The Origins of Aristotelian Science

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This book may nOf be reproduced, in whole or in part, includ ing ill ustrations, in any form (beyond that copying permitted by Sections 107 and 108 of the U.S. Copyright Law and except by reviewers for the public press), without wri tten permission from the publishers. Set in Li nonon Saban type by G&S Typesetters, Austin, Texas. Printed in the United States of America by BookCrafters, Inc., Chelsea, Michigan. Library of Congress Cataloging-in-Publ ication Data Ferejohn, Michael T. , 1945The origins of Aristotel ian science I Michael T. Ferejohn . p. cm. Inclu des bibliographical references and index. 1.

ISBN 0-300-04649-9 (a lk. paper) Aristotle- Contribution in theory of knowledge. 2. Aristotle-Contributions in logic. 3. Know ledge, Theory of- History. 4. Logic, Ancient. r. Title . B49 t. K6fA7 1991 12.I',6'092.-dc2.0 90-40942.

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The paper in th is book meets the gu idelines for permanence and durability of the Comminee on Production Guidelines for Book Longevity of the Council on Library Resources. 1098765432

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Contents

Acknowledgments

IX

Introduction

PART ONE THE STRUCTURE OF DEMONSTRATIONS One: Demonstration, Division, and the Syllogism Two: Demonstration and Definition

15

38

PART TWO THE EXPLANATORY CONTENT OF DEMONSTRATIONS Three: The Character of Demonstrative Premises

Four: Type

I

Pcr Se Predication

75

Five : Type

2

Per Se Predication

92

Six: Type 3 Per Accidens and Type 4 Per Se Predication Seven: Demonstration and Negation

Notes

139

Bibliography Index r vii

165 169

1.3-'

65

[09

Acknowledgments

The first systematic work on this project was begun in 1981 -82, while J held an Andrew W. Mellon Facu lty Fellowship in the Humaniti es at Harvard. I am grateful to the Mellon fOtlndation and Dr. Richard M. Hunt for thcif sup port during tha t year, and to the H a rvard Philosophy Department for its kind hospita lity. While there I benefited greatl y from discussions on germinal ideas of the present work with John Murdoch, Martha Nussbaum, and Steven Strange. Since then L h3ve received hel pfu l comments and suggestion s on earlier ~e rsjons of variolls parts of the book from Robert Bolton, Daniel Devereux, Michael Frede, Cy nthia Freeland, Robert McKay, Philip Ro ln ick, and Thomas Upton. Specia l thanks are due to David Charles and James Lennox, who read :lnt! commented on the entire manuscript. I especially want to thank my lcachers, John Kekes, Nelson Pike, and Gerasimos Sant:ls, for their unflagging ellco uragem en t and sup port during the difficult times, and G regory Vbstos for showing me by his own example the close connection between good phi losophy and good character. In the late stages of its preparntion, the project has been facilitated by a number of Duke University Research Council Grants, and a Juni or Faculty Research Leave in fall 1987.

Introduction

Books about Aristotle's Posterior Alw/ytics h~vc traditiol1::dly confined themselves to the ancient and respectable, yet relntively modest role of commenrary.1 Remarkably, there has yet to :lppeaf a full -sca le account that even attempts to free itse lf from Aristotle's peculi:1f (perhaps even eccentric) order of exposition in this difficu lt work by placing ;111 o f its contentS into a unified and intelligible analytical fr::lIn ework. Put sim pl y,

this is the void which the prese nt work is intended to fill. In the most general terms, my aim here is to present a nd defend

:l.

co mprehensive inter-

pretation of the theory of "demonst rative knowledge"

(iJ

c:hro15f:/,KTLK-ry

i7Ttwr7J1,L'T}) as that theory is presented in the Posterior Al1alytics and selected parts of the Prior Al1alytics. Now it is quite impossihle to s tudy vertt;), "essence" (TO Ti .ryil elvat ), and "substance" (overia), bll t Aristotle's preferred mean s of design atin g them in the Organon is with the simple Ilom in alized in te rrogative, " the what-isit" (TO Ti eern). The fund amental distin ction between properties that are within the what-is- it of a th in g and others that are not then forms the co nceptua l basis fo r a th eory of predication in Posterior A llalytics 1.4 th at disringuishes necessary, " per se" (Ka(fov-ro), predications, which are the proper conce rn of dem ons trative science, fr om merely contingent, "per accideHs" (KoTa aW.L{3e{3"f/Koop6s) are "useful" (xp-r,a-Lp.m) in such investigations. 11 Furthermore, Prior Analytics 1.27-31 sheds some light on the specific function rbis procedure is supposed to serve within the demonstrative process, since it is presented in those chapters as part of a wider di scussion about how, as Aristotle 's foundationalism and logica l theory requires, one can and should go about selecting appropriate premises of syllogisms in ge nera l, and appropriate ultimate premises of demo nstrative syllogisms in particu l ar. '~ It is importa nt, however, not to expect more of these chapters than they are intended to acco mplish. A well -known passage in Posterior AnaIytics 1.2 sets out six different co nditions that a demonstrative premise must meet: "Now if know in g is as we have laid down, demonstrative knowledge must come from [premises} which are (a) true, (b) primary, (c) immediate, (d) better known rhan, (e) prior to, and (f) causative of,

I

20 )

Demoltstration, DiIJisiol1. tmd the Sylloglslll

the conclusion" (71 bI6 -20) . It would be a mistake simply to assullle that if Posterior Allalytics 2.[3 and Prior A1tolytics 1.27- _)2 give us;, method for co ll ecting premises that have these characteristics, then the method in question is one that selects (or a ll of these characteristics. 11l ~ deed, quite to the contrary, I shall argue presently that the divisional method promoted in these chapters is one for assuring the s;ltisfaction of cond itions (bl and (el alone. To begin with, truth, the first condition listed at 71lH6, is no more than an unanalyzable conseql1ence of Aristotle's very minimal rcquire ~ ment that a demonstrat ion mu st constitute a proof (o r sound argument) for its conclusion. For it is hard to im agine that anything illull1in;.lting could be said about how one should go abollt finding true statements that would not proceed by saying how to find statements that have ccrt..ov) sin ce the o nl y class th :lr incl udes squares and to which the predicate applies is the class o f rectangles itself (under this or sorTIe other description ), wh il e on th e stro nger im crprctati o n the fact th at every rectangle is a rec tan gle is enough to rem EO"TtlJ), there is;l significant la ck of parallcl between the surface grammar of th e two types of co lloquial sentence. Th e predi cate part of a co lloquial sa id -of predication, such as ( I ) Man is (a n) an im al,

or (2.) Socrares is (a) man ,

is t ypically a nom inal form (o r, as we mi ght spec ify further, a so rtal expression, thoug h thi s classifica tion is not so obviolls in a la nguage lacking the indefinite article). Coll oquia l inheren ce predi c:ltiolls, on the othe r ha nd, have as t heir predicate parts adjectiv~l or verha l form s. But why does Ari stotle e1ecl' to exp ress thi s gr;llllmatical distinction by means of th e pa rtici pation cond ition given at 2;1 19? The :-tllswer to thi s, I believe, lies in the fac t th at in the OrgtlJ/ol1 only nom in al form s (roughly, QVDf..LCXTa) are what may be legitim a tely repb ced by defining /ogoi . Thi s is apparently a consequence of Ari stotle's tendency to think of the ohjects of defin ition as things rather than ex prcssions .~ In the case of;l ty pi c:d snid of predication, the predicate is a lready in nom inal fo rm, :md therefore the Clpplicability of the defining logos to what is signi fied by th e subject fol lows unproblema t icall y from Aristotle's o ft-re peated insistence that an adequate definitory logos is always sub stitutahl e for the nam e of what it defines. \ But now co nside r the case of a typicIJ()p.o:ra, th en this sente nce would satisfy the parti cipa tion condition, sin ce the phrase that would be the definition a l equivalen t of " (is) ge nerous" ( rc rh~ps, " tends

I 93 1

Expfmtatory Content of DemollStratiolls

to give freely of himse lf ") is true of Socrates if (3) is true. But this is not Aristotelian. For him the fact that the phrase "(is) generous" is adjectival means that it is not a name and therefore has no definitionally eq uivalent logos. What can be defined, on the other hand, is the entity signified by "(is) generous," namely the igL'i generosity; a nd its defining logos (say, "the propensity to give freely of oneself") is itse lf a nom ina l form, and as stlch is intersubstitutable with the name "ge neros ity." Thus, Aristotle's point in saying at 2.a2.8 that in rhe case of a predication such as (3), «neith er the name nor the logos is predicated of the subject" is that both (4) Socrates is generosity,

and (5) Soc rates is the propensity to give freely of oneself,

are false or worse."

DIFFERENTIAE IN THE CATEGORIES It appears that when Aristo tl e comes to forge a distinction between necessary and contingent truth in Posterior Al1afytics 1.4 (w ith an eye toward isolating those non accidental predi cations suitable for use in demonstrations), one reason he finds theory SI> less t han adequate to his purposes is that he now recognizes a type of sentence that does not fall neatly into the crude said-of versus inherence dichotomy. These ate true senten ces containing sentential elements which signify differentiae (OLUq,OPUL), such as (6 ) Man (is) two-footed.

To be more precise, [here are actually two distinct, though closely related, diffi cu lti es occasioned by the evident meaningfulness of such sentences. Onc is the semant ical problem o f providing an adequate explanation of th eir [ruth cond ition s. The other, whose eventual solution w ill have a di rect bearing on the first, is the ontologica l problem of sayi ng where differentiae fit into the classi ficat ory metaphysical scheme of the Categories. Even before conside rin g his reactions to. them, it is not hard to guess how Aristotle coul d have found himself in the midst of these difficulties. In tbe Topics and elsewhere, his favorite manner of definition is per genus et differentia. Moreover, inasmuch as this style of defi ning is the heart of th e method of division practiced by Plato in the Sophist and Statesman, it must surely be counted as part of the baggage Aristotle carried away from the Academy. But it often happens that there is a price attached to Aris[ 94

I

Type 2 Per Se Pret/i,'afion

totle's acceptance of Platonic doctrines. In rhis case, he th ereby commits himself (0 recognizing the truth of sentences like (6) and therefore to the existence of such "things " as " tw o~footed ne ss." Thlls, in order nO( to S3C~ rince the ge nerality of tbe Categories program, be is forc ed to find a place for both o f these in that framework. Wku we h,we here in effec t is .an in sta nce whe re what Aristotle tak es over from Plato comes into confli ct with his own in dependently devel o ped doct rines. Moreover, I sh:l /l a rgue prese ntl y that despite Aristotle's confident state ments to the co nt rary, th is conflict is not really resolved In the Categories.' It is true that in Categories 5 ( ,:12. 1-2.8) we do find rhe pronollncc~ ment that differentiae are SOlid of the species they differentiate, ;'Iud this, by (56), would entail that differentiae are h01ll0c::ltcgorial with th ose s pecies. Furthermore, there is no m ystery about why Aristotle s hould W;:lIlt this to be so. Since reference to a differenria is as 111uch a p ~l rt of th e defi nition as the name of the genus (according to th e Platoni c legacy), then surely differenria predications should be nccorded ;t tremlnent th ~tt respects their status as definitional (a nd necessa ry) truths and does not dUlllp th em unceremoniously in to the class o f :lcddental inherence predications. But for all this, there are also very powerful re;1sons why Aristotle is not free simply to cla ss ify differentia predications os s:lid -of pred ic.1tions. Chi ef among these is th e fact thM they do nor really sMis fy the participation condition. Aristotle does quire a bit of pushin g and pull ing trying to get such se ntences to pass this test, but in the end (as Ackrill points Ol1t~) these efforts must be regard ed as so much desperate cosmetics. Bri efl y, h is trick is to test for satisfaction of this condition only after first puuin g the differenria predication through the regiment:ltioll phase of rhe truth analy sis discussed in chapter 4, so that (6) is recast .1S (6') Two·footedness is predicnred uf

111/111 .

Following this regimentOlrioll, a differentia predication comes out conta ini ng only nominal forms, and in this form such prcdiC:Hions certainly do satisfy the partic ipation condition. Howeve r, this m:lllCliVer is only open to Aristotle at the cost of having to dispense with the particip:u ion condition a ltogethe r. For lhere is nothing 10 preve nt eX;lctly the sn llle move in the case of a paradigmati c inheren ce predi cat ion. For in st:mce, one cou ld use virtually the same reasoning just dispbycd to show that sample se ntence (3) satisfies the p" withi" G 3re intersubstitutable. In employing this principle he evidently means to distinguish this type o f dichotomy from tbe accidental so rt th at might be susta in ed temporarily, if say, all men were for a tim e either sitting o r standing to the exclusion of all other physica l attitudes. For, as Aristotle is no doubt aware, this latte r

[ 102 J

Type 2 Per Se Predicatioll

trans ient state of affairs wo ul d not justify connaring the propenies of sit· t;ng and not·stm/dillg within the hum~m spec ies, nor wo uld it even justify the assertion that these properties enta iled aile a nothe r. Aristotle's argument, then, is that STRO NG MLEM and (PO) together with the implicit assumption that any pair of type 2. per se attributes form an A·pa ir of opposites. yield the conclusio n th at such attributes belo ng necessaril y to the mem bers of the genus to w hi ch that A ~ pa ir is appropri . ate. As it applies to the pair odd and el'en, Aristorle's actua l exa mple at 73b2.2.-24, it purports to show that beca use these two attr ibutes for m a n A· pair appropriate to the gen us I1Im/ber, it follows t hat they belo ng nec· essaril y to numbers. But which numbers in particular? It is nor yet dear what exac tl y the argument is supposed to show. In the passages quo red ahove (7.~ hI(, -19, 2.4 , 74 b6-7), Aristo tl e's conclus ion is represented as t he thesis that a cer· tain group of attributes belong necessJrily to thei r subjects. Howeve r, ill view of the fac t that the anno unced primary purpose of Posterior A,I1l· Iytics 1.4 is to isolate a class of necessa ry statements that can fUllct ion as syllogistic prem ises in demonstration (73 a2 T- .'i), we still mll st a'fwl [Ire well within the range of the actual ancient usage of that term, how are we to decide between whac appear to be two equillly plausible intt'fprewtions? The way our of this quandary is again to be found in Aristotle's rel11arb.ble knack for prov id ing just the right example at just the right tim e. In this case his choice of exa mples constit utes stron g evidence that the class of type 4 per se predications d iscussed at Posterior AlInlytics 7 3h 10- 16 is IllC;]l1t to indude a type of statement he elsewhere describes as "generally true," or "true for the most part" (i7Tl. TO 7TOAV) . And since 1 shn ll also argue that these last are patently the type of causn l general izations Arisrotlc includ es within the scope of his theory of demonstmtion, this will support the callsal jn ~ terprctation of senten ce (6). It must first be noticed thai Aristotle's F.7T1. 'TO 7TOAU predications typically have very general subjects, chat is, suhj ects th :lt apply to a great many cases. II Wh..ti truths hut th at Aristotle ev idently also places under the heading of type 4 per se predication . T hese are sen ten ces that :.lttrihute to so me subject ;1 cert:lin subtype of wh en he refers to as "propria" (Ulter ). Such predicntions receive their fu ll est treatment in the To/);cs (especia lly;'lt (02aI8, 12ob2}, and throughout Book 5), but they nre menrion ed by n;'illle in th e Posterior Allalytics at 73a7, and again at 96t126. What's more. Aristotlc's most frequent examp le of a scientific explicandum in the latter work, (12.) Triangles have [interior ] angles equal ro two righ t

angles,

invo lves one of his favo rite examp les of an i:8wv. Accord in g to Aristotle 's intit al introduction of propria at Topics 1.5.102:118, they arc distin guished by two conditions: if one thing is a propriulll of a noth er, then the express ion that signifies the first mu st not sta te anything in the essence, or "the what it was to be" ("TO Ti T,V eil1at) II. of the second, ;lIld the first mll st belong only to the second. T hi s second condit ion is then redcscrihed as the requirement that propria mu st he "convertible" with their subjects, which mea ns that (or every tru e propriul1l predicatioll there is ;] corresponding trlle universal bicondirio l1;'1l comnin ing th e same terms. The example Aristotle provides in this p;lSS;lgC shows de:lI"ly wh;'lt he has in mind: (l .~)

Man is ca pable of lea rning gr:l1ll1l1:lr.

Since none of the various defin itions of Illall presented in the Corpus makes reference to the capacity mentioned in (l3), ;'Ind since (accord ing to Topics 101b]8) a definition sta tes the TO Tt Tjv t:i'1nL o( its definiendum, we may assume th;'lt ( I .,) does meet thc first condition givcn ~lt., f R. Moreover, in Aristotle's own words, " if [;1 thing] is a 111;111, it is capahle of learning grammar, and if [a thing1 is capab lc of learni ll~ gr;ullllwr, then it is a man" (Topics 102a2.1 - 2.3). T hi s is qu ite dearly what is mca nt hy the second condition, sin ce it simpl y mean s that rhe Glp;'l c ity for learning grammar belongs to all men and to men alonc.l ~

I 12.1 I

Explanatory Content of Demonstrations

Now, as Aristotle himself recog ni zes at Topics 5.I.12.8bISff., these two condit ions are so general that they ca n be satisfied by predications of vastly disparate charac ters, and only some of these he thinks to be of interest to sc ience. In particular, these are predications that involve what he calls at 12.8bIS "per se propria" (Ka9'avro f5ta), where even though the proprium in question is not in the "what it was to be" ofthe subject (as is dictated by the first cond ition on propria ), there is nonetheless so me conceptual con nection between subject and predicate that accounts for the truth (indeed, the necessary truth) of the sentence. Clearly, sentence (13) is of this type, since although grammati cal capac ity is not mentioned in the definition of man, there is an obvious concep tual connection between something being a man and it being able to learn grammar. 18 There can be no question that these predications of per se p ropria make up a n important group of propositions of Aristotelian sc ience. They are especially important to the mathema tica l sc iences such as geometry or arithmctic, w here the aim is to demonstrate the truth of certain necessary (as opposed to merely causa l), but nondefinitional propositions from a se t of given definitions and axioms. This again is evidenced by the

fact that (12) Triangles have [interior] angles equal to two right

angles, Aristotle's fa vorite exa mple of a sc ientific demonsrrandum in the Posterior AnaJylics, involves one of these per se propria. Since the definition of triangle contains no referen ce to interi o r angles, the predi cate of this sentence can not signify anything in the essence of its subject, and so (10) is not a definitional truth. Furthermore, there is very little doubt that Aristotle views thi s as a case of convertible predication. And sin ce he is no douht aware [hat th e axioms, definitions, and postulates of geo metry can be shown to entail that whatever is a triangle possesses the property mentioned in ([ 2.), he would certainly classify that property as a per se propnum. On the othcr hand, Aristotle also explicirly recognizes that there are other true predications besides those that ascribe per se propria, which likewise satisfy the two general conditions on propria, but in which the connection between subject and predicate is entirely fortuirou s. 'Y For example, he indicates at Topics 129a3 that if a sentence such as ( 14 ) Socrates is wa lking in the Agora,

I 124 )

Type 3 Per Accidens and Type 4 Per Se Predication we re to be uttered at a time when Socrates was in fact the only pedestrian thing in the Ago ra, it would have to be regarded as invol ving the attribution of a proprium, albeit a temporary one. And thi s is as it should be, since on such an occasion (14) wo uld plainly satisfy both co nditions for propria predications given at T02.aI8 . For walk in g in the Agora is ce rta in ly no part of the essence of Socrates. yet on that oc, .. sion he is precisely the extension of the predicate of (14). But even though th is sentence is st rictly speaking a proprium predication, Aristotl e main tains throughout the Corpus that something's wa lk ing or being in 0 ce rtain place are the kind of genuinely accidenta l states of affairs that hold no scien tifi c interest. Hence, such accidental sentences as (T 4) shou ld qui te naturally be absent from th e theory of demonstrative knowledge ou tlin ed in the Anofytics. By cont rast, th ere is ampl e ev idence rhat necessary predi cation s of propria of the per se variety are sup posed to fi gure importantly in Aristotle's theory. Besides the fact noted earlier that the mathematical proprium mentioned in (.1 2.) is the most frequently cited examp le in the Posterior A110iytics of a per se attribute whose existence ca n and sho uld be demonstrated, there is also a host of programmatic pilssages from both Analytics leadin g to essen tially the same conclus ion. For instance, at Posterior A1tolytics 2. TJ.96hlj - 26, the passngc in whi ch Aristotle explJins how his version of the method of division can prove use ful in undertaking the systematic study of a genus /" he says th:1t one should try, among o th er things, to discove r the "proper affec tio ns" ([Ow' 1fod1T}) of o ne's sub~ jecr.!1Likew ise, in Prior Altaiylics I.27, whose concerns I have argued (in chapter I) are closely parallel to those of Posterior A"afylics 2..lJ. he makes much the same point in almost the same words: "We mllst differentiare among the co nsequ ents [of a given suhj ectl those which are in the what-is-it, those which are predicated as 'pro pria ' (i61.(1), and those which arc pred icated as [merely] accidenrally" (Prior Al10fytics 43b712). For presumably, if it is hi s intention all along simp ly to colbpsc all propria into accid ental attributes for scientifi c purposes, there wo uld be no point in distin guis hing th e seco nd an d third cla ssifications men tioned here. Fu rthermore, a biological example supplied by Aristot le ill IJosterior Anafytics 2.14 gives a pretty cl ea r idea of eX:;1( tl y how propri:1 will figure in the co nstruction of demonstrative sy llogisms once a sHhjec t-gcJlUS has been syste matized according to the guidelines set OUl' in th e previous chapte r. At 98ar7 -2.o, he indi cates th at it wO Hld he reaso nab le to pro-

[ lZS [

Explanatory Content of Demollstrations

ceed by first identifyi ng certain charac teristics of anim als th at always accompany possess ion of horn s, such as having a third stomach or h aving a sin gle row of teeth, and then arguing (sy ll ogisticall y) that any subtype of horned animals mu st necessarily displa y these same cha racterist ics. Now if, as see ms plausible, we take thi s as a description of an approved form o f demo nstration , and also assume that the attri butes in question are necessary [lila of horned animal, we ca n understand Aristotle here as certifying de monstrati ons such as th e follow in g: (i) Al l cows a re horned, a nd (ii ) al l (and only) horned an im a ls ha ve a third sto mach,

so {iii } all cows have a third sto ma ch,

where what is being demo nstrated is th at a per se prop ri um of a certa in kind is >1150 a necessary atrr ib ute (though not of course a proprium ) of one of its sub kinds. This th en has far-reaching and impo rtant consequences fo r the acco un t of the stru cture of demonstration given in part I . Fo r since the primary (affirmati ve) demonstrative premises considered in chapter I we re limited to state ments that are immediate but not convertibl e, the onl y so rt of de mon st rative syllogism in Barbara represented there: (i)

All B is A, and

(ii) all C is B, so (iii) all C is A, W3S

a type in wh ich the rclati o ns among its co ntai ned te rm s may be rep-

resented by the fo ll ow ing vertical sc hema:

c I 126 I

Type 3 Pcr Accidens alld Type 4 Pel' Sr Predicatioll H owever, in ligh t of the examp le at 98 al7-2.0 , we can now see th :lt in addit io n to this entire ly ve rtica l type of d emo nstration , Aristo tle al so recognizes the possibility of another sort, in w hi ch the terms of B:J.rhnr;:l are related as follows:

/

B --A

/ c

/

whe re the late ra l co nnec tion between A and B is meant to represe nt th e relatio n of mutual entai lment (that is. convertihili ty) betwec n a kind (B) and one of its per se prop ria (A). Bur now, thi s opens the furth e r poss ih i l ~ ity of an exclusively lateral form of demo nstratio n, represented hy the schema, .

A- -

c/ n

/

/ in w hi ch o ne exp lains the possess io n of one per se proprilllll (A) of a given kind (C) by reference to the possession of anothcr of its per se rro~ pria (B). W hat is striking about this form of demonstration is t hat it accomp lis hes all of its ex pblnatory work at :l s ingle divi sio nal nod e. As applied to Aristotle's exa m ple at 98:l 17- 2.0, this Jl1i~h t invo lve, say, CX ~ pla in ing the presen ce of a third stomach in horned animal s by means of dental configuration: (i) All (:t nd only) things wit h :t single row of teeth have

a third stomach, and ~dl (:tnd o nl y) horned anill1:l1s haw ,1 singlt· row of teeth. so (ii i) all (and only) horned anim a ls have;l third stol1l.u.:h. (i i)

o r perha ps the dental co nfi guratio n migh t be explained hy lll e;:1IlS o f t he thi rd stomac h . ~! It is appa rently beca use of the obv io ll s import ~lI1ce of sl1 ch sentences

I

127

I

Explanatory Content of Demonstrations

to Aristotle's science, most especially to his mathematics, that Mure includes per se propria predications among the type 4 per se predications discussed at Posterior Analytics 73b10 - 16. H Although he docs not make his reasons for doing so explicit, they are no doubt analogous to those given above in the case of 87Tt. TO 7TOAV predications: since we have seen that such statements make up an important class of scientific propositions in the Posterior Analytics, Aristotle must have included them somewhere in his catalogue of scientifically appropriate statements in Posterior Analytics 1.4. Moreover, the fact that he actually uses the expression per se in the Topics to distinguish thes.e necessary propria from other types provides additional grounds for thinking that they are discussed somewhere in Posterior Analytics 1.4. But since he makes it a characteristic feature of per se propria predications that tl1ey are not definitionally true, their inclusion in types 1 and 2. is ruled out, and this leaves type 4 as the only remotely plausible place where they could be included. A UNIFIED ACCOUNT

At first sight, it is admittedly hard to believe that Aristotle could indiscriminately lump per se propria predications and bTl. TO 1TOAV predications together under a single heading in view of the fact that they seem so obviously different in character. For it seems that any proprium predication, including those of the per se variety, must be strictly universal by virtue of the convertibility condition, whereas the lack of precisely this feature is what Aristotle uses to distinguish E7Tt TO 1TOAV predications from necessary truths. It seems incredible that Aristotle could identify these two disparate types as type 4 per se predication without so much as a word to indicate the differences between them. Yet despite its incredibility, there seems no way of escaping this conclusion. Certainly, the arguments offered above to support Mure's inclusion of per sc propria predications among type 4 per se predications carry great weight, and yet we have seen that there are analogous and equally good reasons for interpreting Posterior Analytics 73bIO - 16 as being concerned with S7T1. TO 1iOAU predications. In addition, the conflation of the two types is supported by the fact that th·ere is an almost perfect parallel between the examples given of type 4 per accidens predication at 73b6 - 8, and the sentences contrasted with 61T1. TO 7TOAV predications at Prior Analytics 3 2b 15. Moreover, there are reasons independent from what is going on at Posterior Ana/ytics 73bIO- I6 for thinking that Aristotle doesn't distinguish between these two types of statement. Even [ 128 J

Type 3 Per Accidells alld Type 4 Per Se Predicatioll

though he recognizes bo th types as scientific. and discll sses each as such sepa rately (indeed. sometimes even in a single work; co mpare Posterior Analytics 73a7 with 87b2.0). th ere is not a sin gle passagc wherc he mcntions both, or says anything to indicate that they arc disti nct types. In fa ct, to my knowled ge, th ere is no place ill the entire Corpus where th ese two o bviously important types of sc ientific statements are set side hy sid e. Fortunately, a ve ry plausible way of dealin g with thi s difficulty is provided by Mario Mignucci (198 1). On Mi gnucci's suggestion, it is not necessary to understand Ari stotle at 7j b lO- 16 as :mempting to pla ce two very different sorts of predication under a single heading, becau se he holds that behind every "for-the-most-part" predica tion there lurks a pe r se proprium, or to put it eve n more strongly, that any "for-the-most-part" predi cation is actually a disgu ised for m of a pred ica tion that assigns a per se propri um to its subject. To see how thi s sugges ti on addresses the diffi culty just descrihed, co nsid er agai n one of Aristotle's p;1radigms of R71-L 'TO 1TOAU p red icat ion: (8) A man grows ch in wh iskers las he ages ]. ( Posterio r

Allalytics 96a 1 0)

I have already argu ed t1uJ.[ Ari stotle do esn't interpret thi s as a mere sta temen t of statistical frequency but rather und erstand s it as ex press ing some

so rt of causa l necessity betwee n aging and th e cmerge nce of w hi ske rs. However, a number of recent st udies suggest that Aristotle's basic model for understa nding ca usa lity is not as a relation between events (whethcr construed types or wkens), but rath er as the opcrations of " causa l powers" residing in [il e " natures" o f the subject-subst:'lil ces in whi ch th e ca usa l effects in qu es ti on obtain. l " On thi s understand ing, We can understa nd th e emergence of ch in wh iskers in p:Jrticui:.1 r ns th e exerc ise of so me causal power, P, invo lved or co ntai ned in th e na tu re of mall. This is where M ignu cc i's suggestion co mes inro play. For it is now plausible 10 interpret Aristotle as ho lding th at P is possessed hy every single specimc n of ma n wi th out excep tion, and accordingly to describe those occ;:lsio nal spec imens without whiskers nor as lacking P, out as instances where P, though possessed, fails to be manifested. On thi s suggestion then, co rrespondin g to thc b Tl. 'TO 7TOAU truth of (8) A ma n grows chin wh iskers {as he agesl,

Aristotle also recogni zes the morc fund a menta l truth of some such sen· tence as

I 129 I

Explanatory Content of Demonstrations

(8') Every man has P (which for the most part is manifes ted hy the grow rh of chin whiskers at the approptiate time). What is more, even though this power might be regarded in some weaker sense as esse ntial to the kind man, Aristotle wou ld certainly not see it as in the what-is-it of that kind as that narrower notion was interpreted in chapter 3. Therefore, on the additional assumption that the power to grow chin whiskers is special to man,2s it would follow that (8') predicates a per se proprjum of its s ubj ect.l~ Having now examined each sense of per se and per accidens exp li cated in Posterior Analytics 1.4 separately, we ca n take a final overview of the whole co mplex doctrine by classifying the various kinds o f true predicat ion we have encountered in the last three chapters according to their suitabi lity to se rve in demonstrations. Among those state ments that can occur as demonstrative premises, but not as demonstrative conclusions, we have placed "definitional" predications,!? that is, type I per se predications (whi ch may either place their subjects in their superordinate genera or constitute "constructive" definitions); whereas among sentences that can occur as demonstrative conclusions are both type 2. per se predications (predications of differentiae to subsets of their sub jects), and type 4 per se predications (p red ications of per se propr ia, and also &1T1. 'TO 1TOAV truths), On the other hand, the two types of predication that can not have any place in demonstrations are type 3 per accidens (that is, intercatego rial predications with nonsubstantia l subjec ts) and predications that are not per accidens in that sense but arc per accidens in all three other se nses of that term (that is, genuine inherence predications).

[ 130 I

SEVEN Demonstration and Negation

NEGATIVE PREDICATION IN DEMONSTRATION When Aristotle says in Book I , Chapter 14 of the Posterior A110lytics that demonstration characteristically proceeds by first-figure syllogisms, he does not specify further that the preferred inft: rcnrial form is limited to Barbara, the only purely affirmative mood with ;111 l1ni vcrs
[ 150 [

Notes to Pages 76-79 2.. This translation is from Ackrill ( 1963). 3· M o ravcsik (1967) ·

4. Ackrill (196)) , 7 1. 5· Ackrill (1963 ), 78. 6. It might be argued against this interpretati on of Cate~()ries 4 that ArIStotle's characreri2.arion of affi rmations (and den ials ) at 2.a2.- H as "wh;tt arc tru e or fa lse" is merely m eant to distinguish them from terms. which are described ri~hl afte rwa rd (at a8 -9) as not incapable of hearing trnth-values. O n thi s view. the remark is seen as closely parallel to De lnferprerarioll e I . 16a '4-19. a passage where Aristotle is concerned simply to introduce the central subject of the work (statements) by distinguishing them from va rious o ther kinds of lingu istic entities. The prob lem I find with this alterna tive is that it docs nol attach any import:lnce to, or g ive any explana tion nf, the fa ct that th e Categories chapter (unlike De bllerpretatione I ) expl icitly stares both that the possihil ity of truth o r falsity is generated by the in terweav ing of uncombi ned expressio ns. nnd (i mmediately beforehan d, at b2. 5 - a 4) tha t each o f th ese uncombined expressions signifies an entity in one o r another of the categories. The proximity of these points creates the presum ption that they a re intended to he closely con nected, a nd o n my view they are: the semanti c va lues (truth and falsi ty) of comb ined expressions (s tatemen ts) are partly determined by th e sema ntic vnlu es (signific3t3 ) of the unco mbined ex pressions (terms) that comprise them. Incidentally, this inrerp retnti on of Categories 4 makes the chapter an Aristotelian echo of Sophist 2.(, ID -2.63B, where Plato says not only that truth and falsity apply exclusively to complex ex press ions (statements ) produced by the in terweaving of nt least one verb (pr,p.,a ) and one noun (o voj.La), but a lso th ar thi s is because a verh sign ifies a n action, a Iluun signifi es a sub ject of acti o n, and a true (or false) swtemcnt is one wh ose verb sign ifies an action that is in fact performed (o r not) hy what its noun signi fies. 7. T hat [h is sema ntics is limited to what I have ca lled atomic sentences is evidenced by the choice of examples at 13 18: " Man runs" (aIJOpW7TOC; 7Pf:X&t ) and "Man wins" (a v(Jp w1ro,> IIlKf/). At 2:16 - 7 he indica tes that " denial s" (a7T()q,aCT&t'» as well as "r'lI1t:~. I ... 2..111 .~.

' 5 llll (,

Syllof,isrn. theory of: lngic of dr llltlnstra· tinn. 5. ' 7; II1mbl. fq. '49//;; a ffirm ,lti v~ vs. negalivl.'. I \ I - \ 1 SyBogisticislil. st ri ct. 'i. I II, \ 1. 141111. '45 "4 ,; on existence :\s.~lIl11ptilln~, H- .15 •.~ I. 14(1111 \; un r.khnititlns. 40 -4 1. Sl-.'il. 1461111;011 Wllllllon axioms, 14 .~/14' Symhols. vs. in;lrtit:l1l:1te tJlli.~e s, 1(,1119 Sy.~tem ;ltit:ity: in demonstration. 7, 4') - ~ I. ~ 2.. SI' t' dfsfI Illterrel ,ltillll :ll model of jllsrincHioll Terrac!totoIllY. of (.",'II'gllrics, Ko-}l1. 15211 1 ~. 1.~l-54"J.K, l .'i1 "J.l. 1.'i .1112.:-I The