Daniel T. Devereux, "Inherence9~ 113-131; Gareth Ma~9 e;~·-104; Michael 1 ries:' Ancient Philosophy 12 ( M~tters:' Apeiron 22 ~ ) { _165.1he conof Categories la20ff and Wh~ 'd al "Phronesis 38 (1 . 37 . g non-substan· · a1 I div1 u s. fo pos1t1n Wedin, "Nonsubstantl n 'd other reason r . gl the reasons are . t h'1s ch ap ter provt e an siderations m ·cal scheme. Interesttn Y• tial particulars in Aristotle's categorl ·es independent of the text 0 f the Categort •

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THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

of the senses already articulated but rather ascending in generality to a genus that subsumes the two senses already articulated as well as shape. I propose that the genus under which shape, form~m and form-e all fall is principle of order ('tO~t~). Aristotle, it must be admitted, does not stress the connection between order and the two types of form. But his definition of disposition (ota8'flEO't~) in Metaphysics V does provide some evidence for such a taxonomy. A disposition, he says, is an order of that which has parts with respect to place, potency or species (Meta. 1022bl-4). Two of the sense of order are easily discerned from the text: an order with respect to place is a position; and an order (or a principle of order) with respect to a potency is plausibly interpreted as a form~m.The third type of order, namely order with respect to species, however, presents some difficulty. It might seem obvious that an order with respect to a species would be a species. And it is easy enough to see how a species is a principle of order - it is a principle of taxonomical order. However, some important commentators do not understand Aristotle in this way. Most notably, Aquinas understands an order with respect to species as a differentia in the category of quantity. 14 Now, one type of differentia in the category of quantity is shape - for geometrical figures differ from one another in virtue of their shapes. So, one might interpret Aristotle as holding that one type of disposition is shape. Regardless of whether or not Aristotle has shape in mind in this passage, however, it would seem that a shape is a kind of order-it is the order of the parts of a material substance with respect to themselves. Is On this understanding, shape presents a nice contrast with position,. which is a spatial ordering of the parts of a material substance With respect to something extrinsic to them. Let us suppose, then, that conceptually, at least, there are the following types of order: taxonomical, dynamical and spatial. The following differentiation of the genus order is thus in order.

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3 Pal Form order taxonomical dynamical spatial a. intrinsic-shape b. extrinsic-position

c II . onomy of the meanAnd with such a differentiation, the 10 owmg tax ings of'form' falls into place.

Principle of order-Form With respect to knowing (1) Art With respect to becoming (2) The end of change With respect to being Taxonomical- Form~c (3) Species (4) A.Oyoc; h A.6 o (5) That which is signified by t e y c; (12) Essence Dynamical - Form~m 'b'gone. (6) The cause of a whl o es en~ ontinuous. (7) That which makes somethi~g c h' 'ch tter IS. at mg. (8) The cause by wh1 rna th' 's existence. f (9) The first cause o ~ m~in does not have a nature. (10) That without whtch at g (12) Essence Spatial (11) Shape

CONCLUSION 14 Thomas Aquinas, Commentaries on Aristotle$ Metaphysics, trans. John P. Rowan (Dumb Ox Books: Notre Dame) 1995, P· 373.

15 I shall give a fuller treatment of this passage in chapter 5.

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and as an ovemew o It will be useful both for the chapter~ to ;;;etaphysical theses th~t what I have already presented to reVIeW d. this chapter. It is underuundergird the taxonomy as it h~ e:;{~e;of the world. Just how to able that Aristotle held a teleo ogt

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

understand his teleology is controversial; but that the world exhibits some sort of teleological ordering is central to his thought. Perhaps the most significant result of this chapter is that for Aristotle form is the primary metaphysical entity responsible for such an ordering. In its fUndamental sense, form is a principle of order. With respect to being, form~c and form~m are the most important types of such a principle, though there is conceptual room for shape as well. Formm and form~c are both crucial to Aristotle's hylomorphic ontology. Form~m enforms matter and orders the composite of that form and matter to the species, i.e the form~c, to which the composite belongs. And it does this because the possession of certain capacities, according to Aristotle, is both necessary and sufficient for species membership. Furthermore, such a view does not overlook the role that the parts of a material composite, i.e. its matter, plays in determining kind member~ ship. For, the parts themselves are functionally determined - that is, they are the parts they are only in so far as they have certain capacities ~ and it is form~m that bestows upon such parts their capacities. This is why form~m is correctly characterized as the cause by which matter is a thing. By enforming some matter, it creates a unified continuous whole that has both, as a whole, certain distinctive capacities and parts each of which have capacities that make them the sort of thing they are. And the resulting composite thereby has the structures needed to place it in the species, i.e. the form~c, to which it belongs.

CHAPTER4 PRIME MATTER . th ht of as a kind of recur~ ristotle's hylomorphism can be oug th theorv. a material o din to e .,, sive ontologtcal theory. Accor g d The matter of f £ an matter. d matter. Such a substance is a composite 0 ~rm f £ rmb ant ather has a base the composite, then, is itself a composite 0 o nfirute1y u r fform and matter. structure, however, does not connnue I lf t a composite o case, namely a matter that ltse IS no o tter A proper b ailed pnme rna · Traditionally, such a matter has een co th fore requires an un~ ' and an un~ understanding of Aristotles' h Yl omorphismth' ere chapter 1 h I d d m e ast ' derstanding of form, whic proVl e . o this chapter. derstanding of pnme matter, whoIChI discuss mtl is a vexed one, both Now, the question of pnme rnatter m Ansto eterpretive difficul · oes lnterpreovely and philosophoICallY· The mam m f prime matter as o concern whether Aristotle accepted the enstence d mixtures thereo£• I n · 1 something distinct from the basiC e1e mentsd an t deal of attenoon. ° has receive a grea th th e 1ast fifty years, this quesoon . o has been oroughly 'd ronent to It . d ~~ In particular, the textual eVl ence pe me, that little m discussed and assessed, so much so' It seems to tinizmg Aristotles be had by scru the th ther band, concern pendent progress on the Issue IS to 0 texts. The philosophical difficulties' on Te ditionally, pnme matter coherence of the concept o f pnme matter. th o raitself is abso1ute1Y form~ ki d f stuff at m Is supposed to be some n tuffbe~ bical less. But what, really, could such a sth rpretive and philosophil t:_A os p o~ 1 In this chapter, I address b0 th e mte primary W'-us ° Issues concerrung pnme rnatter' though th my philosophi--" cauY interesung show ata 15 sophical in nature. My atm to th debate. contributors to e 1 Cf. Ch.3 note 3 for some of the matn

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account of prime matter can be articulated that strongly coheres with, even if it is not necessitated by, Aristotle's texts. I begin my discussion with an examination of one of the best recent attempts to make sense of the concept of prime matter - that of Robert Sokolowski. I shall call Sokolowski's view the extension interpretation. 2 According to the extension interpretation, prime matter is what Aristotle sometimes calls what he sometimes calls J.!eyeeos; and what we would call extension: My reasons for discussing the extension interpretation are two-fold. First, according to the interpretation I defend, although prime matter is not extension, it bears an intimate relation to extension. Hence, by first focusing on extension, I shall lay the groundwork for the view that I shall eventually defend. Second, the extension interpretation raises certain philosophically interesting issues. In particular, it raises the interconnected issues of the nature of extension and the way extension can be integrated into Aristotle's theory of material substances. I shall argue that Sokolowski does not adequately address these issues and shall then go on to address them myself In so doing, I aim to provide a philosophically robust and perspicuous account of extension, one that not only is interesting in its own right but also provides the basis for a perspicuous account of the nature of prime matter.

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SECTION I-SOKOLOWSKI'S CHARACTERIZATION OF EXTENSION Sokolowski bases his interpretation of prime matter on two passages. !n Metaphysics VII 3, Aristotle performs a thought experiment in he strips away all qualitative and quantitative determinanons of an obJect. What remains, he claims, is matter that is capable of receiving attributes accidentally hut possesses none of the attributes in itself Aristotle says:

w~ch ment~y

2 Robert S~kolowski, • Maner, Elements and Substance in Aristotle;' Jour~al of the Hutory ofPhilosophy 8(1970): 263-288; Richard Sorabji, "The PresIdential Address· Analys fMa An 0

A rutote . 1~Rn . Soc~ety . • 86(1986): es 1-22. tter,

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4 fJII Prime Matter d d th have been removed, we But when length and breadth an ep . th" which is 1 s there IS some mg ft 1 do not see anything e over, un es . in is in itself neither bounded by these ... Consequently, thhlS last(Mth t g 1029al6-18). · nor any 0 f the ot ers e a. a this nor a quantity

About this passage, Sokolowski writes: . . d d b determined dimenThe matter left over is somethmg boun ~mensions, but it is sions. In itself it does not have any speci ~ k d off into de. · · ble of bemg mar e extension m . capable of receivmg them, I.e. capa al d has . Th"IS Imp . 1"Ies that matter y modify the state . drea l"d terminate sizes. I itself. The powers of hot an d cold' flmd an . so . all 3 of matter but they do not extend matter ongm Y· M ' ks · th f Aristotle's remar m e etad nu·nate dimensions Sokolowski interprets the referent 0 . d f that has no eter physics passage as a kin o matter . th gh form. fb . d d t rrrunate rou . . but 1s capable o emg rna e e e tuff th . "tself is indeternunate . atmt . . The picture of pnme matter as a s . li . . g principles, 1s rem· bY various , discus. mad e d eterrrunate but that 1s . . nunn ·th"n Aristotles ski cites Wi i 1 forced by another passage oko ow sion of place in Physics IV 2. Aristotle says: f h th place o "d h" s in this way, e , eac ) b th m·terval (3taO'tTII.la Hence, to those who consi er t mg [thing] is the form; but I·f P1ace see msto eth" e · other than the ex. IS . the rnatter• For d d IS dISdetermined bY th e of an extended thing, tt . h · boun . matter h . e. an ch a thing IS tended thing, it is that w IC IS 1 d a limit; su form, for instance by a pane an h r "t and the atttibutes 0 f the

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and the undetermined; for when t e I~ ept the matter (Phys. sphere are taken away, noth.mg rematns exc 209b5-11 ).

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s: ' ...nua as e . . 1 the word utaO" •• ,,... , differs In th1s passage, Anstot e uses . d b form. ~taat11Jl0 · and atmatter that is bound ed and d eternune .Y when the 1·itnltS

° ally indefrom the extended thmg and iS what, rematns a then is an tniO . ed ~taO"'tTl~ ' ' ..mon tributes of a sphere are remov • f akina. carves out a r-o: t:Y • te. stZe, · a m anner o spe terminate stuff, and form, m osite has a deterffilna th d th ul . c rm matter comp . them m e . f e res tmg ro . tl does not mennon o 1t; an shape and presumably, though Ansto e f . . above passage, causal powers. ski forms a concepnon 0 pnme th From these two passages Sokolow d ot say much more about e . Although he oes n matter as extension. 0

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exact nature of extension than what appears in the above quotation, he does provide the following characterization. 'For Aristotle, the underlying matter is simply formless, unqualified, space,filling stuff.'4 This description of extension as formless, unqualified, space, filling stuff is quite suggestive. And in some ways, it is very much on the right track. Nonetheless, it leaves much about the nature of extension unexplained. What exactly is to be made of the idea of formless, unqualified, spacefilling stuff~ Such a stuff is unlike other more ordinary stuffs. Bronze, for instance, is a stuff with determinate formal characteristics. So how and why is it legitimate to call extension a 'kind of stuff'~ In addition to being incomplete, Sokolowski's characterization faces a difficulty. By describing extension as space,filling stuff, Sokolowski implicitly forces upon Aristotle a distinction between matter (extension) and space. Extension, it would seem, is the stuff that fills space; and so, if Sokolowski's description of extension is taken at face value, there must be some space distinct from the extension that fills it. But, Aristotle, in Physics IV 6, 10, argues at length against the view that in addition to matter there is space, or as Aristotle calls it, the void ('tO Kev6v), that matter occupies. Thus, if prime matter is extension, it cannot be space,filling stuff. This difficulty with Sokolowski's characterization is no mere quibble but points to a rather serious question about the coherence of Aristo' de's views about space. Perhaps the strongest evidence that Aristotle would appeal to matter in order to explain the spatiality of material objects occurs in Physics IV. In his concluding remarks about the void in Physics IV, 9, he says: From what has been said, then, it is dear that a void does not exist

separ~tely, neither simply nor in what is rare, nor potentially, unless

one wtshes to call the void a cause of locomotion. For then the mat, ter of what is heavy or light, qua such, would be the void; for the dense and the rare with respect to these contraries is productive of locomotion ... (Phys. 217b2Q,25) In this passage, Aristotle says that the void does not exist; but if one were to call something 'the void: one could only mean the matter of what i~ h_eavy and light. Aristotle, in a manner of speaking. has turned the votd lnto the matter of sensible objects. 4 ibid.

4 ~ Prime Matter

l . th spati, al atter in order to exp am e. earlier passage in Phystcs VI, That Aristotle would appe t~ m_ ality of objects finds corroboraoon rn an 9. I b d is the same. This is clear from The matter of a great and smal o y h matter comes to be . from water, t e . the following. When atr comes di mething else to tt. 0 n something not by somehow appen ng so b t"n actuality; and the .all comes to e I the contrary, what was potentt yfr . Likewise, when the arge same happens when water co mes om atr. all fr 0 m the large. S"mil 1 ar1y, 1 allandthesm h comes to be from t e sm all r or a small vo ume 0 f b . b omes sm e f when a great volume o atr ec h . potentially both ecomes air becomes greater, t he matter t at ts h t changes fr om cold to ..ts th e samemattert a both. For just as tt . . otentially both, so too whn e hot and from hot to cold because lt lS P h e is nothing in the matthe hotter comes fr om the h 0 t ' because t terhot when it was 1ess hot ter which comes to b e h 0 t which was no th tter of a great a ·n that e ma . Aristotle begins this passage by s ~ g diately illustrates thts by and small body is the same and then f 1mme . becomes greater, the matter saying that when a small volume o atr s great. Aristo d e thus seems itself, which is potentially great;.eco~~ has the potential to infe~~ to be suggesting that matter itse lS w ak is spatially malleab_ e. d . tAnsto or decrease in vo1ume. M atter' so . to 1f speuire' one to rnterpre . the 1tse req th latns t by course, this passage d oes no d lving matter at exp . he . is .an. un herwever, 'as believing that extenston Sokolowski (along. Wlt h" . I my oplmon, o f t nsion rn t lS spatiality of ob~ects. n tl h d the concept o ex e d others) has shown that A_ristod edida not posit extension as the grouhnat ·f Ansto e t the somew sense. Furthermore, 1 uld be forced to accep . ct has of the spatiality of objects, he wo brute metaphysical fa b . . that matter as a . .thout there e, unsatisfactory postnon ·al propernes Wl . th" . different span ttribunng lS ~he potential for haVIng .n such a potentiality. Hence,; but charitable mg any ground to explat n1 texruallY grounde . d e seems noto y concept to Ansto . rms .ali of objects rn te as well. . d xplains the span ty . 1 teness of if Ansto e e . 1£ the rncomp e a1 to space 1tse ' . It is not But note th at of extension and does not appe all the more wornsome. 11 . becomes . d f atter as we Sokolowski's interpret:::thing can be bo~ a kin ~; to complete obvious, after all, how .ali of material objects. In as the ground of the span ty (Phys. 217a2Q,217b4).

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this account of extension, therefore, we need an explanation of how the void can be turned into matter. It is to this issue that I now turn.

. fi d with respect to one another First, its regions need not remam .xe uld b two feet from each over time. So, for example, two regtons cho h e t another time. Sec. d h £ from eac ot er a other at one ume an t ree eet . f st'on but are par. . d re01ons o exten ond, matenal obJects o not occupy material obiects d thts conception J I d tially composed of them. n ee ' on f . Clearlv: such a . d e ·0 n 0 extension. ,, are a composite of form an some r gt h . b bly primitive, that 1 . one t . at IS pro a· s of extension). view requires some sort o f re anon, · this case regton holds between forms an d matter (10 . A . h biects on the ab,{. . lanon s wtt o J Call such a relation the enJormtng re . ' . inherit their spa. b' thts conception . 0 solute space conception, o ~ects ~ f . On this conception, tial relations from the span'al re1atl0 ns o regtons.. different regions ively occupymg . however, they do so not bY success th ssi'vely change thetr · ns at succe but by being partly composed o f regto

SECTION II EXTENSION In his thinking about spatiality, Aristotle obviously did not have recourse to contemporary mathematical sophistication, though as I shall argue in a moment his conception of extension can be developed in a mathematically rigorous fashion. Informally, however, we can contrast this conception with the more familiar conception of absolute space. Consider, therefore, some arbitrary regions of absolute space, A and B. Because these regions have fixed relations between them, if A is two feet from B at some time t, then it is two feet from B at all other times. This fact about absolute space leads naturally to an account of the changing spatial relations between material objects. Material objects inherit their spatial relations by occupying these fixed regions. Hence, any two objects occupying A and B at any time t will be two feet from each other at t, though at some other time they can come to occupy different regions thereby inheriting the spatial relations that hold between those two regions. Like absolute space, extension is a space-like structure in that it con5 tains regions. But, it differs from space in two important respects. 5 Before providing a characterization of extension, I should note an objection to the idea that Aristotle had a theory of any space-like structure at all. There is no question that Aristotle had a theory of place that is designed to accom_modate the metaphysical commitments of our ordinary talk about where thmgs are. Such a theory is designed to explain, for instance, the truth of ~he st~te~en~ that Socrates is in the Agora. It is not clear, however, that Aristotles thmking about spatiality involved anything more than his theory of p~ac~. And so, one might argue, an appeal to extension so as to explain the spati~Ity ~f ~terial objects is an over-interpretation of Aristotle. In response to this obJection I shall make two points. First, there is the textual evidence adduced .by Sokolowski that Aristotle did have the conception of extension and that It ~as a matter-like something at some level ofhylomorphic analysis. And there Is also the textual evidence from Physics VI, 9 that I have adduced. Secon~, the int~retation of extension I am offering obviously fits into the la~ger Interpretation I am defending in this book according to which Aristodes hylomorphic ontology as providing the ground for many of the structures

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relations h e matter-like. To see . b mes muc mor So characterized, extens10n eco th bronze of a statue. this, consider a less remote ki n d f matter- e't elf can be said to Neither the shape of the statue no r the statue 1 s d that is diflic ult b nze to use a wor . occupy the bronze. Instead ' th e ro ' ark of this fact IS . h statue. 0 ne m . to define adequately, constttutes t e d h ever the bronze ts, . h is locate w er . . that the statue, as well as tts s ape, . Hence, if extenston ts the statue ts. and the bronze is located w h erever . like the bronze, must . pound, then lt, h the matter of a hylomorp IC com £ And as a result, it must go · lt · ts · the matter o • l the relations t h at h 0 ld constitute the compostte · d be where the composite goes. 0 r, mo re accurate b c ..Y• d but must mstea . st not e nxe 1 . s between regions of extension mu l . the differing re anon . as to exp am capable of changing over time so .

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between the maten'al ob'~ects I·n quesnon.. d ·s not much more than a . ture can . w h at I h ave characteriZe 1h As I have said that t he pte ' I want to s ow picture. In what follows, however, temporary math ematical . al d evelopbe fleshed out consi'derablY Wl.th some ali con a mathemanc 0 b appe ng t th apparatus. In doing so I will e . tl . and indeed e ch aracteral l to Ansto e, . tl • gener b ail rnents obviously not av a e ter to Ansto es al ization contains some creatures t hat run coun'de for instance, appe s . · I provi ' ways of thinking. The charactenzanon . . crure m 1 lace IS a stru . . ial scheme. Quite dear y, p m what follows, that are inherent m h1s categor h ld become clear fro . Aristotle's categorial scherne. A0 d'a1ass ou d in extension. such a structure finds a very natur groun

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to the notion of a point and so is naturally assimilated into an ontology of points. Aristode, however, though he accepts that there are points (Meta.l016b20-31 ), denies their substantiality (Meta. 1077b12). Despite the difficulties with points, however, and despite the risk of anachronism, there are good reasons for engaging in this project of clarification. First of all, it is difficult to see what extension might be. Several philosophers have appealed to the notion, but without some robust characterization of the sort I shall give, such an appeal can appear to lack much content. Second, the account of extension I shall give provides a perspicuous way of understanding not only Aristode's concepcion of the spatiality of material objects but also how he might have understood various phenomena associated with spacial motion. Finally, and most importandy, my account of Aristotelian extension will prepare the way for some speculations I make in the final section about the nature of prime matter as distinct from but importandy related to extension. The structure of Aristotelian extension can be captured first by characterizing a richer structure (arguably latent in common sense) and then by abstracting certain features from that structure. Let us begin, therefore, by appealing to a four-dimensional structure M of 6 points. 1he four dimensions are the three spatial dimensions and the temporal dimension. To give the structure a temporal dimension it is natural and in accord with Aristode's own view of rime to suppose that for any two points, p and q, within M there is a well-defined interval of time. As a result, for any point p there will be a set of points simultaneous with p. With these stipulations, the structure M can be thought of as stratified into a succession of instantaneous three-dimensional spaces called hyper-planes of simultaneity each of which bears determinate temporal relations to all the other such spaces in the manifold. Once the sttucture is partitioned into three-dimensional hyperplanes of simultaneity further features can be added. One such feature is a distance function d(p,q) defined on any two points within the same hype~-plane. ~is distance ~nction provides the hyper-plane with a metnc. And With such a metnc, the space will exhibit what contempo6 My charact~ation of absolute space draws heavily from Michael Friedman,Foundattons ofSpace-Time Theories (Princeton,1983).

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_a:. d conformal properties as well rary mathematicians refer to as amne an 'd f anifold. . reqmre . d bY the very 1 ea. o (a m c as the topoloo-ical propernes al) o· . (affine) ' angulanty conrorm That is the notions of straightness ' . al) b d fi d within the space. and nearness ( topologtc can e e n~ E clidean spaces 'b d f The structure descn e so ar contains separate u be com. ther These spaces can that bear temporal relanons to one ano .· d eli more feature bined into an enduring ab so1ute space by m u . ng oneth This fea0 f ·multanelty toge er. 1 that'connects' all the hyper-panes Sl ill c ll th ·s convention? . alld , . . ' d i w roow 1 . ture 1s nowadays c e a nggtng, an different points just m A rigging is a relation that holds between.altwlo . Hence one can pan ocanon. ' . h case those regions occur m t e same s . ·me among points . cnon across t1 think of the rigging as creatmg a conne . f as orthogonally . now conceive o of space that runs m a way we can . I rtandv: the riao-ing · ult ne1ty. mpo ,, through all the hyper-planes o f slm a . ' . al lations to oththe1r metnc re connects points in a way that preserves . th hyper-plane of 'f d are m e same d er regions. For instance 1 P1 an ql h h d P is connecte . eli d fr 0 m eac ot er, an 1 th simultaneity and are a stance d and q are in e 2 · nected to q 'an Pz 2 to p2 by the rigging while q 1 1s con eli tance d from each . th dqarea s same plane of simultaneity, en Pz an 2

=-

other. . . l all .t 'the fixity princic ll · nnop e-c 1 Let us formulate the ro owmg P If two points are conpie' -that characterizes this aspect of sp~ce. R holds between them, . . e the relanon th 1 nected by the rigging Just m cas . ul 'tyJ·ust in case ere a1 0 f slm tanel . two points are in the same P ane b tween any two pomts, th distance e . d non S holds between them, an e

x andy, is given by d(x,y), then: ) "' ( R y )), then S ) & (x1 R x2 ..,.. Y1 2 (x 1,x2,y 1,y2) (if ((x 1 S y1) & (xz Yz d(x 1,y 1) = d iff d(x 2,y 2) =d) . that any two points . . c a1 way of saymg . anlhe fixity principle 1s JUSt a rorm other pomts at riao-ing to two h at a single time connected by t e

=-

=

' . . ' emerged within a cert.ain 1 7 It should be remembered tha; ~e ~ ~;rntended to refl;: anJs::: historical context, and my use 0 .e t I 's views on space and 0 er . between ArlStOt e about the relationsh1p cally important treatments.

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other time will be the same distance apart as the two points to which . they are connected. 8 The structure so far characterized is one way of viewing what mrght be called 'absolute space: And as I said, it is plausible to suppose that such a view of space is latent in common~sense conceptions. Aristotelian IJ-EYE8o<;, however, is not absolute space. As the informal discus~ sion of extension brought out, when we move to Aristotelian IJ-EY£80~ we can keep the idea of a structure stratified into hyper~planes of si~ multaneity; but we must abandon the fixity principle. Suppose, then, that there is a structure M that contains simultaneity hyper~planes. And suppose that a rigging connects the points in the various simultaneity planes. But suppose that the fixity principle is false. In other words, suppose that it is possible that (x 1,y 11x21 y) (x 1Sy1 & x2Sy2 & x1 Rx2 & y1 Ry2 & d(x ,y ) = d & d 1 1 (x 2,y) ;t: d). At this point, the mathematical detour we have taken can now begin to pay off. For, we have reached a structure that can play the role of extension. With this characterization in hand, we can see how a mat~ ter like stuff can nonetheless be the ground of the spatiality of material substances. To see this, let us consider two types of motions that such a manifold might underlie. First, consider spatial motion. Let us posit a primitive relation of enforming that holds between a form and a particular region of points. And let us suppose that there is in addition to the form and region of points a third entity, namely the composite of form and matter. Un~ der such a supposition, there could be a composite A of form F and 1 8 Now, as characterized so far, space seems to be a four~dimensionalist sort of entity, which, one might argue, is problematic from an interpretive point of view. I have already noted that the appeal to points is at odds with Aristotle's ontology. But, once one appeals to points, it would certainly be more in line with Aristotle's views to have them endure over time. For, there are several passages (e.g. Catg. 5a26~7 and Phys. 218a2-3 and 5~6) that can be taken to suggest that Aristotle is a presentist. One can, however, remove the four-dimensionalism of the structure by allowing points to exist in different hyper-planes of simultaneity. To do this, one needs to construe the rigging as the identity relation. In this way, one can suppose that points endure over time. Under such conditions, adherence to the fixity principle entails that the metrical relations of any two points are permanently fixed.

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£ F d region r Further, let us region r1 and a composite B ~f ormand an that occu~· within regions, suppose that there are two pomts, P1 P2' h di e between A . h one m easures t. e stanc r and r respectively b Y w h tc c t firom B The 1 2.1 h · t A 1s two ree • and B. Finally, let us suppose t at at nme .1 th A is a composite of fact that would make this to be the ~ase l;or;tF and matter r2, and form F1 and matter, r1, B is a composttehof b 2 n"me t and time 1 se t at etween d(p1,p2) = two feet. But now su~p.o e feet from B. Assuming that tz, A changes its location so that tt ts th~e A h as matter r ' and . h t t nme t as 1 1\s form enforms regton r 1 so t a a uld ak it the case that A likewise for B and r 2' then the fact that wo_ mf ceorm and region r 1' . . h A . compostte o a r• IS three feet from B ts t at ts a . d d( ) = three feet. In B1s . a composite . o f a crorm an d re01on r an P1'P2 t::r 2' f h · al obiects succes~ . . do asp ystc J this way, spatial motion IS not concetve h other are fixed. eac l . ns between sively occupying regions w h ose re atto "al composites having . . . · d of as maten Rather spattal motton ts concetve h th can change over · b etween eac o er matter whose metrical relanons time. . o characterized can under~ A second form of motion that extenstonths . ubical composite, c there are three lie is increase and decrease. Suppose that ere ts athat . A, of form F 1and region r 1at orne t1. And suppose the volume of A. 1he . h measures f lines-x, y, and z-of A b Yw h tc one d t of the lengths o x, Y uc be determined by th e volume of A would thus be equal to the pro uld and z. The lengths of x, y, and z, thoug~, wo f those lines-call them 0 fA would be d(x.,~) distance function applied to the endpomtls ds the vo ume o x x. y y and z >z. • In other wor ' . t and t , the dis~ a'-o' a' b' a'o th b tween time 1 2 uld * d(y ,yb) * d(z ,>z. ). Now, suppose at e ult the volume of A wo a a -b As a res ' tance between x and ~ decreases. "nk• b t again the shrinki.ng decrease. A, m u extensiOn. · 1t would . aoth er word s, would shn d ' lving · Nunerr · would be the result of a change 10 l A occupying a regton · al obiect, name Y ' the regton · f space J all than not be the result of some Ph ystc . wneren _~,.r tandsm er of space at time t that ts

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2 It• occupies at time t 1. . l arrives at a space~like srruc~ . · nop e, one fix By relinquishing the tty prt . . g r..aions that are the mat~ s contamm -r,. f the re~ ture that can plausibly b e seen a . B ause the pomts 0 . d f ec kin mposttes. th aions can act as a . o ter for various form~matter co . . do not obey the fixity prt·nople, e rec- of senst"ble composttes. gtons . h forms derhes t e h c angeable structure th at un

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They are capable of taking on different volumes and changing their distances between each other. In this way, the regions of this space-like entity can be the matter for form-matter composites as well as confer spatiality on material composites. As a result, one need not posit a void that physical objects occupy. Rather, the void has been turned into matter.

SECTION III WHAT IS PRIME MATTER: I have argued that Aristotle had the concept of extension, that one can characterize extension mathematically and that the resulting theory fits easily into a hylomorphic ontology. I have not yet addressed, however, the question as to the nature of prime matter. In particular, I have not addressed whether prime matter is, as Sokolowski claims, extension. Now, it is difficult to provide much textual support for such an identification. As is well known, many scholars think that Aristotle's texts do not support even attributing to Aristotle the view that there is any more remote matter than the elements. I disagree with such scholars but am nonetheless willing to admit that Aristotle's texts cannot provide much support for any theory about the nature of prime matter. There is, however, a philosophical reason to resist the identification of prime matter and extension. Philosophically, the idea of prime matter is the idea of something that in itself is formless but that has the potential to take on any form. Extension as I have characterized it, though, does have in itself formal characteristics. It is, for instance, necessarily composed of regions that bear metrical relations to one another. In response to such an objection, one might try to deny that the metrical relations in question are forms in the right sense of'form' thereby retaining the idea that prime matter does not have any forms in itsel£ But, Aristotle's favorite example of a form is shape - and surely if shape is a kind of form, then metrical relations between regions would qualify as a type of form. So, even if Aristotle accepted the view that extension is matter at some level of hylomorphic analysis, the identification of extension and prime matter looks philosophically

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. . n we face an obvious quessuspect. But if prime matter ts not extensto ' tion: what is it~ h thematical charac. d return to t e rna th In response to ts we nee to 'd d I haracterizing extenterization of extension that I have provl e · .n c ctured in some . f et of pomts stru sian, I appealed to the nonon as .d _ the set of points . way. There are two components to such anul1 .ea structure, I sat'd, lS . d efi ned on t h em · The res hong 1 tions from extenand the relanons extension. Now, were one to a bstract away t e re a might think. But th f 'nts Or, so one . sian, one would arnve at e set 0 pot ·h rrives at is a struced w at one a . . . mfact, once the relanons are remov ' . And such objects 1 . . .c properoes. tureless set of objects with no mtnnsl . b orne spatial reail pomt ears s th could not be points. For, necessar Y any . d fined on them, e . 'th t any relaoons e us J·ust call them tJ.on to something. Hence, Wl ou . S let ailed pomts. o, resulting objects can h ard1y b e c

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objects. th t we understand Aristothe completely unWith this distinction in mind, I suggest la 1 . al corte ate to ed telian prime matter as the onto ogtc , c the relations defin on · 't h e matter ror th that allows fo r the structured set of obiects t h at 1s J thi goro er d them. It is the fundamen~al bare some o;d be, so to speak, the g_roun _ very possibility of extens1on at all. It w th uld charactenze ex: . a1 ructUre at co for any contentful mathemaoc st .al substances. . all tension and hence the spatiality of mfate~ matter is philosophi~ .Y · · no pnme Of course this charactenzaoo 'd that prime rnatter1s1n · the ' f the 1 ea forms. At 73a28. 10 satisfying only if it can make sense ~. all F' 0 1 itself formless but stands in poten~ dtyfint .cion of some predica~e lfs 1 Postenor · Analyttcs, . Ansto · tle gt·ve h1s e that F belongs to Gin 1tse .d d · 1f..' .He says 1 three-sl e be1onging to a subject G m . ttse f G as, for ex:amP e, for if and only if (1) F is in the defimnonGo . the proper subject ofF, as, f . 10 . the definition of tnan . g1e,•or (2) f IS ·ghmess. In the first 1s . sense . elfoF biect o strat be 1n 1ts example, a line is the proper su ~ a1 . elf a species can d ot· •· . , G that ts so ItS . d d so oes n tn Itself, only a genus, • . . highest kin an d run·e eoes IS a er p bFor, a genus that is not also a sP plausible to consi th . d s not seem __ ;t., all ose o have a definition. Now, lt oe that could unur us it . 1 ks any nature if . . not a gen ' theless even lt lS fin' . n ·nee matter a genus, since 1t ac · Nonekind it must ' 1ack a de 100 ' 51 jects that would belong to lt. highest , should be clear that, like a

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it lacks all structure. After all, without any structure, what could possibly be its defining formal feature~ It is not so obvious, however, that prime matter could not be in itself F in the second sense. One might argue, for instance, that it is the proper subject of those relations that are constitutive of extension. After all, prime matter does serve as the matter for such formal features. Despite this possibility, however, there are reasons to deny that prime matter is in itself F even in this second sense. These reasons stem from the way in which prime matter could be a subject of properties. Ancient commentators often distinguished between a primary and a secondary bearer of properties. Consider, for instance, a bronze statue, Arguably, it is the statue, which for the sake of this example can be considered a composite of the bronze and the shape, that is the subject in which the shape inheres. Nonetheless, there is a sense in which it also makes sense to say that the bronze has that shape as _well. The_ Medievals marked this duality by calling the statue the pnmary subJect of the shape and the bronze the secondary subject of the shape. And in general, one might consider the matter of a formmatter composite the secondary subject for those properties for which the composite is the primary subject. Matter, however, at least some matter, is itself a composite of form and matter. Bronze, for instance, according to Aristotle is a composite of a form that is a mixture of the elemental forms and some more basic matter. Hence, the bronze would be a primary subject for such forms, while its matter would be the secondary subject. Given the way the Medievals make this distinction, it s~ould be clear that anything that is a primary subject of a ~roperty Is a composite of form and matter. Prime matter, however, IS not a composite of form and matter and hence cannot be a primary bearer of properties It m tal · b . • . us ways remain at est a secondary bearer of properties. So, for Instance, extension is the primary bearer of those ~O:Uctural features constitutive of it, while prime matter, even though It IS the. matter for such feature, is only the secondary bearer of those properties. It can only ever borrow its character from those entities that are ~e primary bearers of various properties.

Retu~mng, _th~n, to our original question, we can see why prime

~tt~r ~s ~ot In Itself F in the second sense of that notion. Any genus at Is In Itself F in the second sense must be a primary subject of F.

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For, if it were only the secondary subject of F, surely it would be the primary subject and not it that would have the right to the label of being the proper subject of F. Hence, the fact that prime matter could only ever be a secondary subject of properties counts against its being in itself F in the second sense. We can see, then, that it really is the fact that prime matter is natureless that rules out its being in itself F in either sense. Because it is natureless, it cannot have a defining formal feature and so cannot be in itself F in the first sense; and because it is natureless, it cannot be a primary subject and so cannot be in itself F in t~e seco~d sense. Of course, despite the fact that prime matter is not in ItselfF, It can nonetheless stand in potentiality to all form. For, an entirely structureless set of objects can nonetheless be augmented with further structure so as to create genera that are capable of being studied.9 Indeed, as I have argued in this paper, prime matter can be augmented wi~ sn:uctural · e matter m th1s sense . so as to create extensiOn. . H ence, pnm re1at1ons does indeed stand in potentiality to all other forms. At this point, it is possible to respond to an objection commo~y · d against · · · h t press the question: what ratse pnme matter. 0 ne m1g . ul IS . matter.~ I sIt, · ror c instance' a partie. .ar~:~ the ontological status of pnme . It. a umvers . al ~ Or IS . It . devo1"d of ontoloaical charactenstics. If not, Is o. . . . . uld · problemanc. Any answer to these questions, It wo seem, IS . If It IS a . pamcular or universal, it must h ave some d efinite ontologtcal h nature. d . . But this is at odds with its nature1essness. I£, on the other an , 1t IS

"d sa response to Daniel Gra9 This understanding of prime matter provi e . . h "The Paradox · matter 1s mco erent. ham w ho argues that the concept of prime . (1987)· 475-90. h of Prime Matter," Journal of the History of Phi1osop ~ 25 ·al characb ounded m some actu . . Graham insists that a potenttality must e gr d b d "d of accual char. . Hence, prime matter, w h"ICh IS . suppose to . e evOI tenstic. d · a1 Although "ali all form IS para OXIC • acceristics and yet stands in potenti ty to lin f ning gains its uch a e o reaso G ah r am is not explicit about th e ma~er, s ct of matter. If, on the other plausibility from a focus on the physical aspe . th matical perspective, han d, one approaches pr1me · matter from a. quasi-rna e . f tureless set of obJects . all . h nonon o a scruc th ere Is nothing incoherent at m t e ed . uite literally forced 18 that can be augmented with scruccure. Inde. 'othne qcrure from a set of . ks of removmg e strU to such a concept when one thm points.

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devoid of ontological characteristics, it would seem to be a metaphysical phantom, something that we cannot really know. In response to the objection, one must first distinguish between two ways of referring to matter. One can refer to the matter of some composite, for instance the bronze of such and such a statue; or one can refer to matter as such, for instance bronze. Now, I contend that the following two claims about bonze are true: 1. The bronze of such and such a statue is particular. 2. Bronze is neither particular nor universal. If one were to think that bronze had some sort of independent existence apart from the objects it constituted, one might be required to reject 2. But there is nothing problematic in refusing to grant an ontological status to something that is being referred to as an abstraction from those conditions that make its existence possible. So, we have analogously,

1. The prime matter of a statue is particular. 2. Prime matter is neither particular nor universal. Hence, there is a sense in which prime matter is particular and a sense in which it is not. And just as in the case with bronze, it is in no way problematic to refuse to grant ontological status to prime matter in so far as it is being referred to apart from those conditions that make its existence possible. A problem, however, remains. For, we are admitting that prime matter in sense 1 has some sort of ontological status; and doesn't this violate its very nature? No. Because its particularity is dependent on its being enformed. This follows from the fact that prime matter (as such) is neither universal nor particular, while the prime matter that constitutes a statue is particular. Hence, particularity is not intrinsic to prime matter, and so there is no violation of its naturelessness. Finally, unlike bronze, prime matter in both senses is devoid of primary actual (as opposed to potential) characteristics. For instance, both bronze as such and the bronze of such and such a statue are primarily hard. But, there is no primary actual characteristic of either prime matter as such or the prime matter of such and such a statue. So again, the naturelessness of prime matter is preserved.

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SECTION IV PRIME MATTER, MAT H EMATICS AND MATERIAL SUBSTANCES · h · h this account of pn·me matter can It is worth noting the way m w lC f h u·cs and his account . 1es' th eory o mat be integrated into A nstot . ema · I am offering, di to the mterpretanon of material substances. A ccor ng . . . b h the mathematical hi. ·al posmon m ot prime matter occup1es a specl f bstances. In fact, one erarchy of objects an d t h e maten·a1 structure . . tho su · which these two . mterpre · tat1on IS . e way m interesting aspect of t h IS J!ll" fA . tl , ystem dovetail. . . Ulllerent parts o nsto es s h t a mathemanc1an As one moves up t h e genus I sPecies strUcture al d th anee less strUctured• ore gener b studies, the structures ecome m . han e bly and am assumture mterc d (Here I am using genus an struc . angea ) Each structure h as · a1 perspective. ing an Aristotelian math emanc all fother structures . · yaparto characteristics in itself but also IS pote~ti d t have in itsel£ Pure that lt oes no in which it actually has reatures h" h one can abstract so £ tures from w h thermore, each structure as ea ali ICIf the chain of genera ·gher gener ty. must arriVe . at some . f h 1 as to arnve at a structure o . £i . 1 however, one c and species is not to go on m mte y, . . elf a composite of rorm most general structure. Now, I·f t h at genus if. IS. ltSto be a genus at all, then st be lt IS . and matter, which I suggest lt mu . c as to arrive at some fr 0 m ItS rorm so it must be possible to abstract S h a something wo uld not utterly structureless someth.m g or other. uc. tl"cs but would nonethe' be a genus, would in itseIf h ave no charactensspecific structures. Such less stand in potentl"ality to any of the more It is that set of ob"~ects that . prl·me matter. . a something, I contend , 1s results from de-structuring extension. . s the positing of a struc1 rphism reqwre , h tl l Aristotle asserts th at .com-f Likewise, Aristo es Yomo eral p aces, I that is itself a compos1te o tureless type of matter. n sev . 1y, however, . of form an d matter have matter . fi rote . t to go on m d posltes cture lS no · h form and matter. If sue a stru . elf a composite of form an as one must arrive at a matter that is not ki .ltSright to think · of extension n1ike 1 matter. Now I think that Sokolows s rphic analysis. But, u ' very bas1c · 1eve1 ofdhy1omo . so as to arcture extension matter at some can e-stru Sokolowski, I think that one

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rive at prime matter that serves as the ultimate matter of a material composite. When one turns to Aristotle's theory about the relation between mathematical objects and material substances, one can reinforce the view that prime matter and extension are crucial in both Aristotle's theory of mathematics and his hylomorphism. Aristotle thinks that mathematical entities do not independently exist. It is not that mathematical entities do not exist at all; but they only exist as dependent entities whose mathematical treatment requires the abstraction from some of the conditions that are necessary for their existence. (Meta. 106la28-36, Meta. 1078al-5, Meta. 1078a25-6, Phys. 193b31-4). A surface, for instance, is dependent on a physical substance whose physicality requires its ability to move. A mathematician, however, treats the features of a surface in so far as the surface is a quantity, not in so far as it inheres in a mobile substance. 10 In this way, although mathematicians do not treat mathematical entities as if they exist in the physical world, such entities do exist in material substances. With such a characterization of mathematics, one would expect there to be something in material composites that corresponds to the various objects that mathematicians study, though one would expect the existence of such entities to be dependent on mobile substances. In the case of extension, one could take such a stuff to be the intelligible matter Aristotle mentions at Metaphysics 1036a3. Extension is intellectual matter because, in its pure form, i.e. in the form in which mathematicians study it, it is abstracted away from any conditions of mobility and sensibility that characterize its actual existence. Mathematicians study the features of extension qua quantity, not qua matter of a mobile, sensible substance. Indeed, in chapter 6 I shall argue that quantity as such just is extension. So, the study of quantity turns out to be for Aristotle primarily the study of extension. In this way, extension is not only a highest kind that mathematicians study but also the most basic matter that admits of some essential structure. Extension, of course, does not actually exist in the form in which mathematicians study it. Rather, it exists in material composites as the matter for sub-

~0 It should be clear the way in which this interpretation intersects with the Interpretation of Aristotle's philosophy of mathematics that I articulated in chapter2.

4 Pal Prime Matter

97

stantial forms. As the matter of a material composite, extension has in a secondary sense characteristics that the material object has. _It woulh~ . 0 f mo biliru be for instance, the secondary sub~ect ·r It is preasely . t hIS ' nature of intellectual matter, one rrug · h t argue' that provides t e dual rationale for Aristotle's remark at Metaphysics 1036a3: · mte · 11·tgt'ble·' examplesbof .sen-I Some matter is sensible and some ts sible matter are bronze an d woo d and any movable matter, 'bl . ut mteh . Ie th.mgs but no t qua senst e' as tn mat ligible matter exists in senstb ematical objects for example (Meta. 1036a3). As should be clear by now, h owever, 1 think that one should not .al stop . al case or the maten. case. at extension in either t h e math ematic th . . Standing above extension ma ematlcallY and below extension di rna· prime matter, accor ng to . tetially is prime matter. L ike extens1on, . . . material composites. 1ts exthe interpretation I am offenng, extsts m . . . . ht have are enistence however and any formal characterlsttcs it rrug. . nl h ' ' on the forms t h at en£orm it• And so,frlt lS o y w en tirely dependent 'al all h £ mal content om a maten one completely abstracts away t e or all th usal powers composite, that is only wh en one abstracts away 'al e ca posite that ' and the spatial structures t hat ch aracten·ze a maten com · · its · pure ro c rm, prime matter. one arnves at, m

CONCLUSION . matter that I have given, it is With the accounts of form and prime h' cture of a material h 1 orp 1c stru now possible to see what th e Y om h. £ dation of a material composite looks like. At the hylomorp i~ oun tter is what can be substance is prime matter. E n£°rming pnme . rnaconso'tutive of extenof relaoons considered a form-m, name1Y th e set . and such relations. . 0 f pnme matter sion. Extension is the composite al traries and mixtures . . h the element con . E nforrrung extens1on, t en, ar~ and d enforms prime matt~r' 11 thereo£ For instance, the patr hot ryN w: the matter of a liv. . fire element. o ' rth · fire or water. Instead' and the resulting composite iS a ,atr, .ing material substance 1s, . of course' noteatuffs like blood, musd e and 'al composite dethere is at the first level homeomerous s b. rrucrure of a maten b 11 This account of the hylomorp tc s h' h Kit Fine convincingly esta • pends on a leveling account of mixture;,w ;~·tosophical Quarterly 76 (1995) lishes in "The Problem of Mixture~ Pac~.c 1 266-369.

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

g8

tissue. Such stuffs are composites of extension and certain capacities distinctive of living beings. So, for instance, blood is a composite of extension and the capacity to transmit food in its penultimate form to the extremities of the body. Such homeomerous stuffs are the matter of the anhomeomerous parts of the body. And, once again, it is certain living capacities that enform such stuffs. So, for instance, an eye is a composite of certain homeomeorus stuff and the capacity to take on the form of objects without their matter. A body, then, is a collection of anhomemeorus parts; and the form of a body is the soul, which again is a unified set of capacities. The following diagram illustrates such relations.

99

4 fll; Prime Matter

in~ One final comment is in order. Although I have distinguished th the diagram the soul and the living capacdities thha~ eknfofrmth;s: ase~~~:~ sion and homeomerous parts, one shoul .not .t m b o the various d th relanon ts etween Wh pendent existents. at exac Y ~ th A · tode discusses · diffi ult tssue one at ns capacities and t h e soul ts a c ul in some sense at DA 41lb13~31. It would seem that .. e eWhnnre so the correct in~ . diVI'du al capactnes • atever permeates each of t h e m th 1 distingw·sh , . . . ne can none e ess d terpretation of Aristo es posltlon ts, o u h the soul is itself in some such capacities conceptually, even tho g . . 12 sense a unity of all sueh capactttes.

rh

.

Prime Matter + Spatial Relations

I

Extension + living capacities (and/or elemental contraries)

I

homeomerous stuffs + living capacities

I Collection of anhomeomerous parts (body) + soul

I

substance-member of a natural kind A few comments about this diagram are in order. At each level, some matter is enformed by a form~m. The results from chapter 3, however, suggest that the resulting composite of matter and form~m should have a form~c, which is a species. And indeed, with one wrinkle, this is the case. I shall argue in chapter 6 that the composite of prime matter and spatial relations, namely extension, is in fact the genus quantity. But because quantity is a highest kind, it does not belong to some other genus. A composite of extension and living capacities, on the other hand, namely some homemoerous stuff, is in some species. For instance, flesh is in the species flesh. Such a species, however, is not in~ dependent of the natural kind to which a living substance belongs. In fact, the definition of such a species would include the concept part of such and such an animal. And because a part of a substance is not itself an actual substance, flesh is not an actual substance. Similar comments apply to anhomeomerous parts. Finally, the composite of a body and soul has as a form~c the natural kind to which the composite belongs.

. lici • Homonymy in the Philoso·

12 Cf. Christopher Shields

Or~:~np';~'i 9J'), ch. 6, for the best recent

phy of Aristotle (Oxford: Claren discussion of unity in Aristode.

CHAPTER

5

QUALITY

W

~th substant.ive accounts of form and matter in place, it

lS now poss1ble to tum to the categories so as to see the A. extent to which its various structures can be traced to nsultodtle's hylomorphic ontology. Aristotle recommends that inquiries h so start Wlt . h w h at is better known to us and proceed to what is hietterd kn . own b Ynature. For the remainder of the book, I shall follow b 'ds a Vlce. I begin with what is better known to us, namely the ac· cr ental categones · o f quality and quantity and then move to the cat· egory of substance. I~ this chapter, I argue that the category of quality admits of a deri· vdan~n from the nature of form. In my view, the possibility of such a envanon · h as been obscured by two factors: (1) the lack of a dear account of the nature of form; and (2) Aristotle's presentation of the of quality in the Categories. As .hould be dear, I have .J...ady

~ry ~dre,...t the first i,.ue; and. ., shall becom< app=nt by the end of

£ ' chapter, the taxonomy of fOrm I prorid
I~ 1~

q~-

genus/ species structure in the category of quality· . chapter eight of the Categories, Aristotle divides the genus, mto four species: (1) habits and dispositions; (2) natural capabili· tles and incapabilities; (3) affective qualities and affections; and (4) s?ape. Because Aristotle does not explicitly subsume any of spe· cres under further genera, it is natural to interpret them as the highest species under the genus quality. If so, the following diagram represents

the~

the genus/ species structure in the category·

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

102

Quality I. Habits and Dispositions II. Natural Capabilities and Incapabilities III. Affective Qualities and Affections lV:Shape This interpretation of the category of quality is so naturally suggested by Aristotle's discussion that most commentators do not question it. Porphyry, for instance, in his commentaries on the Categories, simply asserts that there are four species in the category of quality and then goes on to discuss Aristotle's treatment of them. 1 Likewise, Aquinas, though he tries to derive the four species in a reasonably systematic manner, does not seem to question that there are just these four main 2 species. And more recently, J.L. Ackrill's commentaries on the Categories shows that he thinks there are these and only these four highest species in the category of quality. 3 Because such an interpretation is so naturally suggested by Aristotle's text, and because it is at least implic· itly presupposed by most discussions about the category of quality, I will call it the canonical interpretation. The canonical interpretation, though a natural reading, leaves the category of quality in a rather uneasy light. Why? Because it is not at all obvious what the justification or even the motivation is for divid· ing quality into just these species. Indeed, when the species are simply ~sted, it is hard to deny that the list appears rather arbitrary. Why, for mstance, should natural capabilities and incapabilities be considered a highest species under the genus quality:' Or what reason is there for thinking that there are no other species under quality:' . The apparent lack of any systematic derivation of the list of species ~~ ~e category of quality has not gone unnoticed by scholars. J.L. Ackrillts representative: When Aristotle says that quality is 'spoken of in a number of ways' he does not mean that the word quality' is ambiguous but only that 1 Porp?yry, On Aristotle's Categories, trans. Steven K. Strange, (Ithaca: Cor• nell Umversity Press, 1992), p.l39. 2 ~qu~as, Treatise on the Virtues, trans. John A. Oesterle, (Notre Dame: Umverstty of Notre Dame Press, 1984.), PP· 4•5, 3 Aristotle, Categories and De Interpretatione, trans. J.L. Ackrill, (Oxford: Clarendon Press, 1963)

5NQuality

. al' H proceeds to list and diScuss there are different kinds 0 f qu lty. e rinciple. four kinds. He does not 'deduce' them or connect them on any P ... [emphasis mine]

103

4

• krill's that is behmd Ac d d ction And it is no doubt the lack of sueh a e u . · h'IS commentaries: . tle 1ater m criticisms of Aristotle a 11t

. nt to show that [habits and He [Aristotle] gives no special argume . riterion for deciddispositions J are qualities. Nor does hheb~ve andiy. cposirion]· why, for . . · t a [ a 1t-or· s ' ing that a given qu al1ty ts or lS no d lass quite distinct _ tr · al' · be create as a c example, should arrecttve qu tt1es • • from [habits and dispositions] ?5 uality; at best unJUSO• Ackrill finds Aristotle's division of the genus, q A d it would ' call th e fied. Montgomery Furth , h owever, goes further. n far as to F rth has gone so seem, is being polite. Montgomery u dey horde: 'I shall ) monstrous mo species in the category o f quality a th . ale (if there be one . lik eranon d largely dispense with quesnons e • •· th trous motley hor e . gl ory e mons for comprehending into a sm e categ . d I think, that these at· yclept Quality ... '6 And it must be admtckrilltte .' 'ght to point out that . d A . lSrl . tttudes are to some extent warrante • d d . of the four speoes. 1' 't e ucnon Aristotle does not provide an exp lCl ggest that, lacking any 25 6 Indeed, Aristotle's own remarks at lOa • su nfident that h'IS list . he was not co th systematic deduction of the speoes, ded . questions about e . th I ck fa ucnon, . was exhaustive. And giVen e a 0 'de naturally anse. legitimacy of the divisions Aristotle d~es ~roV1 e not unreasonable, in Although Ackrill's criticisms of Ansto e ~ ;nterpretation to the . alternaove ... . this chapter, I argue that there IS ~ all the regimented interp_retatt~n, canonical interpretation, what I will c d Vl.ng the dissaosfacnon war remo . ted indeed be mcorpora that can not only go some way to. th at he and others have h ad Wl'th 1t chbut can · derivable from hylomor· ·at s erne IS into the thesis that the categon phism.

Ackrill

4 Ibid p.104. Jl. d sux9Eat~ as •states'and ds t#~ an · · ' to pro· 5 Ibid. p.104. Ackrill translates. the wo~ted 'habits' and 'dispostnons 'conditions' respectively. I have mterpo vide continuity with my translations. h • An Aristotelian Metaphysfi and Psyc e. 6 Montgomery Furth, Substance: 0~ J>ress, 1988) 14. . (Cambridge: Cambn'dge Umverstty ICS,

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

104

My main argument for the regimented interpretation proceeds in two stages. First, I examine the details of Aristotle's discussion of the first three canonical species and conclude not only that they are subsumed under the single genus of dispositions but also that the genus of dispositions admits of a more or less systematic and symmetrical differentiation. As a result, the category of quality should be understood as being primarily divided into two species: shape and dispositions. And because the genus of dispositions is systematically differentiated and Aristotle does not differentiate shape at all, any arbitrariness in the category of quality must be located in the division of the genus, quality, into the two species, shapes and dispositions. In the second stage of the argument, I propose a hypothesis about the way Aristotle understands the nature of quality itsel£ a hypothesis that leads to a very plausible division of quality into shape and dispositions. What is the hypothesis~ Not surprisingly, it is that quality as such is a principle of order. The connection to form, then, is obvious. If I am right, quality as such simply is a type of form. In addition to this main argument, an implicit argument runs through the chapter. Given Aristotle's settled taxonomical method, one should expect the specification of differentiae in marking boundaries between the species in the category of quality. It is surely noteworthy, however, that Aristotle supplies no such differentiae for the canonical four highest species. Indeed, such a fact ultimately lurks behind philosophical dissatisfaction with the canonical interpretation. For without such differentiae, it is difficult indeed to see what Aristotle could say to a detractor who doubts that there are just the four canonical species in t~e category of quality. The regimented interpretation, however, do~s arn~ulate such differentiae and in so doing not only accords with Anst.otles general taxonomical method but also provides the philosophical resources to respond to those who are doubtful of the divisions Aristotle makes.

SECTION I THE FIRST THREE CANONICAL SPECIES

~tho~gh Aris~otle says that the first species in the category of quality Is habits and dispositions, it is dear from his remarks that he thinks

SN Quality

105

habits and dispositions are in fact two distinct species that fall under a common genus. Aristotle begins his discussion by providing a way to differentiate between habits and dispositions. He says that dispositions are easily displaced while habits last longer and are more difficult to displace (Catg. 8b28). And he provides examples of items in both species: scientific knowledge and the virtues are habits (Catg. 8b29), while a hot condition, a chill, sickness and health are dispositions (Catg. 8b36-7). Aristotle's explicit differentiation of habits from dispositions, then, as well as his use of examples to illustrate the differentiation show that he thinks the first canonical species is a genus under which fall the two species habits and dispositions. What, then, is the genus under which habits and dispos~tions b~th fall:l Aristotle's concluding remarks about the first canomcal species strongly suggest that the answer is: dispositions. At9al0, after repeating his differentiation of habits from dispositions, Aristotle says: But habits are also dispositions, though dispositions need not ~e . are m · so me way dis habits; for although those who have hab1ts posed according to them, those who are disposed need not have a habit (Catg. 9al0-13 ). · what he has just I n this passage, Aristotle seems to be contradicnng said. If habits differ from dispositions in the way he says they do at . . tly d atm · at 9al0-13 that habits aref 8b 28, Anstotle . cannot consisten . . b di . . d t be habits But the threatI o disposmons ut sposmons nee no • . . disappears . . a speo"al ki nd of ambigw"ty is noted. E seif contradictton . . . a genus where tn his works, Ansto tle uses the same word to. refer h .to III h 1 e th F ·nsrance tn P ystes ' . 1 d an a species falling under at genus. or d . Ph · ' uses the word 1d Vll
THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

!06

Once such an ambiguity is accepted, Aristotle's remarks in this pas· sage make perfect sense. If habits and dispositions are species under the genus, dispositions, then all habits would be dispositions though not all dispositions would be habits. Moreover, Aristotle can be seen to be providing a justification for including habits under the genus dispositions. Aristotle says that those with habits are disposed in some way according to them. So assuming that things are disposed in virtue of dispositions, habits must fall under the genus dispositions. On the most plausible (and only charitable) interpretation, then, Aristotle thinks that the first canonical species is a species of dispositions under which fall those dispositions that are easily displaced, i.e. dispositions, and those that are long lasting and difficult to displace, i.e. habits. Once the first canonical species is understood as dispositions, it is a small step to place the second canonical species under a common genus with the first. Aristotle contrasts the second canonical species from the first by saying that things with such qualities are not merely disposed in some way or other but rather have a natural capability or incapability (Catg. 9a16~9). 8 He says, for instance, that some people are natural boxers or are by nature sickly (Catg. 9a19). This suggests that the ~econd canonical species consists of dispositions that are nat· ural, .while the first canonical species consists of dispositions that are acqwr~d. And .Aristotle's examples of items falling under the first two cano~cal species confirms such an interpretation. Science and virtue are his examples of habit; and in the Nicomachean Ethics Aristotle says that science and virtue are acquired (En • 1103a15). Fu~ermore, the examples of dispositions that Aristotle provides-a hot condition, a chill, a sickness and health-are also acquired. The items under the second canonical species, on the other hand, are all items that some~

8 I a taking the 1tfolf' in the s ' ' ' ~ ~ " ~ totot>trov . -., Uyeentence, ye nro~, eJCaatov trov notov •~ ou ~ _,_ yap ~ tro : BtaJCetcr9ai ~ .. , . tOt>~ 1t0tT]cra ~ tat, ai\J\.U exetv cjlOOtlCTJV T1 aov~ VOJ.Ltav tt. p' nB' " !:.!.tcp Buvalltv , So take th 'C' tro~ TlJ.lT]ut:;V nacrxetv; as signalling a contrast. n, e sentence reads·'Each 0 fth · · fb ing disposed but rather In . VJ.rtu : ese Is not sa~d merely in virtue o e· f h · be affect d.' 1b . e 0 av10g a natural capacity to act or not to disposedein . e crufcialh ~ntrast, then, is berween being disposed and being VIrtue o av10g a natural · . . capaaty or IDcapacity.

107

S~Quality

· a runner' being sickly thing has naturally. 9 Being a natur al b o~er, b ~~~g or being healthy are all non-acquired dispos~n~ns.b A . de of any . the 0 miSSIOn yth riStO · fact be It would seem, then, that desptte .cal species, ey can m genus that subsumes the fi rst two canom . . A d this is done, di p 0 sinon. n once subsumed under the same genus- s th . nder that ge~ ,rr · · of e speaes u it is possible to provide a d urerenttatlon .. ill 't elf have a f dispositions w 1 s nus. (As will emerge later, t h e genu~ 0 d al dispositions; and differentia). It divides first into acqwred an .nadtudir. st'tions that are · acqwre spo then acquired dispositions diVI'de mto th 1 g lasting and . . . d' . . d those at are on easily displaced, 1.e. tspostttons, an difficult to displace, i.e. habits. . al · s namely affec~ . d anoruc speae , Like the first two species, t h e thtr c d der the species . .. . · 1 'bly subsume un th ttve qualmes and affections, ts P aust ed directly under e dispositions. It should not, however, be su~suml h uld not, in other 0 · al spectes •. t s h' same genus as the first two canomc h I't along with . hi rchy m w lC , words, be placed in a genus/ species era h'gh st species under a . ts· one of three e th e first two canonical species, d I c llows. resente as ro genus. Such a structure wo uld b e rep Dispositions I. Acquired Dispositions II. Natural Dispositions . III. Affective qualities and Affections · under highest speaes . a Rather, it should be considered as on~ :.:,~d then be divided mto genus of dispositions. The other speaes would be represented . Such a structUre the first two canonical spectes. 0

f

as follows. Dispositions 'ned) I. Dispositions (of a sort to be spb~cl and Dispositions) ·· (Ha ItS A Acquired dispostttons atural . d softness are n -----that hardness an . · his com· 9 At Catg. 9a25, Aristode also says A . de there to be dir~J Hence. I capabilities and incapabilites. I take ~tohas that are not acqut_r . · lighdy tnents at hardness and softness somethmg . d' So interpreted' 1t ts a s 'ght . of'acqutre · A person nu • mterpret'naturally' as the co_n~ vin a quality by nature.uldn't have such a Weaker notion than somethmgs a .g though he wo for instance, have a non~acquired laztness, quality by nature.

-THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

ties)

109

108

B. Natural Dispositions (Natural capabilities and Incapabili-

II. Affective Qualities and Affections

The subsumption of affective qualities and affections under the genus, dispositions, is recommended by the fact that Aristotle's examples of affective qualities and affections are objects of perception. In the Categories, he says that among the items falling under the third canonical species are sweetness, bitterness, sourness, heat, cold, whiteness, and blackness (Catg. 9a29-31). And in the De Anima, Aristotle says that sweetness and bitterness are proper objects of taste (DA. 422bl0-2); colors, proper objects of sight (DA. 418a26); and heat and cold, proper objects of touch (DA. 422b26). Hence, assuming that the Categories and the De Anima can be given a unified reading, affective qualities and affections are proper objects of sense. Such an interpretation is also supported by Aristotle's discussion of qualitative change in Physics VII, 3. He says there that qualitative change occurs only in the third species of quality and that such a species consists of those qualities that are sensible (Phys. 245b4-246a4). So affective qualities and affections are objects of sense. But Aristotle's discussion of the sensible objects in the De Anima makes it dear that they are dispositional in nature. It is the nature of color, for instance, to be able to set in motion a transparent medium as long as there is light (DA 418bl ). Color need not be setting in motion the transparent; but it is essentially capable of doing so. And so it is essentially a disposition of some sort. Hence, because affective qualities and affections are proper objects of sense, and because proper objects of sense are dispositions, affective qualities and affections are dispositions. It can thus be seen that consistency between the Categories and the De Anima entails the incorrectness of the canonical interpretation. De Anima 418bl-2 treats the idia of sight as essentially dispositions, but the canonical interpretation treats the third canonical species as distinct from dispositions. Hence, some sort of regimentation of the category of quality is needed.

By itself, the fact that affective qualities and affections are dispositions does not require the acceptance of the latter of the two possible of the genus, disposition, represented above. But there Is a reason to prefer the latter differentiation, a reason that stems from

~erentiations

5~Quality b' ts of perception The proper o ~ec the nature of the objects of percep .' . produce a kind of mo. to cl e, are disposmons . th e tion, according to Arts . tothem in this way 10 . . the tion in perceivers. He not 0 nlY charactenzes th th' d canonical spectes 10 . di . of e Ir De Anima , but in his scussion . tion He says: . . h a characterJ.Za • Categories he provtdes JUSt sue . alities because ailed affecuve qu h Similarlv, heat and cold are n~:r.c d' someway,butrathert ey '' have them have been auecte hm f the ones menuone · dare those that are called affective qualities because eac o nsation (Catg. 9b5). . . h respect to se Productive of an affection wtt . which are sensanons, d _a· thus pro uce Affective qualities and arrecnons h sensation is an occurrence .

a kind of motion, in perceivers. But su: a th t has the proper obj~ct . oth er than the subject a nsanon in a subject that 1s t: instance, causes a se d of honey, ror . . to pro of perception. The sweetness . 1£ B t disposmons .. uce in something other t h an th e honey th ttseb'• ctu with the di spos1non can 'th h th . the subiectWl motions in subjects ot er an e su d ~e motions m ;J di · . 0 f dspostbe differentiated from t h ose that pro uce . al species constst . . to pro uce the disposition. And t he fi rst two canontc · a disposinon Anda . £ instance, IS di 'cion. tions of such a sort. Sctence, or b' ct with the spos~ . the . · .the su ~e oduce boxmg . monons tn 10 motion, namely intellection, . . di posmon to pr being a natural boxer IS a s d nder . . subject with the disposmon. . thus all be su.bsume th u dis. al spectes cancan be divt . 'ded mto . ose 1he first three canontc · n and d this genus th disposino the genus dispositions. An . th biect with e . 'th the th subject Wl . s m e su ;J positions that cause monon b' ct other than e ·cai species, 10 · · a su ~ecies is the thir d canont those that cause monons . divided into di . . 1h l 0 f these spe t: rmer IS spostnon. e atter . while the ro . abilities, and al . . ali . d affecnons, .. d mcap I.e. affective qu ties an al capabiltnes an d as 1 have th '·rrue ofbemg · ose that are natural' I.· e• natur b' and dispos•·t·10ns• An • . d · ha tts · · ns m VI those that are acqwre ' t.e. ed from dispos•t•o ' . . ns 1,££ tiat dispos1t10 • ready said, habits are wneren ul displace than l ·on of genera diflic t tO exp OSI longer lasting and more unforrunate . us is a genus . . h has been an , 1h matn gen . d At this pomt, t ere all d 'dispositions. . e each of which ts ap Y that are entitled to be ~ 'deed . to twO spect~ di 'ded into twO s~. IS · divt tn · tshichVlitself has a speaes of dispositions; 1t f these speaes 0 called 'dispositions'; and o~e f dispositions w th the structure may . one of whtc . h ts · a 8•peaeso oes th the reservao·on at 1 of dispositions under lt. Wi

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

IIO

become overly rococo, I will try to mark these differences with the following labels: Dispositions, Dispositions, Dispositions and Dispositions. Rather than describing each of these species, I will present the following diagram that should make clear which name refers to which species. Quality I. Dispositions A. Dispositions- Dispositions that cause motions in the subject with the disposition 1. Dispositions-Dispositions that are acquired a. Habits-Dispositions that are long lasting and difficult to displace b. Dispositions-Dispositions that are easily displaced 2. Natural Capabilities and Incapabilities-Dispositions that are not acquired B. Affective qualities and affections- Dispositions that cause motions in a subject other than the subject with the disposition II. Shape This diagram already represents an improvement over the canonical interpretation. Where the canonical interpretation takes the four spe~ cies as basic and underived, the regimented interpretation has already located a considerable amount of interesting structure in the category. The differentiation of the genus, dispositions, though, is not complete: more structure can be gleaned from Aristode's discussion of affective qualities and affections. Furthermore, the structure might be inter~ preted in such a way that affective qualities and affections admits of a differentiation that is roughly symmetrical to the differentiation of dispositions. And once such an interpretation s accepted, the entire genus, dispositions, admits of a symmetrical differentiation. Aristode's name for the third species indicates that he thinks it is divided into two species. He calls the species, 'affective qualities and :urections'; so it is natural to suppose that there is a genus divided Into one species called affective qualities' and another called atfections: And if the regimentation of the category of quality so far proposed is correct, the genus under which affective qualities and affections fall is the genus dispositions to produce motions in subjects other than the

~d

III

5 ~ Quality

di .. N . hould be clear from the agram subject with the disposttton. ow, It s I I the genus dispositions to . the same eve as th above that such a genus IS at . th e as the subject with e b. t that IS e sam . d . h th" I tter genus is differenoate produce motions m a su ~ec IS a d· disposition. It sh o uld a1 so b e clear t, at al' d that the natural tspo. • . d' and natur an , d by the differentiae acquire . d difficult to displace an ,rr · d by 'long lasnng an . . sitions are d urerennate · a1 differenoaoon o f • . , if th re is to be a symmetric .. d easily displaced. So, e d h" h affective qualines an . .. h genus un er w IC • the genus, dtspostttons, t e . d "th features analogous to ac~ . c 11 h uld b differentiate WI . di 1 d' affecoons rau s o e di 1 • and 'easily sp ace · . , 'difficult to sp ace, .d A . tode does seem to proVl e quired: 'natural: 'long lasting, And, indeed, in the following passage, ns just such a differentiation.

, . · acbe in ones consntunon For if paleness and darknessl~~T~::tive Jqualities; for we are said cording to nature, they are cal h If. for instance, because of a to be qualified with respect to t h~m. h ,ppened to become dark or long sickness or scorching somet_ mg . ~ al condition and perhaps pale and did not easily revert t~ lt~~r~~:se would be called'( affec~ remained that way throughout tts e, ily lost and quickly revert . . , . . . But all those that eas , ... an d not '[affec~ tive J qualtnes all are d 'affections . ortgm . · al conclition are c e to thetr tive] qualities'(Catg. 9h 22 ~zg).

10

~rr . qualities are that arrective.rr. . d seems to say ali. In this passage, A nsto e . . e of the fact that anecnve qu differentiated from affections m virtu are long lasting and difficult , constitution · · by nature · other ties are in ones il or di placed. He seems, m to displace while affections are eas y s 'de a differentiation of the £ es to proVl .. words, to be using the same eatur J,rr. ntiate the genus, disposttto~s . sed to cunere b admit~ genus in quesoon as are u. 'th the disposition. It must e d . · a subtect w1 · a1. Un er that cause mooons m '.1 • not exacdy symmetric J,rr. tiaoons are. · the same ted that the two cuneren · a subject t h at IS . . se motions m . the genus, dispostttons to cau . . th e is one specieS correspond~ ds . . h th dispositton, er th rrespon as the subJeCt w1t e ra1 and another at co th . . · that are natu . d On the o ther hand , under . e ing to those dtspostttons to those dispositions that are ac~wr~ ·a subiect other than the sud~Ject . '.1 ding to those tspo· genus, disposittons to cause mooons m·es correspon . there IS . one speo with the disposition, il"ective' into the text. . terpolat ed '·am 10 As can be seen, I h. ave m "ch I will provide shortly.

. requtres . JUS . tificanon' wht tton

This interpola·

a

II3 THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

II2

sitions that either are natural or are acquired and difficult to displace and another species that corresponds to those dispositions that are acquired and easily displaced. Nonetheless, the similarity between the two differentiations is hard to deny.

SECTION II THE THIRD CANONICAL SPECIES! SOME DIFFICULTIES The symmetry that results from the proposed differentiation does make the category of quality interestingly systematic. And insofar ~s charity recommends attributing to Aristotle interestingly systemanc differentiations rather than haphazard ones, charity recommends the proposed interpretation. Nonetheless, a careful examination of the text reveals that there are some difficulties with this interpretation of the third canonical species. And as a result, the interpretation I am proposing is not straightforwardly supported by the text. The difficulties emerge from the fact that the interpretation I have proposed can only be gleaned from the above passage if one in~erp~­ lates the word 'affective' before the final occurrence of the word qualities: The original text actually reads as follows: those which arise from [causesJ which disappear easily and which soon revert to the original conditions, on the other hand are called 'affections' and not qualities ... Now, there are what I take to be compelling grounds for allowing the interpolation. Aristotle begins his discussion of affective qualities and affections at 9a28, several lines prior to the above passage. And there he says that affective qualities and affections are the third species of the genus quality. But affections could only be part of a species under the genus, quality, if affections are qualities. And so internal consistency demands allowing the interpolation. Nonetheless, some difficulties remain. Although allowing the interpretation avoids inconsistency, Aristotle's remarks after this passage are problematic. At 9b30-3, Aristotle seems to argue that affections are not qualities by appealing to one of the characteristic marks of qualities. According to Aristotle, things are

5 et1 Quality . . b h argues that things . . f ualines; ut, e • called such and such m vt~e o. q f h ving affections. He says. d h m virtue o a are not called sueh an sue . . of them [affech and such m virtue all d For we are not sai~ to be suewho blushes because of shame c ;.a tions ]. For neither IS the man rns ale because of fear calle . 'a blusher; nor is the man w~o tuh ~aid to have been affecte~·m' er d 'affections' and not 'qualittes Pale man,' but each o f them ts rat all . some way. Such t hmgs, then' are c e

ak "milar argument about east m · tle goes on. to · for instance, may be more After this passage, A nsto certain states of the soul. A man m p:un~ult be called irascible ( Cfratg. . cc .ons irritable for a while b ut wo uld. not as ha·sreexclusion of arrec~ , om 10a7-9). Aristotle's justificanon for tlhat the lack of'affecttve b~fore . suggests, however, . the genus, qualtty, . ot merely an oversi"ght on Ansto' ali . , . the previous passage ts n . t the interpolanon. qu ties m count agams . f the 0 de's behalf And this would seem t al "dence counts m favor o • · th tot ev1 . h · terpoDespite these difficulnes, de . dicated, not allowmg t rthem ore · Fu erm • interpolation. As I h ave alrea y. m tl contradiction. to Artsto e a . . . lation forces attnbutmg . dude affecnons from the genus, d So 11 rv~ng to ex · ly .nawe tl if one reads Aristo e as t. ' "d red to be senous tl ,• st be consi e fr Ansto es ar quality, his arguments m~ lation that arises om th need for the evidence against theakmterport:u"nly too weak to defeat "d e an easy . c · 1 e -ce . proVl es. far as gumentation ts r:ur y w . d interpretatton . all h regtmente And so, mso consistency. Fm y, t e. fAn"stotle's argument. . tan"on alth diffi lnes o d mterpre ' cu. orts the regimente .derably the diagnosis of e y to illuminate consi allowing the interpolanon su~p . provides a wa 1 lowing the interpo ano~ . th" portion of the text. ualities by ong m ts · are not q tl · issues Aristo .e iS t~ea .fy the daim that affecoo~s .rtUe of states that all d such and such tn Vltl illustrates this Aristotle tnes to JUStl not c e d A ·sto e . n f hame is not saying that t h mgs are . al ndition. An 00·cnn co b use o s th oho blushes eca who turns easily revert to e . th person w · a person claim by saymg . at. a e of his blushing. Nor lS les do not provide called a blusher m virtual But these examp ' face is not a c man.the state of the persons t be called a pale because o f rear a p eth ose at f h e may no a good reason to supP blushes because o s am called red-faced, even quality. A person who uld nonetheless be the state of a blusher; but such a person w~ttle while. Hence, because if he is only red-faced for a (Catg. 9b30-3).

a

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

114

momentary blusher's face passes the test for being a quality, it should be considered a quality. From the perspective of the regimented interpretation, an even fuller diagnosis of the argument can be made. Because the momentary redness of a blusher's face is a disposition to produce sensations in perceivers, it is a quality that falls under the same species as the redness of an apple. Not only are both rednesses qualities but both are dispositions that produce motions in subjects other than the subject with the disposition. But, because it quickly reverts to its original condition, the momentary redness of a blusher's face, unlike the redness of an apple, is an affection, not an affective quality. Being a blusher, on the other hand, is a disposition to produce motions, namely reddenings of the face, in the subject with the disposition. If such a disposition is natural, it is in the second canonical species; and if acquired, it is in the first canonical species. So the fact that a person would not be called a blusher in virtue of the redness of his face would only go to show that such a redness is not a quality in one of the first two canonical species. And indeed, it is not.

SECTION III THE THREE CANONICAL SPECIES RECONFIGURED The examination of the first three canonical species has thus revealed order where there first appeared chaos. The first two canonical species have the sort of differentiation proposed in section I. And with only some difficulty textually, they can best be understood as dispositions to produce motions in subjects other than the subject with the disposition and as divided into such qualities that are either: (1) acquired and easily displaced; or (2) natural or acquired and difficult to displace. The first species consists of affections; and the second, affective qualities. The following diagram. captures the differentiation of the first three canonical species.

us

5~ Quality

Quality I. Dispositions . .. h cause motions in the subA. Dispositions-Dtsposltlons t at .. . ct with the disposltlon Je . .. h acquired 1 Dispositions-DispositlOnS t at are 1 . d long astmg an . a Habits-Disposmons .. h t at are . difficult to displace . dis laced . . . -Dispositions that are easily P . . b. D1spos1t1ons bT . -Dispos1t1ons 2. Natural Capabilities and Incap~ I~tles that are not acqUire . . b'ect • •. . . . s that cause motions m a su .~. B. Dlsposinons-DISposltlon h b' t with the Disposition other than t e su ~ec . 1 . . · s that are either ong 1. Affective Qualities-DlspositlO~ d lasting or not-acqUire "1 displaced . ·· that are easi Y rc · Dlsposltlons 2. tuiecuonsII. Shape · diagram is far e represented b YthlS It should be clear that the strU~tur th he structure involved in the · and symmetncal an t ·· · of more systemanc f the cnnosms . I n also answer one o canonical interpretanon~ t ca th Ackrill says: Aristotle raised by Ackrill. Recall at b d as a class affi . ualities e create Whv1 for example, should ecuve ~. s~u b· d disposition · ' quite distinct from ha Its an . th ·cal interpre£ gamst e canoru Although this question has some .orce a wer it. According to the . d . rpretanon can ans .. proration, the regtmente mte . al'n'es are dispostnons to .. 1 · affecnve qu regimented interpretaoon, th biect with the di spostnon . . ther than e su J • sm 0 duce motions in sub~ects . . · ns to produce monon while habits and dispositions are dispostno ding to the regimented . .. Hence, accor . . the subject with the dispost~O~· f th genus, disposittons, contams ~,a: noanon o . e affective qualines · as a class interpretation, t h e wnere . ds for treanng all the J. ustificanon one nee . .. s ard an. d dispostnon · b quite distinct from ha tts an . can also go some way tow The regimented interpretano~ Ackrill claims that Aristotle does A krill's wornes. uali from any sort swering ano ther of c . . th category of q ty not deduce the list of spe~e~ m f ~e genus, dispositions, though, .c: of principle. The differennanon o . under it. The species are denv . f the speoes be seen as a deducnon A

°

11

J. L.Ackrill, Op Cit, P· 104·

----~------------------------------~· THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

II6

from natural divisions that flow from the nature of the genus. And since three of the canonical species fall under dispositions, at least three of the species in the category of quality have in some sense been deduced. So Ackrill's worry has been partly answered. It must be admitted, however, that the deduction so far provided is not a complete answer to Ackrill's worry. The genus dispositions itself as well as the species, shape, have yet to be deduced from any principle. As a result, there still seems to be an arbitrary division of quality into the species shape and dispositions. To provide a complete response to Ackrill, therefore, we must turn to a deduction of dispositions and shape from the genus quality itself

SECTION IV DISPOSITIONS AND SHAPE The regimentation of the category of quality I have so far proposed is, I think, well supported by Aristotle's discussion in the Categories. The examples of items falling under the first three canonical species are all understood by Aristotle as dispositions. And once the subsumption of the first three canonical species under dispositions is accepted, a rather symmetrical differentiation of the genus that follows the contours of Aristotle's own differentiations can be provided. Unfortunately, it is not possible to glean from Aristotle's discussion in the Categories the constitutive differentiae of dispositions and shape. And in some sense this differentiation is the most troubling one. What, after all, could the justification be for dividing quality into shape and dispositions? And not only is the answer to this question not to be found in the Catego· ries, it is also not obviously found anywhere else in Aristotle's texts. Because of the difficulties in finding textual evidence for a division of quality into shape and dispositions, at this point my reading of Aristotle becomes much more speculative. I do not think that it is re· quired by Aristotle's texts. Nonetheless, I do think that there is a way to understand quality that can make sense of a division of quality into shape and dispositions. And so the speculation can at the very least be seen as a fruitful one: if accepted, it would provide the resources for a complete and systematic deduction of the species in the category of quality.

5 ~ Quality

II7

b .

ring Ar. . . can be completed y mterpr~ . d r perhaps a pnnclple of The differentiation of quail~ . . . h uahty lS an or er, o li 'tl istotle as thmking t at a q Al h h Aristotle does not exp Cl .Y order, of that which has pa:rs· fit. ~ug £dispositions (oux8Ecru;) m . h s de mt1on o · define quality in th lS way, I c ch an interpretation. the Metaphysics can provi'de some support ror su In Metaphysics V, Aristotle says: . h as to place or d f what has parts, eit er Disposition means the or .er (Meta.1022bl-2). as to potency or as to species ~,a: . that divide d three wrrerentiae This definition consists of a genushan h' h has parts. And the three . d oft atw IC the genus. The genus Is-or er otency, and (3) as to spe· differentiae are ( 1) as to place, ~fc~sh:: ~arts, thus being divi~ed des. The genus, order of thatdw h' h order can order somethmg. . t 0 war w IC d anplace toward a potency and in virtue of those t h mgs ' An order can order someth'mg towar a

i:

toward a species. cies under the genus order of Aristotle does not name the thr~e spe ncertainty as to what ~e u congem·a1 to th e thesis that which has parts. A nd there. IS some tation third kind of order is. But the mterpre . found in Aquinas' com· fi the interpretation of this paper stems rom h . Aquinas, picking up on Aristo· d th · t1es' Metap 'JStCS. "J:. c; an ef mentaries on Ansto . b tween the word e..,t 0 f th connection e h th' d kind o de's own statement e b2-3) takes t e Ir 1022 . . . , uta ,;:, ·eEOtc; (Meta. ' f tity•12 But d1 • . the category 0 quan word ,c:hsposlt1on, . of the differentiae mtension of this . kind 0 f order an . order to consist

think it is possible to broade~ thefe~ th material substances and v~bnl. . to be th e differennae . made plausi It . ho anounderstandi ng IS d de consider 13 S 0 beets . al uc . fanor eran ous mathematic ~ •. . between the nooon as if one allows a certain vacillanon Because differentiae can be ~een a the notion of a principle of.oalrderb. ranees in their respective kinds, 1 aten su s principles that P ace m h . trans. John P. n Aristotles Metap 'Ystes, 12 Thomas Aquinas, CommentarBy o ks 1961), P· 373. . 0 b Ox oo ' · h the mter· Rowan, (Notre Dame: um . is I think, consist~t Wlltl (Oxford: . I am proposmg ' ' M h']stcs vo . ' 13 The interpretanon R ...... ns, Aristotles etap . h pect to a spe· d · W.D oss, ··-· ' b pretation foun m · · R speculates that Y•0 rderw1t . fres the species in a 24) 335. oss b dinanon o rdination and su or ch a coordination, the Clarendon, 19 , P· cies' Aristotle means the ~~ that which guarantees su · genus. Because a dif£erenna 1suld be a dilferenna. . . of sueh an order wo prmc1ple

°

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

II8

5

II9

~ Quality

differentiae can be seen as a principle that orders material substances toward their respective species.

b s and geometrical . that num er h meption of •peec • mpports. the d view f ntitie.. Among t h e quantities, d

This way of understanding order towards a species finds support in Aristotle's discussion of quality in the Metaphysics. At 1020bl-3, Aristotle says:

obj"'" ue the fundament.! kin '

One meaning of quality, then, is the differentia of substances, while another concerns immovable mathematical objects as in the case of numbers which are said to be of a certain quality (Meta. 1020b2-3).

In this passage, Aristotle divides quality into the differentiae ofsubstances and features of mathematical objects, a division that mirrors the division I have made within orders toward species. And interestingly, just after this passage, Aristotle illustrates what he means by the quality of mathematical objects in such a way that the origin of shape begins to emerge. At 1020b3-7, Aristotle says: For example, the numbers which are composite and not one-dimensional, of which the plane and solid are imitation (these are numbers which have two and three factors, respectively), and in general, that which belongs to the substance of a quantity (Meta. l020b4-7). Aristotle here illustrates the qualities of quantities with the examples of plane and solid numbers. A plane number is a number with two factors; a solid number, a number with three. This example is illuminating, for in it Aristotle applies to numbers a description that has a geometrical origin. He describes a number with two factors as a plane number. This dearly reflects the fact that to the extent that mathematician, in AriotorJe', time had
theo'Y of &
Now, if n=be,, have difii,rentia< with a geometrictl origin, and g«>metncai obje"' have 8eometrictf dilrerentiae, then, .,,uming that and l!<=etricaJ objec., are the fUndamental kind. of quantities, will be the fundamental quantitative differentne. And, Anuotk, !i.t of quantitiea in the with the

~=ben

g~ometncal ~ere~tia.e

Categw~.,,

~~;'body, numbet, time, pi~ an f

according to Aristotle, are: lme, su .a 'surface and body are kinds ~ •peech (Catg. 4b23-4). Of courne, hne, definics, place~ geometrical objects. Place is not:~' as tains (Phys. 212a20-21). An

m immobile bounda
K

::::;..e that it i• plawibl~

to

;::'P.J

a boundary has enough afli.mtyb takio~ to geometrical differentiaThe. ~ pose that its differentiae · will e . n . a number of mono · n . . at xs, finallv as defined in the Physics, timedis number must be consi~erthed ,, f b . an so .. m e it is defined in terms o num. er' H ce the list of quannoes . al all · to nme. . enthat ' numbers and geometnc to be definition Y pnor d th Categories supports t h e I.nterpretanon . . And since, as I h ave note ' .e d obiects are the fun amenta1 quanones. di g to Aristotle h ave a geometn· fu daJ b uld accor thnt Aristotle t hought the n differentiae of num ers wo cal origin it is plausible to suppose a metrical in nature. b' ~ ' . f uantities are geo etrical o mental differentiae o q he differentiae of geom d line and So what, then, wo~d be t or instance, between a curve and a triShapes. What is the differencLe,ik£ wise with a square differen. 1' ~ 1h · shapes. e f ualines mto a straight me. etr . d , own division o q . a division angular surface. So Aristo es . f mathematical obJea:s, vides tiae of substances and differentiae d o ith respect to a species, pro d nder or er w that I have subsume u h d pecies suff h 'es s ape. d towar s of orders, orders the origin o t e speci this discussion of or For the moment, let tl h re are two other kinds . rns out, are di A .sto e, t e h. h as It tu fice. Accor 1 ng to nd ard a potency, w IC 'A der toward a d ers tow · s n or toward a P ace an or ders toward a speoe . dered toward d easier to un erstand than . or if Socrates, parts areh'orb k and legs .. For mstance, that IS ac d place is a posltlon. . I ted in such a way th other han ' . h' h he IS oca m n e the room m w IC h . lving in the roo · 0 f orion (Meta. d then e IS ' • ciple o m are on the . . grounf ·'ts senses a potency is a pnnf disposi'n'on for some because m one o I otency is a sort o h. that falls m l019a15), an order as .to al r words, the sort o~ mglf this is cor· kind of motion. It is, m ~ ~ the category of q f ty.di.· position. We dspeCiesm . no a s . . b'onity in the nono fini . above differs the first regimente other am Io, . the de non . rect, there IS yet an that llisposition m ecies in the category would have to supposetha . the name of the sp . · ' t lS from the Clispostnon

~ects.

~u~ace

er~

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

f

.

120

o quality. But this is not over! troubli A d . f h fi Y . ng. n xf the ambiguity is accepted the oricri · In · the category of quality' ha b o·nc o dt e . rst re01me o· n t ed specxes s een roun • It IS one of th . d of that which h e species un er the genus, order as parts. 14 We are close to seeing how "d "fi . principles allows forth ..J,a- an x_ e~tl canon of quality with ordering . e wrrerentxanon of th al" th ts one final distinctio th d e genus qu tty. But, ere n at nee s to be mad f h . d ..J,ae. woo t e spectes un er order of that which h as parts, wrrer from th h · d · al The order toward a pi . e t tr In a croci respect. . . ace xs not ground d b "al e Y an mtnnsic feature of a substance alone but th ra er essentt Iy includ th . I t h e place toward wh. h h b es ano er Item, name y tc t e su stance is d d Th h b or ere · e ot er orders, on the other hand d 'oseemto egr ddb . . substances. Although d oun e Y mtrmsic features of or ers toward pot t"al" · d some sense relational . h en 1 ltles an species are in nonons-t e specifi . f th ki involved mentions so hi I catton o e "nd of order met ng e se-the o d d d . r ers are groun e by intrinsic features of the s b u stance Itself A s b . d d a species in virtue of it h . .• u stance ts or ere toward c s avmg certam intr. . c reatures specified by th ..J,a. mstc reatures, namely those ·a~· . e wrrerenna· and "t. tt tty In virtue of its h . . '. I ts ord ered toward a poten. avmg certam mtrins. £ t10ns. And it is plausibl xc eatures, namely disposir e enough to supp h h ose t at s ape is an intrinsic reature of a substance S . • o It seems that on fi al ..J,agenus, order of that which h . e . n wrrerentiation of the entiation made the £ 11 . a~~arts, ts possxble. And with this differ' o owmg terarchy can be given.

v

I. Order of . that . which has parts A· lntnns1c Order i. with respect to potentiality dis . . ii. wi~ respect to species posmon for a kind of motion

~· ~erent~ae of substances . differentiae of mathematical b. ----~a=r.::it::hmetic properties d . o ~ects-shapes and d enved &om geometryl5 14 1h. IS un erstanding of the fi derstanding, op cit. p373. rst two species follows exactly Aquinas' un· 15 Someone might ob"~ect that this unde wh A. . at rlStotle says at 10a16-20· • 'R , .~standing of shape conflicts with seem to uense' 'rough' and •smooth' might ai F signify . quality, but such ·thingare,diffi o-ven. or It would seem that each s er om the classification so far refspect to one another: From this Preveals a certain position of the parts with o parts with respect to one another assage, falls one .might th1"nk that the position outside of the category of quality

fi.

5 PI! Quality

121

B. Extrinsic Order-position

It is now possible to see how an identification of quality with ordering principles allows for a complete differentiation of the genus quality. Suppose that qualities are intrinsic orders (or principles of order). Such orders will divide into three kinds: dispositions for motions, 16 differentiae of material substances, and shape. Now, at Metaphysics1020bl5, Aristotle says that differentiae of substances are qualities; and so it is a virtue of this division that they are contained in it. But, because differentiae are essential features of material substances, they do not fall in the category of quality and so would not appear in a list of species in the category of quality. The other two species, on the other hand, would be in the category of quality. And it should be clear by now that they are the first two regimented species in the category of quality. By identifying qualities with orders (or principles of order), it is thus possible to provide a complete deduction of the species in the category of quality. The first two species are deduced from the genus, order of that which has parts. And the species under the genus, dispositions, are deduced in the way illustrated in the previous section. And not only can a complete differentiation be given but the differentiation has two additional merits. First, the differentiation of each genus in question flows from the nature of that genus itsel£ The division between dispositions and shape flows from the nature of orders: they can be with respect to a potency or with respect to a species. And ~e P~~ary division of dispositions flows from a categorial fact a~out ~sposmo~s: they can cause motions either in objects with the disposmo_n ca~s~ng the motion or in objects other than the object with the ~sposm~n causing the motion. Second, and equally as important, the differen~ae involved in the divisions satisfy the requirement that they fall the genus being divided. Being directed toward a potency or directed

~utstde

and so that shape cannot be the order of the parts of som~ing. It is ~ror­ tant to note however, that Aristotle here uses the word 9EOW and not E~tc;. 'order: which is the word Aristotle uses in his definition of ou19E
• 123

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

122

toward a species are not qualities. Nor is the location of a motion being caused by a disposition a quality. 17 Now, although I have been speaking of identifying quality as such with principle of order, it should be obvious enough by now that I think quality should in fact be identified with form as such. For, as I have already argued, in its fundamental sense, form is a principle of order. So, the conceptual clarification of the nature of form and the regimenting of the category of quality have coalesced so as to support the thesis that at least part of Aristotle's categorial scheme bears such an intimate tie to hylomorphism that the former can be derived from the latter. I shall end this chapter with the following thought. I have noted Kant's criticisms of Aristotle's highest kinds. Of course, one can direct 17 It is noteworthy that my derivation of the species under the genus, quality. is not the first such attempt in the history of Aristotelian scholarship. T~0 other attempts, both of which can be found in Aquinas, Treatise on the Vtrtues, trans. John A. Oesterle, (Notre Dame: University of Notre Dame Press, 1984.), pp. 4-5, are worth noting. Simplicius provides the following deriva· tion. "Some qualities are natural-those that are in their subject by nature and always; others come from without-those that are caused extrinsically and can be lost. Now the latter are habits and dispositions, and they differ insofar as they can be lost easily or with difficulty. Regarding the natural qualities, some belong to a thing insofar as it is in potentiality to something, and thus we have the second species of quality. Others belong to a thing insofar as it is in act, and these are either deep-rooted or only on the surface. If deep-rooted, we have the third species of quality. If on the surface, we have the fourth species of quality, such as figure, and form, which is the shape of the living being:' Aquinas, afrer criticizing Simplicius' derivation, provides the following derivation. "Now quality, properly speaking, implies some mode of a substance ... Now the mode or determination of the subject by way of ac· cidental being can be taken in relation to the very nature of the subject, or according to the action and passion which follow upon its natural principles, which are matter and form, or according to quantity. If we take the mode or determination of the subject in regard of quantity. we have the fourth species of quality ... But in the second and third species of quality we are concerned with the mode or determination of the subject in regard to action and pas· sion. Hence in both species we take into account whether something is done easily or with difficulty, whether it is transitory or lasting ••• The mode or determination of the subject in view of the nature of the thing, however, belongs to the first species of quality, which is habit and disposition.n

5 et; Quality

. d in the present case, one 0 f the categones. An . such a criticism at any .d uality a highest kin d,)· We have, . h k hy we should consi er q this question. For, trug t as , w . th mpt to answer ki d however, made progress m . e a~e answer: quality is a h~ghest ~ we can now provide somethmg_o an f hylomorphic ennty, _name y . . .d · al to a basic type 0 th esnon but because It IS I ennc pletely answer e qu h uld form. Of course, this does not com can now ask why form s o rather pushes it back one step - for, o~emetaphysical entity. In ch~pter be considered one of the basic types o however, we can at least gtv~ a 7, I address this question. F~r now, t of Aristotle's scheme. Grali~n~g . "fication · for this.aspec 1 ov: the category of qu. ty al IS provisional JUSU f h" h 1 morphic onto o~n' al h the mtern the cogency o IS y o hi hest kind but so as . tl , disnot only justifiably regarded as~ g cion is latent in Ansto es structure that, with a little regtmenta '

cussion of it.

CHAPTBR6 QUANTITY

~hapter,

n the last I argued that the category of quality admits of a systemattc derivation from the nature of form. In this chapter I . show that the category of quantity admits of a systematic deriva, from matter, though as shall become apparent, form is implicated ~ the derivation in a way that matter is not implicated in the deriva,

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tton of quality. Interpreting Aristotle on the nature of quantity is complicated by the fact that he provides two different treatments of that category: one in Categories V and one in Metaphysics V 7. Interestingly (and perhaps not surprisingly) the treatments differ in important respects. In the Categories, Aristotle provides two different differentiations of q?"'tity. Acronling to the 6rst, quantity dividos into ronrinuous and discrete quantity; the former then divides into line, surface, body and time, and the latter into number and speech. According to the second, quantity divides into quantities whose parts have a relative position with respect to one another and quantities whose partS do not (Catg. 4b20,2). Although the differences between these twO differentiations are interesting, for the purposes of this paper I shall focus on the first. For, in the first instance, the differentiations appear to be compatible; and second, by presenting the division into continuous and discrete quantities before the other division, Aristotle, it would seem, gives pri, ority to the former. In this chapter, therefore, not only will I assume that the two differentiations do not need philosophical correction to make them compatible but I will also follow Aristotle's lead and take the division into continuous and discrete quantities to be the more fundamental.

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A much more trenchant difficulty emerges, however, when one looks at the differentiation of quantity Aristotle provides in the Metaphysics. There, Aristotle divides quantity primarily into numerable quantities, which are pluralities, and measurable quantities, which are magnitudes (Meta. 1020a9). Hence, unlike the Categories differentiation in which Aristotle first divides quantity with the differentiae continuous' and ruscreti, in the Metaphysics Aristotle first divides quantity with the differentiae 'measurable' and 'numerable: Furthermore, the divisive differentiae of measurable and numerable quantities in the Metaphysics include the notion of a limit. For instance, a body, according to Aristotle, is a limited magnitude in three dimensions; and a number is a limited plurality (Meta.l020a14). In the Categories, however, no corresponding concept occurs. The Metaphysics differentiation thus appears to be richer and subtler than the one in the Categories. For what is to come, it will be useful to present both the differentiations of quantity in their full form. The differentiation in the Categories is as follows. quantity continuous line surface body time place discrete number speech And in the Metaphysics, it is as follows. quantity measurable - magnitude (~y£9oc;) limited (1tE7tEpaa~vov) in one dimension-line in two dimensions-surface in three dimensions-body unlimited (a7ttpav'tov)- ~ numerable - plurality limited (1tE7tEpaaJ.Ltvov)-number unlimited (a7ttpav'tov )-~

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J'tr . ·ons of quantity in the CatThe differences between the Qliierennan . d 1 _ . f e be explamed by a eve op egories and the Metaphystcs can o cours . tl b h wrote the h. h Ansto e, ecause e di mental hypothesis accor ng to w IC h . l h d available to . . d h Metap ystcs ater, a Categories early m his career an t e h . al · w· ries a difh · al d metap ysic mq ' him, as a result of his later P ysic an h h te the Metaphys. f cepts w en ewro ferent and more extensive set o con bl . d I am not . ik me as reasona e, an 1 ics. Such a historical specu anon str es I dd ss the following a thretwo differentia. It. . I n t h'IS ch apter' however, averse to acceptmg . . h lanon between eb tween the two philosophical question as to t e re . . conceptual connecnons e the differences tions: are there interestmg . 1 . . a systemanc way differentiations that wo uld exp am m . . the discrepancies ..r th £ llowmg answer· between them? And I orrer e 0 . . the Categories and his between Aristotle's treatment of quannty ml . d by his identifying · be expame treatment of it in the Metap hystcs c~th . as such. According h · WI extension quantity as such in the Metap ystcs all . . s m· a primary sense quannne . , . hall e to Anstotles later view, Is argu ' th b . with them deter. al forms en, nng b arise from extension. Su stann ' ·at form belongs to prime . d' . that when a substann . . n ffilnate Imensions so d di t quantity anse, I.e., o scree d . an d li and on the other han matter both continuous quannty the one hand there are solids, surfaces an fnes, te bodies scattered th .stence o separa . tl f e eX1 • f antity that Ansto e there is number because o the spec1es o qu . all . In space. In this way, one can see l nfolding systemanc Y . more or ess u articulates in the Categortes as 1 from the natures of form and rnatter• h t to which . . the issue as to t e exten . . 1 It may at this point be worth mentionm~ce ts of actuality and pote~tiallty form and matter and the closely related co P is not mentioned m the are present in the Organon. Although . A matter lytics 94a20-95a10 th at Aristotle . ev1'dence at Postertor fna lanarion by th e nme · he wrote Organon, there 1s had developed his four-cause scheme o eb~ sly includes both form and the Posterior Analytics. Such a scheme o VlOU to which Aristodes• use 0 ffofour . d the extent urmatter. Scholars have questione 'd that he had a fully deveIoped th ( is ev1 ence · terpret causes in the Posterior A nal'Y acs the Oraanon. Some m . e. . hen he wrote '6 I ·10terpolation, cause scheme of explanation w h p t•rior Analytics as a ater heme . . ofthe fiour causes in t e. fa-ory os ~ account of t he fo ur-cause sc Ross discussiOn D 'd . d unsatiS ... · cf. av1 some, as a rudiment~ry ~ sical-metaphysical treatises. athan Bames, that Aristotle uses m hiS phy Co LTD 1947), pp.51-2; Jon. . Press Aristotle (London: Methue~ & A ~lytics (Oxford: Oxford Un•=ty and tr. and ed., Aristotle: Poster~or ~ The distinction between 1975), p.215, Graham, 0P· cat., P· 57·

129 THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

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SECTION I SOME PRELIMINARIES In order to discuss adequately the relationship between the Metaphysics and Categories differentiations, some preliminary comments about Aristotle's treatment of quantity in the Categories are needed. One important aspect of the Categories differentiation concerns the fact that time and place need not be considered basic quantities but can instead be understood in terms of other quantities, namely number and surface respectively. In the Physics, Aristotle defines time as the number of motion with respect to the before and after2 (Phys. 219b2). Hence, time is at least conceptually posterior to number-it is the number of some definite thing, namely motion. Hence, an account of Aristo· tle's conception of number in general should account for the nature of time. Despite the fact that time's definitional posteriority to number allows one to focus attention on number itself, one complication does at this point emerge. In the Categories, time and number occur in distinct non-subordinate genera. Time, according to Aristotle, is continuous, but number is discrete-so the definition from the Physics, which would make time a kind of number and hence a discrete quantity; does not seem to fit with the Categories differentiation. A remedy for this difficulty exists, however, that uses distinctions Aristotle makes in his Metaphysics discussion of quantity. According to Aristotle, time is continuous because motion is; and motion is con· tinuous because the underlying continuum in which it occurs is. potentiality is clearly in the Organon though it seems restricted to contexts in which Aristotle discusses necessity and contingency; C£, for example, De Intepretatione ( 19a30-19b4, 22b30-23a25) and Prior Analytics (25a37). 2 Although ri Vll
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d . for these too l'k otion an ume, f h others are said to be qu~tities I e ; are continuous in ~i~':' o t e are said to be quantities tn a wathyan attributes are divts!ble. Byh · h . ese are fact that the subjects o f w h IC b' t but the interva1 throug 'subject' here I mean not the movtng :oi~~S- 31). which the obiect has moved (Meta. . Ul'ty Although

J • .th respect to ltS connn · . un· Hence, time has a dual aspect Wi . . ally discrete, because itS d o is intnnstc . . Hence, even it is a kind of numb er an s . al hares in connnutty· . the · connnu · ous ' it so. s m . iS derlying subject -subordinate aenera o though time and numb er apPear m non f a kind of number· Put an· th b thought o as ber but as e till Categories, time can s e . much as a num th uz· other wav, one can t h i'nk 0 f ome not. so This in turn reduces e P. ) ~' . ely monon. th mber-senes numbering of somethmg, nam discrete ( e nu ·• 0 · . by nature zlement as to how someth mg . _ after all continuous quan . s can characterize someth.mg continuous asures (and the enumeraoon · discrete me ties can be measured usmg _,_ place . f 0. e maA.es thereof) plus fractions. ~ 'thi ·nstance 1, 1_ his definition , fi .. fplace,~e ·rv. m s1 fu L-ental quann.,, . . fplace Aristotles de muon th defimoon o h more naaxu f . e however, e 'th only a derivative upon anot er · · n 0 tim • the connecnon. . But wi surface. Unlike the d efirutlo ly apparent ge. does not make immediate cion does emer · onless k ch a connec .mary mo0 that place is the pn this definition, little interpretive wo~ ' su In the Physics, Anstotle says_ s (Phvs. 212a20). In b t rather with hi h contatn .J d f rface u boundary of th at ';' c . lace with a kin o su 'bl understood as Aristotle does not identify P boundaries are plausl ~ be identified a kind of boundary; but sue~ f wine, for instance, . 1be surfac· f portion o . the wine. surfaces. The place o a b tcle that contams ntinuous. 1he with the inner surface of the fo rse only be roughlydcothe boundaries 'ght o cou . · An es involved in a place rm m I am sitong in· d ceiling of the . s the roo all floor an place of my computerthl rf:aces of the w uls,d sl·st in surfaces. . . uldbe esu . con _c. es m this case wo . boundaries wo ,4: ulty that sunac · • room N onetheless, the mner J run 1.nto the ,Cllluc rface fo r 1n • . · o.oes · ner su ' This sort of idennficauon 1he wine bottles i~ b ttle. Aristotle, . 1 tionless. 'th the wme o cul He are not obvtous Y mo ·t moves wi this difli tf· 1 · nless ,_.J stance, is not mono di -. ctions neeacu to remove tially and (2) th'lngs however, provides the (so)~L: .. gs that move essen ve accidentallY he een 1 uuu thi that mo And among ngs distinguishes b etw that move accidentallY·

°

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distinguishes between (a) those that can move in themselves, things like the parts of a body and a nail in a ship and (b) those that cannot move in themselves but do so always as attributes, things like whiteness and knowledge (Phys. 211a19~23). Now, a surface is in the category of quantity and so, as an attribute, falls into class 2b. In other words, qua what it is, that is qua attribute, a surface is motionless - insofar as it moves, it does so only accidentally, that is only in relation to the sub~ stance it is present in. Hence, in the sense that place is motionless, so too is a surface; and so place can be understood as a kind of surface. Because place and time are derivative quantities, focus can be di~ rected at the other more fundamental species in the category. There is, however, one final oddity in the Categories list of quantities. For, removing place and time does leave species, namely body, surface, line and number, that seem to fall naturally enough into the category; but it also leaves a species that does not so obviously belong, namely A.Oyo~ (speech). It is not clear why Aristotle considers A.Oyo~ a quantity in the Categories, and interestingly he omits it from his discussion in the Metaphysics. Aristotle explicitly says in the Categories that A.oyo~ is sp~ken speech (Catg. 4b32). So understood, A.Oyo~ is something like a s~nes of sounds, which, as a result of conventions, is semantically sig~ ruficant (De Int.16al~20). As such, however, A.oyoc; consists in proper obje~s of sense, which belong in the third species in the category of quality: affective qualities and affections. And so it is difficult to see how i~ can be a b~ic spe?es in the category of quantity. In h~t of th.e difficulties concerning the placement of A.Oyoc; in the categ~n~s, I will leave it as something of a puzzle and not try to in~ ~lude It In the derivation of quantity. Hence, I will focus on the species: ody, s~rf~e, line and number, and in particular on the way in which the dert~tion of ~ese species can be informed by the differentiation of quantity that Anstotle gives in the Metaphysics.

SECTION II THE CONNECTION With these initial comm ab th . . . ents out e Categories differentiation m Ia P ce, It 1s now possible t 0 tu b th th Meta.,h · dC m to 0 e connection between the r ystcs an ategories differentiations and the way in which the

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. bl 0 to approach these Issues lS species in quantity are denva e. ne way . 1 ,,r · · In . . . f th Metaphystes Qlllerentiation. 0 by noticing an mtrigwng feature de l al' differentiated by 'tude an pur Ity are the Metap hysics, b oth magni . · limited plurality; ..~,.r . 'li . d' A mber for mstance IS a the Qlllerenna, rmte • nu . d GI'ven the gener~ c r ''t d magnitu es. . · · and a privative and body, line and surrace are Iml e ..l!
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SECTION III A DERIVATION With a general picture of the category of quantity in place as well as substantive accounts of form and matter, it is possible to tum to tum ~0 a more precise articulation of the connection between the Metaphystcs and Categories differentiations of quantity. One initial set of conceptual connections that serves to link the differentiations are those between measurability and continuity on the one hand and numerability _and discreteness on the other. Aristotle explicitly notes these connecnons in his discussion of quantity in the Metaphysics: 'A quantity is c~ed a 'plurality' if it is divisible potentially into parts that are not c~ntmu­ ous and a 'magnitude' if it is divisible potentially into parts which are continuous' (Meta.l020a10-2). Aristotle does not explain why ~e~e connections hold; but given certain every day conceptions of what It IS to measure and count, the connections are plausible enough. When we measure, we usually measure some continuous whole and what we use to measure is also usually continuous. For instance, were we to measure a table, which is something continuous, we would place some continuous unit of measurement, for instance a meter stick, next to the table so that one end of the table is square against one end of the meter stick, and we would mark off where the other end of the table lined up against the meter stick. Of course, one might measure discrete entities, for instance the combined lengths of two cars, but to do so one would measure the cars independently and add their lengths. Such an account of measuring is, of course, focused on spatial measurements. And indeed, one might object that non-spatial measurements need not be of continuous entities. The weight of a pile of sand, for instance, can be measured by a scale even though the pile of sand is not a genuine continuous unity. For this reason, it is best to interpret Aristotle as dividing quantity with spatiality primarily in mind. Aristotle's views about numbers likewise reflect some fairly quotidian facts about human practices, though, his account of numbers, as shortly, is in some tension with other aspects of will become apparent 3 his metaphysics. His linking of numbers with discreteness reflects the 3 C.f. Julia Annas, Aristotle$ Metaphysics: Books M and N (Oxford: Clarendon Press 1976), for a helpful discussion of Aristotle's treatment of numbers.

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all directed at discrete

. Y · · under f t that unlike measunng, counring IS gener al discrete ennnes . af ac , ollect sever · ena o entities. When we count, we c ally bring their own ~nt al

C single count noun. ount nouns gener one criterion of diverst."ty IS gener f lu-identity and diversity; and becaalluse . olves the subsumptton ~ a P · gener y mv ly discreteness, counnng . gle count noun. So, for mstance, d 1. . nder a sm . "d all boun co rality of discrete entmes u. ated but indivt u y two we might collect two spanally separ un 'book' and say: there are d the count no th do suplections of paper un er books on the table. ks b ut numbers are sparse,b ey umber thinks num. ers1092bl9n . tl , mar a o AlthoughAnsto esre di towhichhe port the interpretation accor ng He says at Metaphystcs th" a. for . l count noun. al of some ml>' entities under a smg e it may be, is ways . , Aristotle here 21: 1\nd a number, whateve; rts of earth, or of umts. F or other. example, of parts of fire, or o pfasomething. that is of somlike 'animal' or b nouns e e always 0 says that num ers ar , ot ordinary count . , B t this is due to . l f ch Fs are n rth' d'umt. u f Hts examp es o su f fi , 'part of ea , an M hysics ratios o 'book' but rather 'part 0 _re, this point in the etap the fact that he is discussmfgfiat to two parts of earthh. . V. 6 Aristotle . h rts o re , . M tap 'JSICS , elements like t ree pa s of'one m e l016bl7-23, he In his discussion of the sense cion of number. At sheds further light on his concep th first measure says: . . 1 f some number. F~r the first measure . b prmc1p e 0 . know 1s e . To be one 1s to e a b" ct by wh1ch we ble in concemmg is a principle; the first oh~e rinciple of the know:ame in all genera. in each genus; hence t B P the one is not theh "t is the vowel or . h one. ut . anot er 1 th each. thing 1S t e"tis the quarter-tone, m d . motion still ano er For m one case 1 . h . is another, an m . we1g t 1t the consonant; m . involves (Meta.1016bl7-23). . o which coun~ng f V iew according t all a'princtple o num · ulates a measure, whathe Aristotle here arne . cth s gh it must be mea-. h . h erves as a nn""· some unit w tc s c nn of measu D' ou f easurab1e quann· ·saro ·gom her: (Hence, counnng 1 from the measunn. that will serve as an suring in a different sense involves something quarter-tone, one ties.) The measuring alw~y:uch whether i~ b~ ~~~en, one can _go on example of one such an With such a pnnghohp does not use this sort e ch etc. d suches. Althou vowel, one consonant, rai su an to count seve .·

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

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of language, one can interpret Aristotle as articula~ng. the vi.ew ~at numerable pluralities arise from the existence of cntena for I~ennty. Because there is a criterion for being one consonant, it is possible to mark off a plurality of such ones thereby assigning them a number.4 Aristotle's account of number thus places two requirements on ~y numerical plurality. First, there must be some unit in the plurality. This requires there to be some criterion by which something can ~e said to numerically one. Second, each of the members of the pl~~ty must fall under some single universal F. With both these condinons satisfied, it is possible for each single member to be numeric~y onethis is made possible by the existence of a criterion for numencal ~n~­ ness-for each member to fall under the single universal F-this IS made possible by the fact that F is a universal-and hence for there to be some number n ofF's in the plurality. . Aristotle's theory of number is dear enough; but at this point a ~­ ficulty arises in virtue of (1) Aristotle's explicit criterion of numencal identity in the Metaphysics and (2) his recognition that numbers number entities that are not obviously capable of satisfying such a criterion. At Metaphysics 1016h33, Aristotle says: '[ThingsJ are numerically one 5 if their matter is one In saying this, Aristotle seems to be appealing 4 Aristotle's discussion in Metaphysics X, 1-2 corroborates such an interpretation. For instance, he says: 'Therefore, all things are measured by unity': (Meta. 1053a18) and 'Then, too, a measure is always homogenous with what is measured ... ' (Meta. 1053a25). 5 There are other passages in which Aristotle links numerical diversity with the having of distinct matter: 1018a8-12, 1025b27-31, 1074a33-3 5, and most importantly 1034a5-8: "When the whole has been generated, such a form in this flesh and in these bones, this is Callias or Socrates; and they are different on account of their matter (for it is different) ... " A rather extensive debate has occurred concerning the question as to whether matter in Aristotle is a principle of individuation. A.C. Loyd, "Aristotle's Principle of Individuation;' Mind 79 (1970): 519-29; and G.E.M. Anscombe, "The Principle of Individuation," SPAS 27 (1963): 83-96 accept such an interpretation. H.F. Chemiss, Aristotle's Criticism of Plato and the Academy (Baltimore, 1944); and W.S. Sellars, "Substance and Form in Aristotle;' journal of Philosophy 54 (1957): 688-99, on the other hand, argue that what makes Socrates and Plato numerically distinct are two numerically distinct instances of the same form. E. Regis, "Aristotle's Principle of Individuation," Phronesis 21 (1976): 157-66, argues that neither interpretation is correct. I do not need to take a

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al kind will in general

her of a natur , th . . . that a single mem to e mtumon d rinuous w h o1e. All of Socratess

have matter that forms a uni~e co~ reaion of matter-his hanuldsdare r,ers, parts, rror instance, £orm a contmuou h' h e continuous WI'th his sho lik . h h'IS arms ' w tc ar continuous wit the other h and ' are not eetc. The parts of PIato and Socrates, on 'fi d . · h ach other. th h · ng of uru wise connnuous wit e al ss with e avl b e f onene . · · n a out ric Aristotle's linking o nume mon sense mtuitto

matter, however, though it satisfies :e~::t the sort of enriAtie~ th~; d . uld seem to But nsto numerical i entlty, wo . . s that have matter. d not can be numbered to those en~~e that can be numbered tl ~t dofiru'th re ennttes A · to es e (Meta clearly thinks that ere a M . s for instance, as ns b have otton ' 6 S can tones in any o vious way • mbered. o too ) So it• tion of rime makes clear, can be nud overs (Meta. 1074a15 • f . . de's account o and unmove . m exists in Ansto 1016b24) categones, ' fu damental tenston would seem that a n d in a ul . ately remove number. d h wever, if not nm d cies , One

rh

The tension can be e:se tl' , ogeneral philosophical ten ~~ id~nrity .th Ansto es al of numenc way consonant WI • fundament sense b extended in might suppose that there IS ab ces which can then e · · le that attaches to mate rial su stan ' th. ks matter is a prme~p

hether or not Aristotle ~: show that he at the stand on this issue, for w fr m the Metaphys rically distinct · have nume . h assages o of individuation, t e P . rial composttes f Socrates's parts distinct mate fa that two o fo very least thinks two I out that the ct th fact that a single rm matter. It may ultima~e Y.:;al must be trace~ to o;the unity and diversity are parts of the same tn:ther words, the prinat:. If so, Aristotle's rema: informs those parts. In. al composite may be a . ne cannot be understo f of the parts of a maten 'cally one if its matter tsNo etheless, the oneness o h th . al unity. on ra1 connnutty . . can. serve t at some mg is numert . . 1 of numertc . , , as his articulating a pnnc~ e nse of its havmg a natu an ambiguity tn one an individual's matter in ;;,~in fact, Aristotle n~~Metaphysics 10~6b ~ as a criterion of oneness: to the above pas~ag': one if it is a quantltyhanl h along just t ese lines pnor e say th at anythmg tsunless the ob'~ect is a w o. e 'A . . one sense w .d I can rematn he says, gam, ~ ther sense we d 0 not say , B so t as I have sal , continuous, but tn ano it has one form. u ' 1 of some kind, that is, un ess . sense. In Physics th . e. neutral on e tssu . could have rnatter.m some f the poten rial qua . th rnonons aa:ua~izanon o . X tiality in Metaphysccs I 8. 6 One might think : motion as the III 1, Aristotle ddin imiJ,ates matter to poten potential and then ass o

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various ways to entities that are not material substances. The extension would be most appropriately Aristotelian if it were effected by homonymy relations. Aristode, for instance, provides criteria for the oneness of motion, one of which is the oneness of the subject of the motion (Phys. 227b30). If the oneness of the subject of the motion can then be understood in terms of oneness of matter (or enformed matter), then at least with respect to motion, numerical oneness can be homonymously related to Aristotle's explicit criterion of numerical oneness. The complete effecting of such relations for all the sorts of entities that Aristotle thinks can be counted would, of course, be a rather monumental task; and it is not one that I will undertake. Noneth_eless, so as to alleviate the tension in Aristode's theory of number I will_supp~se that numerical oneness and hence numerical plurality apply m their fundamental sense to substances and in a derivative sense to any entity for which an appropriate criterion of numerical identity exists. The_ vie'; of measurable and numerable quantities that emerges, then, Is this. A measurable quantity is a continuous chunk of matter, and a numerable quantity is a plurality of such chunks of matter that all fall under the same count noun. Notice that the similarity measurable and numerable quantities consists in their both chunks of matter with their dissimilarity arising from their beIng either one such chunk or many such discrete chunks falling under a single universal count noun Such a simil . b . ak . "bl th . . • anty egms to m e vtsI e e way m which quantity B fr . al . ows om matter. For, m gener , two speaes fall under a single g · · f . enus m VIrtue o some similarity between them. In this then, the genus is quantity, and the similarity be. . tween the speaes direcdy invol . ves matter-a measurable quanttty IS a ;ont~nu:unkss chunk of matter and a numerable quantity is a plurality of matter. So the genus quanti·"' . h h. h "fi o sue c u h · . -,,I.e. t at w Ic uru es t e two species m question, is matter involvi·ng If ify c • one were to spec t h e reature corresponding to the genus d · at· · 'an one were to allow wanton nomin IZation, one could say that the genu . d matterity. s quantity correspon s to

be~een ~em~

c~se,

Following this line of thought, let us supp th th th c the similanty · . . between mea rablose dat e matter at accounts ror · · Is . extension. . . su be e an numerable quantities In Itself, extension would li "d mt ess. It would be

"th t the 1" ·dess metaphysical blob. WI ou something of an amorphous lffil . . l l t limiting principles . .ti g prmcip es, at eas . presence of some sort ofl uru n d . · ould not contain . f di . t boun anes, It w snnc . unified continuous that mark off the regtons o anyntities that co uld b e . . . distmct regtons and h ence would not contain . 7 tain contmuous e . . ctured via the introregions. So it would not yet con d h extension IS stru measured. But suppose t h at sue I uld have to be structure . h t ffonn? two th 0 duction of form. Wh IC sor hi h according to e ac. -c ms matter, w c , d h by the sort of form t at uuor . c Such an intto uc. th chapter 3, IS rorm-m. . . . l uld create distinct regtons count of form sketch e d m e cion of form-m as an informing pnnctp e wo composites. It would, . . s form-matter d h . extension an w ose of matter that consntute variOU di hose matter IS in other words, create b o es w db se forms-m infonn conf t. n f matter by a p1urality 0 f forms-m are principIes o mo IO. • An . ecau 0 . . matter, the mforrrung underlymg . posites each o f w h"tch has tmuous com f discrete ali forms-m creates a p1ur ty o 8

th composition of form-m and continuous underlying matter. & With discrete bodies resulting om be d A plurality ofF's con· readY to be num ere · . und er the extension the world IS d matter falling · of form-m an ' sists in discrete composites b c m c for F must b e universt e ror - ' . al . al types of fonn, uruvers • form-e F. The fonn in question mdu h. h this understanding of quanth sal, and fonn-cis, of the two fun. ament

There is an interesting sense. m ~ .IC d indeed it may threaten_ . e an a single genus. Plurahoes tity introduces an asymmetry mto. tt,under "bil" f the two species falhng . . Aristotle, however, acpossi Ity o ble quanones. ed . nns . would seem cont ai.n measurahi h items cannot b e defin dm te It . I·ts pre ecessor tially contains . cepts a princip1e according tow c ·f th one item poten l of a single genus I e l ality arguab y potentially contams . .

fthe plurality, the um 6cation . . that are part o d the measurable quanones . nus is threatene · of the two species under a smgle ge . h distinct regions in p~ten'}'· formless extenston as h distinctions m 7 One might suppose that however, it would not have sue Until it is informed by form, . fo within ali sing requtres rms actu ty. . etation I am propo - I do not think, th the mterpr forming man.... 8 It may seem at . lied prior to their en . retation I am proposing. a species to be multt~esis is required by the ~~ osterior to a universal however, that _such a -m could be underst p The multiplicity of forms form-m informing matter·

(DA 414b31). And because a Pur

_i,..,

138

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

Tho difficu~~ howev~r, is not intractable. In the first instance, measura~l: art-whq~antilti~s contham parts, which are numerable. So if there are f h o e re ations t at threaten the uni p at least symmetrical· pluraloto ty o t e species, they are · 1 1es contain magnotud d o d 1 S es, an magn1tu es contain 1 alo P ur ltles. econd, It 1s possible to unify th f edlicidy quantity as such with ;;::: 0

0

0

0

~ty ~y

0

id~ntifying

0

:x~:::~::z

~:tl:rer~~~::;(;)::Fo:!:~o:i~g sligh~y awkw~rd formulation of

~:~~::::~~'~mpo~ites ohf :h:~:=~:~o~~~~t;::: ~~=~~ uurerentiae, w en added t d 0

bl o extensiOn, o create the spedes measurable and numera e quantity 1 the following structu respective Y· Hence, we have re. 0

0

Quanttty Unlimited extension (".;ye9o~"") £ r.., en ormed by form-m _ measurable (~ye9o~ ) quanttty ' t.e. hrmted magnitude 0

0

0

0

0

in one dimension-line in two dimensions-surface in three dimensions-body enformed by forms-m th e resultmg comp by some form-ebl ~sttes 0 f whotch are enformed numera e quanttt b Y ' loe. limtted pluralirv t.e., num er -,, 0

0

0

0

0

One pleasing aspect of this hierarch the privative differentia'unli d' M YIs Its pnncipled elimination of fied with limited magruotudrmtthe • heasurable quantity is now identiera ert an oh o and numerable quantity is n od ofi d w~t magrutude simpliciter; od ofi ow I enti e with li o d l I enti cations are made Possioble b ecause unli rmte d p urality. These genus which, because it is mite Is now part of the matter as such b Sity, be limited by form Th 'must, Ymetaphysical necesofi • Is structure also P od JUSt! cation for two Arist li roVI es a rather stunning ote an posmon 1 ves in the category f s, at east as they manifest th emse 1 0 stantioality decreases as one a quantity. ds • Accordi ng to Aristotle, sub2b22). And in this hierarch sheen a g~nus-species hierarchy (Catg. o y, Y ascending to th hogh arnves at a very indete....... ; e I est genus one nate sort of ' matter, which would be very Insubstantial. Furthermore b od d ' y Io entifying the genus quantity with unli rmte extension, and by d enymg the possibility of an actual infinite, 0

0

0

0

0

0

0

0

0

0

0

0

0

•

....

0

0

6~

Quantity

139

Aristotle guarantees that quantity cannot exist as such without being determined by a differentia. The identification of quantity with unlimited extension thus allows for a derivation of the species in quantity. The main divisions in the category of quantity have already been derived. Continuous quantity and measurable quantity are convertible-and they arise from the limiting of extension by form-m. Discrete quantity and numerable quantity are likewise convertible-and they arise from the limiting of form matter composites by forms-c. And because number, owing to the elimination of A.6yo~ is the only species under numerable quantity, we can suppose that numbers (ofF's) just are limited pluralities of a certain sort. The divisions among the types of continuous quantity, then, flow from the dimensionality of extension itsel£ Body is limited measurable quantity in three dimensions; surface, limited measurable quantity in two dimensions; and line, limited measurable quantity in one dimension. 9 The virtues of the present account should be evident. There are, however, two remaining difficulties that must be addressed before it can stand firm as an interpretation of Aristotle. The first difficulty concerns the fact that the constitutive differentia of plurality contains plurals, namely 'forms-m' and 'compositeS. Were this structure intended as an analysis of number, which it is not, it would be charged with a blatant circularity. But even though it is not an analysis of number, the following question does arise: how can the differentia of plurality make appeal to what appears to be not just a quantitative notion but a notion involving plurality itsel£ namely forms-m and composites~ And once this question has been raised, does it not equally apply to the other differentia, for that differentia contains a singular, namely 'form-m: But is not a singular likewise a quantitative notion? In order to answer this question, one must remember that according to the interpretation in this paper number in the species of quantity is the number of composite material substances. The appeal to numerality in the differentiae is an appeal to a unity and plurality of forms-m, which are principles of material substances. (The plurality of composites of form-m and matter reduces to the plurality of form-m-for

0

0

9 Aristotle seems to think that the tri-dimensionality of extension can be

known a priori (De Caelo I, 1).

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME 140

many composites are many forms~m informing extension.) Now, that Aristode allows types of entities other than material composites to be numbered has already been shown. As long as there are criteria of identity for such entities, they can be numbered. Hence, it is legitimate ' to appeal to a number of forms~m.

That the plurality of forms~m is presupposed by the derivation does, however, require some categorial facts concerning form and matter to be underived. These facts, though, are facts about hylomorphic enti~ ties; and so such a requirement coheres with an interpretation accord~ ing to which hylomorphism is a prior and more fundamental theory than categorialism. According to the interpretation in question, the categorial scheme is intended to represent the basic structures of ma~ terial composites. That some aspect of the scheme, in this instance the notion of a plurality, must be applied to hylomorphic entities does not vitiate the contention that, as a representation of the categorial struc~ tures inherent in material composites, the scheme can be derived from hylomorphism. One final issue must be addressed. It may seem that according to the interpretation I am offering substances are in the category of quantity. For, a composite of form and prime matter would be a substance - and I am claiming that the species in the category of quantity unfold from such composites. As I have derived quantity, however, I have appealed to form~m informing extension so as to create bodies. Here, however, the results from earlier chapters resolve the difficulty. The derivation I have provided does depend on principles of substance-but once the principles have been allowed to structure a world containing mobile material substances, one significant feature of such substances must be abstracted in order to arrive at species in the category of quantity, namely motion. As I argued in chapter 2, the abstraction of motion requires t~e abstractio~ of ~orm. As I argued in chapter 3, the type of form reqwred for monon Is form~m; and such a form is responsible for the substantiality of a material composite. Hence, its abstraction results in the category of quantity, which is not subordinate to the category of substance and which can ultimately be identified the most indeterminate type of matter that has enough struCture to be a genus.

CHAPTBR7 SUBSTANCE . 's cate orial scheme, or at least have so far argued that Ansto~e d is: tematically connected the part of it that I have examme , ysult admits of at least a d asares ' to his hylomorphic ontology an far are incomplete in two ways. partial derivation. But the results ~o I have not explained how form First, and perhaps most importan y,fu, damental category: substanc~ I d t 0 the most n· unresolved. 1hemain thesis and matter are reate · s rematn Second, some very general I~sue "al scheme admits of a syste.matic; of this book is that Aristodes c~tegon I Such a thesis is monva~ed l rp h hic onto ogy. · anon b oviding some sueh d env derivation from his Y omo in part by philosophical concerns :ri~~:heme can be challeng~d. :;: the Kantian criticism of the cat~ . rtant structures to Ansto . many of Its Impo IS cause the scheme owes . the Kantian claim that the scheme . de's hylomorphism, on~ ca~ reJectan deeper explanation .than An::ch a a hodge~podge affatr with~uthil:sophical brainsto~ngb B::n onto brilliant though haphazar ~ shes the philosophical ufo th ex~ . nl ·a1 For, It pu . . •fi cion r e w· thout an a priort JUSO ca ' b. ctions defense IS 0 y partt : Aristode's hylomorphism. 1 eone sympathetic to Kants o ~epriori c d matter, som w·th ut some a istence o~ rorm an ds to criticize Aristode. I o might argue, might snll have groun f form and matter, someonfroe hylomor~ . denva · ble m 1 "cal argument cror the existence o th gh it IS · a1 cheme, ou ds an onto ogt Aristode's categon s . •fi d since it depen on thd s unJUStt e . phism, is elf l:n the requisite justificanon. f substance and the scheme that Its ddr both the category 0 f form and . h I a ess fo th existence o In this c apter, . . J'ustification r e focus. g directly on . m larger Issue o fth e aprtort . directly. lnstead 0 f m o so however, matter. I d '

!

no~e

143 THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

142

these two topics, I instead focus on a topic that is in some ways one ~f the fundamental issues in the interpretation of Aristotle, namely hts attitude toward the plenitude of being. In addition to being an int_eresting issue in its own right, I shall eventually argue t~at interpren~g Aristotle in a certain way regarding this issue results m a systemanc and arguably a priori treatment of his category of substance as well as his introduction of form and matter in to his philosophical system.

SECTION I LOVEJOY, HINTIKKA AND THE PLENITUDE OF BEING More than any other scholars Arthur Lovejoy and Jaako Hintikka have discussed whether Aristode accepted a doctrine of the plenitude of being. In his classic work, The Great Chain of Being: Lovejoy articulates the doctrine as follows: no genuine potentiality of being can remain unfulfilled, that the extent and abundance of the creation must be as great as the possibility of existence and commensurate with the productive capacity of a 'perfect' and inexhaustible Source, and that the world is better, the more things it contains. 1 As this passage indicates, Lovejoy links a philosopher's acceptance of plenitude with his belief in the existence of a fundamental source of the world, which, because of its overflowing nature, guarantees that every potentiality of being is fulfilled. As a result, Lovejoy does not attribute plenitude to Aristode. Because Aristode's unmoved mover is eternally contemplating itself, it is entirely self-contained - unlike Plato's One, it does not overflow itself into other realms of being. Hinitkka, on the other hand, attributes plenitude to Aristotle. 2 Not surprisingly, he does not trace Aristotle's acceptance of plenitude to an overflowing source of being. Rather, he argues that Aristode was committed to plenitude because he accepted a modal thesis according to which to be possible is to be true at some time or other. In defense 1 Arthur Lovejoy, The Great Chain of Being: A Study in the History ofan Idea, (Cambridge, Mass: Harvard university press 1936), p. 52. 2 Jaako Hintikka, Time & necessity: Studies in Aristotle's Theory of Modality (Oxford: Clarendon Press, 1973), p.95.

7 fit; Substance

ges that taken A . ikka ites the following passa H of his interpretation, mt c . h a modal principle to rtogether strong1Y support attributmg D sue Gen et Corr. 338a 1-3' 335aistode: De Caelo 281a28-282a25; 1~26b;7-37, 1064b32 ff.; De Int 2-b7; Met. 1050b7-8, 1047a12-14. Phs 203b30, 221b25·2::2~9; De 18bll-15; Top. 112bl, 115~17 -18, o~al principle in place, lt ts easy n t A . d to plenitude. .For, rar . n. 644b21-3. And wtth them uld be comrrutte enough to see why Aristode wo Th P must be true at some orne. suppose that it is possible that P· en. me or another tum out to be Hence, every posst"hili"ty must at some tl l d true. . .tkka adduces d oes see m to count The textual evidence that Ht~l S houldn't we simply co_nc u e heavily in favor of his inte~retan:n~ ;;ll, maybe. But, there ts ; ; : th h · · ht and LoveJOY wro g . . this matter less at e ts ng intikka's posmon on . ddress in a . . does not obviously a did sidual issue that makes H. . £actory - hls posltlon . tode . not c thinking that Ans d completely satts . y's reasons ror 1 . de to Ansto e L fu s to attribute P enltu uld b the satisfactory way oveJO e . accept plenitude. Lovejoy re As~ de's unmoved mover co because he does not see how d I nsto uld of course, be an ordering d pnnin "al b tances an so, .al worl • t co ' source of the maten . f desire of maten su s fl wing, it ld b the obJect o · ·s not over o d ccordciple - it cou e . s· but because lt 1 di t their monon , , bil being Instea ' a some sense, rec 1 . al source of mo e f. bile being as a could not be the ontotloSJ:c ly took the existence othmo . at least one ght that ere lS L · Aristo e s1mp ing to ovejoy, l ust have thou th eed not have of mobile being, at n brute fact, and, as a resu t: m . .. e1 the extstence posstbthty, nam Y f entation. But, b . d th" line o argum b ponse to lS . d his views a out o tame • Hintikka does h_ave; .rescceptance of plemtu ~mental concern because he ties Ansto es a onse sidesteps the n lling. The difd · the resp b · sly compe d so is not o VlOU li f argumentation modality an nme, . that motivates LoveJOY anlight by considering a ~e o Suppose for the , . rpretanon. . b b ght to Hintikkas mte b . does not exiSt. ficulty can e rou fa to vor obile emg . that at first seems . . possible that m . b trUe at some nme e . d t . that 1t. lSthat to be possl"blelStO sake of re uc to il be" g does not eXIst. mpoon hich ob e m . ·me at w m f motion (Phystcs Then, on the assu must be a o the measure o th or other, ere d d fines time as d far from represent"toe te such a possl"hility· An so, But, because Ans . .. 219b2), he cannot accep

r:

THE FOUNDAT IONS OF ARISTOTLE's

i

7 Pt1 Substance

CATEGORIAL SCHEME

ng a possibility that need h 144 fact obt . h . not ave but does a d fi . . am, t e eXIstence of mobile b . . s a matter of contingent ~ moon of rime and the modal . ei~g Is necessitated by Aristotle's Im. . prmciple that Hinitkka attn·butes to

h

· seems, provide . 1h ' .Is argum ent, It ; ~~ore evidence against Love. ereas Lovejoy interprets Ar· , 1t I , be agreeable to Hintikka emg a b Istot e as taki ng t h e existence . of mobile. b . s a rute contingent fact h. :~s-~n f~ct committed to its nec:s;i IS .:gument shows that Aristotle ~ utmg plenitude to Aristotl . ty. dnd so Lovejoy's reason for not ~anwtetillsettled. For even if we acc:p:stuhn ercu~. But the issue is not yet · that concern at · Is · necessary, we th s . ask the question d Lmobile . b emg e oveJoy, namely what explains e existence of mobile being. I n response t o t h.Is question H" ikk 1he. necessity of such a fact h' mt. a might very well say: nothing nation · needed. Just as' the e nught is b h that Is fa thargue,_ provides all the expla-· fact ot th necessary b. and not explainedctb at tnangles h ave three sides

~ Interpretation and so would

furthe;~ mo Iile being exists is necessa: anyd ~rther fact, so too the act. n the £ y an IS not 1. d b is rooted in a defi .~rmer case, Hintikka mi h exp ame y any

uence of A . tlnltlon; and in the latt g t _argue, the necessity · er case t · · . qtime. Such nsto es• VIew about the relat· b , I IS a tnVIal consea response h Ion etwee ·b·t· by considerin h , owever, is not the onl n I Ity and pretation tha~ t e ~ther ~ossibility, the road ~ne possible; indeed, Loveioy's retru~s Anstotle's commitm w e paved for an inter:~ concerns · d e but meets . m a much more dire ent to pierntu Takin th . ct way. . g e existence of mobil the Intriguing possibili th e bemg as a brute ne . . ty at, despite its ne . cessity overlooks mits of an expl ananon s h . cessitv it as odd · • uc a VIew nu·gh . -,, noneth eless ad' smce some phil t strik . osophers think that ne e ~~me philosophers things that don't reqwre ex 1 . cessities th swer to the quest· P ananon. For instan are e sort of Ion - what I ce, an ap . 2+2=4?- would di exp anation can w . propnate ansome for th_e that sary, what other different, and ar ~1 n Is needed~ Aristod h . well, It IS necesnot think all negua . ~ more subtle, view about the . owever, had a very cessmes are 0 1s matt F . I n a par - some he th er. or he did For instance all th ' ose mvo ved · ' explanation Oth h m correct definiti ough d t, are brute. • ers, owever, do. For instanc thons o not have any e, e fact that triangles

1

e:c~:at~ t~

philosophe:~~:.

po~si

~act

145

have n:o right angles does have an explanation, namely that they have three s1des. And in general, Aristotle thought that the essence of a genus explains why it has the proper characteristics that it has as a matter of necessity (PA I, 4-6). Once it is admitted that some necessities have an explanation while others do not, however, we can tum to the ~u~stion of mobile being's existence and ask: which sort of necessity Is It, brute or explainabld If the interpretation that I said would be agreeable to Hintikka is correct, we are forced to conclude that the necessity is brute, or at least a trivial consequence of Aristotle's views about modality. But perhaps, it is not. Perhaps Aristotle thought that ~here is some sort of deep explanation for the existence of mobile bemg. In thinking about this issue, it is interesting to note that Aristotle touches on but never settles in any explicit way the question as to whether there is some explanation for the existence of mobile being. In Physics I, 2 and 3, Aristotle addresses those philosophers who deny that motion exists. At 185al-5, he says that someone investigating nature need not determine whether what exists is, as Melissus and Parmenides hold, one and motionless. Now to investigate whether what exists is one and motionless is not a contribution to the science of nature. For just as the geometer has nothing more to say to one who denies the principles of his science - this being the question for a different science or for one common to all - so a man investigating principles cannot argue with one who denies their existence. For if what exists is just one, and one in the way mentioned, there is a principle no longer, since a principle must be the principle of some thing or things (Phys. 185al-5). Aristotle's contention here is in some ways easy to discern- he is simply denying that a physicist must argue against those who deny the existence of motion. In another respect, however, the precise nature of the view Aristotle is advocating resists easy determination. The difficulty arises from what might seem an innocuous aside but what is in the end a comment that has considerable interpretive significance. Aristotle illustrates his claim about physics by drawing an analogy to geometry-he says that a physicist confronting someone who denies the existence of motion is like a geometer confronting someone who denies the principles of geometry. Such a geometer, Aristotle says, need

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

not argue against his skeptical opponent. So far so good. But Aristotle goes on to add that the concern over the principles of geometry cannot be dismissed altogether. Rather it belongs to some different science or to a science that is in some ways common to all sciences. By analogy, then, a physicist need not address someone who denies the principles of physics; nonetheless, questions about such principles could not be dismissed. Rather, some other science or some science common to all sciences must address them. As it turns out, Aristotle reiterates a similar point in very similar language at Physics at 252a32. He says: To maintain that all things are at rest, and to disregard sense-perception and attempt to show the theory reasonable, would be an instance of intellectual weakness ... Further, just as in arguments about mathematics objections that involve first principles do not affect the mathematician - and the other sciences are similar - so, too, objections involving the point that we have just raised do not affect the physicist; for it is a hypothesis that nature is a principle of motion (Phys. 253a32-253b6). Aristotle here again denies that a physicist must contend with objections to his principles, and he again draws an analogy to mathematics. And though he takes care to point out that a scientist inquiring into some particular genus need not investigate the principles of that science, the passage implies that the scientist in question need not demonstrate the principles of his science qua that scientist. A mathematician, for instance, need not demonstrate the principles of mathematics. But by a further implication, some other science does investigate such principles. Analogously, then, a physicist qua physicist need not determine whether mobile being exists; but, by implication, it would seem that, qua some other type of scientist, a physicist does. 3 3 Although the Metaphysics passages only imply that scientists must be

conce~ed abo~t the natu_r~ of their princ~ples.qua some higher more general science, Anstotle explicitly states such Implications at Posterior Analytics 77b3-9: An~ for those one should supply ~ ~rgument from the principles and conclusiOns of geometry; but for the p_n~oples, the geometer qua geometer should not supply an argument; and Simrlarly for the other sciences too. We should not, therefore, ask each scientist every question, nor should he answer everything he is asked about anything, but only those determined by the scope of this science (PA 77b3-9).

147

7 fit; Substance

h th t some type of . k hat Aristotle thoug t a diflic.ult th It is thus tempting to m t . d Moreover, it is not · g was m or .er. explanation of mo b 1·1e b em h th debate between LoveJOY · · tersects w1t e science more general to see how such a quesnon m. . k that some . 1 and Hintikka. If Aristotle d d thm the existence of mon~n, . some way demonstrate an explanaoon . f mobile than physics can m · ould count as . Aristotle, hy is according to then such a demonstrat1on w il being. Furthermore, because first ph hos~p and because first philosoys1cS, the only science more general than h P d monstration wo uld h ave tod conth"s d a. sue a e . g·' an bil1 . h b . phy is concerne w1t emo-. · ate way w1"th bem · dm · somel mom. of the enstence . of mo . e tain predicates assoc1ate 1 . cal exp ana non 1 tion LoveJOY would result in an onto ogt tl the sort of exp ana f th

°

being. Although it may not be exacal ~o the overflowing nature o t: was looking for - it may not appe vide a sufficient respon~e . nonetheless pro unmoved mover - 1t may d "th being itself rath er than Ansto· 1·S concerne W 1 Loveioy insofar as 1t . · : . ~ thi ssue e1cle's formal modal apparatuAs. . tle never does addre~s s 1 -theouc 1 however, nsto 1 H never m a meta Y• th meta-leve. e th · ciples of h nrortunate h b. lains e pnn I vel or at e t er at t e o ~ect e ther science exp k that could . s that some 0 ther wor , gument in some 0 . Aristotles ret1cal stance argue d he gt"ve an ar f tion Desp1te lf physics, nor oes . f th existence o mo • hall allow myse Ianaoon o e th · aper I s count as an exp 1. atter however, in 1S P. rovides compelling reticence about th s m ' ulation that I thmk P ul te that Aristhe latitude for a ce~aintlspec these issues. I shall speghc tshall diverge fb · g, thou . f Ansto eon interpretaoon the lenitude o ~m the rinciple as I artotle did in fact accept P f it According to P f the perfecfr H" tikka's fonnulation o • all PP every degree o om m hall henceforth c , that several interestticulate it, what I s b . tantiated. tion of being ~ust e t~is paper, I shall ar~~utin pp to Aristotle. In the rematnder o result from attn . g hich Aristotle lanaoon tow "bl . onsequences f ing interpreove c b . f the sort o exp . hand it is poss1 e "d the asis o With PP m , th First, it provt es . assages above. 1 resembles those at alludes in the Phystes. p that not only stron~y but also concerns yllogtsm telian soence to construct a s of an Aristo Th alone it seems to me, are supposed to be part orion and being· atht ugh, the lens of PP . between m . ~-' ystem ro fo the connecnon . lications pp has r . Aristotles, metaphysical s e the Imp makes viewmg . cerestinglY, however, ar . attractive. More m

°

• 149 THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

the unity of Aristotelian sciences. I shall argue that PP provides an ontological principle of unity for the various epistemic projects that together constitute Aristotle's system of sciences. PP thus serves as something of a paradigm for Aristotle - it is a principle around which some very basic structures in his metaphysical system turn. Of course, it is one thing for PP to be a paradigm for Aristotle and another for it to play a role in the larger philosophical context in which Aristotle was operating. I shall argue, however, that PP did play such a role. If I am correct, not only can PP be seen as a principle that gives to Aristotle's philosophical system a remarkable internal coherence but it also connects Aristotle to a tradition of metaphysical speculation started by philosophers before him. If I am correct, by giving a dis~ tinctively Aristotelian flavor to some very general metaphysical theses present most noticeably in Plato's middle dialogues, Aristotle supports his scientific theories with a metaphysical apparatus concerning the nature of being. It may seem that the considerations I shall present are the basis for an argument that Aristotle accepted PP. And in some sense they are-I do think that viewing Aristotle's system as if he accepted PP does have a number of interesting and attractive interpretive results. But I in fact think that the correct interpretation is more complicated than this. Although for much of the paper I shall proceed as if Aris~ totle accepted PP in the same way that he accepted any number of other philosophical theses that occur explicitly in his works, several reasons suggest that it is more plausible to view PP as something of an unarticulated regulative principle that guided Aristotle rather than an explicitly formulated principle that he accepted. This is not, how~ ever, to denigrate the role that PP had in Aristotle's thought. Indeed, such principles are often of extreme interest to the historian of phi~ losophy. For they provide a due to the philosophical gestalt in which philosophers from different eras were operating. They are, so to speak, a kind of unarticulated form of thought which have as matter the vari~ ous philosophical theses that occur explicitly in a philosopher's texts. And such, I shall argue, is precisely the case with PP. I shall argue that in addition to unifying a number of themes both within Aristotle's own system and within ancient Greek metaphysics, it also illuminates

7 fit! Substance

tl . 11ectual milieu in whiCh Ansto e fthe1nte considerably t h e ch aracter 0 was operating. .

·

SECTION II UENCES OF PP IN'I'ERPRE'fiVE CONSE Q SECTION IIA THE EXISTENCE OF MOTION A DEMONSTRATION OF . b · ~

erfection of bemg must e m According to PP, every degree :the!t content of this principl~ B~t stantiated. I shall discuss later. e ex lanation of mobile bemg, lt for the purposes of constructmg. a~ of the principle. It can be suffices to be dear about the logtc

;:;m

stated as follows. . d f the perfection of 'f b . F lS a egree o I. Necessarily, for all F, 1 et.ng d b . 1.s instannate . il being, then F~ emg c th existence of mob e . l argument ror e d With such a principle m P ac~ the following premise and con u~ being can be constructed by ng d fthe perfection ofbeing sion. . . mobile is a egree o II. Necessarily, bemg · is instantiated. III Hence, mobile bemg f ttn'buting PP to Ar~ · th · terest o a b 1 · an Aris~ d illustrates e m This argument alrea y bl the sort that e ongs m th . tl Not only does it resem e . lightly more complex than e lStO e. · al form lS S · '1 . . so'ence -its logtc 11 . m but bears obvious Slffil an~ l tote 1an b sy ogts · 'ddl rtions of necessity - but ltS ml e standard Aristotelian Bar : . d . s remises are bo asse . Hence, because middle terms tles, an dlt P o·f the perfection of bemg. lian science this argument is egree ~ . Aristote ' . h term dard explanans m an. f mobile being that lS bot are the stan f th enstence o d lanation o e l · al And this, I conten , pr~videels :~nature and explici~y ontdo Whereas Lovejoy Anstot tan both LoveJOY an bil b · . . rovement over . for the existence of mo e emg, 1s an 1mp ·cai .....nlananon · · kka ak the uld see no ontologt - r . ly attributed to Hmtt t es : d whereas the view. I ten::~ consequence of Aristotle's mo~ . ce of mobile ensten . being amasnow suggesting forges . a deep connecnon framework, the Vlew 1

:m

;!:olli.

I 51

THE FOUNDATION S OF ARISTOTLE's between Aristotl ' . CATEGORIAL scHEME am right A . es tl views ab out being d h 1 so ' allud nsto e .has t h e resources to anprt e"dexist Ito which he thence of 0 motion. If "bl es m the Ph . OVI e e sort f " ' e to explain th e existence . qua fi<St of mobil b _P hilosopher itargument is indeed e emg. P0

Y"" -

THE

SECTION liB UNITY OF ARISTOTEL

Of . course, physics is onl IAN SCIENCES science. And . y one of the . . lt would b dd mam branch f e o were Aristotl h es o Aristotelian mg could be dem br.mches of A . omtr.oted but that the .' to t ink that mobile be nstotelian . eXIstence f s it turns out how science would have to b o any of the other A I h ave articulated ' evet "' it · "· possible to use the e tak . "' a brute &ct. provide the demo ' . ong with certain sub of plenitude A nstotle · nstration · SI Iary · . order to views, m thinks h s m question. h ysics . and theolo t at the th ree t h eoretical . comments he akgy (Meta. 1026al6 M scrences are mathemati. P h m es abo h ' eta. 1064bl) cs, ( ow that he think. th t h. . And num<'OW Meta. 1069a30, DA 4el;a lowmg structures '";'dues the wodd 7, 413a21, DA 41ateo centralin importance

~"

~

"d~rmciple

6u~ ~genus-species

4a35, NE 1098a4).

Substance Immobile Mobile _

u

s::;;oved Mover(s)

Eternal _ H eavens Destructible Unensouled- Sublunary bodies Ensouled- L"1vmgth" . Elements/mixtures Incapable of Perc .mgs Capable of Perce~tlon- Plants Irrational on - Animal Rational Brutes s Humans

'".explanation fot the existen« of the main branches of AristoteHan d ut a gteat e more needs to be done in otdet to see bow it science. B d al so. I have alteady atgued that Ariswde can use the principle of P
~s·

~

~

m~b;le

0

h substance, which strictlY speaking is the subject matte' of 0 Y""· Secondly, the demonstration of the existence of mobile being . at I pmvided telied on a pren>ise acconling to which b
an~thet

sciences study. The fim oedet of business in this task is to articulate more dearly the content ofPP. And in this regatd. it is fitst important t<> note that PP does not commit Aristotle to the dubioUS thesis that being comes in degrees. Rather, aaotding to PP, being h"' a namdy pet· l that the perfection of b<· •ng comes in degt«S is analogous to the clain> that walking comes in degrees of quickness. Wallcing itsdf does nDt come in degte<S' but th< speed at which someon< walks d - AnaJogou.lY. whethet something is does not com< in but the way in which it is does. With that said, we can now ask two questions. First, what. accotding to is the nature ofbeingl Second• hoW are the dog«<' of being dif&.-enti·

~

degffi'''

.ddre""

Quantity Mathemanes, · accordin 1061a28-36 g to Aristotle• studi<s 1 ' PhY'· 193b31-4)· . !:a13,Meta.1026al6),i.e.b physia, mobile (Meta. eta. 1026a20). M oreover, phy o y;.and theology, the sunm stance (Phys. Sics contains all th oved movers ( ose scrences · that

d

7 ~ Substance . era su sume under the genus, mobile substance. So for study the gen b d mstance' b"IO1ogy IS . a part of physics. ' rea Y sat , 1 that PP can be used so as to provide As I have al d "d I th"nk

;:;:""ty

Acistotl~

Aristotl<. ofanother? course. the fint q-tion in the M ated from one and insis" there that being is said in ,.any ways (M
THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

152

them, it surely applies to substance. Hence, 'being' in PP can be replaced by'substance' so as to yield PPS. PPS: Every degree of the perfection of substance must be instantiated. What, then, about the second question~ What counts as a degree of the perfection of substance~ One passage that provides some insight into this question occurs in the Parts of Animals. At PAn 644b21645al, Aristotle argues that the heavenly spheres are more divine than destructible substances (PAn 644b21-645al). The source of such divinity stems from the fact that the heavenly spheres, though capable of accidental change, are not capable of essential change. They cannot, in other words, come into or go out of existence. Destructible substances can fail to be what they are both accidentally and essentially-they can acquire and lose accidental features, and they can come into and go out of existence. The heavenly spheres, on the other hand, though they can change accidentally as a result of their local motion, cannot go out of existence. Aristotle's view about the source of the divinity of the heavenly spheres can be augmented by his view about the unmoved mover. His argumentation in Metaphysics XII, 9 shows that he thinks that the unmoved mover is a perfect substance. According to Aristotle, the unmoved mover must have himself as an object of his thought. Why~ Because the unmoved mover, being the best of all possible beings, must think about the best of all possible objects; and the unmoved mover is the best of all possible objects (Meta. 1074b30-5). The unmoved mover, however, is pure actuality- it does not admit of any potentiality at all (Meta. 1072bl-15). So, just as in the case with the heavenly spheres, there is a connection in Aristotle's thought between the degree to which something admits of the potential for non-being and the perfection of that thing. These textual clues can be augmented by considering in the abstract what it would mean for something's being to be perfected. One plausible answer to such a question that springs to mind is: a being's being is perfected to the extent that it excludes non-being. So, for instance, a being whose being is perfect would altog~ther exclude non-being. A being that is less perfect than a perfect bemg would admit accidental

153

uld dmi . d bein s less perfect still wo a t but not essential non-bemg. An .g

7 (41 Substance

both accidental and essential nodn-bemg. b l'ng is of course, to speak xdu es non- e ' 11 . To say that someth mg e b de precise in the fo ow· hor can e rna f b . · for x to be incapable o metaphorically. But t h e metaP r lude non· emg IS r ing natural way: ror x to exc d b . whose being is perrect . I ther wor s, a emg . . h b . hat it is Such a vieW IS not-being w at x IS. n o would be altogether incapable of not emg w • c 11 · g thesis· expressed by t h e ro owm · {' 'f and only if it is not posT: The being of suhstan~e: x, is perrect 1 sible for x not to be what It IS. . scope distinctions in T .th the appropnate It is important to read WI mind, since T is ambiguous between

. £ 'f and only if necessarily for any atTa: (x)( the being of xIS per ect I tribute F, ifFx, then Fx); and . . d l if for any attribute F, 1f . Tb: (x)(the being 0 f xIS perfectlf an on y Fx then necessarily Fx) th ' d di g _ Ta would have e di . th . tende rea n Clearly, Tb and not Ta IS e ~~stance is perfect. Rather,_ accor ng t~ result that the being of every sub ranee's being is perfect if and o~y the intended reading ofT, a su s uch that it is impossible for It not . . fact has are s the attributes t h at It m . · g· Level 0 bemgs to have them. . r£ ct a leve10 bem Call any being whose b~ing ~ r:ve~ 1 being, then, would excl~de e;~ exclude altogether non-~e~n~. g and a level 2 being would adrrut ~\y sential but not accident elbn . These distinctions are capture accidental and esseno'al non· emg. the following theses. . . 'ble for it not to be what Tl: A levell being is s(2u)ch. t:a~~!)p':::x~:%r it not to be what it is . allY'• but It I it is acc1dent essentially.

'bl for it not to be what it . ch that it is possl e T2· A level2 being tshsu. 15• essentially. · . allY and w at 1t is accident

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

154

A level 0 being would thus be perfectly actual. A levell being would be capable of accidental and not essential change. Finally, a level 3 being would be capable of both accidental change and essential change. If I am right that Aristotle accepted PPS, then he should have accepted the existence of beings at all three levels. And of course he does. The unmoved movers are level 0 beings; the heavenly spheres, level 1 beings; and the destructible substances, level 2 beings. PPS, then, in conjunction with plausible theses about how to differentiate among the degrees of perfection of being allows for a principled division of the genus, substance, a division that accords well with the divisions Aristotle made. Now, Tl-T3 account for the existence of at least three types of substances; but further discriminations among level2 beings can be made in accordance with a principle that appears implicitly in claims Aristotle makes concerning particular species. According to Aristotle, the being of a mobile substance is perfected to the extent that it imitates, as much as its nature permits, the divine perfect being. Mobile substances, in other words, are ordered with respect to the perfection of being in accordance with their degree of imitation of the unmoved mover. The most explicit allusion to such an ordering in Aristotle's works occurs in De Anima II, 4. In his discussion of nutrition and reproduction, Aristotle says: The acts in which it manifests itself are reproduction and the use of food, because for any living thing that has reached its normal development and which is unmutilated, and whose mode of generation is not spontaneous, the most natural act is the production of another like itself, an animal producing an animal, a plant a plant, in order that, as far as its nature allows, it may partake in the eternal and divine. Th~t is the goal towards which all things strive, that for the sake of whtch they do whatsoever their nature renders p ·bl OSSI e ••• Since then no living thing is able to partake in what is eternal and divine by u~interrupted continuance (for nothing perishable can forever rematn one and the same), it tries to achieve that end in the ?nly w~y possi~le to it, and success is possible in varying degrees; so tt rernatns not mdeed as the self-same individual but continues its existence in something like itself- not numerically but specifically one (DA 415a26-415b8).

7 (le; Substance

h

155

t1 . al re roduce because they in eren y

Aristotle here says that amm ~ P all in the eternal and diak h s their nature ows ak . . Strive to part e as muc . a at the oal of all things is to part e m vine. Indeed, he says outnght th gd tible substances cannot di . But because estruc h d thin which is to propagate the spethe eternal an t e vme. live forever, they do the next best g,

cies to which they belong. . to the way in which . tl tricts his attention . In this passage Artsto e res . . f di . ctivity.. But his atn.. · ·rrutation o vme a di 1 . f general view accor ng reproductive actlvltles are an .bl ak as an mstance o a all . ·rtue of degrees of.mu-. tude here is plaus1 Y t en to which the world is ordered teleologic yhm VI ral thesis the views . . A d ·f ne adds to sue a gene d th tation of the divme. n 1 0 th h di ine is imitated an at ~' d the extent at t e v b that being is perrecte to . b instanced, it ecomes every degree of the perfection of bethng mthust ghet that the genus, sub. t1 would ave ou . h di species each of wh1c spossible to see how Ansto e . . . . f . . led division mto b e stance, admits o a pnno~ . . 4 I h ve already argued that su stanc plays rather distinctive actlVttles_~ a b tance and mobile imperfect . bile .penectthsu s bile substance divi.des into first divides into 1mmo al . IS . mo re substance. I have so mennoned atdmo that the latter's bemg eternal and destructible substances: b .ng of the heavenly spheres perfect than the form~r's. Becaus~il esu~:tances, they must undergo is as perfect as is posst~le for ~~n e to Aristotle, is continuous, eterthe perfect motion, which: ac~n/s). Destructible substance, then, nal circular motion (Phystcs li . ' bstances. Non-living substance; divides into living and non- vmhg su f· and they are only capable cho .xtures t ereo ' 1 whi they move to the p aces to are the elements and rru . ~' . · nd msorar as imitating the divme ffi1 . different ways correspond. ns EVEICcl ttvt an be understood m two 4 Aristotle's teleology c f he final cause. The expressio . d the ing to two different conc~ts o :ess res ectively, the dative of.mt~restb:Ween and oEVE ICQ 'ttvO~ wfhdich .expcorr~sp:Od roughly to the dis~mctl~; W. Kullb. f that action. ,. . f th biect o eslre, genitive o e o J • and the aim or o ~ect o d Living Things, the beneficiary offanha~~o~ Cause," in Aristotle on ~at~re anBristol Classical man "Concepts o ~ e b mgh Bristol: Mathesis Publicanonh~-h I am referring tth 1£ d (PittS ur .cal d · g to w IC A. Go e ' e • 169-175. The teleologi or ::.notion of final causation. Press 1985), ?P· rd . with respect to the~ . d fended by David Sed. h. per IS an o ermg th · wh1ch IS e m t IS pa . . mpatible with ev1ew, . ( ), pp.l79-196, Hence, my vieW IS co tb centric? PhronesiS 36 1991. ley, Is Aristotle's Teleology teleology is anthropocentnc. that in the former sense ...

o

:::stZs

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

IS6

their natures order them. Living substances, on the other hand, arecapable of nutrition and reproduction, which capacities allow them to be self-sustaining for a period of time and, as Aristotle says in the above passage, to imitate the divine insofar as they propagate. The activity of the divine mind, however, is a kind of knowing. And so, in order for the world to exhibit all the degrees of perfection, there must be imperfect substances that can know. Knowledge, however, comes in two varieties - knowledge of particulars and knowledge of universals. The former requires sense perception; and the latter, rationality. 5 Hence, PPS requires the existence of imperfect substances capable of perception and rationality. And so, the principle of plenitude, along with a thesis about the ways in which being can be perfected, entails the existence of the subject matter for all the main Aristotelian sciences that fall under the genus body.6 The only remaining science whose subject matter requires explanation is mathematics. It is here that the results from earlier chapters become relevant. As I argued earlier, the subject matter of mathematics results when motion is abstracted from body. Hence, insofar as Aristotle can explain the existence of bodies by appeal to the principle of plenitude, he can explain the existence of the subject matter of mathematics.

5 Aristotle~ compl~te account of the relation between sense, reason, particular~ and umversals ts of course complicated. In some sense, one can perceive

umversals (PA ~00a15: Phys 1~410-20).And in some sense, reason must apprehend the umversal m a parttcular image (DA 43lb2). Nonetheless, some sort of connection between sense and particulars and reason and universals is certainly an aspect of Aristotle's thought.

~ Not~ce th~t this interpretation goes some considerable way toward explainmg Artstotles acceptance of the etemality of the species. C£ J M Cooper, '1\.ristotle on natural teleology'; in Language and Logos, ed. M. Nussbaum and M. Schofield, ~C~bridg~: Camb~dge ~niversity Press 1982) pp.197-222, for an altemanve discusston of Anstotles views about the etemality f · an d teIeoIogy. o spectes

157

7 fit; Substance SECTION IIC PP! ARISTOTLE AND PLATO

. th at I have provided has implications The interpretation of Anstotle . · g Aristo. dl ague Issues concerrun dm d al h e of the world. for some rather large an a Itte Y v . d e ab out th e ration . co erenc de's fundamental att1tu . gue and rife vageneral tenWere I to use terms t h at are, like the issues m question,te th less do seem to conno with ambiguity b ut t h at none e . . Id wer to the question . h that lt pe s an ans . . . t r a rationalist. As dencies of though t, I rmg t say e of an empincts o . tl as to whether Ansto e was mor b t to let the world · · t have een conten . b hil tionalists have had an a general rule of thum ' emptrlcts. s_ · d b rue t piuralmes' w era contain unexpIame . . I s Now in the case 'fyi d explanatory prmctp e • ' al impulse toward um ng an iricist and a ration . • sciences, · the d ebate between an. emp of Anstodes • d s Aristotle take the und the question. I · d fact or does h e ist interpretation revo ves aro l oe . . a brute unexp ame ' subject matter of his sciences as I . al xplanation~ find them capable of some deeper ~nto olgtcd e ery different pictures h estions ea to v th Different answers to t ese qu ld A ding to one picture, e . dthewor. ccor al . tl of the way Aristo e viewe . nl 1 ralistic but is so mca· al' uiryts noto YP · f subiect matter o ratton mq 'th'u any particular soence J 1 . 't0 be sure, Wl m c . Pabie of further exp anation. . . kn able principles, ror m. . . and a prtort ow d th there are necessary, pnrmtive th all triangles are dose ree. 1 'th' geometry at h th stance the princtp e Wl m lanations as to w Y ere are sided plane figures. But, there are ndo exp ding to such a picture, conThe worl , accor f ali . hich are the subject matter o triangles in the first p Iace. 1 · d plur ties, w tl 'gh have Alternatively, Aristo e ffil t . . tains brute and unexp ame . the most basic theor~tical soen:;~ational inquiry is indeed pluralts~c thought that the subJect matter t formulate indemonstra e · and that within vanous so·ences one f thmus b•iect matter is nonetheless · ceo esu;.~ 'th' principles but that the e~ste~ese two world-views represent Wl ~ capable of some explanationdu£; nt attitudes concerning the one ~ the theoretical domain two er~ng to Aristotle, does the ;an]' m the many. To what exten~, accor dmit of a systematic and unt e exthis instance the many soen~es, a tration (or at least a conceprually in this instance a ~mon):f the existence of the genera that Planation, . d set of demonstranons intertwme

•

I

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

158

the many sciences study~ To what extent, in other words, does the one hold sway over the many~ It should be clear by now that I am advocating the latter interpretation. Viewed in the light of PP, Aristotle's system not only displays a remarkable degree of internal coherence but is also an attempt to describe the world as a remarkably coherent unity. To this extent, he was much more of a rationalist than an empiricist. There is, of course, considerable debate about the extent to which Aristotle was influenced by Plato. But, ifi am correct, Aristotle did at least inherit Plato's rationalist impulse as regards the existence of the subject matter of rational inquiry. Moreover, I am inclined to think that the connection between Plato and Aristotle on these matters amounts to more than just shared cognitive tendencies. Indeed, I think that the connection between the two is deeply conceptual, though I also think that the only way to appreciate the conceptual connections is to view both their metaphysical systems through the lens of PP. With PP in mind, one can see that Aristotle, while retaining a Platonic commitment to PP, nonetheless modifies in a distinctive way several Platonic views. In the doctrines I have attributed to Aristotle it is certainly possible to hear at least the echoes of Plato. Form, being and perfection constitute a Platonic triad; matter, becoming and imperfection constitute a second. And the two triads stand to each other as master to slave, as original to copy, as original source of formative power to material being formed. In fact, the idea that pure being excludes non-being is a dominant theme of Plato's middle dialogues. According to Plato, the world of form is the domain of pure being; and the world of flux, which is teleologically ordered in virtue of its imitation of the forms, is a mixture of being and non-being. So, for instance, he says in the

Republic:

It would remain, then, as it seems, for us to discover that which partak~s of bot~, of t.o ~e and not to be, and that could not be rightly designated either m Its exclusive purity, so that, if it shall be discov~red, we may justly pronounce it to be the opinable, thus assignmg extremes to extremes and the intermediate to the intermedi t (478e) a e. As is known, Plato abandons, {or at least modifies) this view in the

Sophist, where he allows the forms to intermingle with non-being.

7 lit~ Substance

59

. . he dialogues, Plato is com(241d) Nonetheless, at various pomts ~~ th d much like the . I . all 0 f whtc soun very mined to the followmg c atms . . d in light of PP: A . tl , system lS vtewe claims that surface w hen nsto es h d . of impure being is b · . (2) t e omatn (1) pure being excl~ d es non- et~g, ld· ( ) the domain of pure be3 intimately linked wtth the matenal wor '. b 'ng inntates pure el • . e being ) ( ing is changeless; and 4 tmpur d A . totle on these points, ·· b n Plato an ns Despite the si mil annes etwee h ld . uite the same fash. . tl d bifurcate t e wor m q however, Ansto e oes not . ks Pl d ws Aristotle mcor. d the lm ato ra ' . h f bstance. Substances, ion as Plato. Havmg accepte · Pl · hterarc Yo su porates them into an ann- atomc al b · gs These fundamen. tl h fundament • . ili' according to Ansto e, are t e . dan em ith the perfecnb ty . . . s tn accor ce w . th tal beings come m two vanene ~: the assumpnon at c d . erfect In ract, on of their being: perrect an tmp : . bstance must come . d f bemg lS true, su l the principle of the Pl emtu e o necessarily change ess, . . P £ t substances are b in these two vanenes. er ec . . h case that they can e . 'ality {tt 1s not t e . . d th · ciple of potennality an hence do not share m potentl and not be), and hence do not have e pnn change, hence share in I rfect substances can . . le imperfection, matter. mpe b ) and hence do have the pnnop not e ' The imperfect substances, Potentiality (they can be and r£ · n matter. ddi · of potentiality and impe .ecn~ ' substances, must have in a non however, as a result of thetr hem~ ._~: cion a principle of substan.al'ty and tmperrec f those 1 to a principle of potenn £ Th. principle is a source ~ tiality and perfection, namely orm. ce:~nto their respective kinds b~t . . . that not only place subs tan f the unmoved movers acnvmes l sser degrees o also are imitations to greater or e · · eternal perfect acnvtty. 'ddl Plato's view that pure bet'ngdoes

Aristotle, then, accepts the ffi1 e the view that the world ~f nonnot mix with non-being as w~ll a: I gically ordered by relanons ~f . t' e the material world, lS te eo o al o accepts the later Platos b emg, •• b · g He s ' 1' . 't tion of the world of pure . em . ki ds But he rejects Platos tst ~~ a that the world contains htgh~st : d. in s~ doing he denie~ that ~:h7ghest kinds, which i~dudedsthbet:!· is :pros hen homonym. Fmally, ing mstea a rfe beings to meet being is a genus ar~ d he allows impe ct . . h he and perhaps most tmport.:J• These theses, then, combt~::lt t . 'de a differentiation o e genus the criteria for substance. d as to provt d · · 1 of plemtu e so th o'cal sciences stu Y· pnnop e that the eore substance into the genera

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

160

SECTION V THE PRINCIPLE OF PLENITUDE AND HYLOMORPHISM The focus on plenitude and its relation both to Aristotle's system of sciences and his hylomorphism is, to be sure, idiosyncratic. The last section should make it dear, however, that considerable light is cast on Aristotle's system of sciences when one views it through the lens of plenitude. Likewise, an interesting perspective concerning Aristotle's hylomorphism emerges as a result of plenitude. Although commenta~ tors generally think that Aristotle introduces form and matter as a result of considerations about motion, there is another route to their introduction. I have argued that mobile substances are inherently striving to be as much like the unmoved mover as their natures permit, thereby perfecting their being as much as possible. But, one might ask: what, according to Aristotle, keeps mobile substances from completely imitating the unmoved mover:' The obvious answer to this question is: matter. That matter keeps substances from perfect divine imitation crops up in various places in Aristotle's works. Perhaps the most interesting instances of such a doctrine occur in Aristotle's metaphorical descriptions of the fatigue caused by the presence of matter and potentiality. In Metaphysics XII, 9 Aristotle argues against the presence of potentiality in the unmoved mover precisely on the grounds that such potentiality would wear him out: 'First, then, if he were not thinking but a potency, it is reason~ able that the continuity of his thinking would be fatiguing him' (Meta. 1074b28~9). And in his discussion of actuality in Metaphysics IX, 8, Aristotle says: 'Nor are they worn out by this activity, for their mo~ tion does not come from a potentiality of two contradictories, as in destructible things, so as to make the continuity of such motion tire~ some; for the cause of this is substance in the sense of matter or po~ tency, and not in the sense of actuality' (Meta. 1050b24~8). Aristotle also argues that deformities in nature are the result of form's not being able to master matter (GA 768b15~768b35). And he argues that the divine contemplation that humans are capable of is subject to the limi~ tation imposed by the presence of the body (NE 1178b35).

161

7 fit; Substance

_c

.

·n hand

. . ci le of imperrecnon 1 ' With the idea that matter 1S a pn~ldp E ery substance is a being · natu r ally unro • f v bile substances, or b e, the following doctrmes · the case o mo · and as such must either h ave, m . . 1 of being. Such a pnn~ d vers a prmc1p e . bil imperfect beings, 1.e. mo e in the case of the unmove mo ddi . ciple is form (Meta 104lb8). In a hnon, d itis precisely because er In ot er wor s, e substances, must h ave matt . . t have matter. And so we se · 1mpe · r£ect that 1t mus fphysical metaphys1c · al and mobile substance 1s · ful ergence o ' _r • here in Aristotle a beaun conv h a principle of imperrection, __ c b · g must ave _c b ethical themes. Imperrect em . "ple of change, imperrect e~ ·sa prmc1 f which is matter; because m~tter 1 bile being, is the subject matter o ing, which is convertible W1th mo . rfect being from completely 1mpe d b · perfect atter keeps . an 1m physics; an ecause m nly ever attatn . If. bil substance can . xhibited by the unmoved mover. . perfecting 1tse ' mo e imitation of the perfection of be1hn~ ~ terpretation without accepnBng Of course, one could aceept t 1s m that I have prov1·ded . ut h and matter . f the characterizano~ o orm . th urposes at hand very we11. Ac~ h

°

su:

these characterizat1ons do su1t h e P 4 and 6, prime matter as · m · c apters-c d . t the interpretation . of which accounts ror cor mg o . the enrormrng d di It is in other words, linke tho ~ is intimately related to extensiOn ' matter m . th"1S way co eres the plurality o f mater1"al substances. . . rime . Fu rthermore, charactenzmg vers1ty. h theP unmoved mover must lack. . For, with Aristotle's views about w at d mover, as a result of its beulmg Pf:: A . de the unmove ) d as a res t o according to nsto ' "al"ty (Meta. 1072b9 ian I ks xtension fectly actual, lacks p~tenn hence being unmovabl~, ac ~nciple of causing eternal monon an . e matter is the ulnmate ~ the fact (Ph 267b27). But because pn_m. I linked to extens1on, . ys. . . db ause it is so mnmate y liminates extens1on potennal1ty, an ec ust lack prime matter e th h nmoved mover m tual stroke. h at t e u ·at· fr om 1t . 1·n a single concep d 4 al so coheres with t e and potenn 1ty . ed in chapters 3 an form~m is a prin~ Form~m as characte~lZ F ·n the first instance, . be the b s So 1t can . d d pmg. or, 1 picture tha~ 1S :~ ;e being of material s~ st:ur:; substances must ciple of uruty a . and perfection that 1~ . intimately linked principle of actuality And indeed, because 1t 1~ s~ te the unmoved b bstances. al b tances 1mrta have to e su fa that materi su s lanation. Form~m, "th "virv, the ct . finds a perfect exp W1 aeti .,, ofthe1·r activines , . . . tone and the same . V1"rtue ·a1 substances acti"vtnes, IS a mover m as the source of a maten

l

THE FOUNDATIONS OF ARISTOTLE'S CATEGORIAL SCHEME

162

time, the cause of a material substance's being a member of a kind, and hence of that material substance's existing, as well as the cause of a material substance's imitating the unmoved mover, and hence of that material substance's instantiating the degree of perfection of being that its nature allows. Additionally, if one progresses along the conceptual path introduced by the idea of form-m, one will arrive at the concept of the unmoved mover. A form-m is a principle of dynamical activities. Now, in the material world, a gap exists between the principle and the activity-the actualizing of the activity need not always occur. Various reasons for this gap might be proposed; but the most Aristotelian reason would be the fact that a principle of dynamical activities must exist in matter. Matter, so to speak, holds form back. Its presence must be overcome. A principle of activity enmeshed in matter must expend an effort to realize the activity for which it is a principle. And without an eternal source of power for such an effort, the effort will not always be forthcoming. To speak of an effort required to overcome matter is of course to speak metaphorically; but I have already noted that Aristode such language in his discussion of the unmoved mover and actuality in the Metaphysics. So, to continue with this metaphorical language, if there were any gap between the unmoved mover's actuality and his potentiality for that actuality, an effort would be required in order to actualize the potentiality. But, because the unmoved mover has no share in potentiality and hence no share in matter, the gap between the potency for an activity and the activity itself vanishes leaving in its wake an effordess, seamless eternal activity. Of course, the activity cannot be dynamical-it cannot involve the spatial world. For such an activity would require matter. Rather, the activity is pure thought thinking itself. And so, the idea of form-m, when carried to its conceptual extreme, leads direcdy to the idea of the unmoved over.7 7 According to the interpretation I am offering, Aristotle's hylomorphism and the principle of plenitude intertwine so as both to explain the existence of the main genera of the Aristotelian sciences and to generate several of the main contours of Aristotle's categorial scheme. Yet, a large question, namely what is substance. Now, anyone familiar with the literature on this topic knows what a thorny question this is; so thorny, in fact, that I certainly cannot hope to provide an adequate treatment of it in this book. I will, however,

7 Pal Substance

. k. ired fort e present c of such a claim must indicate what sort of view I t hm IS requ 1 • . but a d erense . do think that the view is in fact Anstot es, wait for another occasion. fli'cting attitudes about . 1 ' pparent1y con f c cus on the concept 0 In order to disentangle Anstot es ~ . b I thmk It est to ro f . l ·f and only if no part 0 x the nature of primary substance, , ) S b ina. x, IS compete I . th completeness (tt:.A.ttoc; • orne e o- . , tolo~ then, contams ree 1 o'' . d he 12 15) Anstot es on is outside of x (Meta 1021b - ·. terial composites, an t · I e forms-c, ma d fin' · n . typ es of complete bemgs - species, · · . th c 110 wing sense - a e ItlO. · IS · completem al an I· unmoved movers. A species d fi ero . . of human is ranon · the e mnon · e of it is non-relational. For mstan~e, . of what a form-m is. For mst:mc if' mal. This is quite unlike the s?e.cificanon fa forcn-m, is the first actuality o a soul, which is a paradigma_nc msta;ce ~ t the specification of what a soul a body potentially possessing life. The act tl : f some other thing, namely a . · · 1 h fact that a sou IS 0 . f that tertn IS essentially mvo ves t e . . A .stode's techmcal sense o . . body, makes such an entity a relat~ve m r~site is complete. When speofyi:~ -he is human· On an A~st (Catg. 6a137). Likewise, a material comlpd · ne wou say h · tannates what for instance, Socrates IS, 0 . ot extrinsic to w at ms ' a1 b · human IS n . · Socrates. . 1 anything extrmSIC to . k d telian view of univers s, emg . h it is lin e to . does not mvo ve it. Hence, what Socrates IS h . . li'ke a form-m m t at f like · i youth' ' Finallv an unmoved mover, t houg It IS An unmoved mover IS, '' l di ced from matter. .all .ed to some mg activity, is complete y vor h t it is is not essenti y tl .al composa form-m without the m. H~nce, w 1ate. Unlike forrns-c and mat~n . to them. · t o IS comp e h' s excnnsiC extrinsic to it; an d so It o ssentially tied to t mg . essentially d f, ms-m are e forrn-m IS ites, both matter an or h h's is so with form-m: a as 1 argued in · ned w. y t I.nsic to it. LI.kewiSe, · matter, both types of I have already mentio related to the matter that IS exthtn c m that enforrns it. Hence, 'all t'ed to e ror chapter 4, is essentl y 1 . d bstance? I think entity are incomplete. . b tween a complete bem~ an s:as the paradigWhat, then, is the rel~t1:~e ea material composit~ the complications it is as follows. For Arist ' In the Categories, he 1gno es of substance · f substance. th only twO typ matic instance o a d atter. Hence, e f their particulanty, · h form an m A d because o · having to d o Wit . d their species. n material compos1tes. are material compos1te8 an bscance is bestowed up~n de also substances imary su di Ansto ' fol . the honor of be1ng pr r are accor ng to h the reason is as howeve , ' h · k, t at ft 1 Forrns-m and matter, can be made, t m d (ii) Aristotle o en A case inciples of substance; an( d often should) be (Meta. 1029a3). Why? h' h. d rnattet are pr . 1 fF can an lows: (i) fo~ an rding to which a ptin~P ~ oderivative upon that w 1C h 15 accepts a vteW acco gh ch a designanon 15 bscance. though t ey designated an F, thou form-m and matt~;r~~:f what is most propmost properly an F. H hood from being the pnn p derive their substance-

w;::

e::

- - --~ ---------- - - -

-------

---

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

SECTION III SOME META~INTERPRETIVE ISSUES Attributing PP to Aristotle results in a deeply unified interpretation of some of the basic structures in his metaphysical system. And this, it seems to me at any rate, counts considerably in its favor. There are, however, four questions that are very pertinent to these issues and whose force may very well disincline someone from accepting the interpretation I am offering. First, why would Aristotle have accepted such a principle? Second, why did he not explicitly profess allegiance to the principle? Third, if Aristotle did intend to explain the existence of motion from theses concerning being, is he not committed to a kind of Platonic doctrine according to which physics is part of metaphysics. Finally, is there not something a bit suspect about thinking that Aristotle would have deduced the various genera that are the subject of his sciences? After all, a priori, there seems to be no obvious reason why there could not have been more species that exhibit more degrees of perfection than the ones that Aristotle focuses on. I conclude this paper with some possible answers to these questions. erly substance, namely a material composite. Furthermore, form-m, because it is prior to matter in the sense that what matter is depends on form, is, of those entities derivatively named substance, primary. This is the conclusion Aristotle reaches at the end of Metaphysics VII. Despite the fact that form-m is in one sense primary substance, however, there is the question as to what the primary instance of substantiality is among complete beings. And indeed, one might think that this is the most important question concerning substance, for it is only complete beings that have what it takes to be non-derivatively called substance. Only a complete being can be self-sufficient, for to be complete is to contain within oneself what one is. And being self-sufficient is, so to speak, what being a substance is all about. So, to d~ter~ine what rry>e of enti,ty is substance in the most important, i.e. non-denvan.ve, sen~e of substance, ~n~ must find that type that is, among c~mpl~te ~emgs, pnmary. An~ here, It Is clear that Aristotle thinks that par~IC~lan~ I~ ne~essary to be pnmary subs~ance among complete beings. This IS Implicit I~ hi~ treatment ~f substance m the Categories and explicit in his argumentation m MetaphysiCs VII 13. Hence, among complete beings, those entities that are particulars are primary substances. As a result, both material composites and the unmoved movers are primary substances-both types are particulars; and both types are complete.

165

7 fill Substance

. I t h 1·nk' lies in . the fact. that the The answer to the first question, . A . . . . f metaphysiCal opnrmsm. . d h ablys Princxple of plemtude IS an expressiOn o . of two amtu. ales t at . argu . that such it is the natural accompamment , ( ) . 1 mc optxrmsm both Plato and Aristotle shared: i an eptstemo 00(-.. ) thical d . "bl • and 11 an onto-e l complete knowledge of the wor IS possic e, d th extent that one . h , b . ·s perrecte to e view according towh IC. on~s emg.~ akes it difficult not to accept has knowledge. Acceptmg (t) and (u) m al tu e of the world . . rfi . h ost gener struc r plemtude. For, 1mpe ectlon at t e m . I . al difficulrv. If being •r . t ble eptstemo ogtc would create an msurmoun a . , b . g must always rec "bl q ua being is not perrecn e, t h en everythmgs . . em ..c d to the extent "f h"n 's bemg xs perrecte main imperfect. Hence, 1 somet 1 g f th ld complete knowlkn 1 dge 0 e wor ' l that it approaches comp ere ow e "bl 1b if complete knowledge b 1· poss1 e. us, edge of the world would e ..c d the extent that it has . , b ng xs perrecte to f is possible and somethmgs ex .1" "bl So accepting o . . b . must be perrecn e. , erfectibility of being if not knowledge, then bemg qu~ emg (i) and (ii) requires accepnng at least ~e ~ d of perrecnon. . . the instantiation of every egree n1 b art of the story, smce lt . li f ningcano Y ep b · Of course, thts ne o reaso . n1 . gle being whose emg "bil" th t there xs o y a sm f leaves open the possl tty ~ tl have thought that every degree o is perfect. So, why might Ansto. e t"ated~ Here, I think, one must 1 · t be mstan • f b the perfection o emg mus . tl , orldview to the world as a . . . "nAnsto esw . d f ·turn from partxcular ennnes 1 th ld as a whole is a kin o urn . I th"nk that e wor rth whole. It is possxb e to 1 f r£ cion of being. Fu ermore, ty that can itself exhibit degrees. o ~e eculd have held that the world

n: .

it is plausible to s.uppose th~~rl:~ec:::. Indeed, this, 1~ the beli~ as a whole exhibxts o~tologt . P whose being is perfected, ts ~ natur. in the existence of a smgle ennty. I gical and metaphystcal opnaccompaniment of ~nbridl~?t:t~~~ ~at the being of ~e world is mism. But, it is not tmplausx e t e of being in it is instantiated. Qua more perfect in so f~r a~ every de~e lacking a degree of being. To use being, such a world IS ncher than ral "thout an army is a less perfect an Aristotelian metaphor, a g= 1075a15). Generals should than a general with an y ldi rs . umty have so e · Hence, were one to accept lead - and to lead, the~ mu;.tth world as such, then one has reason to the ontological perfectionfobe. e And as I have said, it seems to me · deo mg. ' believe in the PIerutu

(;;:ta.

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

I66

that Aristotle would have believed in the ontological perfection of the world as such. These reasons for thinking that Aristotle accepted plenitude provide the beginning of an answer to the second question, namely why did Aristotle not explicitly state and accept PP. Although I have been talking as if the acceptance of plenitude was somehow at the forefront of Aristotle's mind in his metaphysical speculation, I do not in fact think this to be the case. If Aristotle's acceptance of plenitude resulted from his metaphysical and epistemological optimism, we should not necessarily expect to find him explicitly stating the principle. Such optimism, it seems to me, would most likely have been hidden from him simply because he lived at a time during which it would have been entirely natural to be optimistic. Indeed, his own intellectual successes would surely have added fuel to his optimistic outlook. And it is commonplace that the optimism of the young is often only visible to the old. Indeed, I am inclined to view plenitude as something like an unarticulated regulative principle for Aristotle. Alternatively, one might say that such a principle was part of the formal element of his worldview, the matter being the world itself In other words, I wish to suggest that the idea that being comes in degrees of perfection was a pervasive lens through which Aristotle as well as at least some of his philosophical predecessors viewed the world and that such a lens served to structure their theorizing. As a result, Aristotle would not have articulated the principle explicitly; nonetheless, its presence as a structuring force would have permeated his entire system. Viewing plenitude in this way allows one to answer the third and

f~urt~ questions I have raised. Because plenitude is a regulative prin-

ciple, It would not figure into the kind of deductions that constitute the Aristotel.ia~ science~. As a result, plenitude, like the principle of non-contradiction, provxdes a general parameter within which Aristotelian scien~e p~oce~ds. So, even though I earlier recreated a syllogism that looks hke xt mxght allow one to deduce the existence of motion from doctrines concerning the nature of being, such a recreation was really heuristic - it makes very dear that there is a strong connectiOn between plemtude and motion. Hence, physics is not literally part of metaphysics, for Aristotle. Nonetheless, one can see very

fo~

purpo~es

167

7 fit; Substance

al clearly via the syllogism I recreated how PIem.tude acts as a gener

.

8

parameter for his other sciences. . . · ceptance of the per. hich an Imp1ICit ac f th An example o e way m w A . de's thought, it seems to . served to structure .nsto A · totle accepted wh at fectibility of b emg . cles, b.IOloo-ical treanses. . al me, occurs in Ansto o. hnsview that bioIogre th scala naturae, I.e. t e . I b all d later came to e c e e . ht be called biological perfection. n kinds exhibit degrees of what nng h k be a natural phenomd to what e too to al 1 addition, Aristot e appe e . If ·n degrees, in his attempts enon, namely vit al h eat, wh"ICh Itse comes l . I that one finds in the b"10 ' · d grees of comp exxty tl · li "tly to explain t h e varymg . e . dies therefore, Aristo e Imp ex_ logical realm. In his hiologrcal stu . d' ees of perfection, and wxth · g comes m.d degr nomies that exh"b" accepted the id ea t h at bem 1 It de . . t only provi e taxo th . . part such a presupposmon no h . al mechanism at xs m ysic al found a p grees of perfection b ut so responsible for them.9 . d e can offer an answer to the With this view of plenitude mlh~ dw is a regulative principle, we · d • Because P e last question I raxse . emtu in deductions of th e ge nera. that tl should not expect to see convmthc g should expect that A:nsto de . contams th an Aristotelian sciences studv.,. Rald er, we what genera It see lenitude. We sh o uld ' 1·no . er would have looked to the wor . to of then to see those genera in thenkligthht genera represented vanous · 1 t thi at s · slv.,, we can words, expect Anstot e o . d as I argued preVIOU de rees of the perfection of bemg; an g · de in Aristotle. .h hould see PP as a see such an atotu the extent to whxc we s . tikka interOne last commen~ a~outd As I have mentioned, Hm he docregulative principle IS m :cc::ding to him, Aristode acce;:::e time. "bl if and only if it occu~s ~ right Prets plenitude modally. th" ·s possx e t m 1ts own trine that some . m~ 11 however, is not only suspec rring - but is h dal pnnop e, l "th ut ever occu Sue a mo . uld be possib e WI o . tl 1 .ms that there - surely somethmg co A . ode himself. Ansto e c ax rted by nst in fact controve . l allows prin. . when Ansrot e ------:.-:difliculty in derernunmg J Hankinson "Aristotle 8 There is constd~able be used in another. Cf.. ti uity, Bob Sharples ciples from on~ sc!~';~~losophy and the Sciences In n q Kind Crossmg' m . · on 005) d V"tal Heat m Ansed. (Ashgate 2 · gth. "Living Capacities an 1 1 9 1 discuss this t~pic ~ ~ ( ~), PP· 365-379. tode," Ancient Philosop 'Y

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RA

2

r69 THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

'I

r68

could beacoatthatcould be cutup but never is (De Int.l9a12,14). To be sure, Hintikka goes to considerable length to explain why Aristode would have accepted a modal form of plenitude that allows for the sort of exception Aristode alludes to. And he is joined in this pursuit by Sarah Waterlow. 10 Both Hintikka and Waterlow try to find some form of the modal principle which is not so obviously counterintuitive and which an be seen as arising from Aristode's logical concerns. In my view, Hinitkka and Waterlow are misguided precisely because they do not see that plenitude is a regulative principle for Aristode. Given that the world is ordered via degrees of perfection, one might very well expect to find that as a general rule of thumb possibilities end up being instantiated at some time or other, especially if those possibilities are relativized to types. It would be odd in an ontological, ly perfect world were some type to have a potentiality that was never actualized. And indeed, when the possibility in question seems very deeply embedded in the structure of the world, one might think that plenitude begins to shift from the mere regulative to the contentful. So, for instance, given the centrality of the motions of the heavenly planets in the structure of the world, we should expect that if it is possible that they cease moving, they will. And Aristode does appeal to such principles in his demonstrations of the existence of the un, moved mover in Physics VIII. One should not expect, however, to find in Aristode some set of theses, metaphysical or otherwise, that would entail what is at any rate a highly suspect modal principle, just as one should not expect to find an a priori deduction of the genera that the sciences study. If I am right, therefore, an appreciation of the way plenitude influ, enced Aristode's thought is crucial in understanding his approach to various inquiries. Aristode would not have explicidy stated plenitude but his allegiance to it would nonetheless be visible. And indeed, I think one can see it in his works, not on the surface, but below it act, ing as an anchor to his theorizing. To use Aristotelian terminology at this point, according to the interpretation I am advocating Aristo, 10 Sarah Waterlow, Passage and Possibility (Oxford: Clarendon Press 1982). I should note that Waterlow disagrees with Hintikka on several important interpretive and philosophical issues. But her general approach to plenitude in Aristode is similar to Hinitkka's.ln particular, she overlooks the possibility that plenitude is not doctrinal for Aristode but rather regulative.

7 ~ Substance

. hiloso hical system and . th matter of his P P . d · "nd de's explicit docmnes are e . d ithout plerutu e m ~ . ' 'T" • rpret Ansto e w cnve 1s plenitude its form. J.O mte th fr an Aristotelian perspe . . therefore is to do something at omf h" system while ignonng 1ts , . . t the matter o 1S problematic - 1t 1S to trea form.

CONCLUSION

.

hich

·rul ·on of the way m w with a brief recap1 an . unfold from the din It is worth condu g d hi hylomorph1sm . . 1 f eo Aristode's categon·a1 scheme an b s· f discussion of the pnnap th

. d dthena ne . · bing at principle of plerutu e an f th Aristotelian worldvtew 1S a e hie to the top o f e somewhat anthropomorp . Plenitude itself. At r£ 1 is 0 course, ch a contenoon. is, qua being, pe ect. t But, let us grant su . es it In insist that such a being is g. t be as Aristode charactenz :al 'th poteno ' b ing mus It then seems that sueh a e t be infected W1 any . th t . ·ry m~t no th vteW a the first instance, its acttVl chano-e. And, if we accept. eb. ct must b" ct cannot o dh that 1ts o ~e . ity. Hence, 1tS o ~e bl of beings an enc~ th direcdy at such a being is the most nob. ects then we do arnve ra ;.r be the most noble of all o ~e ved mover is thinking i~ ·~ principle Aristode's view that the unmo. for Aristode, a teleo ogt kind of be, Now, the unm~ve~ rov;~:· order of the worl~· ~ ~rm,m· The and hence is a pnnaphe octerized as very much likede er resides in th mov mov . · pdy c ara ing, then, 1t 1S a form'm and e un • ) insofar as no only difference between a over is complete (t~A.etoc; ence, it stands (Meta. 102lb12,15). Htially related tO the fact that the unmovr part of it lies outside o like~ts the soul, which are essen forms,m. in contrast to ub ....,. ....... that are, ·res s s.....~ some matter. l . de however, reqUl Now Aristode ar, The principle ~f p e~er:ce capable of change.f -L.~ .._, (Phys. 26()a20, . . penect an . ...me o ~---eot us grant them for qua bemg, 1m . lac is the primatY ·r rmP e contentious; bu~ ~--~ must have gues that change . arguments are be;nu lS 1111¥""··--26la26). His L...:na whose --oWbat cou1d such a mat' 1hen, every ~-eo . ,__ d the moment. fo change m P - .~·.A . chapter 4, oes the matter that allows ~ hawever, as I aiS....- m .. __ .J extension . £xten81on, . __ .J de,suu~ . ter be~ ExtenslO~· •ts of potentiality· Ins~de, we are forced to admtt not stand at the litni th principle of plem~ . this way is every de, does. So, if we accept . en is prime tnatter· ym that underlying atenJiO .

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• 171 THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

'l i

170

gree of the perfection of being instantiated. Between prime matter and the unmoved mover, then, are the varying types of substances whose degrees of perfection depend on the extent to which they imitate the unmoved mover. Such imitation, however, essentially involves some sort of activity and so requires a principle of such activity, namely form-m. In this way both form-m and matter are introduced into the world. And with these hylomorphic principles, it is possible to see the way in which the categorial scheme unfolds. Substance is the fundamental type of being and is divided into its main species in the way I described above. In general, the connection between form-m and species membership is guaranteed by Aristotle's acceptance of a functional determination thesis and the fact that form-m is a principle of activity. Form-m, however, not only is the underlying principle that places substances into their respective species but also is responsible for the accidental activities of substances. Such accidental forms provide the basis for the category of quality and can be divided in the way I suggest in chapter 5. And, when form-m is abstracted from material substances, one arrives at the category of quantity. And the divisions in quantity can be explicated in the way I suggest in chapter 6. It would seem, then, that the main contours of both Aristotle's hylomorphism and his categorial scheme can be seen as unfolding in a more or less systematic way from considerations concerning the perfectibility of being qua being. If one grants the principle of plenitude, then a rather stunning metaphysical system emerges that is in its a priority almost Spinozistic. With the principle of plenitude in hand, Aristotle has the resources to argue for (1) the existence of the unmoved mover (or at least some being whose being is perfect); (2) the existence of motion and hence the existence of form and matter; (3) the existence of the main branches of his science; (4) the existence of t?e s~bject matter ~f mathema~cs; and (5) the intra-categorial divistons m the categones of quannty and quality. Furthermore, with the appropriate conception of substance, Aristotle has the resources to avoid Spinozistic monism. Finally, Aristotle's categorial scheme _ or at least pa~ of ~t- can. esc~pe J_
'

~·

7 ~ Substance

ul

d ether surprising if an unartic ate Of course, it should not be tog philosopher's thought th . . 1 h t serves to structure a regulative prmctp e t a . . nflict with that philosopher's o er will, when articulated exphculy, co . I th'nk that this is the case · · s Interestmgly, t if d explicitly state posmon · i1 h' al difficulty that emerges . t1 F h · a ph osop tc . with Ansto e. or, t ere ts cr . According to it, there ts a , h . t tion I am onenng. one accepts t e mterpre a ul . 1 ounds Aristotles metafact about the world as such th~t nmate y grges· where in Aristotle's B h uesnon now emer • f physical system. ut, t e q ld falP It certainly is not said-o anysystem of categories does the w~r S : t be a primary substance. . ythmg o tt mus thing. Nor is it present man : . of the genera that con't fall~ It ts not many ld But in which genus d oes t . . uld ppear that the wor as . 1' . es So ttwo a allTh stitute the Anstote tan sC1enc . . , tl , tegorial scheme at . e 'fi . lace in Ansto es ca b exhaustive classt canon such does not h ave a P h . meant to e an d th categorial scheme, . ow~ver, ts ld And so the inability to fin e of the kinds of bemg m the w~r .difficulty. . world's place in it presents a ser~o~s ultimately owes its jusofiThus, if Aristotle's metaphy~:des~=~ itself owes its justification cation to the principle of pleru .r 'bil' of the being of the world, . b t the penecn tty th kicked to considerations a ou . bed a ladder only to have e~ Aristotle would indeed have climdd t from under oneself ts probkicking a la er ou f it away. 0 course, ythin to hold onto. And Aristotle . lematic only if one does not ha~:Oan n:tion in order to avoid ~mg. might at this point appeal to a pt of the world as a whole ts an He might try to argue th~t the conhce might try to argue that as ~uch, . nd likeall Kant, . 0 f hlS · categones. . .th. ne the purvteW idea of pure reason, a one should not expect it to f: wt ~ns the disintegration of the opttKantian twist already begt . rpreting him. Of course, dA. tleaslammte di uch a . that characterize nsto h sical optimism - accor ng mtK sm not without his share of metap regulative ideal. To what deant was ld · at least a r d· d d 'dea of the wor ts 'd d optimistic an m ee to Kant t h e 1 • d be const ere tl ver Kant's atotu e can. tl , ) optimism has subsequen y e h gree, ow , ll Ansto es . to what degree his (as we ~ for another occasion. occaston. rtainly toptCS been eroded are ce

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s

•

INDEX actuality, 11-12, 55, 57, 60, 63-64, 83,127,137,154160-163 affections, 9, 60, 101, 102, 107-115, 130 affective qualities, 9, 101-103, 107-112, 114-115, 130 Aquinas, 7, 16-17,26-27,76, 102, 117,122 Aristotle, 5, 7-17,20-23,25-47, 49-54, 59-68, 70-86, 88, 90-92, 95-96,99, 101-109, 111-113, 115-121,125-152,154-171 being, 7-8, 15-17, 19-21, 23, 26-27, 33, 40,42-43,46-47, 54-56, 58-60,64-67,69-74,77-78, 81-83, 85, 93-94, 103-104, 106-107, 109, 114,117, 121-122, 131, 134, 136, 139, 142-156, 158-171 body, 5, 8, 21-22, 25-29, 31, 33, 35-41, 43-48, 55, 57-58, 60-67, 69-73,75,83,98, 119, 125-126, 130-131,139,150,156,160,163 body-s, 38-46 body-q,38-40,42-44,46 capacity, 22, 43, 62-63, 65, 67, 73, 98,106,142 categorialism. 7, 9, 11-15, 17, 20, 140 categories, 5, 7-19, 21, 23, 25, 29, 44,47,49,53,74-75,101-102. 105, 108-109, 116, 118-119, 123, 125-130,132.135,163-164, 170-171

cause, 40-41,52,54,56-60,70-73, 77-78,82, 109-111, 115, 121, 155,160,162 composite, 11, 42, 45-46, 48, 52, 54-55, 57, 60, 62,64-69,71-74, 78-79,81,85,88-89,92,94-98, 118,135,139-140,163-164 contraries, 54, 64 65-66, 68, 82, 97-98 disposition, 76, 108-111,114-115, 117, 119, 121-122 essence, 23, 26-27, 44, 51-54 55-61, 64,70,73,77,145 existence, 11, 57,59-60,66,70-71, 73, 77, 79, 94, 96-97, 127, 134, 141-145, 147, 149-154154, 156-158,162,164-166,168,170 extension, 14, 22, 36, 40, 46, 48, 74, 80-86, 88-93, 95-99, 117, 127, 131, 136-140, 161, 169-170 form. 5, 11-13,17-19,22-23,25, 28, 30, 34,40-71,73-79,81, 85, 88-90. 92-93, 95-98, 101, 103-104, 122-123, 125-127, 131-135, 137-144148-149, 158-164,168-170 fonn-m. 22, 61-62, 64-74, 76-78,91-98,137-140,161-164, 169-170 forrn·c. 22, 61-62. 64, 66-67, 69-71,73-74,76,78,98,137-138

THE FOUNDATIONS OF ARISTOTLE's CATEGORIAL SCHEME

genus, 21,25-29, 32-34, 39-40, 43-48, 50-52, 59, 73, 76, 91-92, 95,98,101-113,115-117, 120-122,133, 136-138,140, 145-146,151,154-156,159,171 habits, 9, 101-107, 109, 115, 122 homonymy, 67, 72, 99, 136 hylomorphism, 9-23,25,47, 49, 79, 95-96,103, 122, 140-141, 160, 162,169-170 Kant, 7-8,171 life, 63-64, 111, 163 line, 7-8, 15, 19, 29, 35-37,43,51, 71-72,88,91,93,119,125-126, 130-131,136,139,143,165

175 174

~Index

62,64,66,69,71,75,77,80,82, 86,90-91,93-94,97,101,104, 106-109,111,116,119,121-122, 125, 128-129, 142,145-149, 151, 154-155,160,162-163,166,171 number, 9, 32, 51, 56, 60, 75, 102, 118-119,125-131,133-136, 138-140, 148

prime matter, 5, 22, 46, 48, 6 6, 79-83,85-87, 89-99, 127, 140• 161, 170 6 principle, 8-9, 17, 28, 37,40-4 ' 48, 51, 63, 66, 71,73-74, 76 -78• 87-89,103-104, 115-119, 122• 133-135,137,143-151, 1 54 , 156-157, 159, 161-171

ontology, 10,13-17,21,51, 78, 84, 86,88,90,101,123,141,163 order, 19, 29, 32, 46, 48, 51, 60, 66-67,69,71-72,74,76-78, 82-83,98-99, 104,114,117-122, 128,139-140,147, 150-151,154, 156, 162-163, 167, 169, 171

48 qua, 7, 30 -3 5, 37-38 , 41-42,44, 50 • 82,96-97,130,135,146,l , 165,169-170 . 5, 7 -9, 17- 19' 22-23, 53, qu alIty, 74-75,101-105,107-1 23• 125,

particular, 16, 25, 27, 34, 49,61-62, 64,66-67,70,74,79-80,88,90, magnitude, 29, 56, 58,126,131,138 93-94,130,146,154,156-157, mathematics, 21-22,25,29-32,34, 165,168 40,44,95-96,146,150,156,170 physics, 7, 17,27-28, 30-31,45-46, matter, 5,10-14,17-20,22-23, 48, 66,81-84, 105, 108, 119, 25, 31, 36, 40-41, 45-46, 48-49, 128-129,135,143,145-147, 52-55,57-74,77-99, 101, 122, 150-151,155,161,164,166,168 125,127,131-132,134-145, place, 8, 25, 32, 40-41, 45, 54, 62, 147-148, 151,156-164,166, 75-78,81,84-85, 101, 106, 117, 169-170 119-120,126,128-130,132,143, metaphysics, 7-8, 10, 12-14, 17, 23, 149,157,159,169,171 27-32,35, 37, 41, 43, 45,47-51, Plato, 10, 61-62, 134-135, 158-159, 53,60-61,64,66,70-71,73-76, 165 80-81,96-97, 103, 117-118, plenitude, 19, 23,142-144,147, 125-128,130-135,146,148, 150-151,156,159-160,162, 151-152,160,162,164,167 165-171 motion, 17, 25, 30-31,40,42-45, plurality, 35, 53, 126, 131, 133-134, 47-48,66,71,86,88-89, 108-109, 136-140,161 119-122,128-129,133,135-137, potentiality, 11-12,63-64,83,91, 140,143,145-147,149-150,152, 93, 95,120,122,127-128,135, 155-156,160-161,164,166,170 142,152,159-162,168-169 power, 63, 68, 158, 162 nature, 14-15,20-23, 26, 28, 32, 37, 40,43,45-46,49-53,56,58-60,

21-23, 130,170 quantity, 5, 7-8,15, 17-l9, 25,29-31,35-40,43-48, 53 ·118 , 75 -76, 81 , 96, 98,101,11750 170 122,125-133,135- 140• 1 ,

7

relation, 7, 10, 12, 17•19 21-22,29, , 5, 8 40 47 63-64, 68,74- 5, 80 130 87:88:91,96,99,122,127, , 144,156,160,163 70 74-78,81, shape,9,59, 65, ' 10, 85,90,92,101-1°2• 104, 1 115-116, 118·12; 33 39-40, species, 8, 22·23, 3 ~ :52, 59-60, 43-44 46-47, 49 • 2 , 98 101-11 , 65-78,91,95, , 131 136-140, 114-122,127,130154-156, 163· 1~· ;2 14-15, substance, 5, 7-\ .30 ,36-50, 18-19,21-23, 5 61 64-67, 53-55,57-58, 60· 98, 101, 103, 69-76,79-80,96-0 i40-143, 145, 118, 120, 122, 13 , 159-165, 167, 147, 149-155, 157, 169-171, 173 7 96 119, 122.

1

7d

su~~S,29,35·:3i 139,159,168 125-126, 12S·

,

. 27, 33-35,37,45-48, 147, syllogism, 149, 166-167 78 155-156 teleo1ogy, ' 51 84-89, time, 7-8, 11, 352,13~ 135 142-144, 118-119,12- ' ' 156, 162, 166-168 9 60-62,64,69-70, universal, 34, 4 ' 136-137, 156 134 74 93-94, 139 • . ' 63 99 132, 135, 138- ' unity, • ' 148,158,161,165