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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.
C IP
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To Donna
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
I 1
J
Introduction &7TLcrn1J-LT/, which can be translared more or less accurately in some Aris·
totelian contexts as "science." When combined with the fact that Aristotle is deservedly renowned both as archetypica l philosopher and as progenitor of many of the modern sciences, this can easily give rise to the
idea that his treatise on
e1T'
of science as that description would be understood in modern contexts. Tempting as it may be, this assimilation seriously misconstrues Ar istotle's aims in this work. If by a "science" one means to deno te a scientific discipline, that is, a d iscrete area of investigation or expertise delineated from others by having both a distinct subject matter and its own charac teristic methods of investigation, then it is simply wrong to think that any such highly specialized concep t is present from the outset of the Posterior Analytics. Instead, the treatise shou ld be viewed as an occasion on which Aristotle begins to move toward an articu lation of thar concept. H ence, as my title is meant partly to suggest/ this book is not about Aristotelian science itself, but about how that ve ry idea grew out of its philosophical antecedents. At the same time, this is not to suggest that he ever achieves, or even approaches, fu ll articulation of this concept in the Posterior Analytics. For whi le there are a number of passages where Aristotle can be seen dis~ tinguishing and even o rganizing f:7TLCJTi}J-LexL according to their subjec t matters, I nowhere in the work does he evince much theoreti cal interest in questions about how the practicing researcher of some area of study goes about (or should go about) co ll ecting and organizing data or producing general results. In fact, the two Analytics on the whole seem to have ve ry little to say about the investigatory methods of science in genera l, much less about any differences among those of the special sciences. Instead, th ese works proceed from the stand point of a "finished" sc ience whose resea rch is complete, and are largely focused on questions a bout the characreri!ai c pau('rns of reasoning through which one might prove, or "demonstrate" (a7TO()f: iKI1VJ-LL), thtu ce rta in independently discovered particular facts of inrerest follow from, and are thus exp lained by, general scientific principles already in hand. 4 But if it is granted that the trearise represents th e initial stages of the movem ent toward the modern conception of a science, this rai ses the question of what provides the impetus for this movement in the first place. We wi ll want to know what basic iss ues and prob lems lead Aristotle even to begin the process that culminated in the emergence of this techn ical concept. The key to this issue lies in acknowledging that there is
I2 I
Introduction
an earlier usage of the term E.1TtUTijJ..L7I . discern ible in m:1I1y of Plato's wri tings, which stands in rougb alignment with rh::lt of the mod ern En~ glish noun "knowledge." \ It will not be necessary to digress into ;t full~ length philologica l study of this expression just to make my ceotrnl point here, which is that the occurrences of i7n~J..LT1 in the fi rst three c hap ~ ters of the Posterior AHaiyttcs, where the mnin rorics of the book are in~ trad uced and motivated, conform genernlly to this earlier nontechnica l usage, and so are better tran slated as "knowl edge" than as "science." One good indication of this is the striking para ll el between Aristotle's arguments in Book 1, Chapter 3 agai nst various " nonfoundntiona list" t h e~ aries of justification and treatments of esse n tinily the same top ic found in recent epistemologica l literature. For the ultimate premises of those Aristotelian arguments flow out of ce rtain reasonab le pretheoretic ideas about the general nature of know ledge and justification, and nOt from any s re~ cia l features of the distinctively Aristotelia1l theory of "demonstrative knowledge" (c.i1ro8etKTtK-ij E.1TuT7"'i]J..LT1 ) whose presentation officia ll y begins in Chap ter 4. But if it is wrong to construe the main subject of th e Posterior Analytics as phi losophy of science, it would be eqllnlly mistaken to classify the work as a piece of genera l epistemology. While it is tru e that Aristo tle begins his treatise with a discussion of what he sees as ce rtain general constraints on any adeq uate theo ry of know ledge, it is also (rue tll:!t thi s initial stage of his inq uiry is extremely short-lived. From there he moves sw iftly, begin ning in Book I , C hapter 4, to th e task of actually constructing an account (based on his own theory of sy ll ogistic deduction) of "knowledge in the unqua lified sense" (e7rurrr,J..LT1 a1TAwr;) th~lt he believes successfull y meets these constraints. This overv iew of the Allaiytics as located wi th in, and pa rti ally traversing, the area between general epis temol ogy and philosop hy of science, ill~ forms most of the material in this book. Each charter is organized arounJ an attempt to show how o ne or more- of A . . isrot lc's genera l philosophical views on the nature of knowledge and its neighbori ng conccpts ultimately contributes in imponanr ways to the theory of demon st rati ve knowledge which he ultimately develops. There is, however, a sense in which the Posterior A,zalytics has somc~ thing of an amalgamated cllamcter, and th is witl add a further comp li cation to the proceedings. As so often happens, Aristotle is ev id ently co ncerned in this area to make hi s own independently developed views consistent and coherent with what he sees as right o r rcdccl1101ble in Pla-
I3I
illtrodtfctioll
tonism. For thi s reason, some of the prefiguring views to be discll ssed below are positions simply taken over from PI am without visible demurrer, while others are distinctively Ari stotelian in origin, and in some cases even a nti -Platonic in spirit. A large part of my aim here, then, is to show how Aristotle's theory of demonstrative knowledge is generated ou t of a confluence of his own original thought with philosophical views inherited from the Aca demy. There is one final asp ect of the Posterior AnaJytics which should be introdu ced as a preliminary matter. Given Aristotle's notoriou s promiscuou s movement between rile form al and material modes of speech, it would be difficult to characterize his philosophical methodology as having made what ha s been called in this centu ry "the linguistic turn." That said, there is non etheless substa nti al point and profit in noticing that his general theoretical approach in many of the so-called logica l works of the Orga/lOIl has features in common with that of contemporary philosophical logic. To he sure, he never formulates exp licitly, nor does he reli giously o bserve, a ny hard and fast di stinction between sentences on the one hand and the extralinguistic {acts or propositions they might be thought to express on the other. All the same, he often finds it important and usefu l to se lect and prefer what he evidently rega rds as the most metaphysically perspicuous ways of expressing certain kinds of facts, and to that extent he seems committed, at least implicitly, to something like a doctrine of "logical form." What is even more to the present point, there arc a number of passages in the early works (most especially, th e Categories, De 11lterpretatione, and rhe Posterior Analylics) that are best understood as part of an ongoing effo rt on Aristotle's part to work out the details of a theory of predication. As it will apply here, t hi s means that most or all of what Aristotle says about the nature of scientific knowl edge in the Posterior Allalytics ca n be cast without intolerable di sto rtion into talk about the requisite features of the kinds of state ments he thinks suitable for expressing or conveying such knowledge. Acco rdi ngly, the formative effe cts of his various philosophical commitments on his theory of demonstrative knowledge will fall out below as a set of syntactic and se mantic restrictions on what he w ill a llow as legitimate s~ ientific predications. The broad context of part I of this book, "The Structure of Demonstration ," is dominated by the a rguments i.n Posterior Analytics, Book I, Chapter 3, mentioned earlier for the following thesis: (AI) Any genuine system of justificatio n must be
foundational. [ 4 J
[litrod/letion
Specifically, it will be argued in chapter I, " Demonstration, Division, and the Syllogism," that this foundationalist posi tion actually l1<1s two quite distinct, though easily confused, conseq uences for Aristotle's theory of scientific knowledge. In the first place, inasmuch as the logi ca l machinery of demonstration is provided by the theory o f the sy llogism presented in the first book of the Prior Allaiytics, (A I ) requires that the demonstration of any given explicandum must rest ultimJteiy on sratc ments thJt are not themselves derived sy ll ogistically from still more basic premises. Predicta~ bly, Arislotle identifies the feat ure responsihle for <111 ultimate premise being "syllogistica lly primitive" in this way as its being "immediate" ( ciJ.leO'o~ ), by whi ch is meant that there is no middle term that can be in ~ terposed to form a mediated predi c:ltional link between its sub ject :ll1d predicate terms. Our of rh is naturally emerges his view that each d emol1~ strative science has associated with it J distinctive se t of stJte ments that are immediate in just this se nse and therefore fUllction as th e " pril1l ~l\'y premises" (rrpwTolI 1TpOTCYUe tC; ) Ollt of which all :-;yllogistic dCll1on s tra ~ tions within that science are constructed. However, in addition to this intrascientific type of foundarional is m, which is clearly linked {Q th e syllogistic require ments of the Aristotelian theory of demonstration, 1 will argue that there is another morc generi11 epistemological foundational ism also present in the Posterior Al1alytics. and the tendency to confuse the ty..IO has confo und ed Illany ~lllcienr and modern attempts to comp reh end the work. This second position is that a demonstrative science (or ind eed any genuine justificatory system), now taken as a whole (primary premises included), must proceed from "start~ ing points" (ap)('ai ) that th emselves are not, and cannot be, proper parts of that science. This is just to say th at hy virtue of th e ve ry nature o f ju st i ~ fication, no sc ientifi c enterprise could possihly function as :l bootstrap operation some how capab le of generating or grounding resulrs ex nihilo. Rather, Aristotle in sists, it can be entered in to only by ::1Il cpistemic sllh~ ject who is already in possession of an adequ:He stock of preexistent (rhat is to say, ptesc ientific) knowledge nor itself in need of justiflc:ltion. Some recent writers have tried without Illu ch success to equate these external epistemological starting points of a demon strative science as a whole with the internal logical starting points- prilll:J ry premises- of individual sy llogistic demonstrations within a science, and it must be a d ~ mi tred that th is id ea !los been encouraged to some extent by Aristotle himself. Against this mistaken view, which I call "striLt syllogisticism," I shall argue for a two~s tage interpretation of demonstrative sc ience." On this account, the construction of scientific expla nation s begins wi rh what
I 5I
llitroduct;oll
I call a framing stage, which will be rep resented as a nonsy ll ogistic proce-
dure descended from the Platonic method of "division" (5
Genuine knowledge must be of what is universal
an d (Pl.) There can be no knowledge of pa rti cul ars, a nd to his own radically anti-Platoni c metap hy sica l theses: (A2.) The things which are most real are (particular) prim ary subs tances
and (AJ) There can be no "separated" universa ls. These seem in gly incongruous com mitm ents le ad him to id entify (o r in vent) as the paradigm for sc ientific predications a rather cu rious type of state ment that I cha ra cte rize as the referential universal. A sente nce of this type is un ive rsal in form, but unlike its Post-Frcgean cou nterpart, existentia lly loaded in the sense that it in volves di stri bu ted reference to all of the particulars lha t fall under its sub ject te rm , and so entai ls or presupposes t heir ex iste nce. As they will be explicated here, Aristmelian OPOL wi ll then turn out to resemble primary pre mi ses syntactically in th at both are uni ve rsal statements that exptess immediate con nectio ns between terms. On t he other hand, the two types of state ments w ill a lso bc distin gui shed fro m onc a nother on semantic grounds because opo , do not in -
[ 6 J
Il1trodllCtiolT
vo lve any reference to particu lars (a nd hence are not referential universals) , but are instead free-floating, or Platonistic, uni ve rsa l predications that could be true even in a universe containing no mundan e partictdars whatever. Along the way, I will also argue that this cru cial di stinction between Pl aton istic definition s and referential universa l immediate premises is a cent ral element in Aristotle's subt le and co mpli cated final position in Posterior Analyl;cs 2.7 - fO o n the question of whether, and in what sense, definitions a re demons trab le. By the end of part I it should be clear that Aristot le characterizes the fin al products of demonstrati on as knowledge in the strictest sense possible for two complementary reasons, both of which stem ul timately from features of the framin g sta ge of demonstration. In the first place, as has already been remarked, unlike the OPOt that go in to this procedure, the primary premises that come o ut of it, and therefore the exp lican da that follow from those premises, are all refetential uni ve rsals, and so are ab out the most real objects in Aristo tle's early ontology. But marc t h~ n that} it will also be seen that th e framing sta ge ~Iso sys[c m ~ ti zes the suhject-genus of a demonstrative science insofar ~s the se t of prim~ry premises it yields can be thought to represe nt iJ taxonomic orderi ng of that genus by the immediate connections expressed by those premises. But this means that the whole p rocedu re o f co nstructing nn Aristotel ~:ll1 demonstration does not just ex pl ain facts indi v idll~lI y; it also locntes the explained fact within the appropriate st ructured lie ld of sc iencific in terest. This bri ngs Ari stotle 's th eory into li ne with :In attra ctive episremo logical pos ition prominent in the final part of Pl ato 's Theaetetus: (PJ) One cannot possess knowledge of a p:1rti cular (,let without possessing know ledge of the entire syste m o f fac ts o f which it is an element.
Pa rt 2. is a close study of Aristotle's views concerning the spec ifi c so rts of immed iate connections he is willing to perm it between the terms of ncce ptablc demonstrative premises. T he main point of depilrtllte for this study is Aristotle's endorsement of yet another familiar Platonic epistem ological requ irement: (P4) Knowledge is of what C:1 I111ot be o therwise,
and its nearly immediate consequences thnt th e co nclu sions, and a fortiori, the premises, of sc ientific demonstrntions must in so me sense o r other be necessary. Th is endorsement len ds Aristotle to require not onl y
[ 7
I
11!troductiOIl
that his th eory of predication provide co nditi ons of truth , but also that it make a d isti nction between those statements whose tru th is a matter of mere happenstance (which therefore, presumably, arc not sub ject to scientific ex planation ) and othe rs whose truth is a matter of necessity
(a nd which therefore do fa ll properl y within the doma in of Aristo telian science). In fact, I shall argue that the Organon contains two distinct theories of predicatio n which refl ect this di stinction, and that these two theories differ d ra stica ll y in their overall sophistication and th eif sensitivi ty to significa nt differences among the rypes of state ments they treat. One of th ese, whi ch I claim is on ly im plicit in the first five chapters of the Categories, wi ll be ex posed in chapter 3 as a relatively simple theory that in the end does no better than to provide a se t of necessary (but no t sufficient) catego ria l con ditions for necessa ry truth. Agai nst this backgro und, Aristotle will be portrayed in chapter 4 as making another, more subtle, approach to the sa me topic in Book 1 , Chapter 4 of the Posterior AnaIytics. In particular, he is there able to provide sz4ficie nt conditions for necessa ry truth by bringi ng into play an idea that is barely embryonic in the Categories (but that eventually blossoms into one of his most important metaph ysica l doc trin es), namely that for every genera l (natural) kind of thi ng, there co rresponds a unique cluster of cha racteristi cs essential to (and in some sense even responsible for ) something's belongi ng to that kind. In la ter works, such clusters are referred to var iously by the use of such terms as " nature" (fj>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/Ko<;), truths that li e outside its domain. In chapter 5 it will be argued furth er that because Aristo tl e takes over ~ ce rtain Platon ic view about definition, (P5) A definition involves the specification of a genus and a differentia,
his new theo ry of predication gives a sepa rate anal ysis for another group of necessary premises, nam ely those involving th e predication of differentiae, which do not fit comfortably within the si mpler theory of the Gate-
(8I
Illtrotilfctioll
gories. In addition, the theory of the Posterior AnolYlics w ill be seen in chapter 6 to make further advances over that of the Categories by extending the range of scientifica ll y respectable truths to include, as nn additional type of per se premise, pred icatio ns of w hat are c:1l1ed in the To/) ;cs "prope rties," or "p ropria" (rB~a), statements expressing ca usa l (as opposed to "analytic") connections, and even certai n gene ral state ments that seemingly do not express invariable connection s, but a re merely true "for the most part" (bTL ro 7TO~U). In conrrast to these rebxatiolls of hi s requirements for sc ientifi c premises, Aristotle's discu ssion ~f one other sense of the term per se in Posterior Ana/yties '.4 w ill be interpreted as an attempt to exclude from his theory a certai n so rt of apparentl y significant predication that is also left entirely out of account in the Categories. Chapter 7, "Demonstratio n and Negation ," concerns the question of how negation (or more precisely, negative predication) figures in the t heo ry of demonstrative know ledge given in the Poster;CH· Allalytics. We sha ll see that. wh ile Aristotle has a theoretical need to include sll ch predi cations as legitimate demonstrative premises. he a lso has good philosop hi cal rea sons to be trouhled by their presence. He is un comfo rtabl y aware of PlatO 's efforts in t he Sophist and elsew here to rescue the concept of negation from the "Pa rmenidea n" ind ictme nt th:1 t its usc inev itahly leads into deep and inescapable paradox. More specificn ll y, I shall argue that one of rh ese alleged paradoxes in particular involves what I call the problem of "se mantic fragmentation." This is a ce rtain mea"illg defect whi ch Plato believes to come out of employing negative predicates as " indefi nite" (dOp tCT'TOIJ ) terms in contex[s where they ;:Ire supposed to denote unrestricted (or insufficiently restricted ) comp lements of Wh:lt is denoted by the positive predicates they contain. O n th e .lccount to be given here, Aristotle foitows Plato not on ly in seeing sema ntic fragmc nt
meaningless. W ith this diagnosis, the so lution to the difficulty is obvious: simp ly make sure your theory of predication does not permit the occlirrence of negative predicates except where their denotations arc suffic iently restricted.
I9I
Illtroduction Aristotle's way of ac hi evi ng thi s, which is ou r special concern here, is in effect to compartmentalize the whole field of demonstrative science into
the so-call ed special sciences. He does this by requiring that each &n.crriU..L'Y/ be pertinent [Q a unique genus of things which it studies and that the demonstrations of that E.1TLUTTJJL71 contain no term (pos itive or negative) whose denotation is not wholly included within that genus. Since this book is limited in scope to a discussion of the interco nn ections among the logical, metaphysical, and epistemological doctrines of Aristotle's early works (especia ll y those of the Analytics), [ shall avoid making referen ce to hi s later writings except fo r purposes of illustration or merely circumstancial textual argumentation. However, I should close these introductory remarks by mentioning two familiar issues in Aristotelian scholarship that will not be pursued here. First, it will not be asked whether the theory of predication set out in the Posterior Allalyties suffers any substancial revision by the time Aristotle writes the notorious mi dd le books (E-E)) of the Metaphysics. More specificall y, I shall not attempt here to decide whether his eventual attachment [0 th e matterform analysis of substances (which is conspicuously absent from the Organon) eventually requires him to repudiate, or merely to extend, his earlier theory in order to analyze "predi cations" expressi ng the newfo und relation of material constitution . Second, nothing will be said here on the undeniably important question of whether the a priori theory of demonstrative science presented in the Analytics is in the end compatible with theoretical remarks about explanation or actual explanatory prac¥ tice in Aristotle's later scientific (especially his biological) works. Again, this book is intended as a study of the orig;Ils of Aristotelian science. not of what it eventually becomes. The rationale for both of these omissions is essentially th e same: part of my aim here is to counteract what I perceive as recent popular tendencies in both of th ese area s to read Aristotle "backwards" by being too eager to find in the earlier works signs of com¥ plicarions and difficulties in his views that do not in fact become evident until later in the Corpus. In saying this, I certainly do not mean to deny that there are ever occasions on whi ch Ari sto tl e says less than he believes abollt peripheral (or for that matter, central ) problems and issues raised by the doctrines he expounds. But even so, I believe it is necessa ry to approach a difficult work like the Posterior Ana/yttes in the first instance on its own terms by trying to understand it as presenting an intelligible and essentiall y self-contained theory, and not merely as a superficial and inade· quate preview of later, deeper, and more subtle doctrines that it does not
I
10 J
Introdu ction
actually discuss. Indeed, without such a free-standing interpretation of the Posterior Analytics that respects its integrity as an independent work, I nnd it hard to see how one could even form (much less answer) meaningful ques tions about whethe r or how its doctrines arc modified, extended, o r abandoned in later treatises.
I
11
I
ONE Demonstration, Division, and the Syllogism
It would perhaps not be too far wrong to describe the POStcri01- Allolytics as an ugly stepchi ld in the Aristotelian corpus. Since :lllcicnr till1es the work has suffered from a reputation for bein g unpolished in style, tCllt:lrive in tone, and even lacking in organiwt ion, judgments which ha ve served theif makers as an excuse to pick and choose the P::1rts of the treatise they find intelligible, interesting, <1l1d important, and to disrqprd other parts as so much confused exposition on the part of Aristotle or his transcribers. One particularly unfortunate outgrow th of this attitlJdc h ::15 been the idea that to look for a comprehensive fr'l1llcwork th:1t organizes all the apparently diverse discussions occurring in the work is to c.:onduc.:t a hopeless search for something that simp ly is nor there. In the introduction to his 1949 edition of the Analyth"5, Sir David
Ross offered quite plausible mitigation for defects in the !-:tyle .1I1d tone of the work, respectively, by pointing alit that there is a reasonahly wide variation, having very little to do with contenr, in the degree to which different Aris totelian treatises are "re.1Jy for press," and th:lt the intrinsic.: difficulty of the topics treated by the Posterior Allalytics (c.:omp.1red, for example, to the Prior Analytics) in any event makes it very C;lS Y to understand why Aristotle should exp ress the views developed there ill ca utious and tentative language. Here I propose to answer the remaining complaint, that the work is disorganized, by :.uguing that th e Posterior Al1a-
[ 1S
I
Structure of Demonstrations
iytics is in fact constructed around a quite powerful (if not always per· fectly visible) organizational scheme. On the view I sha ll be advancing, the treatise is not si mply a loosely connected set of local discussions on a very broad and undefined group of topics. Instead, it can be understood as a syste matic atrcmpt by Aristotle to give and defend answers to two very closely related questions that naturally flow o ut of an investigatory current stemming from Plato's Meno and running through his Republic and Theaetetus: first, what are the essential features of "knowledge in the unqualified se nse" (i7fl.rrri}p.1'j a7r'\ws-), that is, the very highest and most secure form of knowledge available to humans, and second, how can these features be secured within the context of Aristotle's own logic and theory of predi cation? More particul arly, I suggest that Aristotle treats the first of these two questions in the opening three chap ters of the Posterior Analytics. thus developing a set of desiderata which he believes any plausible theory of i7rltrrTII.L7I a7r'\wc; must satisfy, and then spends virtually the rest of the work showing that a theory of his own invention in fact does so. 1
DEMONSTRATLON, SYLLOGLSM, AND THE FOUNDATLONS OF KNOWLEDGE Not coincidenta ll y, what is by far the most strikin g and important of these desiderata makes its appearance in th e very first sentence of th e ope ning chapter of the work: "All learn ing and all tcaching of the discursive sort arises out of preexistent knowledge" (Posterior Analytics 1.1.7 ral - 2..). With its specific reference ro "teaching" ([)t.cScuTKa,\ia) and "learning" (p.a81'juw), this remark sou nds a theme that must have been calculated to evoke comparisons with Plato's introduction at MellO 8SD-E of the do ctri ne of avap.JI-r,(]'Lc; as a solution to the famolls paradox about th e poss ibil ity of learni ng formulated earlier in the dialogue at SoD-E. In chap ter 2 I wi ll argue that these Platonic overtones are meant partly to motivate a distin ction between universal and particular knowledge whi ch will turn out to be an abso lu tely pivotal element in Ar istotle's own [heory. for now, however, it will suffice ro notice two outstanding features of the very special way in wh ich Aristotle himself understands this remark . One is that Aristotle, unlike Plato in Book 6 of The Republic, is here identify· ing the highest form of know ledge as one that is "discursive" (tStQII07JHK1j) in nature, which means that it is a SOtt gro unded on "reasoned jus-
I
16 J
Demollstratioll. Dil/isioll. !md tlu.' Syllogism
tifi cation." This thollghl becomes dear later on in Ch.1ptcr 2. when he describes "knowledge in th e unqualified se nse" (61ru:rn1P.:ry a1rAWIJ) ;l S a sort that arises " through demon stratio n" (ik a1rooeieewlJ), and is picked up in Posterior Analytics 1 .13 and ag.lin in Posterior Analytics 2. L and ;z. .2. , where the point is made that it is one th ing to kn ow that a ce rtain b et holds (that is, to know "that it is" [TO onD, a nd another (presu ma hl y better) thing to know that 011 QCCOlmt of wh ich it obt~li n s (th : a is, its TO Ston) by providing a demonstra tion that elucidates its C
[ 17 [
Structure of Demonstrations Analytics 1.4.25b26; Posterior Analytics I.2.7IbI7), or in other ways makes it clear that the two subjects are very intimately connected ( Prior Analytics I. I.l4a 10j Posterior AnaLytics 1.2.72310- I 5i 2.1 9·99b1 5), Secondly, there 3re places where demon stration is linked to the "figures" (O'X7JJ,LaTa) of the sy llogism (Posterior AI1alytics I.I3.78bI 3ff), most especially the first (Posterior Analytics 1.14.79aI7). Finally, a number of passages appear to equate the construction of a demonstration with the interposition of a "middle term" (J,LEa-O /J ) between two o thers already noticed to be con nected somehow (Pos terior Analytics 2.2 passim; 1.1J.7 8b3 ff ). Quite aside from whether th is geometrical conception agrees with present-day understandings of the logic of scientific exp lanation} the problem is that it seems not to fit very well with Aristotle's own remarks concerning the details of his theory. Such a tight connection between demonstration and syllogis m would seem to place ve ry definite sy ll ogistic constraints on both the form and interpretation of the apxai and the 'Jo...aJ,L{3a/loJ.l..c/la of science. Yet even a quick study of the passages (here called group B) where Aristotle identifies and di scusses these items indicates what seem to be frequent and flagrant violations of these constrain ts. These passages are mostly contained in the first eleven chapters of the Posterior Analytics, with the highest concentrations in the second and tenth. Of special co ncern here will be Aristotle's di scussions of "definitions" (ijpo<; o r OPlO'J.l..O<;; r .2..72aI5-2.5; I.IO.76b3 5), "common [a xioms)" (Til' Kowa; I.IO.76a40i 1.11.77a10-35)} "assumptions of existence" (071. cern; I. 10.76a31-7; 76b3-l3), and "assumptions of meaning" (Ti O'TJJ.Lai/J8lj Lro.76ap-7i 76b3-l3) . The apparent incompatibili ty between these two groups of passages has provoked two extreme forms of reactions among Aristotle's interpreters. Those whom I shall call the strict syJ/ogislicists take very serio llsly the geometrical conce ption suggested by group A and consequently try to understand the texts in group B in a way that gives to lhe vatious kinds of apxai and 'Jo...aJ.L{3a./JOf.LE/Ja discussed therei n an aura of syllogistic respectability. On the other side there are the antisyLlogisticists, who, upon noting the contortions through which the strict syllogisticists put the texts of group B} propose to give up ent irely the idea that demonst ration is significantly based on the theory of the syllogism presented in the Prior Anaiytics, despite Aristotle's clear declarations in group A to the contrary. I My general view is that each side of this deba te is mistaken for failing to take into account a large portion of what Aristotle actually says about ( 18 )
Demollstration, Divisioll. alld the Syllogism
the subject at issuc. ~ This fault is not shared by the interpretation to be defended here, which might be thought of a5 ;\ qualified form of syllogisticism. According to this account, Aristotle does indeed (as the pas sages in group A suggest) regard demonstration as essentially and impor tantly syllogistic in character, yet he is not committed to the proposition (falsified by group B) that all of the apxai and AafJ-i3avOIW'IY. of demonstration are ultimate premises in syllogistic justification-chains. More specifically, my central proposal is that (a) the whole protcss of Aristotelian (hTO()BL~L<; is a two-stage affair, (b) only the seco nd of these is syl logistic in nature (a lthough it is strictly so), and (c) l1l.:lny of the apxai and )..Cf./k{3aVO/kBVa of Aristotelian science play out their roles in the ini tial, presyllogistic stage (or, as I shall call if, the "framing" stage) of demonstration.
DEMONSTRATION AND DIVISION, THE FRAMING STAGE The key to understanding the logical structure of Aristotelian demonstra tion comes with an adequate appreci.:ltion of its architect's ambivalence toward the method of "division" (()LCtipecn~ ) pr:1criccd hy Plato ~ and other members of his Academy.'· To begin with, it is generally recognized that Posterior Analytics 2.5 and Prior Alwlytics 1.3l both record ~l critical attitude on Aristotle's pan toward this Phuonic method insofar as it was advanced as a method of proof inten ded to rival his own method of demonstration. ; He argues in both places that if an individuo.1l step in the divisional process (wherei n some predesignated target is sequentially IDeated on one side or the other of finer and finer differentiations) were to be construed as an attempt at logical inference, it would have to be judged invalid.~ So, for instance, in Prior AHOlytics (.31 he considers the follow ing sequence of divisional steps,
Step N (I) Every man is <1nimal, and (2.) every animal is mortal or immortal, sO C~)
every man is mortal or immortal. In parricular, (4) Every man is mortal (an im al),
Step N +
I
(5) Every mortal (an im al) is footed or footless, and
(4) every man is mortal (animal), so
r
19 )
Structure of Demonstrations
(6) Every man is footed or footless. More particularly, (7) Every man is footed. and argues (a) thai the so-called concl usion of each step ([ 4J and [7J , the state ment carried over to the succeeding step) is never actually proved from earlier lines, but is instead simply introduced in each case as a new and un sup ported assumption {46.bI2.. I8-19),'1 and (b) that even though the disjunctive predications in each step ([)J and [6]) do follow logically fro m prior statements ([lJ with [.1, and [5J with [41, respective ly), these inferences cannot be cases of demonstration because they violate th e rule that any dem onstration of a universal affirmative must be in Barbara, and so must have a middle which is in cluded in its ma jor term (46a39-b4).'H But whi le it is ge nerall y ack nowledged that Aristotle is hostile for these reasons to fnaip&a-I.C; if and when it is proposed as a self-sufficient method of proof, it is not always noti ced that in both A1talytics (especially in Posterior Allaiytics 2.13) he actua ll y advocates the use of something very much like this Platonic device, provided that ce rtain safeguards are observed, for a very specific and limited purpose within his own account of the demonstrative generation of the highest form of knowledge. Thus, at Posterior Analytics 2.13 .96bI 5 he says that when one is "making a system atic study" (7TpaytL01Tf.:Vrl'Tm) of some subjec t (p resumably with the aim of developing unqualified knowledge), it is " necessary " (xp'lj ) to "divide" (B~ehe:i: I') the genus in to its primary, "atomic" (&TO,u.OV) species. The same point is then made even mo re explicit at b25 when Aristotle allows that "divisions according to differentiae" (ai 6& 8t.mpea-et.C; al K(lTa Tar:; B~a4>op6s) 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
I
Structure of Demonstrations be instances of what he ca lls "per se" (K0'8'auTo ) predication. Moreover, it will also emerge during that discussion that this key expression, like so many other im portant pieces of Aristotle's philosophical terminology, is "sa id in many ways" (1TOAAaxw<; AeyeTaL), and that, as a result, the multiple explications it receives in Posterior Analyties 1.4 can be see n to function as somethin g like a catalogue of correspondi ngly different types of non accidental connections that Aristotle allows to hold between the terms of legitimate scientific predications. But this must come late r. For though even at this early stage it is hard to overstate the importance of these issues to Aristotle's tbeory as a whole, the truth is that he simply ducks them in the chapters presently under discussion, where he is concerned exclusively with the broad structu re of demonstration. Thus, in Prior Analyties 1.27 he insists at 43b7-11 that in order to selec t demonstrative premises correctly it is necessary already to have distinguished between the accidental and different so rts of nonaecidental attributes IS of a given subject, but he says nothing about how this distinction might be accomplished. And likewise in Posterior Analytics 2.13, when he declares at 97a24 that one of the three rules to ob~ serve in fo ll ow ing his recommended procedure is to "gras p attributes in the what~is~it" (TOU Aa{3ellJ Ta Kary/yopOV/LBlJO' elJ -rijJ -ri eern) of the subject, he agai n offers no guida nce on how such attributes are to be distin· gu ished from other types. In order to understand this silence, we have to keep in mind that when Aristotle claims in Prior Analytics 1. 27 - 3 2 and Posterior Analytics 2.13 that the operation he describes as "division according to differentiae" at 96b25-6 is a usefu l (and even necessary I") device for the acquisition of the ultimate premises of demonstration, what he is promoting is not actually Platonic Division itself, but rather a certain distinctively Aristotelian adaptation of that method. For even though the two proced ures bear a strong st ru ct ural resemb lance to one another (they both proceed by "dividing a genus down into its indiv isible species," in the exact la nguage of Posterior Analytics 96bI5 ), this shou ld not obscure the fact that they also have vastly different epistemologi ca l functions within their respective systems. As it presented in the Sophist and elsewhe re, there is nor much doubt that Platonic Division is regarded by its author as a complete (that is to say, self-sufficient) philosophical method for producing or discovering a desired definit ion (specifica lly that of the indi visi bl e kind predesignated as the target of the division).1 7 Not only that, but it is also evi~ dent fro m Sophist 253 C- E that Plato sees the prosecution of the method
I 22 J
Demonstration, Division. a11d the Syllogism
as the proper business of the very highest form of intellectual activity (which he refers to alternately in that passage as "dialectic" and "philosophy"), and that he consequentl y views the definitions ge nerated by th e method as the proper objects of the highest ep istemic attitude countenanced in his system: knowledge, in the strictest possihle Pb tonic sense of the term. Now, as it will be interpreted here, the Aristotelian adaptation o f P13 tonic Division advocated in Posterior Al1aiytics 2. . 13 and Prior Allalytics 1. 2.7 - 32 differs from its distinguished ancestor in both of th ese respects. In the next chapter we shall try to ascertain exactl y what it is about the logical character of definitions generated by Platonic Division th M in clines Aristotle to deny them the status of knowledge in his sn' ictest se nse of the term. However, the most immediate and st riking point of difference between th e two meth ods is that Aristotle's version, unlike Plato's, is not a meth od for generating definitions, but instead o ne whose li se presupposes that one has somehow already grasped an appropriate set of immediate principles (some, but not all, of which are definitions I ~), and which then deploys these principles over some field of scientific interest (i n Aristotle's technical usage, a genus) in such a way as to coll ect the ulti mate sy llogistic premises requ ired to construct demonstrative sy llogisms, and so to dev610p a syste matic und ersta ndin g (or knowl edge simpliciter) concerning that field. Consequently, where Plato is able to co nceive of definitions as the products of an entirely sel f-sufficient philosop hical meth od (dia lectic), and so as spec im ens of the highest form of k nowledge, for Aristotle they func ti o n as mere sta rting points: part of the preex iste nt material, ca\led fo r by Posterior Ana/yties 1. 1 and 2., from which know ledge simpli citer- or demonstrative knowledge- is ultimatel y generated. This diffe rence from Plato is so mewh
[ 2.l
1
Structure of DemOllstrations
we know independently th at the question of how rhe definitional starting points of (hT6l)E:L~t8 are initia ll y apprehend ed is put off until the notoriously diffi cult final cha pter of the entire treatise (Book 2, Chapter 19), whose deta ils will be dealt with below in chapter 2. By con trast, as I have suggested, thi s issue is simpl y finessed by Aristotle in Prior Anafytics 1.2.7- 3 2. and Posterior A l1aly tics 2.1 } wh en he issues offhand admonitions that the procedure he is recommend ing must restrict itself to essential (or at the very least, nonacc id e n tall ~) co nn ections between terms without offering the sligh tes t advice in either place on how thi s restriction mi ght be ensured. I have been arguing that, because the method of «Aristotelian divi sion" advocated in these chapte rs does not provide (a nd indeed presup poses) a way of distin guishing esse ntial (or no na ccidenta l) from acciden tal predications, then, sin ce thi s distin cti on is what ultimately grounds con diti ons (d)-(f) at Posterior Anafytics 7Jbr6- 2.2., it follows that the me thod is not designed to test for th ose conditions. Bu t if, as I asserted above, there is no independ ent test for cond ition (a), truth. we may then ask, what is the method supposed to acco mplish ? Accord in g to th e interpretati on I propose, it is offe red by Aristotle as a way of obtai nin g premises that satis fy th e remaining two req uirements listed at 7Ib I 6-2.o, namely that demonstrative premises be (b) "primary" (7TP(~'TOV) in the sense of being (c) "immediate" (ap,ga-ov). In co ntrast to condi tions (d)-(f), which will be understood in part 2. as all pertainin g to certain preferred intensional relations th at Ari stotle insists must ho ld between the terms of legitima te demonstrative premises, the im mediacy conditi on is a purely extensional one entail ed more or less straightforwa rd ly by Aris totle's insis tence at Posterior Analytics 1.[4.79aI8 -32 that sy llogisti c demonstration mu st proceed exclusively in the flrst-figure moods, and more pa rticul a rl y (given that he a lso requires demon strative premi ses to be universapn ) in Barbara or Cela rent.lI In bo th of th ese moods the middle ter m is in cl ud ed in the ma jo r, and eith er incl udes the minor (i n Barbara) or excludes it (i n Cela rent), from which it follows within Ar istotle's fo undational sy llogis ti c scheme that an y primary (th at is, ultimate and indemon strable) premise will express an immediate (that is, unmiddled ) in clusio n or exclus ion relation between its termsY In orde r to see exactly how what I am ca ll ing Ar isto telia n di vis ion constitutes a method for coll ecting premises th at satisfy the immediacy requi rement of 7 Ib2.2., we must take a close look at the safeguards that
I
24 J
Demonstration, Division.
Aristotle insists at Posterior Anolyt;cs
(lHd
the S)'lIogisllt
2. T .1.97:123
- 2.6 mllst he observed
if the method is to accomplish its purpose. I have already argued that the establishment of the first of these, that the procedure must (T) confine itself to essential (or at least, nonaccidental) connections between terms, should not be undersrood as something thm the method itself is supposed to achieve, but rather as a prior achievement that is presupposed by the possibility of the method's successful operation. In contrast to this, <1$ the method is described in Posterior Allaly6cs 2.13 and Prior A110lytics 1.2.7 - 32., it does contain within itself the mC;lJlS ro secure the remaining two safeguards mentioned at 97
I 25 I
Structure of Dem01lstra tions
rel ated by both incl usio n and excl usion relatio ns (so that the genus as a wh ole has a branching stru cture). Now, as before, we first look fo r and find the te rm, A, that is nonreciprocally enta il ed by all the o thers (which again is th e ge nu s itself). However, when we now look for a single term among the remainder that is nonrec iprocaJly enta il ed by all of the othe rs, what we find instead is that there are in fact two (or perhaps more) terms, Band C, each of whi ch is nonreciprocally enta il ed by a certain fam ily of terms with in A, which is to say th at Band C represent branch ing nodes of A. Moreover, the sa me sort of ci rcumsta nce ca n recur if we try to find within th e fami ly o f terms that nonretip roca ll y entail B, a single te rm that is nonreciproca ll y entail ed by all of the others: we might very well discover that in fact there are two or more independent fa milies within B's extension , so that B itself is discovered to have a branching structure. And so th e method would proceed unti l the o riginal co llec tion of terms is ex hausted. With this com plicatio n installed, Ar istotle 's procedure for pl acing the terms of a ge nus in co rrect o rd er begi ns to look even more like a Pl aton ic Di vis ion, since it is now see n to involve a descent through the branching stru cture of a given ge nu s, a descent which wo uld presumably culminate at its in{imae species. But as it now stands, the procedure invo lves no way to ensure that any or all of th e connections uncovered in this descent will be " immediate" in the sense of 7 Ib2.2. Fo r th ere is nothing as yet to ru le alit the case where B nonreciprocally entails A, but only because it nonrec iprocally entails some third term, D, that itself non rec iprocally enta ils A. And by the sa me token, the entailment relations linking D to bmh A and B mi ght themselves in volve any (fi nite H ) number of furt her intermediate tcr ms. T he fundamental diffi culty that gives rise to this sort of case, acco rding to Aristotle's own diagnosi s at 96b35-7, is that the original co ll ection of terms subjected co the orderin g procedure described at 9732.8-35 could not in the first place have contained all of the esse nce-diffe rentiating terms with in the gen us under division. (Clearly, in the schematic case just described, if D had been incl ud ed, it wou ld have turn ed up before B in the orderin g proced ure.) Consequently, he moves to block th is possibility by building into th e version of division he is advocating a way of ensu ri ng the third of the sa fegua rds mentioned at 97a2.3-2.6, namely th at "nothin g be left ou t" (J..l:YJ3ev 7fapa{3avew) of the division, as he puts it in a num be r of places (for examp le, Prior AnaJytics 1.30.46a25, Posterior Analytics 2.5 .9 I b3 I; 2 . I 3 ·96b 36). Notice that in the branching case desc ri bed above, where term A has been d iscove red to be nonrecip rocally entailed by two independent terms, Band C, the problem before us is th at
r 26
I
Demollstration. Dillisirm, (lml tbe Syllogism
these terms may each entail A only through the medi~ltion of other terms (or ser ies of terms) that did not appear in the origina l co ll ection. At Posterior Allaiytics 96b37-97a6, Aristotle actually describes such a case and provides a way of detecting and correcting its defi ciency: For when the primary genus is taken, if olle of the divisions lower
(than the immediate one] is then taken, everything lin the genus]
will not fall into this. For in sta nce, not every .mill1
follows,
/A~ B
C
I
I
I
I
I
I [ 27 J
Structure of Demonstratiolls
x,
/ n/ B
/~
C
The test emp loyed in the quoted passage, then, effectively separates these possibilities, for on ly in th e first case is it true not only that Band C individually entail A, but also that A entails their disjunction, or in other words, that they are jointly exhaustive of A. Thus, Aristo tle argues that even though whole-willged and split-winged each entail animal, and so come somewhere after it in the correct ordering of terms, they cannot be next in order to A, sin ce (due to the existence of wingless anima ls) it is not true that every ani mal is either one or the other. Furthermo re, a second look at Posterior Allalytics 96b37-97a6 shows that what Aristotle is proposing the re is not just a method for detecting omissions in the proper order ing of terms, but also one for correcting omissions once found. Suppose it has been discovered according to the above procedure that Band C do not jointl y exhaust A, and thus that the re must be missing terms between them and it. Aristode's dis cuss ion suggests that onc can set abo ut find ing those missing terms in the sp irit of hi s program by now trying to find a te rm (ca ll it D) not appea ring in the original coll ection that is entailed both by Band C, and in turn entails A. In Aristotle's example, the term meeting these conditions is winged. Now that we know D is one of the o mitted te rm s between A and Band C, but not necessaril y the on ly o ne, we can reapp ly the test for omissions given at 96b37 - 97a6 at twO levels: first by ascertaining whether D is itself jointly exhausted hy Band C (if not, th ere must be missing terms between it and them), and next by first identify ing D's cod iffere ntia,!" E (in Aristotle's, example, wingless), and then determining whether D and E jointly exhaust A. If furt her omissions are discovered during either process, mi ssing terms are added as before, and new tests fo r omissions are administered. So the process continues until, after some finite number of steps/] a complete correct ordering of the terms within A is generated. [ 28
I
Demol1stl'atiOll, Division, alld the Syllugism
To sum up, I have been arguing that because the Aristotelian version of division advocated in Posterior Allalytics 2..IJ and Prior Analylics 1.27 -3 2 conta ins within itself pro ced ures for obtaining a correct and complete ordering of terms {and because it is restricted to terms thnt sig~ nify essence}, it is reaso nable ro view the method as a whole ~s one by which it is possib le to set out all of rhe immediate esse ntial connections among the terms within a genus, and in lhat W:1y to systematize the genus prior to construction of sy llogistic demonstrations pertinent to its contents. This, I take it, is the rational e for Aristotl e's remark :1t Posterior Al1alytics 1.13.96b15 that division of a ge nu s into atomic kinds is necessary when one is "making a study" (rrpoy(.Lo!TelrrrTOt) of that genus. However, we have not yet seen how this method figures in Aristotle's vi ews about how one should go about actuall y co llecting the sy llogistic premises of demonstration s relevant to the genus under study. This final con nection is made in Prior Analytics L27, and Posterior Analytics 2.14, both of which are hest understood as :1ssl1l1ling that the prospective demonstrator ha s already empl oyed Aristotdi ..l11 division to chart all of the immediate connections within the genus of interest. At Prior Analytics I.27.43bI-5. Aristotl e says thilt in order to co ll ect appropriate premises pertinent to a given subject, it is neceSS:1 ry, ~lfter first setting down the subject itself, its definition, and its peculiar properties (that is, all terms that are nonaccidentally coextensional with the suhject!B), to proceed to identify the terms enta il ed by the subject, the terms that the subject entails, and the terms th
[ 29 1
Structure of Demonstrations
tails A and is entailed by C, then simple transitivi ty requires that C entails A. Notice that this tells us there is some syllogistic proof of "All C is AU containing only immediate universal affirmatives as premises, hut it provides no way of identifying those premises. If, however, this passage is to be understood as a pertinent part of the discussion begun in Prior Anaiytics 1.2.7 about how we can actually find the materials for syllogisms (43a2.0- 21), the method by which we can apprehend th e starting points (or ultim ate premises H ) concerning each syllogistic problem (a 21-2.2.), and our abil ity to construc t syllogisms (a 24 ), then it is mo re reasonable to suppose that (he field of terms involved has already been arranged by an Aristotelian division into the correct and complete ordering. On this supposition, Ariscode's point is now a stronger and more helpful one-if in the concurrent processes of tracing A's descendants and C's ancestors through this ordering, one happens upon the same term (B ) from both directions:
c then one has thereby not only discovered that {here mu st be a syllogistic demonstratio n of "All C is A," but also connected A and C through a series of immediate entailment relations, and in this way actually collected all of immediate (uni versal affirmative) premises of the syllogisms in Barbara needed to construct [hat demonstration. Aristotle makes a restricted version of the same point in Posterior Analytics 2.14, after using lan guage ve ry similar to that of 97a28-35 in Ch apter 13 to advocate once morc his ow n ve rsion of division: "For example, if the genus animal is what we should study, [we should discover) what belongs to all ani mals. Having grasped these, [we must identify] what follows upon all of the first of the remaind er (e.g. if this is bird, what follows from all bird), and proceed thusly, always taking the 'nearest' (eyy.ncxra) [d ivision]" (98a4-7). Aristotle then explains how this point can prove useful in demonstrating that certain attributes belong to certain subjects: "Let A
[ 30 [
Demollstration, Divisiolt, altd tbe Syllogism
stand for animal, B for the attributes belonging to every animal , and C, D, and E for the so rts of animal. Now it is clear on accou nt of what B belo ngs to D: on acco unt of A. And likew ise for the others [i, e., fo r C and E]; and the same reaso ning always applies to the terms lower [than C, 0 and E]" (9 4a 7-12). Here aga in the poin t is that, since we have already discovered that B is one of the (nonacc idental ) attributes belongin g immediate ly to an;ma l and that D is an immediate subdivis ion of A (in other words, that bo th "All A is 8" and "All 0 is A" are trtl e and imm edi ate) , we are in pos itio n to co nstru ct a single-syll ogis m demonstration in Barbara of "All D is B," The sa me sort of interpretation can al so be given to th e para ll el po in t Arisco tle makes at Prior Anaiytics 443 1-7 for rh e case where one wants to prove a uni ve rsal nega tive: "Whenever it is required [to show} that some predicate bel o ngs to none of some subj ect, it is necessary to COI1sider the terms whi ch a re entai led by th e su bj ect, nnd those whi ch C:l nn ot belong to the predicate .. . for if any of these is the same the predica te ca nn ot belong to any of the subject." Let li S suppose th:1t the universa l negati ve to be proved in this case is "No C is A." Aristotl e's poi nt is th at if one we re to discover in the correct and comp le te ordering given hy Ari scotelia n division a ter m B th at is an ancestor of C and imm edia tely excludes either A o r some ancesror of A, or schematically, that th e foll owing ordering ob tain s:
then one would possess all the imm edi ate un iversa l premises (on e nega tive, and the rest affir mative) need ed to comp lete a sy ll ogisti c dcmon st ration of "No C is A" (in Barbara and Celarcnt 1<1). I have been argu ing that when Aristotel ian div ision is carried into th e specialized co ntexts of Posterior Anaiytics where Aristotle is co nce rn ed spec ifica ll y with the co nst ruction of demons trative sy llogisms, it heco mes in effec t an abso lutely necessa ry and integral presyll ogisti c stage in thc ove rall process of generati ng scientific know ledge. It is, mo reove r, thi s (raming stage o f dem onstration thM proves to be th e locus of opera tions
I
31
I
Structure of Demonstrations for the various types of apxai and "Aa/J.{3a l/o/J.6I/a cata logued in Posterior Anafytics 1.10. H this two-stage interpretation of demonstration is correct, then it should be possible to understand each type of apxai in terms of the structural features of rhe framing stage an d its place in the ove rall theory of demonstration. The mOSt important of these types, the OpOL discussed at lengtb in Chapters 3 to 10 of Book 2, will be see n in the next chapter to lie at the very heart of the framing procedure. But first, three other types (generic existence assumptions, generic meaning assumptions, and rhe " logica l" comm011 axioms of Noncontradiction and Excluded Midd le) will be interpreted in the remainder of thi s chapter as constituting various background assump tions necessar)' for the completion of the framing procedure p rior to the actual construction of syllogistic demonstrarions.
THE BACKGROUND ASSUMPTIONS OF DEMONSTRATION A good place to start this procedure is with one of the most widely d iscussed and least understood passages in the entire Posterior Analytics. Speaking of tbe lim itations his cheory places on what must be proved and what ca n be assu med by a science, Aristotle iss ues the following seemin gly en igmatic remark: "Proper (tfha) to each science are the subjects whose existence it assumes, and whose per se attributes (V7T
jc((-genus. " (R2) Every science must assume the mean ing of its sub-
ject-genus. ( R .~ )
Every science must assume the meaning of the per se attri butes of its su bject-genus.
(R4 ) Every science must prove the existence of the per se attribures of irs subject-genus.
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DemOIl5t rat;oll, D;I /;5;01l. and the ,,),/101:;5111
Of [h e va rious items mentio ned in these p rinc iples, th e memlillg as~ sumptions mentioned in (R3) will tu rn out to he th e mos t impo rta nt. sin ce they wi ll be seen to prov id e th e sllhstJnti ve conte nt of Ari s totdi ~ 1l &1To8eL~t~. In chapter 2 we shall consider exactl y how th ese sl1hs t~ll t i ve mean ing assu mptions fit into the fO llnd ~ t io ll ~ 1 st ru cture of d e mon stra ~ tio n) an d in pa rt 2 we shall go a ll to exp lore the p rec ise nature of the pe r se con nectio ns conveyed by these ass ump tio ns. Fo r the mom en t, however) ou r conce rn is to deter mine the im porr of Arisrodt:'s asscrri on o f (RI) at 76bS-7) th at every scie nce mu st ass ume the "existence" (TO elvc:n) of th e genu s it st udi es. Jaakko Hi nti kka , who is inclin ed towa rd strict sy l1 ogisti cism, c h a r acte r is t ic~ lI y und erstand s the immedi ate exegetica l q uestion posed by this res tri ctio n in a wa y tha t Icad s him to empl oy an in terpretationa l device tha t is at o nce impl ausib le and unn ecessary. In keeping wi th his general com mi tmen t to inte rpret all a PXO!t and ACXJL/3allOJLf:. lla as syll ogistic "p remises" (7Tponxm·; L<;), he presu mes that the "assumptions o f existe nce" d isclIssed here mll st co nstitute a certain kin d of pred icatio n that ca n both serve as ul tim ate sy ll ogistic premi ses, and at the sa me time ensure existential impo rt fo r th e wid est tc rlll of a sc ience (whi ch imp ort, in Hi nti kka's wo rds, is then "ca rri ed downwards fro m wid er term s to narrower o nes in a sequ cnce of ~ci entifi c sy ll ogisms") .l! Bu t fin din g nothing in Aristo tl e's tcxts t h ~H ex pli citl y meets these speci fi cJ tio ns) Hintikka is force d to supply refe rents fo r (R I) on Aristo tle's behalf. As a resu lt, he hn:1 l1 y identifies rh c:se ;1ssu mptions of exis tence as a peculi ar sort of "nrst premise" th ~H is ;1. lso;1 "ki nd of dd ini rio n (6po<;) lo f the] widest term of ;1 given science."
is to be fou nd amon g the ultimate pre mi ses of th e sy ll ogistic demo nstrations within 5(;. In add itio n, he co nte nd s tha t these to pm os t p remises are un derstood by Ari stotl e to entai l 1Illi vcrs:11 ex istence cbi ms, in thi s C;lse, (2) All Gs ex ist.
Finally, in Hill tikka's view, the ex istenti al fo rce of ( I ) represl'IHcd by thi s impl icati on is the n " percola ted down" to the ultim ate delllollst rata of the justifi catory chain s in which (1) fun cti ons as an ulti mate prcmi se. The most serious prob lem with th is atte mpt to id entify ;lIld explicue
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Structure of Demonstrations
the ex istence assumptions in principle (Rr ) as generic (that is, topmost), immediate syllogistic premises is quite simply that Hintikka's account of the latter is internally inconsistent. For in the schematic illustration above, G is, ex hypothesi, the widest term in 51.>. Now (I), as an immediate prem ise that defines G, must presumably do so at least partly by connecting it with its immediate taxonomic superior. But if this is so, it follows that (I) contains a term wider than G, and so cannot (con trary to what Hintikka claims) function as a to pm ost prem ise (or in any o ther capacity ) within St: . There is so me reason to believe that Hinrikka is sensitive to this diffi culty, since he apparently hedges on his claim that (I) defines G with the following qualifica tion , sayin g, "Yet these (pre mises) have the pecu liarity th at they do not co ntri bu te very much to specifying all the different elemen ts that would go into a full definition (of the essence) of the genus," .1~ and this would ce rtainl y have the effect of blocking the inference just rehea rsed that (I) conta ins a term wider than G. However, even if it is allowed that this does not amount to a simple retraction of his earlier claim that (I) defines G, this maneuver still offers no hope of sa lvation for Hintikka's account. For as he recognizes, denying (I) the stat us of a full-Aedged definition makes it "easily appear ... (as) not a substantial assump tion at all, but rather a mere definitory reformulation of a tautology of the form (3) Every G is a G."H But even supposing that we grant this dubious distinction between definitions and "mere definicory reformulations," Hintikka's "topmost" premises sti ll cannot do the work he has in mind for them. To begin with, nowhere in the Allalytics do we find sy llogis ti c examp les (scientific or otherwise) contai nin g sucb tautological premises. And even worse (for Hinrikka 's account), AristOtle shows himself on a number of occas ions CO be fully aware of the grammatical possibility of fo rm ulae like (3), and he plainly does not regard such logical monstrosities as legitimate instances of predication, much less as acceptab le premises in scientific syllogisms. \~ It is important to keep in mind tha t these probl ems are not properly Ariscotle 's; they ar ise o nl y in the attempt to in terpret h is (Rr ) in accordance with strict syllogisticism. Once the .unnecessarily rigid requirements of that program are abandoned, however, the meaning of (RI) becomes both intelligible and unproblematic. The method of Aristotelian di vision, as I am interpreting it, is to be understood in the first instance as a procedure involving the definitions of things (or kinds of things) rather than words. As such, it is to be sha rpl y distinguished from the activities of
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Demonstration, Divisioll, mId the Syllogislll
the lexicographer, who is concerned to chart relations among linguistic entities without paying much attention to the th ings these entit ies :-Ire supposed to denote ..\ ~ Hence, unlike that other sort of investigation, Aristotle's method is premised upon, and initiated by. confrontation with, or contemp lation of, a group of things that actually exist, or are at least supposed to exist, which one is interested in dividing up into its sm::dlest" natural classifications. IX Any application of the method, t herefore, will naturally involve tbe presupposition t ha t the genus being divided .1ctually docs exist (that is, is a genu s of real things ). Indeed, this much is Jcknowl ~ edged explicitly by Aristmle ill Posterior Allofytics 2. to, when he com~ ments that unless it is known that a thin g exists, any proposed defini tio n of it (even if formally correct) will bll short of stat ing the thing's "es~ sence" (7t Ea-n), and must instead be tbought of as nothing more th:lll an "accoun t of the meaning of rhe word" (AO-Y0O;- mv 7L
be divided. Notice that a parallel rationale can be given for (R2), which, it will be recalled, states that a science must also "assume the meaning of its subject~genus." As was just seen in the criticism of I-Jintikka 's intcrpreta~ tion of (Rr), this cannot mean that the ultimate demonstrative premises of a science must include the definition of its sllbiec t~genus. But here again, the difficulty can be circumvented by mC
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Structure of Demonstrations
could hardly escape Aristotle 's notice, and it is just th is, I believe, that he means to exp ress by (R2). Once th ese two precon ditions have been secured, the framing stage of demonstration then proceeds along the li nes set out above. Beginning at the to p, o ne moves downward through the genus by specifying finer and finer sets of differentiae, taking ca re that the differentiae a re taken in the right order, an d that at each level one takes the immediate, o r "proper," differentiae of th e kind being subd i vided.~' The epistemological effect of thi s process is critical to the operation of Aristotelian science: whereas prior to the framing procedure a given subject·genus might (for all th at is known ) be no more than a mere aggregarory grouping with no interesting in ternal stru cture, afterwards it is revea led to be a hierarchy whose co n· stituent necess ary, immediare connections are exp ressed by (a nd so give ri se to) the ultimate atomi c premises of the demonst rative syllogismchains within the sc ience whi ch studies that genu s. Fin all y, the postu lation of a presyll ogistic framing stage provid es a way of understa nding how the " lo gica l" axiom s 41 of Noncontradi ction and Excluded Middle figure in demonstration , without casting them in the un likely role of syll ogistic prem i ses.~1 For within that framewo rk, both of these apxai are naturally presupposed by the sys tematization of a ge nu s in to a hi era rchy of the so rt Aristotle envi sions. This hardly needs showing in the case of Noncont radiction; cl ea rly no coherent cl ass ificato ry scheme whatever will be poss ible if it is all owed th at one and th e sa me item ca n be simu ltaneous ly included and excluded by another. This point is recognized by Ari stotle at Metaphysics 4.4.1007a2. 1- 36, where (a pparently relyin g on Categories S.}b2S-}3) he argues th at to say A is both B and not B is in effect to make B an acc ident of A. Therefore, he reasons, to deny Noncontradiction is to do away with the essential/acci· de ntal di stinct ion, and thus to rule out the possibility of delineating essential kinds by means of division or any other method. Th e case for Excluded Middle, while no t qu ite so obv io us, is evidently just as co mpelli ng for Aristotle, for he sees the prin ciple as required to secure th e requirement discussed ea rlier tha t the divi sion " leave nothing out." For suppose that in th e attempt to subdivide A, we succeed in dis· covering two (or more) d ifferentiae, Band C, which are know n to entail A and to exclude each o ther. Still , even if we knew th at Band not· C we re equivalent, it could not be in ferred from this that B and C exhausted A (that is, that all noo- Cs in A were Bs) except by in vokin g Excluded Midd le to assume th at every A either has or lacks C. As a matter of fact,
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Demonstration, DirJisiOll, tllld tbe Syllogism
this is the form of an inferen ce Aristotle him self pe rforms at Posterior Analytics I.4. 73 bll-4, concerning the per se ,lttributes odd and even and their logical relations to th e genus of Illlmbers."4 Of course, such forma l principles as have been discussed so fa r :Ire sufficient to determine only rhe broad schemati c st ru cture of ;til Aris{O~ telian demonstrative science. III any particular case rhi s schema will have to be filled in by a set of substan tive principles that provide th e acrtla l conte nt of th e explanations constru cted within the science in question, and this is presumably the fun ct ion of wha t are referred to 3 5 meaning assumptions in (R3). The next order of business, then , is Lo develop sOlne understandi ng of the role these meaning assumptio ns play in the theo ry of demonstration.
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TWO Demonstration and Definition
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I suggested at the beginning of chapter I that the opening statement of the Posterior Analytics, that all discursive knowledge must come out of pre· existent knowledge, is a deliberate allusion to the paradox of learning formulated by Plato in the Meno. What is more, this Platonic theme is sustained and developed throughout Posterior Analytics 1.1 and then resonates throughout the remainder of the treatise. In a manner again strik in gly reminiscienr of the Meno, Aristotle introduces at 71 aI 7- 2.9 a distinction between two ways of knowing a general proposition: (I) the " unqualified" (a7TAwr;) way (w hich I sha ll designate de re ). which entails knowledge of irs application to all the particulars that happen to fall under its terms; and (2) a " merely universal" way, which docs not enta il such knowledge of its particular in stantiations. I He then goes on at a29- 30 to tout ("his dist in ction between de re and merely universal knowl~ edge as just w hat is needed to resolve the paradox of the Meno. It is remotely possible that the purpose of thi s passage is drarnaric rather than sysremat ic: that because the work to follow is, after all, about a certain ki nd of knowledge, Aristotle desires to warm his audience to his subject by trotting out a familiar o ld puzzle about the general subject of knowledge, wh ich is then dropped for good when it has had its salutatory effect. Such easy answers to questions about Aristotle's expository prac· tices are always possible (i f never very satisfying), especiall y when the
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work in question has a reputation for being «tentative and lInpolished," ! but in this case the suggestion lacks plausibility. For at 71a12. - l7, the passage directly preceding the initial appe
THE MEANING ASSUMPTIONS OF DEMONSTRATION Let's now turn to yet another of the metascientific principles inrrodu ced
in chapter
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(R3)
Every science must assume the Illc;lning. of the per se (l
terior Anaiy(ics 1.10.76hS)
The central work of part 2. will be to explore the vario us so rts of non accidenta l connections Aristotle means to include here LInder the hea ding per se, and his variolls motivations for doing so, hur now we want to fOl:uS on how the ass umptions mentioned in (R}) fUllction in the ove r;lll process of demonstration. Besides this passage, there are many oebers (for example Poster;or Analytics 1.10.76a32.-37, b6-rJ, b1 5) which express this restriction, and still others which indicate (w hat evidently comes to the same thing) that " definiti o ns " (OpOl) are among the "first
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Structure of Demonstrations
principles" (apxai) of demonstration (Posterior Analytics 1.2. 72a 1 5 - 25 j l. I O.76b35-38). According to the central ten et of strict syll ogistic ism, we are to understand Aristode to be saying here that definitio ns are among the ultim ate syllogistic premises of demonstration. With respect to syntax, thi s poses no pro blem, si nce much oEwhat Aristotle says about definiti ons throughou t the Organ on makes it very easy to think of them as having at least the fo rm of simple universal affirmative senten ces. 4 Indeed, this much is virtually exp li ci t at Posterior Analytics 2.I}.97b2.6. Howeve r, as soon as qu es tion s are rai sed about Aristode's intended seman tic interpretation of OPOt, and more specifically about their existentia l import, their credentials as appro priate syll ogistic material at o nce become suspect. At Posterior Anafytics I.IO .76b3S-77a5, definitions are explicitl y rul ed o ut as " premi ses" (1TpOT(.lO"e Lo; ) on the grounds that they " make no assertio ns of existence or non-existence" (ov8e v yap elvm 7j p.." ELVaL AEyenn; b35), which is to say that they la ck existential force.:; Moreove r, any doubt that thi s excl usion is based on th e general theory of the sy llogism, and not on any special co nstraints on th e premises of demonstra tive syllogisms, is removed by Posterior Analytics 1.2.7 2.a8 - 2.5, whi ch makes th e reasons behind the exclusion altogether transparent. There Aristotle first reca lls his insis tence at Prior Analytics 1.1.2.4a17 that every sy llogistic pre mi se must be either an "affirmation" (.\0)'00; KaTaaTLKo')) o r a " denial" (ADYOS' a1Toa'TtKoS'), or as he pu ts it at Posterior Analytics 1.2..72.a9, " one or the other part of a proposition" (CbTOcbavO"tS' ), and then proceeds immedi atel y (at 7 2a2o- I) to state as a corolla ry to this th at legitimate sy llogistic premises mu st, again, asse rt that "something does or does not ex isr ."~ To the st rict syllogistic ist, who is co mm itted to holding th at all apxa.i are demo nstra tive premises, this presents the enormous difficulty of showing tha t OPOL do afte r all have a rightfu l place among th e prem ises of syllogistic demonstration, despite all the passages just menti o ned which seem to deny them just th at. Hinrikka attemp ts to get around rhis diffi culty by pointing to Aristotle's well -documented tenden cy to equivocate in hi s own key philosophical termi nol ogy. H e argues in effect that the tcrm opoS' takes on an extrao rdin arily narrow sense in Posterior AnaIytics 1. 2. and 1.10 that picks o ut only so-called "nominal definitions" (AOYOL TOU Ti OIJf.Laivet ra DvoMO'rO'),' which do indeed la ck existential import, and that tbe above passages therefore need not be interpreted as rulin g out all defini tions as premises, but o nly this special subclass of them. By contrast, according to Hintikka, th ere are oth er passages in the
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Posterior A1ralytics (especially I. 2.2.8 3b 32.- 84a6) that in dicate there is at least one other so rt of definition-namely those formulae, ca ll ed Ct.TOJ-LOL at 2..5.9Jb32, w hich express immed iate co nnections between ter mswhich do have existential force, and so can function as pre mises in sy llogistic demonstrations. N It is hard to see how H intikka's strict sy ll ogistic ism can be co mpatib le with his position that there are some Aristotelian defi nit ions that call/lOt fu nction as demons trative prem ises. Nonetheless, I believe he is quire right to argue that Aristotle does sharp ly distinguish betwee n t he OPOL of Posterior AHalytics 1.2. and 10, a nd the " immediate" ultimate demonstrative p remises of Posterior Analytics 1.22 a nd 2.5, and moreove r that he does so precisely on the grounds that o nly th e latter have existentia l force. As a matte r of fact, a closer look at what I have ca ll ed the framing stage of demonstration provides a very plausible explanation of w hy [h is distinction should be so important to Aristotle. Ie was argued in chapter I that the Ar istotel ian ad~lptation of Platonic Division invo lves, not the discove ry of defin itions, but the deploy men t of a set of previously apprehended "definitional assumptions" (opod upon some field of inquiry. That is, I argued tha t where Plato co nceives OPOt as the ul ti mate prod ucts of his preferred epistemologicn l method, for Aristotle they are mere starting points- part of the preexistent material out of which knowledge simpliciter is ultima tely generated. I now wa llt to purs ue the question of what it is about the logical chnracter of definitions that motivates Aristotle to assign rhem this me rely contrib utory ro le ill
his theory of demonst rative knowledge. REFERENTIAL AND PLATON ISTIC UNIVERSALS It w ill be helpful at this point to not ice an important respect in which Aristotle 's proposed so lution to Meno 's paradox in Posterior AnalYlics 1 .1 mim ics the st ructu re of the solution put forward by Plato himself at MenD 85D-E and developed thro ugh his midd le d ialogues. Both sol utio ns depend o n separating two forms of knowledge (o r ::lprarcnr knowl edge), one of which is of universa ls (in Placo's case, of the Forms) and the other of particu lars . But this structura l parallel notw ithst;lIld in g, the fun damental epistemologica l positions from w hich the twO propos'l ls issue are diametrica lly opposed . For Plato it is universal knowledge (of forms) that tu rns out to be not just the highest but the only form of gelluine knowledge, w hi le so-called knowledge of mu ndane participants in Forms
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Structure of Demonstrations
is eventually consigned at Republic 5.477-78 to the category of mere "belief" 16o§a) or "opinion" l,,-iO"n,). On the other hand, Ar istotle, true to his anti-Platonic metaphysical proclivities, makes precisely the reverse assignments of relative value to these two sorts of cognitive state. It is what I have called "de re" knowledge- the sort that entails knowledge of particular cases-that is said in Posterior AnaJytics 1.1 to be knowledge in the "strict" or "unqua lified" (d-n-AW~) sense, whereas the type whose objects are universals is described as knowledge only in a qualified sense 171826 -'9)· Before proceeding further, we should try to get a more precise understanding of Aristotle's characterization of de re knowledge at 7 1a1 7- 1 9 as "knowledge of what was known previously, and at the same time. . . of the things which happen to fall under the universal of which there is knowledge." One possible construction of this description is anticipated and explicitly ru led out by Aristotle himself at 7Ia30-h3. In that passage he argues against the suggestion that the objects of de re knowledge of the ttuth of
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are limited to those individual instances that are known by the subject to be pairs, so that to say that a knows de re that every pair is even is just to say that everything known by a to be a pair is also known by a to be even. The problem with this construction, as Aristotle quite correctly deduces, is that it improperly restricts the su bject matter of (I) itself only to pairs whose existence ha s been apprehended by a, whereas the proper scope of the sentence, and therefore of a's de rc knowledge of its truth (as Aristotle puts it) is all pairs that have been proved to be even. These he insists are not limited to pairs kn own by a, but include all pairs witham qualification. Put positively and in the language of recent discussions of propositional attitudes, Aristotle's point is that de re knowledge contexts are transparent in the sense that if a knows de re th at (I) is true, then it fol lows that for every pair b, a knows [hat b is even, whether o r not a knows of b's existence. In his notes [0 this passage, Jonath an Barnes has tried to capture this feature by giving the fo llowing analysis of a's having de re knowledge of (I), If anything is a pair, (hen a knows tha t i( is even.'
This is very nearly correct, si nce it would in every case warrant the inference from "b is a pair" to "a knows b is even." However. this univer[ 42
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sally quantified formulation, unlike its Aristotelian counterpart, docs not make reference to all the actual pairs there are, and so does not involve presuppositions of their existence. Hence, it could be (vacuous ly) true even if no pairs existed. III For this reason, l think it is better to represent the transparency of de re knowledge by lIsing a more Aristotelian form of sentence to be discussed shortly: Every (actual) pair is known by a to be even,
which entai ls Barnes's analysis but at the same time is intended to carry such existential presuppositions. True to the general quasi-epistemological motif of the Posterior Analytics described in my introduction, Aristotle's proposed treatment of the MenD paradox is based on an epistemological distinction between two types of knowledge, or more accurately, between two ways of knowing the truth of single universal sentences such as (z )
Every man is animal.
Indeed, I have suggested that this serves to underscore the fact that he sees his solution to the paradox as a direct and opposed response to Plato's own. Nevertheless, it is possible to see behind this epistemologica l distinction a parallel semantic distinction between two very different ways of understanding the logical character of (2) itself. On one hand, we could understand it :IS a sentence abollt every single individual falling under its subject term, that is, about every actually existent man, II so that its truth would entail J conjunction of singular propositions. I! On th is construction, the subject term of a universal sentence makes (distrihlltcd ) reference to everyone of its actual instances, and so, by virtue of this referential function, the sentence as:1 who le involves a presupposition of the singular existence of each of those individuals. Here it is important to see (hat one cannot capture the existential force of (2) in modern predicate calculus by simply conjoining a universally quantified version of it with an existentially quantified statement bestowing general existence on its subject: (2') If anything is a man, it is an animal, and there are
men. As with all attempts to translate between the Aristotelian and Post-Fregean logics for general terms, this fails to respect a fundamenta l difference between the ways in which they deal with existence. In the logic of quantifiers, existential import is always conveyed by means of existentially [ 4] [
Structure of Demonstrations
quantified stateme nts of general existence (that is, no nemptin ess of predicate extensions), JI such as " Th ere are men ." On the other hand, in Aristotelian logic it is always ca rried by singular existential presuppositions generatcd by th e fundamental idea that general subjec ts like "Every man," no less than singular subjects like "Socrates," actua lly make refer(~ncc to the individuals to which they apply. 1" One way to see this di fference is to norice that if the membership of the human species were (partly or wholly) different from what it actually is, then the facts expressed by (2) wo uld differ accordingly; that is, the sentence would be about a different group of individuals. By contrast, the propositions expressed by (2 ' ) would remain unaltered in such a case. IS In order to rep resent th is distinctive fea ture of Aristotelian logi c, I shall hereafter refcr to universal sentences under this interpretation as referential universals. Alternatively, sentence (2) could also be understood as making no reference whatever to concrete individuals, but instead as expressing a (necessa ry) relation between the universal kinds signified by its subject and predicate terms. Viewed in this way, the sentence could be analyzed as the second-order statement that the human spec ies is a spec ies of animal. 16 For reaso ns that J hope are obvious I shall ca ll universal sentences under this seco nd style of interpretation Platonistic. With this distinction in place, then, it is possible to understand the episte mological moral Aristotle claims in Posterior Analytics 1.1 to draw from his treatment of Meno's Paradox as the conclusion that universal statements capable of conveying the highest form of knowledge (demonstrative knowledge) must be referential. whereas the preexistent substantive meaning assumptions from which this knowledge is generated are conveyed by Platonistic universal state ments. Thi s then leaves two questions outstanding: how does Aristotle think these Platonistic definitions are acquired in the first place, and why does he relegate them to this inferior position?
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THE ACQUISITION OF DEFINITIONS One particularly elegant feature of the overall design of the Posterior Analytics is that its very last chapter (Book 2, Chapter 19) returns to the thought with whi ch th e treatise opens, namely that knowledge based on reasoned justification must be generated out of preexistent knowledge of its foundations. We have seen that this Platonically inspired idea is rcAccred in Aristotle's theory by the requirement that any demonstrative scie nce must take as given a distinctive set of "starting points" (apxai)
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that are used in th e framing sta ge of demonstrnti on to ge nerate the mos t bas ic premi ses out of which sy ll ogistic dem onstration s within that sc ien ce are composed . But this of course does not even tou ch the residual question of how these initial sta rting points come to be acquired or justified in th e first place. I should point ou t to begin with that because the cI;lSS of Ari stotelian apxai has already been seen to be ex tremely heterogeneous in its l11;l keup , there is no reason to ex pect that this ques tio n wo uld receive a single) simple answer from Aristotle. And ind eed) he appears to recogni ze very different manners of justifica tio n for di ffe rent so rts of a pX('Ii. In particular, his proposed defense in Metaphysics r 4 of th e so-call ed common axio m of Noncontradiction (w hich was class ifi ed in chap ter J as one of the nonsubstantive background assumptions of Aristotelian division needed to generate the premises o f demonstrative syllogisms) appears to proceed accord ing to relatively in fo rmal dial ectical methods of th e sort set fonh in the Topics. On the other hand , he ~eems [0 think that another sort of backgrou nd assumption, those conveying the existe nce of the ohjects o f demonstration, requires no discursive justificati on at ~ II , but rather can be secured simply by perceiving the objects in qu es ti on, or pcrhaps (in th e case of mathematics ) even by simply hypothesizin g their ex iste nce. Bu t whe reas Aristotle's views about the acquisirion of these various sorts of nonsubstami ve startin g points of demonstr ... tio ll them selves remain for the most pa rt in the background of th e Posterior Analytics, he evidentally regards opol.- the ultimate meaning assumptions of demonstratio n-as so central to his theo ry that he chooses to dose the whole treatise with a di scuss ion of how they in particl1lar co me to he apprehended prior to the generation of demon strative know ledge. To he sure, the fact that Posterior Alla/yties 2 . I 9 is co ncerned specifi cally with defini tional apxai does not co me out clearly in Aristotle's initial formulation at 99bTS - I9 of the main question to he pursued in rhe chapter: " Hence, co ncernin g sy llogism and demonstration, what each of th em is and how it comes about, is now appa rent; and likewise co ncernin g demonstr;ttive kn owledge, for [the issuesl are the same. But Iwe must now ma ke clear] concerning the starring poi nts (apxwv), how they come to be recogni zed (YIIWPL,uOt), and wh at is the co ndition (etL'iI -) which recognizes them." It is, however, evidenced in hi s more precise reiteration of rhe questioll at b20 - J..5, where he characterizes the "primary st
I 45 I
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! Structure of Demonstrations
whether it's th e same [as that of nonimmediatesJ o r not, and (2) wheth er there is knowledge (em eT'ni!':'!) of both, or if kn owledge is [only] of [nonimmediates] whil e [the cognitive i~t~, which apprehends immediates] is of a d iffe rent sort." U It is important to recognize that even though neither Plato nor his Meno are here mentioned by name. this fin al chap ter of the Posterior Analytics, no less than the first. takes the famous paradox about learning formulated in that di alogue as its primary point of departure. T his is plain almost fro m its ope ning when, in [he conti nu ation of the passage jusr quoted, Aristotle consciously mode ls his proposed approach on the Meno pa radox by posing th e ancillary question of wheth er the soughtafter account of the preexistent apprehension of im mediate demonstrative first principles will involve (a) postulating the emergence of enti rely new cogni tive itet~ in the subject's soul, o r whether (as in the Platon ic doctrine of Reco ll ection) it wi ll instead requi re (b) the postulation of pre-existent etet~ of whi ch the subject is unaware: "{We mu st inqui re] whether cogniti ve states not {already] in the subject co me into being, or whether they had [sim pl y] not been noticed (AeA.-rjfhro-w) I" to be within the su bject" (99bu-2.6 ). From this point Aristotle proceeds to argu e that the seeming exhaustiveness of the disju nction between (a) and (b) sets up an apparent dilemma, but that this dilemma is in fact only appa rent. He moves directly against (a ) at bz.8 - 30 by reca llin g hi s co nclusion in Book I, Cha pter I (which in rum looks back to the MellO) that it is not possible fo r knowledge or learn ing to arise out of a complete lack of cognition on the su bject's part. His rej ectio n of (b), on the other hand , is qualified : he claims at b2.6-2.7 that it is absurd (a-ro7ToII) to think th at one cou ld happen to possess a cognitive €§~~ that is "more accurate" (aKpt{3ea;6par:;) than demonstration. while remain in g ignoran t that one possessed it. The qualification here is sign ificant, for it turns out that Aristorle's subsequent proposal fo r avoiding the dilemm a is [0 deny (a) by holdin g th at there is a certain preexistent ettr:; fro m which the apprehension of first principles (and a fortiori, all demo nst rative knowledge) ultimately arises) while at the sa me time avoidi ng the absurd form of (b) by denying that th is e~tr:; is an occurrent cogn itive state (in whi ch case, it would presumably have to be more accurate than demonstrative knowledge, and co uld therefore not be possessed inadvertently). Ralher. he maintains, the egt~ in question is a certain kind of cognitive capacity, that is to say, a Svva,utr:;,2° for acq ui rin g such occurrent states. which is not more accurate than those occur-
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Demonstration and Derllitioll
rent states themselves: "However, it is apparent both that one cannot possess such states without knowing so, and also that they cou ld not come to be if one didn't possess any [prior] state
[ 47 [
Structure of Demonstrations
developed mature human specimen (or perhaps, as we might say, any sllch that ma ste red a language with general terms), solely by virtue of having a rational sou l, quite independently of whether it had any inclination or abi li ty for the scientific ente rprise. In other words, as Posterior Allaiytics 2.19 characterizes the mann er in which the definitional first principles of demonstration are initially appre hended, it rums out to be nothing other than the process of general co ncept formation, wh ich is avail ab le to all humans, and whi ch must already have been accomplished before there can be any question of doing Aristotelian science. In the fina l analysis, it is th is pecul iarly human, but not peculiarly "scientific/' activity that Aristotle sees as provid ing the preexistent substan ti ve material out of wh ich demonstrative knowledge is ultimately generated.
I I
THE LOGICAL CHARACTER OF DEFINITIONS The rema ining question posed earlier is why Aristotle denies that apprehension of this preexistent material qualifies as know ledge simpliciter. The answer to this li es ultimatel y in anoth er, related respect besides that discllssed in chapter I, in wh ich the framing stage of Aristoteli an demon stration differs importantly from Platonic oLai-peCTlS. in light of what is known about the metaphysics of Plato's middle period, it would be very hard to deny that for him the ultimate objects of 6wipE:CTtl) must be separated universa ls, that is to say, Platonic Forms. Hence, any sa lient exteHsianal rclations that are noticed among classes of particulars during the process of division must be understood finally as mundane manifestations of eternal, unchanging, and necessary "interweaving" (CTU,u'1TAOK'lj ), that is) intensional, relations among such Fo rm s/~ which are the real subject matter of the OPOL generated by Plaw's method. But this means that once such a Platonic definition has been acquired, any or all of the sensible particulars that helped give rise to it might be forgotten (o r for that mattcr destroyed) without diminishing the quality of knowledge of rhe definition itself onc whit. This of course would not be at all troubling to a Platonist, for whom particulars are after all just imperfect and transitory participants in the Forms. On the o ther hand, it is easy to see why an immanent realist!#' like Aristotle would be qu ite uncomfortable about the adri,:ission of such free-floating universa l knowledge that is not necessarily pegged to any concrete individuals. This, I think, is at bottom why his theory of demonstrat ion systematically gives pride of place to de re knowledge of a-rOJ.1.0L and is inclined to demote merely universal knowl-
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edge of OPOL to the level of preexistent epistemic material out of which demonstrative knowledge is generated.
DEMONSTRATION AND SYSTEMATICITY There is, however, a second and equally important reason for Aristotle to deny preexistent knowledge of OPOL the status of knowledge in his stri ctest sense of the tcrm, and there is more thall a li ttl e irony in the fact that this reason also seems to be taken frolll P1:tto. On the basis of what has been sa id so far, nothing in the theory of demonstration rules out the possibility that one could acquire any number of these (.~pxni and yet not have the slightest idea how they (or any subgroups of them) could be drawn together into some systematic and coherent scheme of scientific explanation. Now it was mentioned earlier thar Plato rcgilrds definitions generated by his method of division as objects of the highest form of knowledge. Furth ermore, in ligh t of certain views ev idenced in the Theaetetus (the one Platonic dialogue devoted exclusively to epistemologic;:ll concerns), it is easy enough to understand the reason for this high regard. This dialogue, like so many othe rs, ends in appa rent perplexity, but nearly everyone agrees that it makes progress in the direction of establi shing that, whatever genuine knowledge should turn Ollt to be, it must somehow involve having "true belief accompanied by a logos." The final perplexity of the dialogue th en arises because the interlocutors cannot seem to find a defensible understanding of wh;:lt should COll1H as the right sort of logos. However, Myles BurnyeJt and others 27 have argued con vincingly that in the closing sect ions of the work, Plato expresses a defi nite attraction to (w ith out quite endorsing) what has been ca ll ed the "interrelational model" of justification, according to which ;:I logos of lh e right sort makes clear the place which the object of knowl edge occupies within a su itably large and systematic field of interrebted ohjects. It shou ld be apparent, however, how a definition of the sort genera ted by the Platonic method of division exhibited in the Sophist might be thought of in just this way, since it takes the form of a logos that spec ifi cs the exact sequence of divisional nodes trJ versed between rhe original genll s subjected to the division and the bottommost item finally defined by it. !~ However, as Burnyeat also points out/~ Aristotle's Posterior Analytics, no less than Plato's Theaetetr/s, is firm in its insistence that the titl e of " knowledge in the unqualified se nse," (or, equivnlentiy, of " understanding" [hno-rrj,ulJ ,uETa )"'0),0<)]) cannot be conferred on a single belief
I
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Structure of DemOllstrations taken in isolation (no matter how "real" its objects ), but must instead be presented in appreciation of the place that belief occupies in a sufficiently wide and syste matic body of other beliefs. In other words, Aristotle, like Plato, subscribes to the interrelational model. Hence, it would seem that so long as appre hensions of definitiona l dpXai are considered as isolated bits and snatches of cognition, they will fall short o f being knowledge in the unqualified sense. If it is correct that Aristotle 's rationale for denying that "merely uni· versa I" knowledge of OPOL is the highest form possible is not just failure of ex istential import but also la ck of systematicity, then it should be possible to see how, in the p rocess of moving from this state to the actua l produc· tion of syll ogistic demonstrations, both failures are overcome. My cen tral proposal is that the presyllogistic framing stage of demonstration is seen by Aristotle as accomplish ing just that. It is a procedure wherein some set of Platonistic OPOL that have been previously acquired (by the process described in Posterior Analytics 2.19) are then superimposed upon some scientifically in teresting genus of individuals whose existence and place in th e broader scheme of things has already been recognized or assumed. This procedure both organizes that genus into a branch ing explanatory structure and simultaneously generates a set of immediate predications, which are referential universals (a nd hence objects of de re knowledge) and can therefore serve as the ultimate premises in syllogistic demonstra· tions of nonimmediate connections within that genus. Hen ce, when the immediate premises of a given science thar emerge from the fra mi ng procedure are considered collectively, they can be seen to reflcct a syste matizat ion of the basic truths about the subject·gcnus into an organized body of sc ientific knowledge in which explanations going all the way back to those fundamental premises can then be co nstructed. And this, as Burnyeat correctly argues, is the only form of cogn ition Ari stotle thinks worthy of being called knowledge in the str ictest possible sense, or as Burnyeat puts it, scientific understanding. Thus, it is possibl e to understand the remark at Posterior Anaiytics I.2.7IbI8-2.o, that "knowledge in the unqualified sense comes from demonstration," as a distin ctly Aristotelian spec ification of Plato's insight in the Theaetetus that genuine knowledge requires the possession of an inrerrelational logos. The differen ce, of course, is that whereas Plato simply identifies such logoi with the Platonistic definitions generated by division, for Aristotle these logoi are nothing less th an the co mpl ete syllogistic demonstrations that (to reinvoke the language of Posterior Analytics 2.1 and 2.)
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DemollStratioll and Defillitioll
allow one to know not just that the fact in questio n is tru e, bu t also why it is tru e. For on the presen t interpretation, the constru ction of such an explanation (more speci fica lly, the acquisition of its ultimate prem ises) req uires th at th e demonst rator have al ready come to app rehend in a systema ti c ma nner all of the salien t necessary interco nn ections o htaining within the field of study. In that sense, the demo nst rative procedure as a whole can be sai d to reveal the systematic relations which the demon strated item bears to other proposi ti ons (most importantly, the ultimate premises) within its app ropr iare science.
TH E PRO DUCTS OF DEMONSTRATION According to Arisrorle's own words at Posterior A"alytics 1. 2..7I b9 - 19, knowledge " in the unqua lified sense" {(hrAw~) is acquired "by mea ns of dem onstration" (~h' cbro8eigewc;). Now tha t the various sorts of apxcr.i of Aristote li an demonstration have been explicated sepa rately, we arc finally in a position to see how they operate together to yield know ledge of the appropriate so rt. That is, we can now say exactl y what it is abollt the demonstrative process that makes Aristo tle believe that its prod ucts should deserve the elevated status of knowled ge a1TAW!). By way of contrast, let us reca ll one likely reason noted earlier for hi s insistence that possess ion of the substantive mean ing assumptions of demollstrationwhat I have been ca llin g im mediate definitiona l ass umption s- does not deserve this statu s. We saw above that the only so rt of know ledge one can have of these starring po ints is (using the distinction of Posterior Analytics I. I) "merely universa l," and so is not "about" an y individuJ I existents that might happen to fall under its term s. By contrast, the immediate pred ications that emerge fro m the fra ming stage are not only uni versal in form but genuine referential universals (o r hypotheses), and th erefore ca n fun cti o n as genui ne demonstrative premises. It is th ese. and not the OPOl frolll which they are generated, that Aristotle ins is ts at 71 bl..l.. must be " better known" than the prod ucts of the entire demonstrative process. Moreover, it is these ultimate immed iate syll ogistic premises (rather than rhe " mere definitory reformulations" th at H in tikka concocts "') that are the true source o f th e ex iste ntial im port th at th en percola tes down to the ultim ate demonstrand a of Aristotelia n sc ience. In sho rt, th en, the concl usions of Aristo telian demonstrat ions are referenti al uni versal sta tements exp ressing medi ated (th at is to say, exp lainabl e) connections betwee n term s. Bu t this, I have suggested, is on ly one of Aristo tl e's two independ ent
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reasons for acco rdin g to demonstrative conclu sions the ti tl e of knowledge
simpliciter. Th e other stems from th e tho ugh t, which I suggcs t is central to the epistemology of the Posterior Anaiytics, that such a conclusion is properly spea king inseparab le fro m th e demonstration supporting it. That is, Aris totle insists rhat epistemological value is determined, not by contem plating the propos ition alonc, but (to revive fo r a mom ent the old Pl aroni c expression ) hy the proposition "together with its account" Cl..u:Ta TOi) AO'YOiJ). But since, according to its Aristotelian specifi cation, the account in question is nothing other th an th e enti re sy llogistic demonstra tion of the proposition, and since, as we saw above, the premises of this demonstration are necessarily acq uired by means of a divisional procedure that orga nizes the en tire subject-genus into a taxonomic structure, it is a sma ll and ve ry natural step to conceive of know ledge of the demonstrated proposition itself as part and pa rcel of one's co mplete and systemati c understanding of th e whole genus in which it resides, and it is not hard to understand why Aristotl e (like Plato befo re him ) should want to make thi s sort of systematic understa nding a necessa ry requirement for the possession of i1rturillJ.,T} in hi s own stric tes t sense of that term.
THE DEMONSTRABILITY OF DEFIN ITIONS However, it m.1Y reasonably be wondered why, if the distinction between de re and "merely un ive rsal" knowledge is as cen tral to Aristotle's theory of demonstration as J say, he seems to menrion it only on the very outsk irts of the Posterior A 1lalytics (in Book I , Chapte r 1), where his concern is not yet to set ou t the theory but to mo tivate it by appeal to the bro:ldest epistemological co nce rns . In Other words, if I am ri ght that th e appl ication of this distinction to definitional k nowl edge especially is cru cial to understanding how genuine scienrific understandi ng is fundamenta lly d ifferent from, and yet genera ted out of, preexisrenr knowledge of apxcx.i, th en pres umably we shou ld find him making explicit and highl y vis ible appl icatio ns of this di sti nction to ma rk off a di ffere nce between prescientifi c knowledge of pseudopredicational, definitional apxai not suitable for use in demonstratio n, and their de rivative and genuinely predicational co un te rparts, which ca n serve as demonstrative premises. Let me first say thM this di stinction is reflected to some extent throu gho ut the Posteri()r Analytics by Aristotl e's regular (if not religious) practice noted by Hintikka of rese rvin g the ter m "definition" (opo, ) to stand for what I am ca lling definitional apxcx.L, and em ploying alternative term i-
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Demonstration nltd Definition
nology (usua1ly "irnmediates" [a,ueCTOtj or "atomics" faTo,uotj) to refer to the imm ed iate definitional predications that fu nction :lS ultimate de-
monst rative premises. T his in fact is the pattern of use ev id cnt in the two passages discussed above in Posterior Anafytics \.2. :lnd LO, where hc ~l S serts that OpOI. (identified there as apxai) arc not genuine hY/JOtheses, but instead "mere theses, " on the ground that they m:lke no :lssertions of existence or nonexistence ..11 In the view I am urging, this is tamamOl1nt to the assertion that such defin itions ca nn ot serve;'ls demonstrat ive premises precisely because they do not carry ex iste nti al import, and so, bi]illg ro "say one thing o f another," .12 are not even authentic predicatio ns. But it may st ill be objected that these passages at hest provide weak circumstantial evidence that Aristotle so metimes presupposes the disti l1l> tion I am ascribing to him . However, we will now he reminded th'lt the original cha ll enge demanded more: if rhe disrincrion in qucsrion is indeed pivotal to Aristotle's theory, then we sho uld find hi m so mewh ere bothering to warn his readers of its presence and importance, and not simply writing as if it had alread y been made cle:H when in bct it hao \l Ot. Fortuna tely, it is not necessary to rely on ly on circu lllstantial cv idence on rhis point, because the re is a place where the distinct ion is set out in quite explici t tetms. What is more, th is occurs right whe re it would be most expected: in the mu ch discllssed (b ut still obscure) th ird through tenth chapte rs of the second book of the Posterior AHalytics. where Aristotle addresses the question of precise ly how definitions fit into the freshly exposited theory of (¥7rc\l5 e t~tS'. The cent ral concern of these ch .. pters is precipitated by Aristotle's declarations in Chapters, and 2. that the pro* duction of demonstrative syllog isms ca n in some contexts suffice to al1* swe r a "What is it?" question. The issue then is to determine exac tly how th e "what-is-it" (TO Ti 6(77(.) of tl given subjec t is "s hown" (l5etl(vvTCu) by syllogistic demon strations in the science that stud ies it (900135 - 36). How eve r, for rea sons hav ing to do with features of Ar istotle's philoso phica l method, the initial stages of this investigation (Chnpters J thro ugh 6) leave unexpressed and un ques tioned the Platonic ;lSSlllllptioll of the So phist and the Statesman that a definiti on is ::J st:ltemcnt of the n f:(Tn of its object, with the result th at the discussion in its carly stages moves back and forth indiscriminately between the original ql1estion of ')oa .~5-36 and other di stinct (though obviously related) qucstio ns abollt thc place of definition in demonstration. Thus, for instance, afrer having argucd in a preliminary way in Chapter 3 for the true (if unexcit ing) claims rh~lt th e classes of definitions and demonstrahle propositions arc di stinct, and that
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Structure of Demonstrations
neither includes the other (91a8- I 2), Aristotle then turns in Chapter 4 to wh at he sees as the more interesting and diffi cult question of whethe r the two classes even intersecr.J.I But as it is configured by the Platonic assumption mentio ned above, th e question actually posed at 9ra13-14 is "whether there is syllogism and demon st rati on of the 1"1, tun." It is not always appreciated how well, from this point on, Aristotle's procedure matches the ge nera l pattern of dialectical inquiry so bea utifully exposited in G. E. L. Owen's landmark articl e, "Tithenai Ta Phainomena." ·l. Acco rding to Owen's account, this sort of investigation characteristi cally opens with an "aporetic survey," in which a number of possible (a nd in many cases, actually propounded) answers to some loosely formulated qu es tion are subjected to close critica l scrutiny. At some point after each of these tvBo~a has been shown in its turn to land in conceptual difficulty, Aristotle begins to se t the stage for resolving these difficulties by recasting the original question into his own d istin ctive semitechnical vocabulary, in this way superimposing hi s own system of analytical concepts on the iss ues he is treating. Now even the casual reader of Aristo tle is aware that virtually every one of his key phi losophical te rms is equivo ca ted upon as a matter of co urse, not just from treatise to treatise, but often within a single work, and sometimes even within a single chapter. This is nO{ at all to charge him with sloppi ness or ind ifference in his terminological habits. On the contrary, his patterns of equivocation are both systematic and deliberate, and moreover are highly valued by him as an indispensa ble part of th e philosophical method he emp loys to bring about dialectica l resolution of the conceptual problems uncove red in his aporeric surveys. For by trans· laring a question under study into his own systematically equivocal lan guage, he effectively disambiguates the question by separating out variou s of its possible interpretations, one of which in the usu al case he identifies as the "strict" (KtJpiw, ), "unqualified" (cX1r'\w,), or "primary" (1TPW'TOV) interpretation. Armed with this disambiguation, he is then in a position to produce what we might call the "full answer" to his question by giving what he takes [0 be the correct answer on each interp retation (with special emphasis, of course, on the primary interpretation). Finall y, different parts of the "full answer" are deployed to show that each of the 8 vB6~a dealt with earlier went wrong because of a failure to respect subtle differences among the meanings of terms, but also th at each is in fact a misfired attempt to express some portion of the whole truth con tained in Aristotlc's ow n final , enlightened posi tion. Thus, in the end, all positions ex·
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cept Aristotle's are literally rejected. bur all ::tre nonetheless ilCcomodated, and it is in this sense that he believes his method "s;tves the phenomena." True to this genera l form, Aristotle's full answer to the question of whether there are any demonstrable definitions is that on some interpretations of the question there are, and on others not. Funhermore, it is not surpr ising that his specification of the various in terp retations involved turns on exploiting amb iguities ill the terlllS definition and demonstratimt. since these are conspicuous ly the only two
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The argument for separating these two senses, lik e so mllch of th e Posterior Allalytics. is conduc ted within the episrelllologic:11 substructure of the th eory of demonstration. Aristotle's concern at 92b4 - 34 is to reconcile twO seemingly incompati ble views he holds ahout the relative pri-
I 55 )
Structure of DemoltStratio1ts
ority of definitional and existential knowledge. On the one hand, he insists repeatedly that (a) one cannot come to know what X is without knowing (e ither befo rehand or concurrently) that X is, (in other words, that X exists; 89b33, 92.bS , 9334). But on the other hand, it is both a feature of his own theory of demonstration and an observation he makes independentl y abou t "actual scientific practice" that (b) a science mu st assume the meanings of its non primitive terms and prove the existence of their significa ta. There is of course th e genera l question, which will be deferred for the tim e being, of whether th ere is any way at all to incorporate these two ideas harmoniollsly in to a si ngl e coherent theory, but Aristotle's concern at 92.b4- 34 is much narrower. His questio n there is whether (a) is consistent with a ve ry special understanding of (b) according to which the assu mptions of meaning it mentions are Pl atonic defini tions (that is, logoi obtained by the method of 8LUipe(;nr:; that give both the n Bern an d the Ti UTjJ.Luivet TO OVOJ.Lu) that also fun ction as ultimate sy llogistic premises. Aristotle's answer to this question is negative, and although his reasoning in Posterior Analytics 2..7 is highly suppressed, it is possible to reconstru ct in the light of his earlier assertion at Posterior Analytics 1.2.. 72.a2.6bS that (c) the premises of a demonstrative syllogism must be "better known than" (yvwptJ.Lwn;pov) and "prior to" (npo'Tspov) its conclusion . He now observes at 92b19-20 that according to "current manners" of defining (and here I believe he is referring to Platonic Division as well as the inductive manner of apprehending definitional connections descr ibed in Posterior A1Wlytics 2.19), one who defines does not thereby prove the existence of the defin iendum. Hence, if a product of such a method were allowed to occur as a better known pre mise in a syllogism that proved the ex istence of its objects, it would after all be possible to know (prior to the demonstration) the Tt BUTI. of those objects without knowing that they existed. Bur this is precisely what is ruled out by (a) . How then does Aristotl e him self propose to reconcile (a) and (b) in the face of (c)? As I have suggested, his crucial pl oy is to insist on a separacion of two senses of the term opo<;: the primary one (employed in 1.2 and 10) in which it is merely a statement·of what a name means, and a secondary (Platonic) sense in which it is also a statement of the what-is-it of whatever answers to the name. He is then ab le to claim that only the second so rt of definition can fu nction as a premise in demonstration, which in turn allows him to mainta in (as part of his "full answer" in 2..10) th at there is an attenuated sense of the verb "to demonstrate" (ar.o8eiKVVJ.L~) in which these definitions can be said to be demonstrated by
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virtue of the ir occurrence as demonstrative premises (2. 10.94a L- 19). \h A negative coro llary to the argumenr of Posterior Anaiytics l.7, as I have reconstructed it, is thar definitions in the strict or primary Aristotelian sense-that is, statem ents that simply give the TI. (T7IJ.L{,
DEMONSTRATION AND ANALYTICITY There is an additional benefit to be gai ned from the present interpretation. An accurate understanding of the respective roles of de re knowl· edge of immediate premises, and merely universa l knowledge of ddin;· tiona l staning points in the theory of demonstration makes it poss ible to clear Aristotle of the charge, which I shall call the allalyticity oiJje<:tiOI1, that he envisions a sc ientifi c prograJ11 somehow capable of explaining CIll · pi rica I facts about the wo rld wholly on rhe b .. sis of nrsf princip les fhat are themselves analytic and thus devoi d of £ncwal COlltC1lr. " This objel.:. tion is motivated by the fact that Posterior Al1aiytics 2. 19. the chapter in which Aristotle attempts to exp lain how the preexistent meaning as· sumpt ions of demonstration are acquired in the first place, set:ms to Ic:we little doubt that be regards these definitional starting points as Pbtonistic according to the above distinction. This ohservntion, which in itself is perfectly correct, is then supposed by Aristotle's critics to necessitate all unbridgeable schism within hi s theory of dernonstr;nive science. In par· ticular, it is thought that the analyticity of these principles makes them logically isolated both from the em pirica l facts rhey arc supposed to cx [ 57 [
Structure of Derno1l5tratiol1S
plain and from the perceptual experiences that are sa id in Posterior Ana· lytics 2..19 to generate them. Let us address the second aspect of this charge first. The criticism here is that a Plaronistic construal of the character of definitional apxai is some· how at odds with the empiricist account given at looal 5(£. of 61Taywyrj, the process by which these starting points co me to be known in the first place. hs obscure martial imagery as id e. this passage does seem to say quite clearly that knowledge of definitional apxai is derived ultimately from multiple " perceptions" (aiuO-rycreL'» of sensible particulars of the relevant kinds. But it is then to be wondered how the truth of ana lytic statements could possib ly be apprehended by a ny such empirical process. More spec ifically. the worry is that because perception is in its essential nature a co nfrontation with a fully pa rticular sensible object, no single perceptual experience could ever produce a cognitive state with universal content, nor could any mere ly combinatory operations upon any finire collection of such experiences. The general argument that any necess ary truth is a nalyti c, and there· fore known a priori, stems from an empi ricist tradition (reachin g back at least to Locke), which has tended to take an extremely narrow view of the nature of necessary truth . According to thi s view. if a sentence (a) does not express a contingent matter of fact about the actual individua ls falling under its subject. then (no matter whether it is a logical tautology or a conceptual truth) it is (b) true solely by vi rtue of the meaning of its terms. As such , it is construed as (c) having no existential force with respect to individuals and as (d) making no factual assertions whatever, but merely as (e) expressing relations between ideas or meanings. But since. on this view, the ,truth of such a sentence is grounded, not in any ob jective fea tures of the ex perienced world, but rather in the structural characteristics of so me artifactual, conceptual, or linguistic sys tem, it is reasoned that such a sentence (f) cou ld not possibly be justified by appeal to perceptual experience. Despite its long·stan ding popu larity, this line of argument is a rather blatant non seq uicur. For unless one begins with the extremely dubious assumption, presupposed by (e), that universal kinds are nothing but meanings residing in heads or lexicons, it sim ply does not follow that a sentence satisfying (a) will hav e any of characteristics (b) through (el . Tn particu lar. there seems to be nothing whatever improper in believing (as Aristotle in fact does) both that a sentence such as (2) Eve:ry man is animal
[ 58 J
I f
r
I I
I f
Demonstration mId De{illitioll
can be constru ed as express in g a necessary relation between two natural kinds , and that th ese kinds along with [heir interrelations arc objective features of the physical world, and not just reflections of our thought or language. But if this is plausible, th ere is no reason Ilot to suppose what (f) denies: that one could (and ind eed must) come to acq ui re knowledge of these necessary co nnections th rough perceptual acquaintance with the world in which they subsist. Of course, this would pose a problem if one also subscribed to an ultraempiricist theory of perception and knowledge according to which both the object and the content of a perceptual experience must be "perfectly part icula r. " Bur this is precisely the kind of theory that Aristotle does nor hold. It is true that he rea cts vigorously to the Platonist's separation of universals from the visib le world, but he is every bit as much a realisral beit an immanent realist-as th e target of those attacks. Co nsequently, his metaphysics allows him to ana lyze perception, as Plato ca nl1 ot. as acquain tance not just with an individual subs tance, but also with th e immanent universal s which that su bstance insta ntiates, si nce they are for him actually present at the site of perception. In b et, he wkes pai ns to remind his readers of this theory of perception parentheticall y in the midst of his description of i1T£r-yw-Y7J in Posterior Allalytics 2.19: "even though it is the particular (TO KaO' eKCf.(.TToV) whi ch is perceived (at(T86v8T£U), the perception (-r, a[
I
59
I
Structu re of DemOl1stra tiOlts niti on .. 1starti ng po ints of demonstrati on are indeed analytic (that is, Platon is tic) statemen ts that can be known at best in the " merely universal" manner of Posterior Analytics 1.1, then they are logicall y incapable of en ta iling de re knowledge of particulars. This objection, li ke the one cons idered above, rests on a failure to sec th at Aristotle's immanent realism cuts across the false dich otomies represe nted by desc riptions (a)-(f) above. Again, on the ul tra-empiric ist attitude toward necessary truth, a true sentence is either about indiv iduals (in which case it is co mingent), o r (taken ex clusiv ely ) it is "merely analytic," in whi ch case it does not reflect o bjective features of the world) and so must be known a prio ri. We already saw that the defi nitional apxai discussed in Posterior Ana/yttcs 2.19 constitute violations of this alleged divi sion si nce they are not about ind ividuals, yet they do represent objective features of the wo rld (relations among kinds), and moreover do co me to be known through perceptual ex perience. Now we can see in addition th at the immediate premises of demonstratio n also violate the empiricist dichotomy, though for a different reason. Since they are referential uni versals, th ey are statements abo ut the actual individuals which come under their sub ject terms, and so they obviously have factua l content, and refl ec t objective features of th e physical world. For as we saw above, the y would be false if thei r subjects failed to refe r, and would ex press different fac ts if their subj eC[s referred to different individuals. Yet Ari stotle would see no ne of this as reason to classify the m as merely conti ngent. In fact, wh en a sentence like (2) is construed as a referenti al uni ve rsal, it refl ects esse ntiall y th e sa me metaphysica l circumstance, that is, the same necessary re lation between immanent kinds, as does its Platonistic counte rpart. Once th is last point is recognized, then it becomes clear exactly where the all eged unbridgea ble schi sm between analytic first principles and th e ex istentiall y "loaded" explananda of scientific demonstration is traversed in Aristotle's theory. My proposal is th at the presy llogistic fr aming stage of demonstration is seen by him as a procedure for transforming me rely universal knowledge of necessa ry connections among kinds into de re knowledge of these very sa me co nnections (a nd others as we ll ). This is achieved by deployin g a set of definitional apxai (prev iously acq uired in the manner d iscussed in Posterior AnaJytics 2..19 ) upo n a field of scientifically interesting objects (w hose existence and place in the w ider sche me have also been previously apprehended ) so as to gene rate a set of existentiall y loaded prem ises express in g immediate and necessary co nnections within th at field.
[ 60 )
,.
DemO/lst ra tioll alld Defillithm
There is, then, a very impo rtant sense in which the qu es tion of wheth er the necessity operative in Ari stotle's theory of demo nstration sho uld be construed as essentialistic or merely analyric is misconceived. The fa ct is that what he regards as the ve ry highes t form o f knowl edge possib le is typ ically conveyed by a special so rt of general sentence (the referenti al un iversal) th at is about indi viduals and yet at th e same time exp resses necessary relation s am ong the natu ral kinds to which those in divid uals belong. One way to put this is to say that such selHences ex press ana lytic (and a posteriori ) truths abo ut actu al indi viduals, qua members of th e natural kinds to which they belong. Hence, their necessity can he sa id to reside both in the analytic connections among those ki nds an d in th e esse n· tialistic connecti ons between substantial 1M kinds and their actu al mem· bers.Jq In epistemo logica l tcrms, this mea ns that knowled ge of such neces· sary truths will req uire both prev ious ap pre hension of necessary relati ons among th e kinds in question (that is, immediate defi niti ol1:l1 apxai). and th e recogni tio n (implicit in the framing procedure) that certain aC Cl131 in· dividuals fall un der those kind s. To return fu ll circl e to the p:lss:lge dis· cussed at the ve ry begi nning of this chap ter, thi s is eX:lctly what is co n· veyed by rhe description of de re kn ow ledge in Posterior Al1aiytics I. T
[ 61
I
THREE The Character of Demonstrative Premises
The account developed so far of the broad structure of an Aristoteli an demonstration has dealt o nly with the logical Ch:1 f
on the grou nds th at even jf its premises are both imm cdiate, it revc rses the co rrect explanatory order between failure to twinkle and llC:1rneSS ex hi bited in the genuine dem o nstration,
[ 65
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Explanatory Content of Demonstrations
(i) Every pl anet is near, and (i i) every near thing fails to twink le, so (iii) eve ry planet fails to twinkle, and so can not be said to reveal the "reason" (TO 8"on) for its conclusion . Moreover, inasm uch as he regularly eq uates showi ng the reason for a proposition with find ing, nO[ jusr any middle between irs te rms, but one that co nsti tutes a "cause" (ai'novj Posterior Analytics I.2.7Ib9-16; 2.2.90a5-24), the problem Ari stotle finds with the first syllogism, in the la nguagc of 7Ib20-26, is that althou gh (we may assume) both of its premises arc true, immediate, and therefore primary, it is nonetheless not a good demonstration because its minor premise, is not prior to, (objec· tively) better known than, or causative of its conclusion. As I hope to show, Aristotle's strategy for ensuring satisfaction of these three re mai ning conditions, all of which pertain to the exp lanatory co ntent of de mons trations, is re (] ected in his broad programmatic re· marks in Posterior Analytics 1.10 when he ind icates that a demonstrative science should confine itself exclusively to "per se" (KaO'aVro) attributes: "Proper (tala) to each sc ience are the subjects whose existence it assumes, and whose per se attributes ({mlr.Pxovra KaO'atira) it stud ies .... Of these subj ec ts both the existence (ro dven) and the meaning (r06 i d vm) are assumed, but as for the per se attributes, only the mean ing (Ti CT71J.Lai vt t ) is assumed" (l.I O.76 b5-7). The central task of this and the following three chapters, then, will be to develop a detailed interpretation of Aristotle's doctrine of per se attributes, with the ultimate aim of showin g how it provides the basis of hi s views about the explanatory force of demon stra tio ns. KNOWLEDGE AND NECESS ITY IN THE POSTERIOR ANALYT/CS
T hroughout the Organon Aris totle gives numero us exa mples of sentences co ntaining the modal-ad verbia l exp ressions O:VO:YK71 and O:l.IO:YK71. What is mo re, he has quite a bit to say in those works about the logical behavior of those expressions. For instan ce, in the twelfth and thirteenth chapters of De Interpretatione, he co nsiders th e in te rd efi nability between " necessaril y" a nd its correlative upossibly" (tv8exo ,uevov); in the ninth cha pte r of the same work he points out differences in the sco pe of the " necessarily" operator between co rrect and incorrect versions of the Law of Excluded Midd le; and in the eighth through the twelfth chap ters o f
ee
[ 66
I
The Cbaracter
of DemOllstrafivl!
Premises
Prior Analytics 1, he conducts a protracted and deta iled invcsrig:1tioll into the validity of vario us modal syllogistic inferences involving apodcic~ tic, or "necessaril y," sentences. But for all this early interest in the subject of necessity, Aristotle never attempts [Q prov id e an exp lanC1[Qry, non modal analysis of apodeictic sen~ tenees until the Posterior Analytics, his treatise on the 1l:1tu re of "del11on~ stration" (&7To5~tgtS'), or scientifi c expbnation. This coincid ence of inter~ est in science and necessity, according [Q Aristotle's own testimony, ste ms from his views abour the objects of knowledge. Although hi s ext::lnr writ' ~ ings on general epistemology, ' compared with those of Plato, are quite sparse, what there is comm its its author without question to the Platonic doctrine enunciated in the Theaetetus tbat the only propositions (states of affairs or facts) that can be known (rather than merely helievcd) arc those that "cannot be otherwise" (a8vJ/O''TOv cXAAWS' F.XI-; tv ). T hi s del(,;' trine, which I shall refer to as th e principle of epistemic cOl1servt1til);sm, (EC) (For every p) if p is known to he the GISt" then r is necessarily the case, is clearly evidenced, among other pla ces. af Posterior Alla/yties 7.p2.0 and 88b3 x, and NicomaciJem l Ethics 11 .~9l)2o. It must be admitted that Aristorle's reasons for holding (EC) a re not very obvious. It is remotely possible th;u he comes to belicve it by mcans of essentially th e same modal fallacy Plato is somctimes :lccuscd of COlll ~ mitting in the Theaetetlls, namely that of confusing the highly con troversial (EC) with another, more plausible (hut less interesting) prin ciple: Necessa rily, (for every p) if p is known th en p is the case.
to
be the case,
To be sure, if it were true, as some have suggested ,! thnt Aristotlc is in ep t concerning the co rrect placement of modal oper;1tors, then thi s mistaken
inference might plausibly be attributed to hilll. However, it "ppears tl,," these criticisms are not ac tua lly warranted by the evidcnce on which they are claimed to res t, 1 and it is in any case preferable to find an exp lan ation according to which Aristotle's reasons for accepting (Ee) :lre more sys ~ tematic and deliberate. One especi.llly plausible explan:ltioll of this sort has been offered by Hinrikka,~ who argues th:lt Aristotle regards the trllt h of (Ee) as requi red to ensure that all known truths arc eternal truths, and that [his latter doctrine is the natural outcome of the dllal tClldcnl.:ies (in both Plato and Aristotle) to think of temporally indcfl nite se nten ces ;:lS
I 67 1
Explanatory Content of DemoflStratiolls
paradigmatic vehicles of comm unication while at the same time analyzing knowledge as some sort of direct acquaintance between knowing subject and known object. But however difficult it is to discover Aristotle's reasons for holding (EC), the effect of that co mmitment on the theory of scientific explana~ tion set o ut in the Posterior Analytics is relatively easy to discern. At the beginning of Chapter 4 of Book T , he prefaces an investigation into the nature of scientific premises as follows: "Since the object of scientific kn ow ledge in the unqualified sense ca nnot be otherwise than it is, what is reached by demonstrative knowledge will be necessarily true. Now knowl· edge is demonstrative when we possess it in virtue of having a demonstra~ tionj therefore, the premises from which the demonstration comes are necessaril y true" (7332.1-25). In light of so me other early passages, the import of these remarks can be made out quite clearly. As rep rese nted by (Ee), knowledge, most espe cially sci.entific knowledge, is of what cannot be otherwise, that is (ac cording to De /nterpretatione q.2.2b5), of what is necessary. Now since, according to Posterior Analytics I.2..7IbI7, demonstration is the justi· ficarory procedure by which such knowledge is acquired, this means th ac the product of a demo nstration must always be some necessary proposition. But since dem onstration, according to Posterior Ana/ytics 7 rb 18, is a "type of syllogism," and its product (chat is, its conclusion ) is always necessary, it follows directly that its premises must be necessary as well (73 32 4).' Right after elu cidating this su pposed impl ication of (Ee), Aristotle de ~ clares at 73 ~12 5 - 2. 7 that it is therefore desirable to comprehend the !la· ture and character of the prem ises of demonstration, and he proceeds w
w
forthwith (in Chapters 4 through JO of rhe first book of the Posterior Allalytics ) to loo k into that very matter, presumably with the aim of pro~ ducing a general characterization of the necessary statements that can serve as premises in scientific sy llogis ms. Throughout [he remainder of part 2, we shall be concerned to understand his views about the nature of these statements.
CATHOLIC PREDICATION I
First of ail, although this is not stated outright, it is clear enough th at the background se t from which Aristotle distinguishes [he sorts of sentences he is interested in consists of true, indicative, present tense, declarative, affirmative, and simple subject·predi cate se nten ces. For these are the only
I
I
[ 68 J
I I
The Character of DemOllStratil'e Premises t ype of affirmative statements that Gin function in syllogisms, as can be seen through an exami na tion of the variolls concrete examples and schemata given throughout the Al1alytjcs.~ Within this background set, Aristotle then endeavors to define a certain subtype, which he (;.1 l1s .. catholic" (KaOoAov) predications, that can stand in sc ientific syllogisms. At 73b2.5 - 27, this feature is said to be a comp lex one involving three subconditions, each of which pertains to the nature of the relation between the subject and predicate parts of the sentence in question.";" For the predicate of a sentence to be truly predicated Ka8oAov of its suhject, Aristotle says, it must apply to th at subject (i) "in every in stance" (KU'Tfl: 7TavT6~), (ii ) "per se" (Ka8'Clvro), and (ii i) "qua itself" ('0 aUTO). As I shall be interpretin g them, subconditions (i) and (iii) both place essentially extensiona l requirements on catholic predication, and so are not centrally involved in questions about their necessity. They therefore may be dealt with briefly and put aside . When Aristotle says that the predicate of a given sentence must be truly predicated KCtTa 7TalJT()S" of its subject, he means that the att ribute referred to by the predicate must .1pply to every single instance of which the subject is true. This should not be taken for a formal requirement that scientific premises mllst take the form of universal sentences, since many of Aristotle's OWll examp les of scientific premises are singular sentences (see, for example, Posterior Analytics 2.1 L94a37-b8), and any true singular sentence does meet the KCl'Tex. 7TClvTor; cond ition. Furthermore, another reason he needs to make this cond ition expl icit is that his general theory of predication le .wes open the possibility of what might be called indefinite sentences, for instance "Man is animal," that co ntain no article or restricting adjective to indicate whether they arc (Q be taken as making an assertion abollt all, most, or merely some of what the subject term denotes. The proclivity to em~ ploy such sentences is ve ry likely reinforced by t he absence of an indefi nite articl e in Greek . But even in modern Engli sh, where there is no such la ck, parallel cases arise. For instance, w hi le the sentence, (I) Women drive racing cars
would in normal contexts be regarded <.15 cquiv
chrOlllOS{)IllCS
apparently expresses a propos ition about all wome n. Aristotle's subcondition (i), then, ensures tha t if an indefinitely quantified statement is to
r 69
1
Explanatory Co,ltellt of Demonstrations
serve as a sc ientific premise, it must tru ly asse rt something abo ut the entire extension of its subject tc rm. By subcond ition (iii), wh ich requires th at th e p redicate of a K0'8oAOlJ pred icatio n must be truly p redicated of its subject "q ua itself" miro), Aristotle means to insist that not o nl y must the predicate of such a statement apply truly (and per se, as will be exp licated late r) over the en tire exte nsio n of th e subjec t, but th ere must also be no class wider than the exte nsion of th e sub ject te rm (except possib ly that of the pred icate itself) to all of whose membcrs th at pred icate also belo ngs (agai n, per se). In other words , it is n ot enough that the predicate of a true KaOOAOlJ sentence app lies both Ka1'Cx -rrO'V'TOS- and pe r se to its subjectj it is also necessa ry that the subject of the se ntence have the wides t ex tens io n of any terms for which this is the case, with the possible except ion of the predicate itsel f. A good way to ill us trate what this thi rd subconditio n of the condition co mes to is the o ne chosen by Aristotle himse lf at 73b33-74a7. T he re he cons iders a sente nce that meets both of th e other subcond itions but not th e thi rd. The exa mp le given is
(n
(3)
Isosceles triangles have angles eq ual angles.
fO twO
right
Now the property referred [Q by the predicate part of th is se ntence is pl ai nl y o ne that is had by all isosceles tria ngles, which ensures th at the pred icat ion is KO'rix 7Tavr05". Further, let us assume th at the predication is also per se (pendin g o ur invest igatio n into that subcondition late r). O n th e o ther hand, the sentence fa ils to be f1 aUro si nce there is a class of thin gs (namely, all tr iangles) that incl udes th e cl ass of isosceles triangles, of whose entire membership the predicate of the sentence is also tru e. Hence, while the pred ica te of (3) is true of its subject bot h Kcrra 7TO'vrOSand KO'(falJTO, it is nor true of it O'Vro, and hence the se ntence is not
n
Ka(}oAOlJ.
There is a ce rtai n ambigu ity in Aristo tl c's di scuss io n of the " qu a itself" subcondition that deserves some com ment. As interpreted above, it req uires that there be no te rm wider than the subject, o th er th an the predicate itself fo r whi ch the predicate ho lds universa ll y. By con trast, some wri ters have proposed a much stronge r construal o n wh ich it requi res that there can be no such term at all, incl uding the p redicate itself. On thi s in terp retation the subco ndit ioll (and th erefo re the Ka86AOV condi tion as a who le) is taken to enta il that all scienti fic predications must have coextens ive ter ms, or in the terminology o f the Topics, that they all must be
I 70 I
I ,I
I
I
I
The Character of DelJlOl1stmtit e Premises J
"convertible" or "counterpredicable" s ta te m e n ts . ~ The difference be~ tween these two interpretations does Ilot show lip very wel l ill connection with sentence (3), si nce it fails to satisfy th e subcond itiol1 on both. COIl ~ sid er, however, a sentence such as (4 ) Every sq uare is a rectangle,
whi ch might be thought to express an imm ed iate relation between its terms, bu t is not a convertible stateme nt. On the weaker interpretatio n advocated here, (4) would be counted 3S satisfy in g subcondi tioll (iii) (a nd in fact would cou nt as Ka9o>..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<)Vl' (4) from the field of legitimate scientific prem ises. My preference for the weaker interpretation is hased on what seems to me overwhelming evidence in the Poster;or Allofytics againsr the view that Aristotle conceives of demonst rat ion as proceedin g exdus ivel y by mea ns of convertible propositions (w hi ch inc identally has the curi o us co nsequence that the s ubject~ m atter of any Aristotelian demollstration would in effec t be confined entirely to relations among cot:xtensive predicates at a si ngle divisional node). To begin with, il is sign ifica nt that he never once says that hi s Ka9d>..ov co ndition entails convertibil ity or cO lln ~ terpredicability, even though he is quite co mfo rtable usin g those te rlllS not just in the To pics but also in the Posterior Anaiytics itself (for in ~ sta nce, at 90b35, 9Ia16, 36). In addi tion, th is view of demonstration as concerned excl usively with coextensive rerms would make it excecdin~ly difficu lt to understand the point of rh e very el ega nt argull1ents he gives in Posterior AHa/yties 1. [9-23 to show that the poss ibilit y of finite d e m on ~ strati on is vouchsafed by the fact th at any upward to downwa rd sequence of immediate predicationa! links must co nta in on ly a fin ite number of terms. Indeed, he says quite dearly at 82315 th at sll ch sequences would not even occur in cases where all terms are co nvertible. But by far the mos t telling o bj ection to understanding th e KCX(JOAOV cond ition as c lltai l ~ ing convertibility is based on the observa tion that in a number of pla ces Aristotle clearly allows demo nstrations that co ntain nOll collvertihle pn:: l11 ~ ises. At Posterior Allaiytics 2.16.98b32, he says that if deciduollsness bc~ longs Ka8o>..ov to a cenai n who le (ge nus), then "if there J rc subspecies lof that genus, it can be shown that] deciduo usness belongs KaOC)>"Ov to th em as well." For it is certainly imposs ible that a single attrihute co uld be co~ ex tensi ve bmh with a certai n genu s and with one of its suhspecies. In
I
71
I
Exp/Oltatory Content of Demo11strations
view of these difficulties with the alternative, it is preferable to interpret the "qua itself" subcondition in the weaker fashion so that it is satisfied not juSt by co nvertible predications (whi ch are of co urse immediate. since there cou ld be no middl e between coextensive terms), but is in effect an alternative spec ification of the condition that scientifi c premises must be immediate in the general sense that there must be no term which inte rvenes extensionally between subject and predicate (that is, which is both wider than the subject and narrower than the predicate). Clearly, this condition is met both by co nvertible statements and by immed iate and nonconvertible ones like (4).~
THE PER SE REQUIREMENT On the basis of the account given in chapter I it should be clear by now how Aristotelian division (that is, the framing stage of dem onstration) is sufficient to provide premises that meet both of the two extensional subconditions just discussed. To begin with, the fact that the method generates inclusion seque nces of terms by itse lf entail s that if A is an "ancestor" of B in the correct ordering, it wi ll of necessity be true of all B. Moreover, Aristotle's procedure for ensuring that nothing is left out of the ordering of terms guarantees that, if B is next in order to A, there can be no terms that extensionally intervene between them, which is CO say that A is also predicated of B qua itself. On the other hand, it was observed that Aristotle's discussion of this divisional method simply takes fo r granted that all co nnections between the term s involved are in some way or other nonaccidental, where that intellsionai requ irement was left unanalyzed. I now wa nt to suggest that in Posterior Analytics 1.4 this intensional condition on demonstrative prem ises is addressed by subcondition (ii) on catholic predications, namely that their predicates apply KetO'CXinO to their subjects. Clearly, this is what is supposed to ensure the necessity of such predications, as Aristotle says quite plainly at 73 bI 6- 19: "Therefore, concerni ng things known in the unqualified sense, those things which are said to belong per se to their subj ects, either in the sense th at their subjects are contained in them, or in the sense that they a re contain ed in their subjects, do so ... of necessity." Then, after offering what appears to he an argument to support this, he reiterates the point at 73b24, by declaring that "thus, ... per se attributes must belong to their subjects of necessity." III In chapter 5 we shall try to understand exactly why Aristotle th inks th at per sc predications are necessa ry. Meanwhile, if we now put together [ 72 J
The Character of Demonstrative Prcmises
what we have learned by exam inin g various parts of Posterior Allalytics 1.4, the results can be summari zed as follows. Aristotle thinks that all sentences that can serve as scientific premises are necessary (73(12 1), ~llld that the ir necessity is a consequence of their being per sc predications. What we must do now is look ca refully at the part of the chapter where
Aristotle explicates the nature of per se predication so that we might gain from these remarks some insight into his reasons for thinking that suc h predications are necessary. It will surpr ise no one familiar with Aristotle's philosophical prose that when we go to the passage where Aristotle first discusses what he means by the expression "per se" (Posterior Analytics I.4. 7 3335 - bT6 ), we find that he actual1y presents no t onc but four separate explications of that term. II We may make the separation of these senses more graphic by performing some minor surgery on the passage: slightly reformulating some sentences into more precise language, physically sepa rating the four different expl ications and their accompanying examples, exc ising superfluous examp les, and attaching subscripted numerals to keep the four senses distinct hereafter. Here then is the postoperative ve rsion of t he passage:
X belongs per se to Y if X is in the what-i:-;-it of Y. Example: Line is in the what- is-it of triallgle. so iiI/(: belongs per se. to triangle. I
X belongs per se, to Y if Y is in the whar-is-it of X. Ex ample: Line is in the what-is- it of straight, so straight belongs per se , to lillc.
X is per se, if X is not s
Type 4 (73bro - 16): X happens per se, to Y if X h[lppens to Y in virtue of (Y I itself. Example: Death happens to a slaughtered thin~ in [ 73 1
Explanatory Content of Demonstrations
virtue of "the slaughtered " itselr [that is, in virtue of a thing's being slaughtered], so death happens per se. to a slaughtered thing. In the next three chapters, we shall look closely at these explications in order [Q identify the exact type of statement Aristotl e has in mind in each case, with the ultimate aim of coming to understand Aristotle's underlying views abo ut the explanatory function of demonstrative premises.
I
74 )
FOUR Type 1 Per Se Predication
The substa ntive account of the nawre of per se predication to be offered here is one according to which th ar doctrine is properly reg;.trded as growing out of a seldom recogn ized rudimenta ry se l1l~llti cs for simple, subjectpredicate, affirm ative sentences, which I shall nrguc is implicitly contained in the first five chapters of the Categories. I My account th erefore begins with an exam ination of those chapters.
THE SEMANTICS OF THE CATEGOR IES The doctrine from which the Categories takes its n:lme is presented in Chapter 4 at Ib15-1alo: Of things said without any combination, each signifi es either substance, or quantity, or qualification, or a relat ive, or where, or when, or being-in-a-position, or having, or doing, or being affected. To give a rough idea, exam ples of sub stance are man , horse; of quantity: four-foot, fi ve-foof; of qualification: white, gramm;ltical; of a relative: double, ha lf, large r; of w here: in the Lyceum, in the marketpl ace; of when: yesterday, last ye:lrj of being-in -;lposition: is-lying, is-s itting; of having: has-shoes-on, has-J rmoroni of doing: cll tting, burning; of being affected : being-cut, hcingburned. None of th e above is said just by itself in any affirmation, but by
I
7S
I
Explanatory Content of Demonstrations
the com bination of these with one an other an a ffirmation is produced. For eve ry affirmatio n, it see ms, is eithe r true or false, but of things said without any co mbination no ne is eith er true o r false (c.g., "man," "white," " runs," "wins").l The most im mediate problem confrontin g a reader of this cha pter is that of determ ining exactly what sort of things are classi fi ed by th is di vision. Aristotle te lls us explicitly thar he is classifying " thin gs said without combination" fTO: KaTer a vev (J1}p..7TAOKi}~ 'Aeyop.. E:va), which Julius Moravcsik \ ha s forcefully argued mu st be sim ple linguisti c items, or term s. Th e argument is that when these items are co mbin ed , what result are sentences, and so the th ings that go into the comb in ation must likewise be lin gu istic expressions. Moravcs ik su pports his claim that the products of co mbin ation are sentences (rather than some extralinguistic enti ties such as propositions) in two ways. Fi rst, he conn ects Aristotle's use of the term T, CTVI-L7rAOKTJ to certain Platonic occurren ces of th e same term that quite clearl y refer to an "interweaving" of wo rds and phrases into sentences. Secondly, he argues th at sin ce Aristo tle holds that the products of combination are "affirma tions" (a:i Kl'lnxc/>aO"€I,,) , whi ch are ca pable of being tru e or fal se, and since he also holds that ir is only senten ces that a re capab le of bea rin g truth -values, it follows thac the materials of combination mu st al so be li ngu isti c entities. These argumen ts are cogent enough, and they can be supplemented by th e obse rvation th ar th e "things" classified in Ca tegories 4 a re entiti es that "si gnify" (cr7l1-L0'iVDVo-L) other things, w hi ch see ms to be a function that could only be performed by linguistic items. But while Moravcs ik is quite ri ght that the distinctio n at Ib2. 5- 2.aIO is linguistic, it should not be co ncluded th at the items Aristotl e groups under the various categories are themselves lin guisti c items. To thi nk that is not to see the co rrect emph as is of the chapter, or of th e Ca tegories as a whole. For as John Ackrill says at the very beginning of hi s co mmentary on the work, "it is important to recognize from the sta rt th at the Ca tegories is no t primarily or explicitly about nam es, bu t abo ut the th ings th at nam es signi fy. . . . Aristotle relies greatly on linguistic facts and te sts, but hi s aim is to discove r truth s about non-linguistic ite m s."~ This point, whi ch I shall argue late r is sli ghtly ove rstated. ca n be appli ed to th e chapter in question as follows. The im med iate objects of th e class ifica ti on annou nced at th e beginn ing of Chapte r 4 (a nd those which co nce rn Morav cs ik ) arc ce rtainly lin gui stic entities. But it is just as impo rtant th at this d iv ision of linguistic entities is wholl y semantical. In class i[ 76 J
Type 1 Per Se Predicatioll
fying "thin gs said withou t comb ination ," which were id enrined ahove as terms, Aristotle makes 110 mention at all of th eir syntac tica l or gr:l mmatical properties. Rather, his sole way of distinguishin g them is by reference to the d ifferent so rts of nonlinguistic entiti es they signify. In effec t, then, the lingu istic ent iti es are classi fied vica rio usly und er such hCildings as " things sa id witho ut combinati on that signify substmrccs." " things said with out combina tion that signify qualities," :lnd so forth. As such, the ostens ive classification of lin guistic items is but a thin ve il for a more fundamental class ifi cation of their nonlinguistic significat:l, and this more fundamental di vision is the ontologica l doctrine of the catego ri es. One major reason this point is not always not iced, I think , stems from Aristotl e's reli ance on linguisti c obse rvations in const rl1 ctin g his list of categories. Whil e the ontol ogical divisio n is logic111 y prior to the linguistic classifi cati on of "things said without combi nati on" (in the se nse that each division in the fo rmer is wholly specified by reference to some division in the latter), Ar istotl e also see ms to think, as Ackri ll puts it, that "the identificat ion and classification of these [non linguisticl thin gs could . . . only be achieved by attention to what we say.'" Thlls it is easy to sec how confusio n about Ar istotle's in tentions can occur. For even th o ugh the immed iate o bjects of the anno unced classification in the chapte r are indeed expressions, and even though Aristotle's method of performing the classification ce ntrall y involves linguistic observatio ns, the importa nt work accom plished in the chapte r is nonetheless metaphys ical : the class ification of non linguis tic enti ties into ultimate onto logical categories. But let us now dig deeper into Aristotle 's genef:11 purposes in wri tin g Categories 4. We have just seen th at hi s prim ary concern is to class ify "things that are" ('TO: o/)'Ta) inro their ultimate genera. Bur docs rhi s mea n th at his interes ts at that point are purely :111d simpl y in mctn ph ys ics for its own sa ke? Some doubt abollt this view arises from the co ncurrent in terest in language in the same chapter, which has alread y been noted. If all Aristotle is doing there is classificatory metaphysics, then what is the point of his mcnrion in g that there are si mple ex pressio ns th olt signify items in each of the various catego ries, olnd that these simple express ions are ca pable of hei ng inte rwoven together into scntl'nccs, whidl he says are the only things that can be true o r tllse? When Chapter 4 is ra ken by itself, th ese peculia rities do little more th an raise th e suspic io n that Aristotle is not merely engaged in classifi catory metap hysit·s as an end in itself. But when this cha pte r is pur be: side Categories 2., th ere emerges the pos iti ve view th;H the ontological doctrine of th e categories in Chapter 4 is actually p;.1tt of a !.trAer effo rt to [ 77 1
Explanatory Content of Demoltstrations
provide what might be descri bed as an informal semantics for simple affirmative subject-predicate sente nces. In the first place, notice that Chapter 2 presents none of the di ffic ulties of Chapter 4 in trying to decide whether Aristotle is t
(henceforth atomic sentences) are either true or fal se. {:z.a6_ 8)h (52) Atomi c sentences are constructed by combination
out of exactly two uncombined express ions (henceforth sentential elements ). (1 a 15- 20, 2.a 4-6) (53 ) Each sententi al clement sign ifies some entity in one
of the categories. (Jb 2.S - 234 ) (54) Some pairs of the entities signifi ed by sententia l elements stand in th e sa id-of relation, and others stand in the inherence relation. All that is needed to make these principles into a fully explicit semantic for atomic se ntences - is a statement t11at re lates the truth of ttue atomic sentences to the two ontological relations memioned in (54). Al though th ere is no such truth analysis actually expressed in Ca tegories 1-4, Montgome ry Fu rth has plaus ibly reconstructed a partia l one on th e basis of Aristotle's discussi on of exa mples there. K According to this recon stru ction, the analysis proceeds in two ste ps, which can be seen by consid ering any true atomic sentence, say one about Socrates. Such a sen[ 78 J
Type J Per Se Predicatio/t
te nee will have th e general form "Socrates is F" (or perhaps just "Soc rates F," since in Greek the copula is dispensa ble), w here F is some suitable simple predicate ex press ion. Th e im portant thi ng to notice here is that substituends for F in thi s schema can include prcdicarive (th at is, verba l o r adjec tiva l) express ions such as "walks" an d "( is) mi l," ;lS well ;l S sorta! nom ina l expressions such as "(is a) n1.1Il." According to Furth , no matter what F signifies (a nd so, whe ther it is predicarivc or no mi na l), S tl Ch '1 sentence ca n first be " thrown in to a sta nd ard and ca non ica l for m, technica lese: 'Fness is predicated of "Karrryopc'iTal." of Socrates."' ~ Thi s ca nonica l translatio n, on the Furth reco nstruction, Gill then be further ana lyzed as expressi ng o ne or the Olher of two "deep st ructures": its truth will be ex plai ned, dependi ng on what the o rigi nal prcdk atc F was, either by the fact that Fness is said of Socrates, or by the bc t tilM rness illheres in Socrates. t!l It sho uld be men tioned here thM there are se ri ous lise-mentio n con fusions involved in Aristotle's use of the verb "to pred ica te" (KCX'17r yop£:iv) in Ca tegories. He uses this te rm ill such a w id e~o pe n sense rh<1t se ntences contain in g it mayor may nO[ have sub ject ter ms th:n refer to lingui stic expressions. Fo r instance, at 2a8 he all ows that white (w hich is said to he presen t in body, an d is th erefore non li ngu ist ic) is <1l so predi cated of body, whe reas 2a20 cl ea rl y indicates the possi bility that :I "n;111lC" (i.ivo,uo:) (a ll also be predicated of a subject. In the ;lbsellce of quot:lt ioll dev ices, this d ual use of the ve rb often produces great con fusion in atte mpts to unde rstand particular occurrences. For exa mple, the sentence "A"imal is prcdicated of man" at 2a38 co uld mean ei ther th:l t the ge nus ani mal is predicated of the species man, or that the term animal is pred icated of m::l.I1 . Fortu nately, the verb to predicate occurs only in th e intcrmediate stJge of the sema n tica l analysis we have been di scussi ng, so its pro hl ems do not reach the cri ti cal aspect of that analysis, the d isjul1l:rive npp iicario n of the said-of and inhere nce tel atio ns over the entire dJSS of truc momic sentences. For Aristotle makes it clea r tha t these are o ntological rcl atio ns that always stand between extralingui stic thi ngs signified hy se nten tia l elemen ts, neve r between sentential elemen ts th emselves, and so h is refe r· ences to these rel atio ns a re not infec ted by the ambi gl1iry observed in hi s use of the verb to predicate. T herefo re, the p robl ems ;lhovc with the ve rb KaTTrYopei.v can be circumvented by sim ply co llapsi ng the two steps into a single truth analysis from which the offending idiom has hee n el iminated: (55 ) If "A is B" is true, then (where "A" sign ifies 1\, ;mt! "B" sign il1es B) either B is said of A or R in heres in A.
[ 79
1
Explanatory Content of Demonstrations
According to the semanti cal principles so far collected from Categories 2 and 4, each atomic sentence is co mbined out of two sentential elements, each of these signi fi es some item in one of the categories, and the truth val ue of the ato mic se ntence is determined according to whethe r the two significata sta nd (in the right order) in either the: sa id-of or th e in here nce relation. But the seman tical theory So is st ill not likely to be ve ry informative until we have some mo rc defi nite idea what these two rela tio ns are. Ackrill II has suggested that such information is not fo rthco min g in the Categories because Aristo tle sim ply discove red th e said-of versus inherence distinction in the ways of speaking current among hi s contemporaries. Now, if this were co rrect, we shou ld rega rd discussions of the dis ti nction as something like theoretically innocent reports of how language is actually used, and there would be no o uts tanding reason to sco ur the text in search of deeper exp li cations of the relations that comprise it. T here is, however, reason to be dubious about Ackrill 's view. Evidence both in the Categories itself and in the writings of Aristotle's co ntemporaries Il suggests that the expressions used to denote these two relations were in fact not commonly used as they are in Categories 2. For instance, Aristotle takes pains at 1a23 to cauti on his readers that when he says one thing is " in" ano th er, he does not mea n that the first is in the second as a part. This seems to he a warning that he is using a term that already ha s a familiar meaning in some different and technical sense. But if the "said of" and "prescnt in" termi nol ogy is indeed a piece of Aristotelian technical (or semitechnica l) jargon, what is supposed to be th e ultimate so urce of its intell igibil ity? The most obvious place to look for a n answer is the so-called tetrachotomy passage (Categories r320 b9), in which the said-of and inherence relations arc first introd uced. In a slightly more natura l order than tha t give n by Aristotle, the tetrachotomy co nsists of four types of enti ty : (i) things th at are ne ither said of anythi ng, nor inhere in anything (l b3-9 ), (ii ) thin gs thal are said of someth ing, but do not inhere in anything (la20-22), (iii) things that inhere in somethi ng, bu t are not said of anything (1a23-9), and finally, (iv ) thi ngs that arc both said of something and inh ere in something (Ia29-h3). An examination of Aristotle's exa mples in thi s passage toge ther with his further co mm ents in Categories 51\ about the elements of the tet rachotomy at least reveals wha t he takes to be paradigm insta nces of each of these divisions. They are, respectively, the following: (i) Primary substances (npwTCH QV(TiaL). These are individuals in the
I 80 )
Type J Per Se Predic,/tioll Category of Substance, such things::ts "the particular man " (0 Ti.S- av()pwand "the particular horse" (6 Ti., l7T7rOS'; la' .~-14). (ii ) Secondary substances (oc: vn:pcu ovo-ien). These are wh::tt Aristotle also so metimes refers to as genera (yiv.,,) and species (f:~o.,,) in the Category of Substance, and are app.uen tly said of both the individuals they contain and the subo rdin ate species they incilld e.l~ Th e examples given are "man" (6 aIlOpw7ro<;) and "animal" (TO ~~Oll; 2.<1 T R). (iii ) NOllsubstantial particulars. These are the an:llogues of primary substa nces in the nonsubstanti:d categories, because they can ollly stand 011 the right side of the said-of relation. Th ey ::1lso inhere in primary suhstances. The examples given are "the particuhlr [piecel of gra ml11::tti c::t1 knowledge" (7j TI.<; 'Ypap..J.l.,anKr,), which inheres in rhe (particuhu ) so ul, and "the particular white" (TO Ti. A6VKOII) which inheres in the (particular) body (1327-,8 ). (iv) Nmlsubstantialulliuersals. These, fil1
I 81 )
Explanatory ColttelTt of Demomtratiolls
early works w ith metaphysics, and it is diffi cult if not imposs ible to import sll ch concerns into them withou t relying on ass umptions and concepts they do not actually discuss. For all we kn ow, Aristotle si mply did not confront the problem of de termining the exact nature of universa ls (or for that matter, the exact nature of ind ividuals) unti l later in his career. In accordance with these observations , I sha ll adopt a po li cy of evading these issues throughout this work, by sim ply underlining references to the entities of types (ii )-(iv) an d leaving open the question abou t th e natures of their referents. However, eve n witho ut knowi ng the exact natu re of all of the types of enti lies divided by th e tetrachoto my, we ca n discern in Aristorle's p resentation of it the intended dependence of the said-of and inheren ce relations on his doctrin e of tbe catego ries. Simply put, the said-of relation is such that its left ter m is always so me hi ghe r kind in some category, and its right term is some kind or particular wi thin the same category, whereas th e inherence relation always has a primary o r second ary substa nce as its right term, and some item in one of the non substa nti al categories as its left term, These dependences can be d istill ed in to the followin g two additional principles of the sys tem S.,: (56 ) If A is sa id of S, then A and Bare homocatego rial. (57) If A inheres in B, then B is a substance, and A and B are hetcrocatcgoria l (that is, A is a nonsubstance).!n To be sure, the di sti nction hetween necessary and contin gent truth is not one of the explic it subjects of Catego ries 1-5. and I have no t been meaning to clai m otherwise. On th e interpretation I have been defending, the sa le fun ct ion of the semantical theory (5.,) con tain ed in those chapters is to spec ify the ontological conditions underlying the truth of all true atomic se nten ces. Even so, it wou ld be hard to deny that some sem itivity on Ari stotle's part to the distinction betwee n necessity and contin gency is re flected by the fact that 5., docs afte r a ll emp loy two different on tol ogica l relatio ns (i n contra st, fo r instance, to Pl ato's single partic ipatio n relation) in orde r to accomplis h this fun ction.!' For it is reasonab ly clear that the distinction between sentences whose truth is ex plained by the sa id -of and inherence rel ati o ns co incides ~t le ast roughly with th at between necessary and co ntin gent truth . Fo r insta nce. such "definitiona l" tru ths as "Man is an im al," "Soc rates is man," and "Wh ite is a color," will be analyzed in Su as expressi ng in stan ces of the sai dvo f relation , whil e merel y accidenta l truth s sll ch as "Socrates is pale," will be expla in ed in terms of th e inherence of paleness in th e subject. For this reason, it is not surprising that [ 82 J
Type 1 Per Se Predicdlioll when Aristotle does have epistemoiogic:J 1 reasons in th e Posterior Allalytics to fo rge an explicit distinct io n between necessary ;lnd contin gent truths, he turns to the bifurcated semantics of the Categories to prov ide the basis for th at distinction. This, however, is not to say that he .. lIows himself to carry the said-o f versus inherence dist in ction as a whole piece into his theory of dem onstration. O n the contrary, it :.ppe:us th:.t matters become more complicated, and demands become greater, whe n the di stinction between necessary and contingent truth moves into the center of hi s focus. We shall see presently thar there are certain constr;1inrs oper'lting in rhe Analylics [hat lead him to elaborate, and in some pbces even to modify, the simple two-part semantics of the Gltegories. During the remainder of part 2, I shall try to show how each of the four se nses of per se just displayed can be const rued as pa rt of this procedure.
THE NEED FOR " INTRA-CATEGORIAL" DIVISIONS We have seen that theory So does provide ~11l :111:1 lysis of t he trllth of the atomic sentences of the Categories, but th:1t it docs so hy making reference [Q two technical Ari stotelian relations (the said-of :1nd inherence relations) whose natures themselves stand in nccd of further cxp lic:1tion. On the other hand, while the supplementary principles (51l) and (57) do go some way toward expl icating these rei
from such false intracatcgorial predications
;.lS
(3) Man is Swaps, (4) Socrates is a horse,
nnr for distinguishing genuine inherence predications from c.::ontingentl y false statements such as (5) Socrates is tall, wh ich satisfy the minimal catego rial conditions specified by the right side of (57). At its root, the prob lem here is that the cMcgori;'ll distinction s hy
I 8.1 J
Explanatory Contell! of DelnO flstratiolls
th emselves are sim ply too coarse to expla in t he truth of atomic sentences, a nd so mu st be augmented by fine r intraca tegoria l distin ctions. Aristotle never gives a genera l systematic treatment of the inherence rel ation, nor eve n attempts to do so.l! T hi s is pro babl y beca use he saw a great many (if not a ll ) ins tances of the in herence relation as the resu lts of the ope rat ions of " ch a nce" (r, rox 7) ). And in view of the disparaging th in gs Aris totle says about the prospects of a ny scientific study of the fortuito us (for exampl e, at Posterior Ana fytics I. 30. 87hI 9 - 28), it is ha rdly surp ris in g tha t he never attem pted to give a co mpletely ge neral accoun t of tru ths th at he th ought to be th e res ults of its operati on . O n the o th er hand, Aristo tle does even t ua ll y say quite a bit mo re abo ut th e nat ure of sa id -of predica ti ons tha n what is given by (56). In b ct, I w ill now develop a n inte rpretatio n of Aristotl e's discuss ion of type 1 per se predica tion at 73a35 -3 8 o n whi ch it ide ntifies furth er conditio ns fo r the said -.of rela tion. O n th e aCCQuO[ I p ropose, these further conditi ons a re not exp ressed in te rms of th e coarse onto log ica l di vis io ns of Categories 4. but rath er in term s of finer, in tracategoria l dis tinctions that I sha ll a rgue a re a lready imp li cit in the methodo logy Aristotle emp loys to develop his li st of categor ies in the fi rst pl ace . As waS mentioned earl ier in con nectio n w ith Ackri ll , this methodo logy centrall y in volves Ari stotl e's explo itatio n of lin guistic obse rvations. It will now be useful to examine in more deta il exactly how he uses such obse rva tions to a rri ve at his list of categories. Alth ough there is not m uch ind icat ion in rhe Categories itself of how Aristot le does this, Ac krill l.! has fou nd ev id ence in Chapter 9 of Topics I tha t he acru a ll y employs two distinct procedures t hat he a pparen tly th inks yield identica l res ults. Both ca n be t hought of as lingu istic in the sense that they invo lve conside ring the range of intui tively appropriate answers to certain ques tions, the main d ifference betwee n th em be ing that in one proced ure d iffe rent q uestions a re asked abo ut a sin gle thing, while in the other a single quest ion is as ked a bout diffe rent t hi ngs. H ence, I sha ll refer [Q th e two p roced ures res pective ly as the multiple-question an d the single-question methods. T he nat ur e of the two methods, a nd the differences between them, will come into view as I present each as an annotated se t of directions for the constructio n of catego ries of being.
I
I ! i
I
Ii I
TH E MU LT IPLE-QUESTION METH O D Step
J:
Take before your mind a single primary substance,S (fo r examp le, a pa rticula r man or a pa rticular ho rse).
[ 84 J
..!
Type f Per Se Predicatioll
It will be observed that this initiJI step presupposes the ability to distill· guish between subst
2.:
List the most hnsic (most gencr;ll)
qll ~st i Clns
th;1t
ca n be as ked ahullt S. The actua l li st of such basic qu es tion s Aristo tle thinks will be produced in t hi s step are: "What is it ?" (Tl. i(TTi;), " How is it?" (7TOtOIj: ), "How much is it?" (1T()(TOIj:), "What relation docs it stand ill ?" (7rp0<; Ti:), "Where is it?" (7TOV:), "When is it?" (miTe:), "'n w h ~lt :1ttitud e is it?" (TI. KttTat:), " In what state is it?" (TL ix eL: ), "What is it doing?" (Tl. 1Tou:i:), and "Wha t is being done to it?" (TL mY
Step J: Corresponding to each of these most basic questions, construct an ontological cbssificntion (thm is, a cntcgory) consisting of entities signified hy th e predi ca te p:lrts of the appropriate :lIlswcrs to that quesrion.
Here I have made reference to the "predicate parts" of th e answers simp ly a concess ion to the peculiar feature of writte n Englis h th;lt questions are usually answered by co mplete se ntences. By co ntras t, there is no rigid 3S
[ 85 [
Explanatory Content of Demonstrations
requiremem in written Greek (or for that matter, in colloquia l English) that meaningful responses have both a subject and a predicate, and so it is very likely that Aristotle thinks [he questions on his list can be answered, fill-in-the-blank style, by responses of one or two words. For example, the question, "What is it like?" can be answered sufficiently by the single word "white." This means that Aristotle could very naturall y think that thin gs fallin g into the category generated by a certain question are those things signified by whole answers to that question. What is requi red for an answer to be appropriate to a question in this method will again depend on whethe r the method is taken as a n ideali zation or not. If it is, and the first two steps are understood to be performed on every substance, then only correct answers need to be coumed as appropriate ones. On the other hand, if the method is not an idealization, and steps I and 2 arc to be performed only on a single (pa radigmatic) substance, the n in order to achieve an exhaustive classification of "all existents" (mlvra 'fa 611Ta ), it would be necessary to regard all possib le correct and incorrect answe rs as appropriate.
THE SINGLE-QUESTION METHOD Srep
I :
Take before your mind all the thin gs there are.
This of course is going to be an id eal ized method. Practically speaking, if Aristotle employed thi s method at all, he probably attempted to gather just a suitab ly representative sample of entities. Also, it must be kept in mind that "all the things there are" (1TaVTa 'Ta. OVTa) must be taken here in the most inclusive sense poss ible to include nO[ just objects but also such things as qualities, locations, states, actions, and so forth. Step
2.:
Select one of these and ask "What is it?" (ri €CT'Ti; ).H Give the most informativt: correct an-
swer to this qu estion, if there is onc. Your answer, if there is one, should take the form "It is _ _ ."1" Now cons ider the thing sign ified by the predicate part of this answe r and ask of it, "What is it?" and answer this question. Your answer should again take the form "It is - - . " Repeat this step until you have fimdly asked a question which has no answer. Let us call such a completed seq uence of qu estions and answers a
chai1l, and represent it by a vertical list of the signifying terms that occur
I 86 I
Type 1 Per Se Predicotioll in it, o rdered so th at the last term to occur is topmost, a nd let LIS refer to the ch ain which is ini t iated by as king abou t so me ent ity X :1S X'S Chai n. Ir might occur to th e reade r here that in some c~scs th is ste p C:1 llnot he co mpl eted (th at is, th at so me ch ai ns mi ght be in fi nite). This app:1relH ros~ sibil ity al so occurs to Aristo tl e (in a slightl y d iffere llt co ntext), a nd he constructs a proof in Posterior Analytics 1.19-22.(8 rln9 - 84 b 2..o) t o elim inate it. 27 Furth er, the possi bili ry of pe rfo rm in g thi s step in a way that produ ces consiste nt resu lts presu pposes th at fo r eac h e nt ity th ere is exactly o ne a ppropriate answer (or, as Aris[Qtlc puts it at Categories 5 .2b7- I 3, o ne " most infor mative" [yvetJptJ.LCoTaTovl a nswer) (Q the q u es ~ tion "What is it ?" W hil e thi s might seem to liS q uite d ubio ll s, Aristotle ap parenrly endo rses so me doctrin e of na t ura l kin ds w hich he beli eves wi ll ins ure thi s res ul t. Step 3: When step 2. has been perfo rmed for each melll be r of the original co llectio n, co nsr ru ct an 011 -
tological classifica tion (a category) A for every exp ression "A" which occurs topmost in ono.! or more chai ns. Th us, for in stance, if YO ll fin d (as Aristotl e ap pare ntl y docs) thM th e chain init iated hy asking "What is it?" of a p:l rt icul ar co lor ends with the same q uesti on bein g asked (but not a nswe red) :lbollt q ua lity in general. you the n constru ct a category of Qua lity. Step 4: Finally. put into each ca tegory A all of the it cll1~ signi fie d in a ll of the chains in which "A" nccll rs topmost. Some exa mp les sho ul d show how this met ho d is intended to opera te. Sup pose t hat a mo ng your o rigin al co ll ection there arc the fo ll ow ing items: (i) Socrarcs, (ii) a particula r ho rse (say, Swa ps), (iii ) the species man, (iv) a parti cul ar co lor (say, w hite!!!), (v) a pa rri cui:lr t:lste (say, so urness 11l~)' an d (vi ) the general color wh i t e.!~ Let us then imag ine that th e cha in s generated by pe rfo rming step 2.. on these ite ms are represe nted as follows: ! ~ (ii) Swaps ' Chain (:1) substance (h) body (I.:) liv ing body (d) ~lIl im ;l 1
(i) Socrates' Chaill (al substa nce (b) body
(el li ving body (d) an imal [ 87 [
Explanatory Content of Demonstrations
(el footed animal (f) four-footed animal (gl horse
(el footed animal
(0 two-footed animal (g)
man
(iv) \V/'item 's Chain (al qua lity (b) sens ible quality (cl visua l quality (d) color (el white
(iii) Mall 's Chain (a ) substance
(bl body (e) living body (d) nnimal (el footed animal (0 two-footed animal
(vi) Sourness 1()'jI 's Chaill (a) quality (b) sensible quality (cl taste quality (d) sourness
(v) White's Chailt
{al quality (bl sensible quality (c) visual qua lity (d) color
Now since the topmost expressions in chains (i)-( iii) are "substance," and the topmost exp ressions in chains (iv) - (vi) are "quality," in order to perform step 4 you pu t all of the items signified by expressions in (i)- (iii) in the category of Substance, and a ll those signified by expressions in chains (iv)- {vi) in to the category of Quality. It will be observed that there arc some item s, such as footed animal, which get put into the sa me category more than once, as it were. This is because certain segments of different chains arc identical. In fact, more can be sa id: if a single item ever appears in any two cha in s, the Aristoteli a n assumption that there is always a unique answe r to the "what is it?" question entai ls that the two chains in question will be identical from the shared item up, This is the fa ct on which the medievals traded when they constructed what ca me to be known as the "tree of Porphyry" out of this Aris(Qtelian doctrine. Although there is no evidence that Aristotle himself actually con nated chains in this manner, it is easy enough [0 sec how he could h~ve. If we simply regard any two Iike·membered cha in segments as (I single segment, we will in effect construct a hierarchica l, or inverted tree stru cture out of Aristotle's classification. Moreover, the requirement of step 3 that all cha in s whose contents are included in a given category possess a common topmost member, plus the Aristotelian uniqueness assumption just mentioned, and the additio nal assumption that each uncombined signifying express ion signifies exactly one entity, together insure that the Aristotelian catego ries are arranged into mutually independent stri ct hierarchies. \ U [ 88 J
Type 1 Pcr Se Predicatio/l As mentioned above, each of the two methods of genernting categories requires supplementary assumptions in o rder to guarantee identical resu lts across separate implementations. Furthermore, there are grounds for doubting that the two methods must, or even C3n, yield the same classifications. \I 1 shall not worry over these d ifficulties here, since my main conCern is not with the intrinsic merits of these methods or with the plau sibi lity of the doctrine of the categories. The preceding rcmnrks have been offered simp ly as a preparatory stage to seeing how deeply implica[cd the doctrine of the categories is in Aristotle's refinement of the Categories semantics in Posterior A110lyfics 1.4.
POSTERIOR ANALYTICS 73"35-38,
TYPE 1 PER SE PRED ICATION The key piece of terminology in the expl ication of type 1 per se predication at 73a35-38 is the peculiar little noun -phrase, "the what-is-it" (TO Ti BU"TtV) . Ackr ill has put forward the quite plausible view that Aristotle has a vacillating attitude toward his categor ies, at some times thinking of them as generated by one of the two methods, and a t other times as by the other. Further, accord ing to Ackri ll, these vaci llations are responsible for an otherwise puzzling incon sistency in Aristotle's lise of the expression "what-is-it" in Topics I.9, At I03b2.} he npparently treats this expression as if it were simply synonymous with "substance" (ovu- iu), since he uses it as a name for his first category (for which he usually reserves th e name "Substance"), Yet just a few lines later in the same chapter, he uses the sa me expression in a way that is apparently much wider: "One who indicates the what-is-it of a thing, sometimes indicates a substance, sometimes a quality, and sometimes somethin g in the other categories" (ro3b27-29) · Ackrill accounts for this terminological instability by hypoth es izing that in the two locations Aristotle is influenced respec tively by the twO different methods he emp~oys to construct his ca tegories. In the narrower usc of the term at .I03b23, his choice of Iangu3ge is influ enced by his thinking in terms of the multiple-question method, where the only appro · priate answers to the "what-is-it?" question are ones that signify substances, since that question is only asked abollt (primary) substances in that method. Hence, in this frame of mind he could quite naturally think of the phrase "what-is-it" as a synonym for "substance," On the other hand, the wider lise of the expression at I03b28 "clearl y indicates," in Ackrill's words,.'! the single-question method , in which the "w hat-is-i t? "
I 89 I
Explanatory
COlltellt
of Demollstrations
question is asked about eve ry sort of entity, and so can properly evoke answers that signify items in any of the c3tegories ..I.I Against this background, I want now to suggest that if the exp li cation of type I per se predication at Posterior Analytics 73a35-38 is recognized as a place where the expression "what-is-it" is used in the wider sense of Topics 1.9. and hence as an allusion to the si ngle-question method, then Aristotle ca n be seen in that passage to have elaborated upon the rudimenta ry semantical system So of the Categories by supplying the finer, intracategorial, di stinction s necessary to give sufficiem conditions for the said-of relation. Let us first get a more precise understa nding of this wider use of the what-is-it. Ackrill himself does not say anything on th is subject beyond lhe remark quoted above. However, by exp loiting the above description of that method, it will be possible to provide a clearer explication. In the occurrence at Topics I03b28, as well as its many occurrences in Posterior Analytics 73a35-br6, the expression "what-is-i t" is pan of definite nOlln phrase formed by putting a neuter singular article in front of it. The who le phrase is then a nominalization of the "what-is-it?" question that plays the title role in the single-question method. Now on the basis of what we know about that method, we can make a pretty fair guess what meaning Aristotle intends the noun-phrase to have. When he refers to the what-is- it of so me item Y. he is us ing a very natural shorthand for referring to the entire class of entities signified during the course of completing the entire seq uence of questions and answers initiated in step 3 of the single-question method by asking "What is it?" about Y. In other words, in this shorthand, X is in the what-is-it of Y just in case X is signified by one of the expressions that occur in Y's chain. We also saw earlier that th e items contained in each Aristotel ian category are ordered in a strict hierarch y, and now we know the idencity of the relation that so orders them. It is the relation (w hich I shall refer to as re lation E) ex pressed by sentences of the form: X is in the what-is-it of Y. If, now, the occurrence of "what·is-i t" in our postoperative ve rsio n of the explication of type 1 per se predication at Posterior Analytics 73 a35-38 is taken as an instance of thi s wider lise, the first glimpse of Aristotle's refinements on the theory Sn emerges. In our initial discu ssion of Sn we saw that homocategoriality of subjec t and predicate by itself does nor distinguish false homocategotial sentences from genuine said-of predications, and that finer, intracaregorial distinctions were therefore needed. Now we can sec that in the Posterior Analytics Ari stotle ha s such finer distinctions in hand in the form of the I 90 )
Type 1 Per Se Predicatioll hiera rchical structure of th e contents of the catego ries as ordered by rela * tion E. Some homocategorial pairs, such as (man, Soc rates) stand in thi s relation, while others, such as (Swaps, m;:lo) do not. Further, relation E, unlike mere homoca tegoriality, is sufficient for th e truth o f se ntences that express it. This is beca use ste p 2. of the single*qu es tion method c<1 11s for o nly correct answers to the "w hat*is*it?" question. Thu s, eve ry pred iGl* tion in which the pred ica te occurs in the ch:lin of the sigll ific:ltum of th e subject is tru e. And since, as we just saw, X is;n th e what*is*it of Y just in case X is signified by an ex pression in Y's chain , it then follows that if X sta nds in relation E to Y, rhen any atomic sentence whose subject signifies Y and whose predicate signifi es X will be true. Hence, Aristotle has all the semantic equipment necessary to analyze the truth of sentences such as "Socrates is man" without at the sa me time co mmitting him self to the truth of false sentences sllch as "Socrates is horse." For while malt is d early in the what*is*it of Soct:ltes, horse just as denrly is not. My suggestion, then, is th at the first type of per se predi cation cx pli* cated at Posterior Allalytics 1.4. 73 :.1 35- 38 is:.1 close descendant of the said*of relation in the Categories,'~ ill1d that Aristotle supplies in th ,l[ passage what is missing from the Categories, a stntemc nt of sufficient cOI1(.ii* tions for the said -of rel ation in terms of intra cntegorial ontological divisions. Moreover, it is these finer*grained divisio ns he ha s in mind when he insists in Prior Allalytics 1.2. 7 - .~ 2. ;:I nd Posterior Al1aiytics 2.13 thilt the organization of a subject*ge nu s, prio r to syllogistic demonstration, by what I have called Aristoteli an di visio n must sysre mnti 7.c the attribu tes in the what*is-it of their respective suhjects. Now since it has already been remarked th at Aristo tl e sees no hope of giving a general systematic account of the only mher type of truc ~1tomic sentence recognized in the Categories (those ex press ing the inherence re* lation ), it might seem that there is now no room for ftlt·her improvements on SUo This, however, is not th e casco Fo r while Aristotle is ::trpnrcntl y quite co ntent in the Ca tegories to divid e all true ~Homi c sentences exhaustively into the two types dealt with by (55), in Posterior A11aiylics 1.4 he evidently finds this cl assification (like the ca tegoria l distinctions th em* selves) too res trictive for hi s purposes. In particular, he there recogn izes the ex istence of other types of true
I 91 I
FIVE Type 2 Per Se Predication
PARTICIPATION IN THE CATEGORIES Besides giving an informal sema ntics for atomic sentences in Categories 1-5. Aristotl e there also offers some obse rvations about the distinctive
logical behavior of said-of predications by formulating two conditions that he takes to be cha racteristic of this so n and not shared by inherence predicat ions. One of these is fairly straightforward. Chapter 3 opens with a statement of the transitivity of the said-of relation: «Whenever onc
thing is predicated of another as of a subject, all things said of what is pred icated will be said of the subject also" (lb9-IO).1 Now inasmuch as transitivity is a purely for mal property that does not distinguish the said-of relation from a who le host of othe rs, it will not playa central role here. However another, more substantial, condit ion is given in Chapter 5 at 2.a19ff: " If someth in g is said of a subject, both its name and its logos are necessa rily predicated of the subject. . . . But as for things whi ch are in a subject, in most cases l neither the name nor the logos is pred icated of the subject." Following Aristotle 's own way of referr in g to this co ndition at Topics 12.1 a I I - I 2, we may call this co nditi on participati011;1In order to see exactly what it amounts to, we must first note that both cond itio ns are ev idenrIy meant to app ly to the colloquial atomic sentences whose truth is expl icated by theory SrI (that is, such combined expressions as "Man wins," and " M an [is] anima l") and not to what Ari stotle regards as the
1921
Typ e 2 Per Se Predicatioll more perspicll o us ca110nical expressions that inhabit instant iations of the
right side of (55 ): (55) If " A is a" is true, lhell (where "A" sign ifies A, ;lnt! "B" signifies B) either B is sa id of A or B inheres
in A. In li ght of thi s, the participation condition CJ n be seen to be esse ntially grammatical. For whi le the canonica l cou nterparts to said -of and inherence predi ca tions a like arc formed by joining pnirs of nominal exp ress ion s by means of the technicalloCl1(ion s of "is said of" (Kaffu7TOKet/"U; /lOlJ Aiyerm ) and " in heres in" (EIJ v'n'oKetf..LelJ4,> 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 typic
Here things are not so simple. If subst itutivity of definitional equi valents were allowabl e for adjectival exp ression s as well as t>IJ()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
I 95 I
Explanatory COllteflt of Demollstrat;ollS
and then arguing that the logos of generosity is subst itutable for its name in (3 ') without loss of truth. At base, the difficulty is this: since differentia predications are like inherence predications (and unlike sa id-of predications) in the respect that their predicates are typica lly not sorta ls, then Aristotle's heroic efforts norwithstanding, the fact is that differentia predi cations will satisfy the participation condition only if inherence predications sa tis fy it also. Hence, insofar as Aristotle is unwilling to give up the participation condition as a means of di stinguishing tbe two types of sentence tteated by theory So. he cannot legi timately treat differenti a predications as expressing the said-of relation .
POSTERIOR ANA LYT/CS 73a38-b4' TYPE 2 PER SE PREDICATION The prin ci pal contention of this chapter is that Aristotle was somewhat more sllccessful in treating differentiae in the Posterior Analytics, and that his explication of type 2 per se predication at 73a38-b4 can plausibly be interpreted as a place where this better treatment occurs. Admittedl y, this passage does not co nta in anything more about the relation between differentia and differentiated species-indeed, discussion of that mat te r is put off until the Metaphysics"- but it does at least go some way toward spec ifyin g the relation between a differentia and the genus whose species it differentiates. Aristotle speci fies the larter relation by invoking an obse rvation he makes in rhe Topics about differentiae that has been largely misunderstood. At Topics 4.6.12.8a26, Aristotle states that differentiae (o r more accurate ly. terms that pick our differentiae) always signify a "q ualifi cation of a ge nu s" (1TOtOT17TO:' TOU yivolJl)). This point is then illustrated by the observation that a person who uses the expression "footed," which signifies a differentia, thereby signifies "some: qualification" (1TOt.OIl n ) of the ge nus animal. Because of rhe occurrence of the expression 1TOtOIl (as well as its proper nominal form 1TOUYr"fjTO:') here. and the fact that this is the same exp ressio n lIsed in the Categories to designate the'category of Quality, this passage has understandably led some to the mistaken view that Aristotle puts all differentiae into th at category, HI which would unhappily suggest that they must inhere in their respective differentiated species. BU[ despite this so mewhat unfortunate choice of terminology, Aristotle's point here in fa ct bas nothing at all to do with his theory of catego ries." Rather, it is
[ 96 )
Type 2 Per .'ole Predicatioll
simply a n obse rva ti on of th e preth eo re tieal bet about la ngu;1ge that express ions signifying differenti ae are always defin;lble by expressions of the fo rm, "3 qua lifiGuion of ," where til stands for the na me of th e genus whose sub species the different!<1 in question differentiates. It appea rs th at in the expl ica ti o n of type 2. per se predication, Aristotl e incorporates thi s o bservation into hi s co nception of neccss;try definiti ona l truth by expanding th e no tion of a w hat-Is-it for differentiae. Thi s expan sion comes naturally if o ne thinks of the w ha t-is-it of X quite ge nerall y as the set of thin gs referred to in giving <111 exha ust ive answer to the question, "What is X?" For whil e, on thi s understanding, th e w hat-is-it of a n individ ual o r a kind will co ntain eve ryth in g of w hi ch it is a me mher or n sub kind (that is, everythi ng signified in the chain gc nerated for it in the single-question method exposi ted in th e last ch<1pter), the wh.n-is-it of a differentia , on the o th er ha nd, will cont~i n not hing more than th e ge nus which it divides. To lise Aristotle's eX;1mple, if one were to ask "What is footedness?" the com pl ete <1I1SWer, ";1 qual ifi..:arioll upon th e genus ani mal," wo uld make re fe rence to just a sin gle enti ty, the ge nus allimn!. O f course, one could 3sk the further, obvio usly relevant, question , "What is anima l?" but in so doing olle woul d, strict ly speaking. have moved ;lW;:ly from the ori gin al question abo ut footcdness :llld taken up in stead th e new question : "What is th at of which foo tedncss is ..1 qualifi cati on?" Now since the wbat-is- it of a differentia is always single- memh ered in this way, its logos will always comain just one Ilalll e: that of the gen us of which it is a qualifica tion . I ! It will be reca ll ed that the probl em detected in th e Categories was that diffe rentia- predi cntio ll s did not fall cl eanly 011 either side of th e said-o f versus inheren ce distin ction presupposed by (SJ). Aristotle there wanted to regard them :!.s definition:!.1 and necessary truths, but they hl iled to sat· isfy an essentia l condition of th e o nl y definitiOiKl 1truths cou ntenan ced by his theory of predication $" . We can now see that in Posterim· Allalytics 1.4 he gets aro un d this difficulty by repudiating the si mple dicho tomy of the Categories and ma king room for anothcr defin itiona l rclation hesides the said-of (type 1 per se) rclati on, one rh:1t holds bcrwee ll ;l differentia a nd th e gen us it d ivides. II Th at he is nh le to describe [h ese two rebtions in a way that makes them appe~r to be rhe in ve rses of O ll l' another, and so to give the doctrine of per se predication the appea ran ce of h:1ving more un ity than it actua ll y possesses, ca ll be credited to ;1 com bination o f lu ck and in gen uity. It might well be interjected <1t this poim that th e solminn just Olltlined
I
97
I
Explanatory Content of Demonstratiolls to th e problems of differentiae is really no solution at all. For while I have argued that Ar istotle was at least able to say something about the relation between differentia and divided genus, he seems to have left untouched both the original se mantical prob lem of explaining the truth of speciesdiffe rentia predications such as
{6} Man is two-footed, and the original ontological problem of fitting differentiae such as tworootedness into his categorial scheme of things. This comp laint is well founded. I do not think that Aristotle's ultimate solu tions to these problems are contained in the works I have been discusjng. Instead, those solutions, which constitute the doctrine of the unity of definition, come with his recognition that the ontological p robl em of differentiae is not a genuine prob le m at all, because differentiae do not need a place in the hierarchical framework of the categories. This is because differentia terms do not signify a distinct class of ovrcx that must themselves be divided into genera and spec ies. They simply denote the ways in which genera are divisib le into species (which is to say, in the language of Topics ,(2.8a2.6, that they denote "q uali ficat ions upon genera"). As such, differentia arc not themselves subject to categorial classification; they are simply the principles by which such classification is accomplished . Along with this dissolution of the ontological problem comes a way of dealing with such species-differentia predications as (6). For since differentiae are now regarded as the principles by which specific division proceeds, there is obviously a one-to-one correspondence between species and differentiating differentiae. This point is recognized exp li citly by Aristotle at Metaphysics 7.1 2.r038aI7. From there it is but a sma ll step to sayin g that each differentia ter m somehow specifies (not to say signifies) the species it differentiatcs, and in fact Aristotle apparently equates species and differentiae in much th is way at Metaphysics 1038a19. On this un derstanding, sentence (6) could be thought of as logica lly equivalent to "Man (is) man," and so as necessarily true. In any case, we are not so much interested here in Aristotle's fina l solution to the problems of differentiae as with discerning how his attempts to deal with them inn uences his charac terization of definitional truth in the Posterior Analytics. The explication of types I and 2 per se predication at 73a35 - b4, since they are expressed in the material mode, can be represented as contai nin g refinements on the semantic treatment of defi nitional truth implicit in the Categories. For we may now replace truth
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definition (S5) with one that recognizes three distinct types of ontological
configuration th at might underl ie
(i) B is in the what-is-it of A (th;l! is, II belongs per se, to A), or (ii ) A is in the what-is-it of B (that is B bclong,s
per St.'! to Al, or
(i ii) B inheres in A (tha t is, B helolJ~s borh per ;lo.:idens I and per a>.:ddclls! roA).
THE NECESSITY OF PER SE PRED ICATIONS It was noted in chapter 3 th~t Aristotle locates the ultim:lte source of the necessity of scientific premises in their per sc ch:lracrcr. But since four separate senses of per se are explicated in Posterior Al1aiytics 1.4, we need to know which of these Aristotle is employing when he says that per se predications are necessary, Does he, in other words, intend his point to apply to just some of the various distinct types of per se predications he discusses at 73a35 - b16, or is it su pposed to apply right across the hoard? The answer to this question is to be found in the expbnarory statement that immediately follows Aristotle's final restatement of th~ per se requirement at 74b6-7. Right after declaring that per se predic;:ltions are necessary, at b7-9 he gives as the reason for this (emp loying the explanatory particle yap) tlwt in such predications either the predic ..lt~ helongs in the whar-is-it-of the subject, or vice versa. Now it is far frolll obvious how this by itself is supposed to explain why such per se predications shou ld be necessary, but a simple comparison of this remark with 73 a .' 5- b4 le:lves little doubt that Aristotle is here making an unambiguous reference to only the first two types of per se predic~tion. I~ It should be kept in mind here that because there are two di stinct types of sentence invo lved, there is no rcason to believe ;:It the outset that the same sort of necessity atta ches to hoth. Indeed, there is evidence indicating just the opposite conclusion. At Posterior Allalytics 73 h 16 - 19, Aristotle offers an ex panded version of the thesis of 7411(-, -9 : "for it is not possible that they [type 1 and type 2. per se ~ttrihlltesl should lIot belong [to their subjects] either absolutely or lin the Ill,mller of] the opposites, For instance, either straight or c[{wed belong to Iil1e; eithe r odd or euen to Humber" ( Posterior Allalytics 7 .l hI9-22., emph
1
E:rplallatory COl/tent of DemOl1stratiOIlS
attribute belongs to its subject with one of two kinds of necessity: such predications arc said to be necessary "either absolutely or [i n the manner of} opposites" (71 c:t1TAWS- 71 Ta a/lTtKeiJu;/la). H Moreover, it ctppears that Aristotle does not intend the distinction between these two types of necessity to cut across that between the two kinds of predications. All four of the aHributes he uses for illustration in the last sentence of the passage are genera ll y regarded by him as examples of "opposites" (al)'nKeip.6I)a), in fact, odd and eve11 are explicirly mentioned as such at Categories 12a7, while at the same time each of them is also among rhe exa mples of type 2 per se attributes given at Posterior Anaiytics 73a40. This by itself shows that th e class of type 2 per se art ributes at least intersects the class of opposites and is perhaps included in it. Put beside th e additional fact that none of Aris totle's examples of type I per se attributes is ever referred to by him as an opposite, rhis gives us enough reason to surmi se that the two distinctions in question are perfectly juxtaposed - th at Aristotle thinks of type I per se attributes as "absolutely" necessary, and type 2 per se attrihutes as necessa ry "in the manller of opposites." Ih But what exac tl y are these two kinds of necessi ty? To my knowledge, there is no passage in the Anaiytics, or for th at matter anywhere in the Organon, where he elaborates to the least degree on his bareboned rema rk at 74b22 that type 1 per se predications are "absolutely necessary." r- Perhaps this is because he thi nks th is type of necessity is so familiar thm it should be readily un derstood without explanation, or perhaps his references to it are meant to reflect some manner of speaking curren t among his contemporaries. A more likely hypothesis, however, is that even if he realizes in these ea rly writings that much more can (and must) be s:lid o n this topic, he simply has not yet reached the point of formulating the pertinen t questions , let alone working out his an swers [Q them. r ~ It was suggested in chapter 2 that in the Posterior Al1alytics he sees the necessity thar attaches to definitional truths as grounded both in analytic rel ations among gene ral (natural) kinds, and in essentialistic connec tions between primary substances and their proximate species, but that he does not clearly recogni7.e at that point that there are two different rela tions involved. This stands in marked contrast to Books Z-8 of rh e Metaphysics, which distinguish between the genus-species and kind-member relations, and foc us on the lane r (conceived there as the relation between a "composite" individual and its "substantial form," o r "essence"). Hen ce, there is reason ro suspect that this issue is so intertwi ned with the genera l problem of giving a satisfa cto ry accou nt of Aristotle's essentialism that its
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Type 2 Pc/" Se Predication
resolution must awa it a sorting our of the comp lex tangle of rhilosophi ~
cal doctrines tha t comprise the centra l books of th e MetalJhysics.
But wh atever the reaso n for the virW:11 lack of edification from Ar i s ~ rotle on the nature of the absoll1 tc necess ity of type I per se pred ica tions, th e prospect of apprehending the rC';1 sons be hind hi s insiste ncr thai type z per se attrib utes belong to thei r su bjects necessarily "in tlu.' manner of oppos ites" is initi a ll y much more promi si ng. In the lill es that follow illl mediately upon the articl1lation of the gener•.ll thesis at 73 bI9 -ZZ., he offers the foll owing explanation, which is c1C:Hly supposed to <.lP ply o nl y to type 2 per se attributes : "For [the opposite of a given attrilm tel is the contrary, or the pri va tion, or th e co ntra dic tory lof th t' ,ltrrillllle ! within the sa me genus. For instance, not~ oddlless is evenness within fthe ge nlls] numb er, in asmuch as the fi rst entails th e seco nd. So, ~ ill ce it is necessa ry that eve rythin g be affirm ed or denied, Itype 2] per ~c attr ihutes ;He IlC C ~ essa ry" (T\l122 -24) . Even thou gh this expbnation is mystify ing in some respec ts, at least its initial assu mption s are fairl y eviden t. To begi n w it h, if the f:i at hZ.4 is pl ausib ly read as "since" instea d of "if!" then it is fa irl y clear that Ari s~ ro de's conclusion depends ultimately on wh;lt sec ms to bc sOlne Illodal ~ ized version of the Law ot" Excluded Middle (l.EM) emhedd ed in that clause, "sin ce it is necessary that eve rything be affi rmed or denied" (h2.4). Now it was seell in chapter I t ha t this law is one of til l' h'l ckg roll nd assumptio ns required both by Pbroni c Division ,lnd by t he ;1llaptatioll of that method which Aristotle incorporates into his own t heory of demoll ~ stration . In deed, it is plausihle to unde rs tand the main sl1hj ect of Po s ~ terior Anaiytics 73bZ.2 - 24 ::IS a special sort of neccss iry rhnt he takes to be uncovered by sHch divis iona l procedures. However, it w ill emerge in chapter 7 tha t bo th Pbro a nd Aristotle h:lVe serio ll s doubts ;lhollt th e mea ningful ness of the law ill an unrest ri cted for m whe re it ~lppl i cs to every subjec t and eve ry attributc wh:usoever. '" Co nseque ntl y, Aristotle for his pan tends always to unde rstan d and ;l pply the pri nciple onl y in restricted form. In fact, hi s .. - :>..4 appea rs to be doub ly restric ted . In t he first place, it conform s to his gelle ral posi ~ tion, annou nced at Posterior Allalytics r. r 1, 77:12. 2- 26, that t he law is mea ningful o nl y w hen restricted to subjects within some spec ified gelllls, in th is case the genus Humber. But mo rt' than that, in thi s p
I
10 1
I
Explallatory Coment of Demoltstratiolls
they are invariably given in pairs (which I shall call "A-pairs") such as (odd, even). (straight, cUrl/ed), a nd (healthy, diseased), each of which exhaustively divides up the members of some ge nus. Let us say that a given A-pair is appropriate to the genus it so divides. Furthermo re, the lan guage of this passage indicates that Aristotle is interested here in pairs of attributes rhat carve out natura l and necessary partitions within th eir respect ive genera. 1t1 For this reason it appears that he is relying not on the relatively weak modal form of the LEM: WEAK MI.EM:
Necessarily, for every member x of G, and for eve ry attribute F appli cable within G, x either has F or lacks F,
whi ch would hold gene rall y for any attribute that could be mea nin gfully applied within G, but rather on the considerab ly stronger thesis: STRONG M I..F.M:
For every member x of G, and for every opposite F appropriare to G, x either necessarily has F or x necessarily lacks f. !I
The evidence for this is to be found in a nother feature of opposi res that Aristotle invokes at 7Jb2j: "E.g. Not-oddness is evenness within [the ge nus J number, inasmuch as the second is entailed by (€7Tercu) the first." T hi s sugges ts th at he sees the division effected by A-pairs as sufficiently nonaccidental to support th e very stro ng intensional relations of propertyidelltity and property-entailment. That is, tbe possess ion of one opposite in an A-pair by a member of the appropriate genus is said here to be entai led by, and even tantamount to , th at individual's lacking its partner. Hence, the modal character of the divisions effected by oppos ites is apparently seen by Aristotle as sufficient to underwrite his lise at 73b23 of a restricted substitutional premise which I wi ll refer to as the Principle of Opposites: (PO) If (<1>. ,It) form an A-pillr appropriilre to genus G, then application s of "'l/" and ."nor Cf>" 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 <:lsce rtain precise ly which statements comprise the sort of predic<1rion argued to be necessary at 73b2 2 -24. Virtu ally all of the exa mples of type 2 per se predication in Posterior Al1aiytics 1.4 are g ive n in the fOrtn of indefinite o r unql1antified sentences such as: (7) Odd belongs to numbe r. (8) Even belongs to number. (7.':139-40).
Such sentences may be right at home in Cntexorics (co mpJ rc t h38ff. ) where Aristotle is interested o nl y in specifyin g the ontological configu rJ t ions that underlie various so rts of tru e predication. But the centerpiece of the Analytics is the sy ll ogistic and its use in scienti fi c d e monstr~Hion, so we know that Aristotle 's rcal concern at nb2.2.-24 is to del11onstr~ne the necessity of a certain sort of syllogistic premise. These wi ll have to ta ke one o r t he othe r of the two general affirmative forms, " All s arc '1'," and "Some ¢Is are '1'," wh ich a re actually dealt with hy the logical theory of the Prior Analytics. What remains, then, is to derermin e exactly which sc ntences Aristot le has in mind when he uses senrellces li ke (7) a nd (R) to exc mplify type 2. pe r se predication. To begin with. the simplest and most obv iolls way of di sambiguating (7) a nd (8) ca n be rejected straig htaway. If th ese sen· tences were understood as simple un ive rsal affir m.H ives,
[ 103
I
Explanatory Colltent of Demonstrations
(7 a) All numbers are odd, (8a) All numbers are even, then we would have Aristotle arguing for the necessity of sentences th at are plainly false, and necessarily false as well. Upon noting this,lonathan Barnes suggests in his notes to Posterior Analytics 73a38-b4 that the im port of Aristotle's conclusion that odd and even belong to numbers "necessarily ill the manner of opposites" (73b I9 -12) is nothing more than the obvious truth that Q11e or the other of this pair of attributes necessa rily belongs to each and every number.!! In other words, Barnes views the argument as designed [Q establish th e necessity of a class of universal affirmative sentences that make disjunctive predications, in this case, (9 ) All numbe rs are odd or even.
This view claims some initial credibility from the fact that the necessity of sentences like (9) is in fact entailed straightforwardly by the premises of the argument. On this reconstruction, the argument presumably commences with a va lid application of WEAK MLEM!l to the attribute odd and the genus l1umber, (10) Necessarily, all numbers are odd or not odd,
to which (PO ) is then applied to yield the necessity of (9). Barnes's view also accords well with Categories 12.a7, where Aristotle express ly affirms the necessity of (9). But despite its prim a facie plausibility, there are twO independently conclusive reasons why Barnes's interpretatio n of the argument canno t stand. The first of these is th at sentences like (9), involving as they do disjunctive predication, sim ply do not have the requisite form to serve as syllogistic (and hence demonstrative) premises. Thi s difficu lty apparently worri es Barnes himself, judging from what he says in hi s notes to 73a35-b4 directly after proposing to read (7) and (8) as equivalent to (9): "Nevertheless, such disjunctive examples are not easily read into 73
I 104
J
Type 2 Per Se Predicatioll text.!4 And this total hlCk of textual support for Barnes's view c.lI1nor be explained away by hypothes izing some eccentric narrowness in Aristotle's choice of examp les. There are a numher of passages in the Allalytics (for example, Prior Al1aiytics 24a16, and Posterior Anaiytics 72<19) that explicitly prohibit the lise of anything but simple two-rerm (that is, single-predicate) sentences as syllogistic premises. Barnes's view the refore requires us to understand Posterior Al1aiytics I.4 as containing a rMhcr blatant case of ig1loratio elenchi, because it has Aristotle at 73b2.2 - 24 endeavoring to support his thesis that certain demonstrat ive pre mi ses are necessary (73a21-25) by arguing for thc necessity of a grou p of sen tences that do not and cannot function as prcmises in demonstration . Any proposal that assigns such a blunder to Aristotle shou ld be regarded as an absolutely last resort. There is another equally compel ling reason that Barnes's interpretation of the argument cannot be right. It represellts Aristotle as helieving that his conclusion, that all numbers are necessarily odd or even, is somehow expressible by his statement (73bl9, 24, 7 4b7) to the effect that each of these attributes, taken separately, is necess •.lrily possessed by numbers. This would involve Aristotle in some v..uiant of the mmbl fallacy of supposing that the necessity of a disjunction somehow distributes to its disjuncts. Yet he explicitly identifies and rejects this fallacious form of inference in his discussion of the future sea battle at De Jllfcrpretdtiolle 9.19a2.9 - 33: "I say, for example, a sea battle must either take place tomOrrOw or not . No necessity is there, however, that it should come to pass or that it should not. What is necessary is that eithe r it should happen tomorrow or not." Barnes is evidently aware of these d ifficulties, for he seems in the end ro regard his proposal as no better than the best in a bad lot. Consider his final words on the subject: "Rcfl.1ining rhe simple predicate 'odd,' we might try taking not number, but a kind of number as subject- e.g.: 'Every product of [two ] odds is odd.' But there is no smell of this in the text" ( 11 5) . Let us pause now and identify the adequacy l:onditions for the task at hand: an altogether satisfactory interpretation of Posterior AlItllytics 1-4 should specify a class of Aristoteli<1n sentences that both (a) involve the simp le and separate predication of type 2. per se attributes such as odd and ellen so that they are well formed for syllogistic purposes, <1nd (h ) 'He shown to be necessary by the premises of the argument at 7.1h2.2. - 24. Barnes eviden tly believes that there are no sentences that satisfy both of these conditions, and then reasons that his <1CColint should prevail by
[ 105 I
Explanatory Conten t of Demonstrations
default inasmuch as it at least respects condition (b) by representing 73b2.2-24 as co ntaining a valid (if misd irected) a rgument for the necessity of sentences like (9). I shall now endeavor to obviate this maneuver by showing that there are in fact Aristotelian statements that satisfy both (a) and (b). When Barnes rejects th e proposal that condition (a) might be saved by understanding the type 2. per se pred ications in question to be sentences about certain kinds of numbers, he pres umabl y does so on the grounds that the relevant text contains no subjec t-terms that cou ld reasonably be thought to signify such narrower subki nds. Thus, when he says in particular th at there is "no smell in the tex t" to indicate that Aristotle is thinking of stich sentences as (I I) Every product of odds is odd,
it is no doubt because the only ge neral terms th at occu r in Aristotle's di scussions at 73338- b4 and b22-24 arc "odd," "even," and "number," and Barnes sees no way to construct a sentence out of these alone which is not about numbers ge nerall y, but only some kind of number. It is significant that Barnes here leaves entirely out of account the most natural and straightforward way of understanding sentences (7) and (8) as sy ll ogistic predications. For there are a number of passages in the Prior A1talyt;cs where Aristotle makes it clear that indefini te predications should as a matter of cou rse be treated as particular state ments (compa re 26a30, 32, )9, b3, 29028)." According to this convention, (7) and (8) would be equivalent to: (7b) Some numbers are odd. (8b) Some numbers are even.
Although Barnes doesn't co nsider these se nten ces explicitly, I suspect he rejects them out o f hand as legitimate examples of type 2 per se predicatio n o n the grounds that wh il e they are no doubt true (and even necessary), their necessity does not seem to follow from the premises of the argument at 73b2.2-24, which would mean that they fai l condition (b) above. This I believe is yet another result of the misguided tendency to understand Aristotelian general sentence forms as trans latable into mod ern q uantifier 10gicY On such an understanding, sentence (7 b) for examp le, is an existentiall y quantified statement, so that its necessity would consi st in the fact that the intersection of odd th ings and numbers is necessar il y inhabited. Admittedly, it is very hard to see how this could follow
I
106 )
i
I I
j
i
I I
Type 2 Per Se PrediClltioll
from any form of MLEM (w hich is
particular.! g However, if (7 b) and (S b ) are now understood ;1S rcfncnti:11 particulars, it rhen becomes very easy to undersr:lI1d how Aristotle could see them as the statements whose necess ity is ;It issue at Posterior Auolytics 73 b2. 2-2.4. For STRONG MLEM and (PO ) together impl y: ( 12) Every number is necessnril y odd or necessa rily
even.
Co nstrued as a referential universal, th is se ntencc .1SSlTts of each and every llumber either that it is necessarily odd or thar it is ncce5s
I 107 I
ExplmlOtory Content of DemonstratioflS numbers . But these two distinct sets of singular propositions can also be expressed respectively by (13 ) Some numbers are necessarily odd, and (14 ) Some numbers are necessarily even,
where these are understood as instances of the referential particular. Hence, since on these co nstruals (13) and (14 ) are implied by (12), it is possible to understand Posterior Anatytics 73 b22 - 24 as co ncern ed with the necessi ty of (7 b) and (B b)."
I
108
I
SIX Type 3 Per Accidens and Type 4 Per Se Predication
POSTERIOR ANALYTICS 7)b6- 8, TYPE 3 PER ACCIDENS PREDICATION For each of the two senses of per se Aristorle explicates at Posterior Ana· iytics I.4.73335 - b4, he also introduces and defines derivatively a com ~ plemcntary sense of "per accidens" (Kara CTvp,{3f:{3YjKOC; ). Th~lt is, something is said to be per accidens in a given sense, just in case it is not per se in the corresponding sense. I shall now argue that Aristotle's disclIssion of the third sense of these two expressions at n b6 - H differs from those of the other three in that the recalcitrant senrences he is concerned to fit into his theory in that passage are not, as in the surrounding passages, a certain type of per se predication, but rather a certain type of per accidens predication. I shall first identify the trouhlesomc "accidental" prcdica· tions involved, and then show how 73b6 - 8 Gill be viewed as an attempt to deal with them. An examination of SUl and especially of (57), (57) If A inheres in B, chen B is a substance, and A and B are heterocategoria! (that is, A is a nonsubsrance),
reveals that the theory sets very definite limits on the possibi lities of inter· categorial predication. The on ly such sentences cOllntenanced are those in which a nonsubstantial entity is predicated of a prilll;]ry or secondary
I 109
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Explanatory Content of Demonstratiolls
su bstance. In particular, there is no poss ibi lity within that th eory of a true intercategorial pred ication whose subject signifies a nonsubstance. However, there is co nclu sive evidence in the Posterior Analytics (a nd in the Metaphysics) that Aristotle recognizes the ex istence of such sentences, and thar he thinks them to be in so me se nse (to be explained below) pe r accidens. For example, at Posterior Anaiytics I. [9.8] b2.4 he says that the sen tence ( I ) The white (TtJ XBVKOV)
is (a) man 1
is a per accidens predication, while the sentence (2.) The
man is white
is not. Much the same point is expressed at Metaphysics r. 4.1 007b3 where Aristotle pro nounces the followin g two sen tences per accidens :
ell The white is cult ured . (4) The cultured is white.
I
Notice thM sente nces like (I), (3), and (4) pose no great difficulties for modern phi loso phi ca l theo ries of language because such theories invariab ly make use of two distinct types of semantical relations. One of these types, which I shall ca ll context-independent, consists of those that hold simply between expl'ession-types and extra linguistic enrities. 1 Fa miliar examp les of this SOft of relation are the naming, denoting, and meaning relations. T he other ty pe, which I shall ca ll context-dependent, consists of th ose that hold between exp ress ion -to kens and extralingu istic entities. Context-dependent relations, of which the most familiar is th e reference re lation , can be described either stra ightforwardly as two-place relations between tokens and the extralinguistic relata, or in a more complex manner by spec ifying an expression-type, the extralinguistic relata, and various other contextual factors such as the occasion of usc, speaker's intent, ostensive gestures, and so fort h, that collectively fix a definite spatial and tempo ral location of a ce rtain employme nt of an express ion -type and thereby indirec tly pick out an expression-token of that type. So, for instance, the very same circumstance may be described either by saying: Smith is the referent of the expression-token " my friend here" (which token emerged frornJones's mouth while he was gesticul ati ng in a certain manner at 3 :00 p.m., August 5, 1988, at the end of th e Newport Pier), or by saying: Jones used the expression-type "my friend here" in conjunction with a certain gestu re at 3:00 p.m., August 5, 1988 , at th e end of the [ 110
1
Type 3 Per Accidells alld Type 4 Per .lie Predic!lfioll
Newport Pier, to refer to Smith, even though the first describes;] twoplace relation between token and referenr, and the second a six -pbce relation among an expression-type, a referent, a speaker, a gesture, a phlce, and a time. Now, if Aristotle's semantical aplKlrJtus contained the distinction hetween context-independent and context-dependent relarions, he could dispose of sentences like ( r ), (3), and (4 ) without much trounle. He could, for example, explain the truth of (T) by first noting that the exprcssiontype white, when it occurs as subject in a true token of that sentence, does not refer to its own llsual denotation, which is of course the nonsubstantial entity whiteness, but rather to some p;uricubr (primJry) substance, and then explaining the truth of that token as due to the bct t'h'lt the substance so referred to is in fact a mall. It is quite apparent, however, thm Aristotle does not have this distinction availa bl e to him either in the Categories or in the Posterior AlIaIytics. The sale semantica l relation he recognizes in these works is the signification relation, and this, without a doubt, is context-independent. 1 According to the semantics of Categories 4, the expression white therefore can stand in only one semantica! relati on: it signifies th e nOllsubstan tial quality wh iteness and nothin g else, it signifies it once and for all, Jnd in a way that is independent of features of any particular oCGlsions of its use. But even though Aristotle does nOt havc the conceptua l gcar necessary to perform modern treatments of sentences li ke (1) , C~) , and (4) , he pllts what resources he does possess to ingeniou s usc in exp lainin g their truth. This explanation, which is accomp li shed solely in tcrms of the contexrindependent signification relation and the Gttegorial scheme, is perhJPs most exp licit in the Metaphysics r pass.lge where he trc;;l ts scntences (:~) and (4) : "1 say, for instance, that 'The white is Cll ltllfCll ; and 'The cul tured is white' [are trueJ because both [whiteness and culturedl arc JCci dents of a man" (roo7b4- 5). Here we have in effrct :111 existentially quantified statement of the truth conJitions for C,) llnd (4 ), which !TIny be generalized to all intercategorial predications whose grammaticJI sub jects and predicates are both nonsllbstantial:
If 'A is B' is true (where 'A' signifies A, 'B' signifies B, and A and B are both in nonsl1bstantial catt.'gorics ), there exists a primary suhstance 5 such that A
S.~
But sentences like (3) and (4) are not the only type of true intercatcgo rial predication that were seen ro have no place in S" . Then. . an: also [ III [
Explanatory Conte/It of Demonstrations
sentences like (I), whose subject signifies a nonsubsrance but whose predicate signifies a secondary substance, recognized at Posterior Analytics 8Ib24_ Hence, the solu tion found in Metaphysics r can be generalized further so that it includes these and provides truth conditions for all intercarego ria l predication with nonsubstant ial subjects no matter what the
categorial status of their pred icates: If 'A is B' is true (where 'A' signifies A, 'B' sign ifies B, and A is not a substance), there is a primary substance 5 such that A belongs per accidens [0 S, and B belongs (eithe r per se or per accidens) to s.
I suggest that it is this genera l trea tment of such sentences that Aristotle is reco mmending, albeit in overly terse langu age, when he says at Posterior Allalytics 8 Jb2.4 th at the rcason (I) is tru e is sim ply that whiteness is an accident of the man. With this understanding of Aristotle 's method of dealing with these sentences in mind, we are now in a suitable position to address two dis ~ turbing little puzzles concerning hi s discussion of per se and per accidens predication in Posterior Analytics 1.4 . The first of these is actually so me~ thin g of an anomaly: the passage where Ari stotle di scusses his third sense of per se and per accideflS does nor fit well with its su rrounding context. Each of th e other senses of these terms discussed in Posterior Analytics 1.4 properly apply to sort of predication (or predicative relation), which is in keeping with tbc general aim of the cha pter to specify the requisite features of scienrific premises. Yet, as Aristotle exp li cates the third sense of these terms, th ey apply not to sen tences but to terms, or what j have called in chap ter 3 sen tenti al elements. To say the leas t, it would be pecu~ liar fo r a systematic writer like Aristotle in (he middle of a prot ra cted dis ~ cussion about predications suddenl y to sw itch tracks for three lines and concern himself with anothcr subject and then to sw itch back again without the slightest warning. ~ Furthermore, th ere is no other location in the Organon where the terms per se and per accidens are used to appl y to terms rather than connections between terms. The other puzz.le concerns the interpr!!tation of Aristotle's remarks at Posterior Analytics 8 Ib24. He says there that sentence (1) is a case of per acc.:idens predication, yet an examination of his discussion earlier at 73a35-b16 seems to ind icate that thi s sentence does not fit neatly into any of the three types of per accidens (namely, types I, 2, and 4) explidtly discussed there. Evidently, he must think that there is anorher type of per
[ 112
1
Type 3 Per Accidel1s alld Type 4 Per Se Predicatio/l accidens predication besides th ese three. But how is the om ission of any mention of th is further type to be explained? Shou ld we S::lY that it is a simp le oversight, and that he simply forgot to indude this type in his list in C hapter 4, even tbough its existence is dearly recognized in Char~ re r I9? Or shou ld we say that Aristotle didn't discover the new type ulltil he wrote C haptcr 19, a nd for reasons now hidd en from us was unwillin g or unabl e to revise the list he had already dr:lfted? Or should we bl:lllle the omission on his ancient ed ito rs? Such explanatio ns, being more on the order of hiogrnphy and psy chology [han history of philosophy, arc, for lack of di scovcwole criteria of correctness, inherently ul1s:ltisfying. They shollid be suppbntcd wherever possib le by more detached accollnts that aim at making sense of the text as it stands witham the a id of such speculative hypotheses. In the present case, 1 shall offe r an aCCO llnt that disso lves thc 3ppe3r;1I1CC of strain between 7Ja3 5- b1 6 and R1b2.4-7 wh il e at the S:l mc time accounting for what appea rs to be an anomalous inrroducrion of th e third sense of per se and per accidens at 7 J h6 - 8. The key to this account is contained in th e single illsight that at 73b6-8, just as in the pa ssages immediately sLltro lindin g it , Ari stotle is primarily concerned with a certain type of predi cation, despite his supe rficial interest there in terms. What is more, the type of per ,lccidcns prcdiGltion he discusses there is prec isely the type he rep rese nts hy ( 1) at 81l12.4, and al so by (3) and (4) at M etaphysics I007h4 -5 .lll oroer [0 sec eX:lctly how these passages are related, it 1l1:1 Y first be noted th :lt the two terms w hi ch Ari stotle labels " per accidens" at 73 b6 - 8, TO f3aoi~oll ::lnd TO A6VKOII, are both nominal phra ses formed with a neuter singul ar adj ectival form signifying a nonsubstallce and a marching article. Such expressions, as we noticed above, are exac tly the type whose occurrence :lS subjects charac terizes sente nces like ( I ), (3) , and (4). 111 bct, th e second of the two is the sub ject of sentences (1) and L~). Now at 73b6 Aristotle gives as the re;)son th ;lI so me terms ~lre per se th at they a re " not said of an yt hing el se as subject" (J..L-ry KnffinTOKf;tJ..Lf:"OlJ AeyeTQt iiAAOV Ttvo'»), a nd from t hi s it may be inferred that he thinks 7'0 J3aai~oll and TO At=:.lJKOV are per accidens precise ly hl'c;lll se they (or more accurately, their significata) are said of somethin g 1.'1se :lS subjecr. But what exactly does thi s mean? It is import~nt not to be mis led here by the unfortunate intrusion of Catego ries termino logy, for here the expression "said of" is evidently used with (I meaning different from what it ha s in the Categories. Here it refers not to what we called in ch~lp rn J the "said-
[ 113
1
Explallatory COlltellt of Demonstrations
.... ,
of" relation, but to inherence, rhe very relation it is contrasted with in the Categories. This can be seen clearly in Aristotle's choice of examples. At 73b7 he gives as an examp le of something being "said of some thin g else as subject" the case of something (presumably an ani mal) walking, and in the Categories scheme this is patently not a case of the said-of relation, but of inherence. Furthermo re, the characte rization given in the same place of terms that 3rc per sc (that is, whose significata a rc not said of anything else as subj ect) is "substance and such terms as signify particulars" (71 (j'ovO"ia Kat o(Ja TO.s~ Tt (JT}/LaiV6t). Apparently, the former are secondary substa nce-terms such as man and horse, and the latter a rc proper names of particular substances, such as Socrates. Now since the sign ifi cata of such terms, being in Substance, are precluded by (57) from inhering in anything, these examples re info rce the view that the expression "said of" at Posterior Allalytics 73b6 refers not to the said-of relation of the Categories but to the inherence relation instead. So Aristotle's exp li cit point, which pertains to terms, is that expres~ sions like 'TO {3aSi.r,p/l and 'TO A6lJKOIJ are per accidens because their significata inh ere in something else. Now comes the crucial step. At Metaphysics Io07b4 - 5 (and with less clarity at Posterior Analytics SIb24-7) Aristotle makes precisely the same point about [he very same expressions, and he does so in language that is nearly identical (except that he replaces the mi sleading exp ression "said of" with the more perspicuous phrase " is an accidenr of"). However, in the Metaphysics passage (and in Posterior Analytics 1.19), Aristotle is no longer talkin g about such terms in iso lation, as he does in Posterior Analytics 1.4, but rather as they occur as subjects in such per accidens predication as (1), (3), and (4). It is therefore reasonable to surmi se that Aristotle's grou nds for cl assifying these predications as per accidens is that their subject terms are per acc idens in the se nse expounded at 7., b6-8, and thar the se nse of per accidens emp loyed at Metaphysics l007b4 - 5 and Posterior Analyhcs 81 b24 is derivative of that sense. Hen ce, wh ile the superficial point of 73b6-8 is again that cectain terms arc per accidens, the important submerged poim that connects this passage with its surrounding conlext is that predications having such terms as subjects are consequently themselves per accidens (in a derivative sense), and hence do not qualify as scientific premises. I said at the beginning of this discussi on that according to the interpretation of Posterior Allalytics 73b6-8 I am defending, Aristotle's main concern in that passage is not with a type of per se predication, but with a type of per accidens predication. Now a stronger point can be put: it ap-
[ 114 J
Type 3 Per Accidens and Type 4 Per Se Predication pears that there is no independent class of type -' per se predic~ti()ns idell ~ tified in Posterior Allalytics 1.4. If there were, then since Ari stotle hold s that per se a nd per {lccidells are com plement~ry in meaning, this would mean that all that is needed to count ~ sentence ~s type -' per se is fhM it not be an intercategorial predi cation with :1 llonsuhst:lI1ti:tI suhjec t. Even if we assume that 73b6-8 is concerned exclusively with sentences whose subjects, no mauer what the catego ry of their sigllificata , refer ro sub· stances (though I have argued that Aristotle himself h~ s no way of nwking this distinction ), rhat would srill leave rhe class of type 3 per sc prcdi ci.l tions so wide as ro include both per se and per
of the other types, Now since, as we sa w at the beginning of ch:lpter 4, the overall pur ~ pose of the discussio n of per se predicmion in Posterior Auolytics 1.4 is to ident ify a group of sentences thar are suitable scientifi c premi ses ( pro ~ vided they are also K(X'ro. 1TClVT()o;;' and awo), it wou ld seem th::lt if Aristotle recogn izes a class of type -' per se predicJtions, he wou ld be giving them this elevated Status. It is hard ly likely, howeve r, that hi s intention is to make such obviously cont in gent sen tences as
n
(5) Socrates is white.
which he categorizes as per accidens in all other se nses of that term, into suitable candidates for scientifi c premises. A much morc plausible view, in light of the fact that 73 b6-8 is concerned explicitly with term s, :ll1d only indirectly with sentences, is thut Aristotle there recognizes 11 0 jl1dc ~ pendent classification of per sc predications parallel to the sc nse of pCI' accidens he employs at Posterior A110lyl;cs 8 I h24 and Metaphysics I007b4. Hen ce, the re is an important difference ill cmphasis between 73b6-8 and its surrounding passages. While in each of those othe r pas ~ sages Aristotle is concerned to characterize J type of pCI' sc predicarion to include in hi s theory of science, here his concern is solely {() identify a certain type of per accidens predica tion he wis hes to excl ude.
DEMONSTRATION AND CAUSAL CONNECTIONS According to the Categories sema ntics, and (55) in parti cula r, there
[ 11 5
I
Explanatory Content of Demonstrations
are foftuirously true, that is, true by virtue of the opera tio ns of "chance" (Tj TVXr,). There he cites as an un desirable feature of a doct rin e under ca n· sideration its consequ ence that th e tru th of predications that veridically attribute (o r deny), the predicate "(is) white" to "particul ar things" (presu mabl y primary substances) wou ld be a matte r of necessity. This, he declares, in turn implies that nothing comes about from chance, a consequence he evidently takes to be false. Clearly, this reasoni ng relies on the assumption that such predications, which we saw in ch apter 3 to be among Aristot le's favorite exa mples of inherence-sen tences, a re also paradi gmatic ex amples of sentences he th inks are fortuitous ly true. This is why he ca n so read il y endo rse the co nd itional th at if they aren' t £ortui~ tou S th en no predications are. fu rth er, sin ce Aris totle here and elsewhere co ntra sts what comes about "from chance" (d1TO TVXi1~) with what comes about "out of neces~ sity" (ig & lJa'YK7J~)" and since we have already see n th at he makes the latte r cond ition a requ irem ent for scien tifi c premises, we shou ld expec t he would not a ll ow fort ui to us truths to fun ction in demon srratjons. And ind eed, he ex pli ci tly deni es both that th ere ca n be scientific kn ow ledge of such truth s, and that they can occur, in dem onstrative syllogisms in Pos~ terior Analytics I.30, and in somewhat more obscure language at Prior Analytics 1 . I 3. 3 2b I 8. These passages prompt th e view th at th e only type of true predications recognized in Catego ries that wo uld be appropriate for demo nstrations in the Analytics a re those ex pressi ng the sa id-of rel ation : For all thi s, there are two very com pell ing reasons fo r thinking that th e simpl e twofold divisi on of p redi cations in the Categories is inadequate for isolating rh e scientifi c propos itions with which Aristotle is co ncerned in the Posterior Analytics. Fo r as we noticed earlier, he argu es at consi dera ble len gth in Posterior Analytics 2.3-10 (espec ially at 90b2891a12) that propositions that are true as a matter of definition cannot, excep t in a distended sense, be the objects or products of demonstration. 1I In resrat in g this view at 93b r 6 after havin g just argued for it, Aristotle makes it clear that the reason such statements are no t demonstrable in the str ict se nse is that th ey can not function as concl usions of demonstrative syll ogisms. But si nce he sees all type I per se predica ri ons as defi nitionally tru e, and sin ce tbere is no recogniti on in the Categories of any other nonfortuitous tru ths besides type I per se predications, it appea rs th at if Aristotl e were to stick with the crude division of the Categories, the class of sta teme nts th at could function as co nclusions in demonstra tions in the Posterior Analytics wo uld effectively be empty. [ 116 )
Type 3 Per Accidens a"d Type 4 Per Se Predication
But of course we already know that Aristotle does not confine himself to the crude Categories division of predications when he comes to outline his theory of demonstration in the Posterior Al1a{ytics. In fact, what has already been noticed about his more refined semantical views in the Ana{ytics implies a partial so lution to the problem just formulated. We S;IW in chap ter 5 that he recogn izes in the Posterior Analytics an additional class of non fortuitous truths besides type 1 per se predications, namely type 2 per se predi cations, which connect a divided ge nus to its dividing different iae. But even with the class of scientific propos itions en larged to include both types I a nd 2 per se predications, that still leaves the subj ect matter of Aristotelian science severely restricted to what we might now call analytic truths. This is because the truth of both these sorts of per se predication is insured by th e netwo rk of wh
I
,!
Explanatory
COli tent
of Demonstrations
POSTER IOR ANALYTICS 7Jb,O-,6, TYPE 4 PER SE PREDlCATlON "X happens per se. to Y if X happens to Y in virtue of [V] itself. Example: Death happens to a slaughtered thing in virtue of 'the slaughtered' itself [that is, in virtue of a thing's being slaughte redL so death happens per se~ to a slaughtered thing. " It mu st be admitted to begin with that thi s expli ~ cation by itself does very little to illuminate the cha ra cter of the sort of predication under discussion. All it says is that X happens to Y per sc. just in case X happens to Y " in virt ue of [YJ itself" (8t'cnho). But since, so fa r as H. Bon itz ha s discerned, ln there is li ttle if any difference in mean· ing between the Aristotelian exp ress ions cSt'ath-o (beca use of itself) and Ka(}'rxirro (pe r se), a nd since the mean ings of both these expressions are in any case equally obscure, this exp li ca tion is not likely CO contribute much to our understanding of Ariscotle's use of per se. However, as so ofte n ha ppens in cases where hi s theoretical remarks leave resid ua l perpl exi ty, Ari sto tle 's propitious insertion of an illumin at· in g example in this passage ena bl es us to get through to his intended mea ning. Although he doesn't actuall y displ ay a type 4 per se predication at 73b 10 - 16, what he does say there leaves little question that he th inks the fo ll owing fits the bill , (6 ) Death happens
(0
some slaughtered [thingl (n
u¢arrolJ.€/lov).
,
However, it is not the example itsel f but the exp lanatio n of its truth offered at b I5 th at provides th e ke y to understa nding Aristotle's use of at'aUTO, and ul timately to und erstand ing t he nature of his type 4 per se predications. The reason that (6) is a type 4 per se truth , he says, is that an ani ma l does not o nl y die when it is slaughtered; it a lso di es because it is slaughtered . As my emph as is suggests, th e cru cial expression in this ex· pla nation is the word "because," w hi ch translates the G reek ~ ,a. Now it is we ll kn own to modern philosophical log icians that "beca use" con· strucrions ca n be used to express a vasespectrum of con nections ranging from enta ilm ent (or logical consequence) a mong proposit ions to the tenuous connection betwee n an a ll but ca pri cious act and a wh im th at precedes it. Moreover, an exactly anal ogous elastic ity has recentl y been ob· served in th e anc ient usage of ISLa. 11 What type of connection l then, does Aristotle mean to express by hi s use of this pre posicion at 73b1 5 ? There a re two initial ly plausible a nswers [ 118
I
Typ e 3 Per Accidells (lIId Type 4 Per Se Prediwtioll
co thi s question, each of which ca n be seen CO fo ll ow from a corresponding way of understanding the verb (T(pa'ew (to slaughter), whose passive finite and infinitive forms both occur in Ari stotle's explana tion of the truth of (6). If the verb is raken to mean somethi ng like "to kill a captive animal," "to kill in a certa in manner, or with a cerrain kind of instrument," or otherwise to involve definitiollJlly the norioll of puttin g the object of the verb to death, then the Sui at hIS would seem to be a logical "because" (that is, would seem to ind icate the spec ification of a logically sufficient co ndition for death). If, on the other hand , (J"(P6,f;lV is understood, as it is by G. R. G. MUfc in the Oxford transh.ltion, Il_ simpl y to refer in a minimal sense to the immediate acts of slnughter, for instance, th e cutting of the throat, then the "because" at In S should be rend with weaker force to indicnte a ca usn l re b tioll between an animal's undergoing that physical operation and its su bseq uent death.
DEMONSTRATION AND "FOR-THE-MOST-PART" PREDI CATIONS Since both of these meanings of cnt>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
I
11 9
I
Explaltatory Con tent of Demonstrations
make it seem initiall y plausible that in singling out this type of predica~ tion Aristode is si mply pointing to the purely statisti ca l fact that there are some instances of high but imperfect correlation between event-types in the natural universe. But this statistical view of thrL 'TO 7TOAV predication is easily d ispelled by the observation that th ere is a conspicuous absence of examp les of predications expressing correlations that could be called purely coincidenta l. Any reasonably perceptive observer-and Aristotle certainly was that- would certainly be aware of some freak statistical regulariti es due to nothing but chance, such as every member of a certain dinner party being born in the same month. Yet virtually eve ryone of his actual examp les of ent TO 7TOAV predication falls cleanly within the class of what we would now identify as causa l genera li zations (for example, Prior A,zalytics 1. I 3.3 2.b7; Posterior Analytics 2.. I 2.96a 10; Metaphysics 6.2.1026bJ4 )· The absence of examples of purely statistical regu larities might be explained by the hypothesis that Aristotle simply does not recognize their practical possibility, but only if it could be established that he requires a relatively high level of generality for the subject terms of £1Tl. 'TO 7TOAV statements. For certainly, as the number of cases examined becomes larger the actual statistical frequenc ies of events converge upon their theoretical probabilities. So if it co uld be show n that Aristotle insists every bTL 'TO 1TOAV predication must have a subject that is extremely gen· eral, and that he regards the threshold of 87Tt. TO1TOAV truth as quite high, then it might be possib le to argue that the e7TL TO 1TOAV classification really is stati stical in nature and he simp ly deni es the practical poss ibili ty of there being any freak corre lation of a sufficj entl y high degree to pass the threshold. However, to my knowledge Aristotle never says or implies that there is any minimum generality requirement on the subject terms of e1Tl. 'TO 1TOXU predications. Hence, if what he ha s in mind is just a statisti cal category, then it is hard to see how he could fail to notice that there are some general (though, of course, not very general) sentences whose truth is purely a matter of coincidence. In any case, there is ev idence that his restri ction of examples to ca usal truths is not due sim ply to a lack of imagination on Aristotle's part. He repeatedly contrasts what is 81Tl. 'TO 1TOAV with what "comes about from chan ce" (Ct7TO TtJxf]S') , both directly (De Generatione et Corruptione 2..6·333b7i De Caelo 2.8.2.83a33; Posterior Analytics 1.30.87b19i Eu· demian Ethics 14.124 7a 32; Problemata 9 J b 31) and indirectly, by equating what is t1TL 'TO 1TOAV with what is true " by nature" (K(l'TO: rjlvG"illj De Gen. Animalium 4.8.777aI9-21), and by co ntrasting the latter with for-
I 120 I
Type 3 Per Accidem alld T ype 4 Per
S~
Predicatioll
tuitous occurrences (Metaphysics 7.7. 1032at2; 12.3 . 1070a6; De Part. A nima/;u111 LI.64 Ib22). This co ntras t ind icates that he co nscio usl y d isco unts the possibility of coinc idental ge neral truth s, an d t h:H he therefore regard s the truth of all €7TLTO 1TO,.\ti statements as due to the operations of nature. As such, th eir character is very mu ch lik e that of genera l truth s now regarded as ex press ing ca usal con nection s. If it is now granted that E1TL 'TO 1TO,.\ti statements express causal co nnect ions, and that Aristotle therefore has good theo ret ical rea son to in clu de th em in the cl ass o f sc ientific p remises and co nclus ions, we have next to discover whether he actua lly does so in Posterior Analytics 1·4· Here we should notice firs t that the doctrine of e7TL TO 7TOAti predication is present virtu all y th roughout the Corpus, the only signincant exception being the Categories, which was al rea dy seen to ad here to the crude twofold divisio n of predications renected in (5S) . In fact, it is found in sHch works as De Interpretatione (19a21 ) :lI1d Prior Anolytics L~2b7 ) that are qu ite ea rl y, even o n the most co nse rv:'ltive chronologi cal orderings of Aristotle's works . Moreover, there are at least th ree good rC:'I sons for chinking that Aristotle consistentl y regards such st:'ltemell ts as sc ientin cally re ~ spectable. To begin with, he often sets them in the middl e position of a threefo ld class ifi catio n, co ntrasting them on one side with necessa ry truths (that is, types I and 2. per se predication :tnd ... certa in type of pro p ria predi cation to be discussed shortly) , which he says are "always [true]" (&€ i ),'~ and on the other side with (ge nuine) accide ntal predicntions that he says can ex press co nn ections that "can happen ill one way or another" (6 Kat. OiiTW~ KaL p..-ry oVrWS" OVlIO'TOllj Prior Anofytics 32.b 12). Whenever he ma kes this threefo ld divis ion. he inva riably insists that on ly the first two types (necessary predications and F.1TL TO 1TOAU predications) can be stud ied by scie nce ( Posterior Analytics 1.30.87b 19-28; Meta physics 6.1.1 017a 16-19). Secondly, many of the exa mples of syll ogistic demonstration he gives in Posterior Allalytics 2. involve co nn ectinns thnt evidently ho ld o nl y for the most pa rt, (for instance, that internationa l aggresso rs beco me in volved in wa r [I J .94a37-691. thnt postp randia l w:llks :.1id di gestio n [b9-19 "], and th at longevity is due to dry consti tution in bi rd s and to the abse nce of a ga ll bladde r in qu ad ru peds [[7.99 bS-71), and thi s is confirmed when he exp li citly describes many of th e actual concl usions he generates in hi s scie ntific treatises as i7Tt 'TO 1TOAU (for examp le, D e Gell eratione Allimalium I.r9.727 b2.9; 4 .4.770h9-1 .~, 8. 777:.119 - 21 ). And finally, in th e Allalytics passages (disclissed ahove in chapte r 1) where he describes his recommended procedure for selec ting demonstrative prem-
I
12 1
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Explanatory Content of Demonstratiol/s
.' "
r
I
ises by Aristote li an d ivis ion, he clearly admits the possibi lity of finding and using e7Tt. TO 7TOAti premises. In particular, at Posterior Analytics 2. I 2.96a I 6- I 7 he merel y insists that the immediate premises of 67Tt. TO 1TOAV conclusions must themselves be e1Tt. TO 1TOAU, and at Prior Analytics 1.27 .43 b3 3 - 37 he makes the same point, and says that for th is reason it is necessary, in the process of collecting syllogis tic premises, to identify those terms that follow "for the most pa rt," or arc "for the most part" followed upon by, a given subject. Yet despite Aristotle's apparently fixed view that e1Tt. TO 1TOAtI connections belong within the field of scientific inqu iry, he seems to ignore th em in Posterior Analytics 1.4, the very chapter where he explicitly id enti fies the statements that can function as demonstrative premises and conclusions. The expla na tion for th is apparent omission, I suggest, is that it is o nly apparent; 61Tt. TO 7TOAti predications are discussed in rhat chapter, though under the heading of type 4 per se predications. T he main evidence for this view, as I indicated above, is derived primarily from Aristotle's choice of examples. We noted earlier th at on one plausible interpretation of Aristotle's explanation of the truth of sentence (6), Death happens to some slaughtered lthing] (n CTc/>arrO/LBVov), which is hi s lone example of a type 4 per se predication, the sentence can be read as expressing a causal relation between the two event-types mentioned in it. An examination of examples of 67Tt. TO 1TOAti predications elsewhere shows them to be of exactly the same type: general statements expressing causal connections between event-types. Among those examples are: (7) A man becomes gray- haired [as he ages]. ( Pdor A lla -
lyrics 1.' 3.32b7) (8 ) A mnn grows ch in whiskers Ins he nges]. (Posterio r Alralytics 96a1o) (9) The weather is hot in the dog days (of Augustl. (Metaphysics ro!.6b3 4)
The similarity between these exa mples a nd (6), tOgether with the fact that Aristotle ha s reaso n to make e7Tt. TO 7TO~V resp ec table, provide good grounds for reading his explanation of the truth of (6) in a causal man ner and for assim ilating e7Tt TO 1TOAV predications into his type 4 per se class ification. This assimilation is giye n further su ppor t by the even more strik ing si mila ri ty between the accidental predication Aristotle co ntrasts with sente nce (7) at Prio r Analytics LI3.32.bI3 : (lO) An ea rthquake happens while an animal is walking,
( 122
I
Type 3 Per Accidells and Type 4 Pcr Se Predh"atioll
and the examp le he gives of type 4 per accidens predi c;'ltion at Posterior Analytics 73br6: ( I I) The sky lightens while so mething walks.
DEMONSTRATION AND PER SE PIWI'IUA This interpretative matter is comp li cated by the bet [hM th ere is ~lIl orhcr type of statement that seems to be quite unl ikc IhT~ TO 7TO>..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<1 1 premises. This is no overs ight. He opens his ver y next chapter by dcdaring th;lt the primary premises of demonstration are not limited to affirl11;ltivc imm edi ate predications, but include immedi:HC l1egative predicniolls 3S well. I Thus, at the very least it is clear that Cdarcllt, the nne wholly universal negative mood in the first figure, No Bs are A, bur (ii ) all Cs are B, so (iii) no Cs :lrC A, (i)
is admitted here as an acceptable form of syllogisti c dcmo llstration. Nor shou ld this really be surp risin g from eithcr :.1 philosophical or a historical standpoint. In the first place, since the initiol, framing stage of demonstration has been represented in chapter l as ;) dirct.:t descendant of Platonic otaipF:(J"u" and th e latter characteristically proceeds by the identification of finer and finer necessary exclusion relations among kinds, it is to be expected that the products of the Aristotelian :'ldaptatioll of that
I 131
J
Explallatory Content of Demollstratiolls
method shou ld co rrespondingly include universal negati ve premises, since these (Ire what no rm ally convey such exclusion re lations. But quite apart from any consideration of the spec ifics of Aristotle's theory, it also seems quite unlikel y on general principles that a theory lac kin g the resources of negati ve predica tion wou ld ha ve mu ch to reco mmend it as a comprchen ~ sive accou nt of scie ntifi c explanation. To borrow one of Aristotle's own biologica l exa mpl es, such a theory co uld not all ow thi s as a legitimate exp lanation: (i) Snnkes are reptil es, an d
give milk, but (iii ) mammaries are for the sole purpose of hold ing
(i i) no repti les
milk , so (iv) sn akes have no mammaries {Parts of Allimals 692.<1 10- 14 )1
PLATO ON SEMANTIC FRAGMENTATION But if Aristo de thus has theo retical need to include some nega ti ve predi cat ions as legitimate demonstrative premises, he also has good reason to be trouh led by th eir presence. This is because he inheri ts from Plato an appreciation of certai n cons iderations th at seem, p rima facie at least, to in fect the ve ry idea of negative p redicatio n with conceptu al difficul ty. No~ tice first that th e method of di vision practiced in Plato's Sophist. States~ m an, and Philebus presupposes th e coherence of negative predica tion. At th e very heart of the method stands a characteristic step in which the di ~ vider comes to apprehend that a " kin d" (yi: vo~) that might have appeared to be monolithi c, or "sound" (v'Y ~'Y/ 'i'), in fac t has a "seam" (8L77'A O'ryV or G'VXII'r}v ), by which is metapho ri cally conveyed th at there is so me pai r of differentiati ng properties or cha racteris tics each of which is had by some, but not all , members of th e ki nd LInder divi sion. Howeve r, th ere is at leas t one passage in the Sophis t where Pl ato see ms to see a potent ial problem wi th the use of negation in division :' This occurs at 22. SB- C, where he has the Stranger and Theaetetus agree th at the art of "anti logic" is d ivided in to two parts, o ne of which, eristic, is described as "techni ca l" (e IJu:XIJoIJ; by which is presumably meant that it is governed by ru les or guidelines) whi le the othe r, wh ich is left narn e~ less, is chara cterized onl y by the essentially privative adverbs "pu rpose~ less ly" (&iK'r, ) and " non techni cally" (ch"i:x vws-). It is the " nameless" part of this divisio n that gets singled ou t for dep recato ry co mment by the [ 132 J
Demonstratiol1 ami Negatioll
Stranger at BIl -C4: "This must be posited ~S::l kind, since om ilCCOUIlf has indeed discerned it as a distincr thing, hut it did not receive ::I llilll1C from those who came befo re, no r is it worthy of getting one fro m LI S now." If we ca n assume th~t Plato's own thought is expressed by Thc;lerctus's un chall enged diagnosis of thi s bck of llameworthiness :It Cs - 6"True [nontechnical antilogic does not deserve i1 name j. for it is divided into parts which are too small and diverse (Knn'l:
Explanatory COltte1tt of Demonstrations
[for instance, as when] seeking co divide the class of human beings into two, [we] divide them into Greeks and barbarians . .. ignoring the fa ct that [the latter] is an indefin ite class made up of peoples who have no intercourse with each other, and speak different languages. Lumping all this non-Greek residue together, [those who try CO divide this way] think it must constitute one rea l class beca use they have a co mmon name, "ba rbarian," to attach co it. Take another exa mple. Someone might think he was dividing numbers into true classes if he cut off the number te n thousand from all others and set it apart as one class. He might go on to invent a sin gle name for whole of the rest of number, and then claim that beca use it possessed the invented co mmon name, it was in fact the other true class of number: "number other than ten thousand." Surely it would be better and closer to the real stru cture of the Form s to make a central division of number into odd and even, and of humankind into male and female.~
ARISTOTLE ON SEMANTIC FRAGMENTATION There are a nu mber of Aristotelian d iscuss ions of negative predicates where he ev id ently concu rs with Plato th at the use of such expressions raises the spectre of se mantic fragmentation . One of thes e is Aristotle's quick cri tic:t1 remark at Metaphysics A.990b14 that the Platonist's "Oneover-Many" principle unh:lppily enta ils the existence of negative forms, which is then expanded in Alexander's parap hrase of the Peri Jdeol1J as follows: "For if someone were to propose [that there cou ld be an idea of not-being (-roil J-LT] el ven lSia)), then there would be an idea of things that are ' non -homogenous' (d:vOJ-Lo)'&vwv) and 'utterly different' (7TavTTI Ota<jJepovTwv) . Such would be a letter and a man, for all of th ese are 11ot"orse." ~
It also appears that Aristotle takes an even darker view than does PlatO o n the dangers inherent in the use of negative pred icates. For there is good reason to believe that he regards this sort of se mantic fragmentation, in its most vicious fo rm , as leading int.o the "Meinongian" problem of adm itting nonexistenrs into one's ontology. This much is at least hinted at in De Juterpretatiolle 2: "Let fter ms such as 'not-ma n'] be called indefinite names (OVOJ.LCX &OptCTTOV ) because they apply to all manner of things, both existe nt ;lnd non -existent (O/ITO~ Kat J.LTJ OVTO~)". (I6 a32 -3 4 ).~ Now this clearly takes matters beyond what is found in the Sophist.
I
134 J
Demonstratio1l and Negd/ioll
Nevertheless, such unmista kable para llels between th ese Platonic and Aristoteli an passages make it practically certain that th e two writers agree that semantic fragmentatio n is at least one of th e diffi culties that must be overcome by any satisfactory account of negative predication. For even though Plato and Ari stotle both sec se mantic fragm entation ~l S ;l potential hazard inherent in the use of negative predi cates, there is no evidence th oU either of them is prepared to foll ow what well may have heen Pannenides's own drastic recommendation , that terms co nstructed out of negative particles should be banished altogether. It rath er appears that both writers recognize an important distinction between cases of negative predication that do ex hi bit semantic fragmentation and oth ers that are quite in nocent of this defect, and they both attempt to immuni ze their respective theories of predicatio n again st this donger. THE ARISTOTELIAN SOLUTI ON, THE COM PARTMENTALIZATION Of SCIENCE In order to appreci ate the nature of Ar istotle 's proposal {() ~H.: hi eve thi s immunization, it will be helpful to co nsider nrst what he perceives as di stinguishing the defective occurrences of negative predi c'ltcS. As the example given above from Al exander (8L 3- 4 ) illusrrates, Aristotle's view is that se mantic fragme ntatio n occurs specifically when some negative term , lI ot-F, is lI sed in such a way that if purportedly denotes the co mpl emen t of rhe denotation of F within some insuffi cicnri y restri cted hac~ ground fiel d. Thus, not-horse is said not to signify nn "idea" (i8i: a )- th~t is, nO[ to pick ou t a genuine property- on the ground thar the class of objects of which it is tru e (eve l)!thil/g that is not ~l horse- the complement of the class of horses within the doma in of existents of every sort) is so wide and diverse (that is, so fragmented) as to include slIch unlikely co ha bitants as men and alphabetical lencrs.- Again, Aristorle's (;md Plato's) objection to such uses, according to the prese nt interprt!t3tion, is ultimately that th e negati ve predic~[e in such contexts lac ks definite mean in g. The argu ment is th at if there are virtu.lll y no limirs 011 wlwt call satisfy th e predicate Hot-horse, th en it does not appear that anything determinate could be attribllted to a suhj ect hy appl yin g that predicate to it. The point, th en, is that Ari sto tl e does not sec semami L: Fragmentation as a prob lem attached to the use of negative terms per se, but rather as one limited to cases where sllch ex press ions are meant to signify ullderres rri cted complements. R
I US I
Explanatory Content of Demonstrations
But if this is seen as the fundamental problem with negative predicates, its most plausible solution requires no great amount of ingenuity: one has simply to make sure that underrestricted complements are not allowed to stand as signi ficata of negative terms. Indeed, there are strong indications that Aristotle finds nothing whatever wrong with the application of negative terms when the background class is sufficie ntly restricted. For exa mple, at Posterior Analytics A.S.73 b2.3 -2.4, he remarks, "the even is the not-odd within number, inasmuch as the one follows upon the other," which clearly suggests that he thinks the term not-odd does possess a determinate meaning (na mely that of the positive term even) so long as its application is understood as restricted to the field of numbers, which form the su bject-genus of arithmetic. Th is passage shows th at Aristotle has no objection to suffi ciently restricted uses of negative predicates. By cont rast, however, ascertaining his attitude toward their usc in underrest ricted contexts is a mu ch more complicated matter. On one hand , he see ms quite prepared in De illterpretatione 2. and .3 co admit what he calls "indefinite" (aopt
A
(i) Every breather is animal , and (ii ) no wall is animal, so (iii ) 110 wall is breather,
bur the first-figure (perfect) sy llogism to wl1ich that is reduced is in Celarent:
r
136 J
Demonstration a/nl Negatioll (i) No an imal is w;lll, and
B
(ii) every breather is :mimal, so (iii) no breather is wall.
With this reduction, the gist of Aristotle's complaint at byo that "the middle stands too far away" (TO 7TXiOIJ C('1TO(T'T7WCtIITCt TO /J-l-:crOl/) is thM the negative connection (between anima l and wall ) expressed by B(i) (or its contraposition) is too remote to explain why walls do not breathe. II By parity of reasoning, however, it is likely that he would make exactly the same complaint abollt the following syllogism in Barh;.lr3 containing negative predicates as opposed to negative predications,11 (i)
C
Every breather is ;mim:ll,
;'Illd
(ii ) every animal is not-wall, so (iii ) every hreather is not-willi ,
which wou ld be tantamount to declaring that the lise of undcrrcstricrcd negative predicates, such as that in C(ii) here, has no proper place in scientifically illuminating explanations." The central argument of chaprer 4 was thar when Aristotle undertakes to give an analysis of the necessity of the most illlport~lnt type of scientific premise (namely, type I per se predications) in Posterior Alla/ytics 1.4, he finds it useful to move beyond the relatively broad cncgorial divi sions given explicitly in Categories 4, and to think of each of the categories (in the way that is impli cit in the single-question method for ge nerating categories) as possessing an internal hierarchical structure of kinds and subkinds ordered by the what-is-it relation. Now we can see in addition that he exploits this same hierarchical conception in the Posterior Analytics to immunize his theory of sc ientific predication against the danger of scmantic fragmentation. This is evidenced most clearly
1
Explanatory Content of Demonstratiolls
exception of those rare occurrences (if any) in biological contexts where this term refers specifically (as in modern biology) to items on the penultimate level of division, it is generally applied by Aristotle as a correlative with the term species at any level of division whatever. Hence, the same item might be ca ll ed a species when considered as a subdivision of a high er kind, hut a genus wh en it is subjected itself to fun her divis ion. But if there is no inherent maximum degree of generality required to qualify a kind as a legitimate genus, then it might be asked how Aristotle's insiste nce that every demonstrative science must pertain to a single genus is supposed to protect his theory from the th reat of se mamic fragmentation. The very way in which this question is puc gets things the wrong way around. As it has been represented above, the defect I am calling "semantic fragment ,aion" is a so rt of indeterminacy in meaning that comes in degrees. So, for example, not-horse within the class of material objects wi ll be more determinate than its completely unrestricted appiicatjon, but less so than when it is restricted to, say, vertebrates. It thus appears that what Aristotle has in mind is a kind of th reshold past which such indeterminacy becomes intolerably problematic. As I am interpreting him, Aristotle does not first decide independently how specific a scientific genus must be and then go on to use this limi t as a safeguard against semantic fragmentation. Rather he reasons in the opposite direction by fixing the line of maximum generality allowabl e in a legitimate scientific genus as that past whi ch the app lication of negative predicates precipitates semanti c fragmentation and purponed demonstrations become far-fetched. Thus, although Aristotle has no hard and fast answer to the question of how spec ifi c a scientific genus must be, he does provide a rule for generating an answer on a case-by-case basis: it must be narrow enough that all the terms, negative and positive, employed in demonstrations conducted wi thin it have determinate meanings.
[ 138 )
Notes
Unless O(herwise specified, a ll translations herei n are m y own, although I ha ve oflen borrowed fro m the Loeb C lassical Llhrary a nd Oxford Ir:1I1sl:l( lons when they seemed impossible to improve upon.
INTRODUCTION 1.
Sec Ross (1949) and Barnes (I97.,)). Hintikkn (1972.) promises a full -length
study of AristOtelian demonstration, bur that work h<1s yet [() nppc'lr. 2.
It is not meant to sugges t on ly th
dre, this is also a book abou t the relation hetween an Aristotelian dcmonslrntive system an d its ultim ate epistemol ogica l "origins" (tha t is 10 say, s tart ing points) . J. Compa re Ferejohn (J98o). 4. This understa nding is confirmed to a large ex tellt hy Posterior AII(1{ytics 2..\ and 2..2, whi ch make the po im that provid ing [t syllogi8 tic dCll1ol1str;Hion of 3 previously known fact (thar is, a TO on) is ta ntamount to elucidating that on account of wh ich it obta ins (its TO SLon); see especially 2..1.89h3 0-3 I; 2..2..89h359035. H ere I mean to oppose not o nly the view tha t the theo ry of demonstr:nion is an attempt to fo rm alize the proper methods of sc ientific inquiry, b ut a lso the curren tly popu lar position advocated in Barnes (1969) and (19~h ) that it is offered as 3 theory of scientific pedagogy that sets o m the mosr effect ive mea ns hy which a fini shed science can be imparted to stude nts. For criti cisms of this latter positi on, d. chap ter x, note 4. 5. According [0 this complex pattern, the term exhihits a peculiar three-wa y
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Notes to Pages 4-18 ambiguity, on some occasions denoting the knowing faculty (SuvaMLI») of the sou l, on others the occurrent condition or state a soul is in when it knows, and on yet others the items of information (pieces o r parts of knowledge) that serve as the objects or products upon which the knowing faculty or state of knowledge is em· played or directed. For a discussion of how this multiple equivociry of E.7rLcrrill.tT/ is involved in Plato's views concerning the unity of the virtues in the Socratic dialogues, scc Ferciohn (1984). 6. Th is genera l interpretation of the structure of Aristotelian demonstration was annou nced programmatically in Ferejohn (1982), parr of which chapter I below rehearses. In fa ct, the present work as a whole is an attempt to redeem promises made in note 27 of that article. 7. Because I maintain that the theory of demonstration is essentially and impo rtantly based on Aristotle's syllogisti c, I do nor share the view of so me recent writers (mos t notably, Barnes (1981) and Smith ([982)) that cenain (bur not all) parts of the Posterior Allalytics were composed prior to Arisrorle's development of the full sy llogistic theory in the Prior Analytics. Besides having a genera l suspicion tha t the construccion of such patchwork interpretations withom the benefit of non doctrinal , or externa l evidence is excessively speculative, J see no compel· ling reason to reso rt to it in the present case until it is shown that there are insurmountable obstacles to understanding demonstration in the way Aristotle himself characte rizes it, as a kind of syllogism (Prior Ana/ytics 1.4. 2.5b 26 - 30, Posterior Alw/yhcs 7Ib7).
CHAPTER {, DEMONSTRATION, DIVISION, AND THE SYLLOGISM I. One feature of the [,osterior Allalytics often pointed to by its detractors is that Chapters 2 and 10 of Book I seem to go over much the sa me ground, making it look as if Aristotle or his ed itors simply threw together a mass of material on rhe same subject without much concern for o rderly exposition. On the view I am proposing, in Posterior Allafytics 1.2., and indecd throughout the first three chapters of the work, Aristotle is concerned with developing a set of epistemological conditions he bel ieves any theory of justificatio n (i.e., lbroS£[~t~ in the non· technica l sense) must meet, whereas in Posterior Altalytics 1.10 he is involved in presenting a specific theory he has designed to meet these requi rements. Thi s, of cou rse, is not to deny that he co uld have that theory in mind in the earlier chapter, but only that he is not yet prepared at that point to expound it. 2.. Smith (1986 ) and chapter 6 of Irwin (1988) conta in different accounts of how Aristotle argues in Posterior Allalytics (.3 agai nst various nonfoundation al ist theories of justi ficati on; Smith also offers some interesting conjectures about who might actually have advocated such views. 3. Ea rlier in this century, this con troversy w:as intertwi ned with a historical debate over the correct chronol ogical ordering of the two Analyttcs. Solmsen (1929) argues on textual grounds fo r reversing the traditional ordering of these
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Notes to Page 19 works re(]ected in their post-Aristotelian titles . (Incidentally, these arguments are recalled and defended in modified form in Barnes [198 I j). Believing that the mature theory of the syllogism was not yet devised when the Posterior Analytics was written , Solmsen is quite naturally inclined towards :lI1tisyllogisricism, although J find very little resemblance between his views and Barnes's "scientitic pedagogy" imerpretation (on which, see Introduction, note 4 and chapter I , note 4). On the other side, Ross (1949) contains deta il ed replies to Solmscn's textl1al argl1ments (see pages 7-22), and also re(]ects a commitment {() strict syllogistici sm in its systematic con(]ation of "primary premises" (7TpWTO,J 7TpOT(hreL~ ) and "first principles" (apxai) in the Posterior Allalytics. For reasons that will become clear later, there may not in fact be any perfect examples of strict syllogisticism in more recent work on the Posterior Allalytics, though Hintikka (1972) is a reasonable approximation. If there ,ue no actual examples, then the position outlined here may be thought of merely as representing a tendency (which Hintikka undoubtedly does display) to give syllogistic interpretations of Aristotelian a.PXai whenever poss ible. Some recent examples of antisyllogisticism are Barnes (1969) and (1981) , and Smith (1982). 4. Since my aim here is to provide a positive account of Aristotle's th eo ry of demonstration, r shall not be conce rned to reheatse all my reasons for rejecting these two opposing positions. The fo llowing section does raise a nl1lnher of problems with Hintikb's account, but those remarks are intended mostly to highlight certain exegetical problems which are subsequently dealt with more adequately within the two-stage interpretation advocated here. I regard
I
Notes to Pages 19-21
5. See Sophist 2.IBff. and Statesman 2. 5Bff. 6. See Chern iss (1944 ). 7. Cherniss (J9 44 ) maintains (54-82.) that the chief intended target of Aristotle's attacks on Staipeav; is Plato's successo r, Speusippus, who evidently did offer it as a self-s ufficient method of proving rhe essence of so me subject (an aim that is underm ined in Posterior Aflalytics :z.. 3 - 10), and not Plato himself, who seemed to rega td it morc as a mnemonic devi ce for apprehending relations among Forms (Sophist 2.53C-E). B. Aristotle also complains in Posterior Analytics 2.5 that there is nothing in the method il self 10 ensure that the divisi ons it generates will all be natural and essential. AristOtle's arrempt to avoid this so rt of deficiency within his own system will be taken lip at some length in Part 2, below. 9. Essentiall y the same point is made in Posterior A1talytics 2.. 5 at 9 I b3 3 -92.a 5. 10. To this Aristotle coul d have added that such inferences cannot even be syllogisms (let alone demon st rative syl logisms) because they also violate the stricture laid down both at Prior Altalytics 1. 1.24al6 and Posterior Analytics 1.2..72.a9 that sy ll ogistic premises always involve one term being predicated of one other term. For (2), (3), (5) , and (6) are all statements in which the disjunction of nvo terms is predica ted of some third term. In cidenta lly, this sa me observation will be seen in chapter 5 to provide a significant reason for rejecting Barnes's proposa l to imerpret an important subclass of Ari stocie's demonstrative premises (namely, th e subtype of per se predications di scussed at Posterior Ana/yties 1.4.73a35-b4) as ha ving disj unctive predicates. I J. In the present im erprerati on, th is concessio n is slightly understated: the full import of the sentence is better co nveyed by the obviously pa rallel ea rl ier remark at 96bT 5. The potential for confusion on this point is undoubtedly magnifie d by the close paron ymous relat ion between XPT! and xpiJrrtJ.l.or;. 12. It is true that the genera l top ic original ly introduced at the outset of Prior Analytics I.l7 and pu rsued throughout Chapters 2.7 and 2.B, how to acquire syllogistic premises generall y, is not obviously concerned with demonstrative premises. However, beginning in Chapter 30 Aristotle makes it clea r th at the scope of his discussion includes the issue of finding suitab le prem ises for demo nstratio n. Hence, at 4634 he cla ims that the general procedure for collecting syllogistic premises set out in previous cha pters is appl icable to every "art" (T€XVlJ ) and "study" (J,ui8TjJ.l.0), and just a few lines later (at aB) he cements the point by claiming that the recommended method is ap propriate in settin gs where one is interested in establishing truth as opposed to mere plausibility, which according to Topics 1. 1. T 00a27 is precisely what di stinguishes demonstra tive from dia lecti ca l reasoning. 13. There is no real question th at the notion of expl anatoriness operati ve in Posterior Analytics T.2 is an objective one: the causativity condition (f) is metaphysica l on irs face, and al though Aristotle docs officia ll y recognize wholly subjective senses of " bener known than" an d (ep istemologica l) " prior ity," he is careful in th(" r r~s ent context 10 exclude these at 7' bp by explicitly maki ng the so rt
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Notes to Pages 2/ -2S of priority he has in mind n consequence of c:ms:ltiviry (w hich , :tgain , is pl a inly metaphy sical). In fa ct, bH -7 2.a5 dis
I.IS·79 a 3.l- b S· 2.2.. It also follow s t hat th e p ossibility of finite d emonstr;nioll (that is, (Inl' co ntaining a fi nite numoer of syllogistic inferences) req uires t hat there be at most a fin ite number of middle terms between the suhject :"Ind preJi C:lte of the demonstrated sta tement. Aristotle unde rtakes to estab lish t his pos!'ib ility as ;1 gener:1 1 theorem (fo r any stn tement wh atever) in the su-ca lled compactness proof of I'o sterior Ana{ytics I. t 9-2. .1 (o n which see nlso Le;lr 119HO]). 2.3. T h ere is some myste ry
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Notes to Pages 29 - 36 2.8. More detail on th e nature a nd demonstrative functio n of such terms will be given in chapter 6. 2.9. Though my gene ral view is that it is wro ng to identify whrlt Aristotle refers to as the (epistemologica l) "starring points" (apxo:i) of a demonstrative science with the ultimare premises of his sy llogistic demonstrations, a comp arison of this occurrence with 4 3b l leaves li ttle doubt that he re he is thinki ng narrowly of syllogistic sta rti ng points (i.e., imm ediate premiscs). 30. The va riation on this procedure given in this passage, and Aristotle's suggestion th at there mi ght be two kinds of proof for universa l negatives, are in co nsequentia l effects of the fact that proposition s of this form are subject to co ntra position of subject and pred ica te. hi Aristotle's system, "No A is C" and "No C is A" arc two distin ct (albeit equ ivalent) propositions requiring distinct (a lbeit equival ent) sy ll ogistic proofs . .~ 1. Unders tandi ng " that whose ex istence is assumed" as a subject-genus is justified by th e close parallel with 76 br 3 - 14. 32.· Hintikka (1972.), 63· n· 1bid .,62.. 34. Ibid. 35. Ibid. (emphasis mine). 36. See Metaphysics 7.1 7. 104Ial2. -20. 31. In chapter 2. 1shall a rgue that Aristotle's version of di vis ion, unlike Plato's, is also to be distin gu ished from the activity of co nceptual analysis because he does nor view it as a method for discovering definitions. 38. Given that the genera l method is mean t to a pply to the mathematical sciences, whose objects are not concrete, it is ha rdly likely that Aristotle wou ld insist that rhe confrontation be perceptual. What is essential is that the divider have some epistemo logica l grasp of his sub jects . 39. It is poss ibl e that this poi nt is grounded fu rth er in Aristotle 's view that one cannot kn ow "w hat so met hing is" (Ti £cT"n- that is, have an account of its essen ce- Posterior Allalytics 2.IO,93b29) without knowing "that it is" (el 60"n ). See Posterior A110iytics 1.1.7131.6-2.9, 2..2..90al -24, 2.8.93a I 4 -29, 2.JO·9 .~b2.9- .H· 40. In fac t, there is some evidence, though it is hardly conclusive, that Aris·
totl e's own classifications of animals in his Historia Animalium presu ppose a system of types of a nimal -differentia e, such as means of locomotion, perception , and rep roduction, whi ch then guides the empiri ca l study of the specific differentiae wi thin these types that are exhibited by various 'kinds of a ni mals. 4 I . Evidently, neither Pl ato nor Aristotle requi res that these divisions be dichotomous. III fact, Chern iss (1944 ) suggests that a large part of Aristotle's dissatisfaction with Speusippus's bta nd of 6taipe o"l ~ stems from the fact that it permits only dichotomou s di visions. 42. The problem of fitting the nonlogical co mmo n axioms, such as the a lternation of proportion als (7 4aJ 7- 25), or the preservation of equality through su b[ 144 [
Notes to Pages 36-40 traction and addition (76;qo-b2), into a syllogistic model of proof is rCOllly one aspect of the general problem of how math elll :ltica l proof and syllogistic demon stration are related. 43. Perhaps the most obvious (and mOSI emharrassing) difficulties for sttkt syll ogisticism involve these "common axioms" (KOLII(r (ygt
CHAPTER 2, DEMONSTRATION AND DEFINITION 1. Compare also Prior Allalylics 2.21 .67<1.) - 27. 2. Solmsen (1929). But d. Ross (1949) and chapter! above.
3· Posterior Analytics 76<132-37; bl-23; 9.;l'29- .n· 4. See especially Topics 6, passim . Aristotle is quite ;lware that si nce a p.1r.l digmaric definition involves reference to the defined species, the r,enIlS, and the differentia, it gives the appearance of containing three rather than two terms, and hence of not being simple enough to inst:llHi:ltc the elementary form of the universa l affirmative proposition of Prior AII,,/ytics ].1.2. That this is merely an appearance is the very substance of the "unilY of definition" thesis Olt De Illterpretatione 5.I739 - 15, Posterior Allalytics 2.6.92;1 .W-H, ;1nd Metdphysics 7.12.103 7b8- 3 8.
5. I am not persuaded by Himikka's (1972) arrempt TO discount this ;lIlJ a parallel passage (Pos terior Analytics 1.2.72:l2.0-21) by claiming that both emp loy elva, in its "predicative" rather than its "existential" role (67). His reasons for this are not obvious, but they may be based on the quasi -linguistic analysis of ell/at and its cognates found in Kahn ( 1973). AccorJing to [hat an;llysis, there is no "independent" use of elVat in early Greek, ;"md::lll sentences of the form "X is" should be understood as equ iva lent to predicmive statements of the form "X is something or other," where this latter means that there is at least OllC prope rty had by X (page I 5, note 8). The problem I find with this ::Il1alysis is that it seems
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Notes to Pages 40-44 to con fuse the obvious truth that [or anything to exist it must have at least one property with the controversial proposal that the statement that X exists is logica ll y equivalent to (perhaps even synonymous with) the statement that X has at least one property. This same objection is developed independently in Roberts (1982).
)
1.
("
i; (
6. The inference may not be imm ediate. Jacobs (1979) contains a plausible argument that the existentia l import of genuine premises is thought by Aristotle to follow from a more fundamental requirement that they always either affirm "something of someth ing" (Ti KaTa TWOS') or deny "something to something" (Tl ci1ro nvos-). whe re the use of the indefinite pronouns imports presuppositions of existence. 7. Compa re Posterior !\lIalylics 2.3 - JO. 8. Hintikka (1972.) correctly observes that the term "fLecroS- is some times also used to denote these statements of immed iate conneelion berween terms, but that in its normal usage (as for instance, at Posterior A1talytics r.2. 72.a8) it picks out propositions that arc "immed iate" in the sense that they are underived. 9· Barnes (1975), 94-95· TO. Moreover, for reasons to be discussed shortly, this problem cannot be overcome by simply add in g a statemenr of general ex istence ro Barnes's analysis, so that it reads, If anything is a pair, then a knows that it is even, and there are pairs. 11 . These will certainly include all past and present men, though there may be some question a bout whether Aristotle's pU7..zle in De lnterpretalione 9 regarding singula r statements about the future rules Ollt the possibility that (2) cou ld also involve reference to alt future men. t 2.. Notice th at this is not to say that under this interpretation sentence (2.) is synonymous with a conjunction of singula r sentences. In fact, another way to characterize the transparency feature discussed above is to say that one could on this in terpretati on know that all of the singular propositions exp ressed by (2) were true without having any idea of which propositions those were. 13. Even singu lar statements like "a is F" are thought to introduce existential import only insofar as rhey entail starements of genera l existence (by Existential Genera1i7.ation). Inciden tally, I can find no evidence whatever that Aristvtle has any such theoretical notion of general existence, though he of course uses sentences that we might analyze as expressi ng it. For this reason (among others) I cannot agree with the proposa l in Hintikka ( 1972) to inrerpret the existence asSllmpti ons of Aristotelian science (e.g. at Posterior Altalytics 76332 -7. 76bI - 23, 93b29-33) as expressible by statements of the form "There are fs" (6 2.-63 ). In chapter 5 I sha ll argue that Aris to tl e even rega rds the ex istentia l import of particular statements, such as "Some numbers are even," as singular in nature and as stemming likewise from the referential funct ion of their grammatical subjects. 14 · On this di sti nction see Kneale (1936) and Moore (1936) . I 5. This of course is not to deny that the truth-values of the sentences are per(ectly correlated. Both sentences will be true in all (and only ) those worlds where
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Notes to Pages 44-49 there are men (i.e., some referents of "Every man"), and all of those are also animals. 16. This may be equivalent, though it certainly would not be recognizable to Aristotle as such, to a Fregean -style statement expressillg a certain con:-;rraint on the possibilities of predicate-sa tisfaction (or kind-membership ) among all (actual or possible) individuals within some domain of discourse: If anything is a man, then (necessarily) it is an animal. 17. Tredennick (1938 ) translates i§t'> here as "facnlty," which is normally reserved fot the Greek SVVCl:p.,t,\. However, in view of the fact that Aristotle goes on at 99b26-34 to argue that this preexistent condition must be some sort of SvvaILL!:;, (that is, an episte mic proclivity, as opposed to an occurrent cognitive state), it is better to understand him as dcliberntc1y employing the wider term f.§t'\ at hI R in a sense that includes, but is not limited to, SlIVO:/.LfW;. 18. On this see Kahn (T981). 19. It is plausible that this use of AQI)OO:I)W is meant to pick up Pbto's use of alJCllJ,.tlJ,.vijuKw at MellO 85E and R6B . 20. The deployment of the potentiality versus actuality distinction to steer between the horns of an apparent dilem1ll:l is of course vintage Aristotle (d., for example, his definition of KtVrjm'\ in Physics .l. I , and his trcatments of growth and perception in De Anima 2.4 and 5 respectively ), which t is regu larly contrasted in later works, does not OCWf at n!l in rhis chnptcr. 21. This would have the unfortunate consequence th:lt in some sense any animal, qua sentient, has the capacity to apprehend slIch principles. 2.2. Compare I00<114-bT7. The interdependence between Aristotle's metaphysics and epistemology on this point will he discl1ssed shortly. 23· The role of intuition in E1TClywy1j is discllssed in derail in Kahn (1 9R 1), Kosman (1973), and Lesher (1973). 24. For an interesting and comprehensive study o( this more elev:lted cOllcep tion of atO'e",cn'\, see Modrak (1987)' 25· Notice that this intensional interpretation of the results of Platonic Divi sion is not affected by the bct that the ellidel1ce the method employs seems to be constituted by more or less empirical observations that certain c\ilsses of individu al s are subdivided into "natural" subkinds (but it[ the S<1me time, my LIse of the adjective natural here cert(linly bears much metaphysica l weight). 26. Aristotle's immanent rea lism and its effect on his epistemology will he discussed at length later in this chapter. 27· Burnyeat (1970), Fine (1979), and Neha1llns ( 19H .~ ) . 28 . There is a close Aristotelian parallel to this Platonic notion of :In inrerreJationa I logos in Metaphysics Z I 2, where it is asserted th;n an adequate definition, by containing the final differentia of the deftniendum, can be thought to make implicit reference to all the differentiae of which that i,~ a specine;ltion. Of course,
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Notes to Pages 49-67 Aristotle never says that such a logos itself conveys knowledge of the highest sort. 29. Burnyeat (1981). 30. See chapter I. 3 I. See chapter 2, note 5 above. 32. Posterior Analytics 2.3.90bH. 33. Actually, this question is first raised and treated dialectically in Chapter 3 at 90b.z.8 - 9Ia12., but Aristotle does not begin to develop his own answer to it until the beginning of Chapter 4. 34· Owen (r9 61 ). 35. The argument is actually a bit more complicated than I have represented it. Aristotle argues that an "immediate" statement can sometimes occur as a syllogistic concl usion, but only if both premises of the syllogism are biconditional, or, as he puts ir, they can both be converted (aJl1"LI'TTpeljlew), in which case there is a petitio principii, and hence no genuine demonstration (9 Ia2 s-b ro). 36. The attenuation requires a play on the terms 8etKIJVJ,LL (" to show or display") and d:7ro8l::iKVVJ.LL (" to demonstrate or prove"), so that a "definition" can be said to be "demonstrated" in the sense that the TL E(]"7'L it expresses is "revealed" or "displayed" by the arrangement of the premises of a demonstrative syllogism. 37. This view, which originated in Lukasiewicz (1957), is propounded in Mansion (1976), mode rated somewhat in Mansion (I981 ), and criticized m Chapter 12 of Sorabii (1980). 38. Of cou rse, the restriction to substantia l, or natural, kinds here is crucial, si nce Aristotle certainly does not think one could gain scientific knowledge of an individual by studying necessary relations among its nonessential properties (Posterior Analytics 1.6.75318-2.7). This is not to say that he believes knowledge of systematic relations among accidents (i.e., nonsubstances) is impossib le (on which, see his discussion of the possibility of sciences of nonsubstantial accidents in Metaphysics r 4), but only that the objects of such knowledge would not be the subjects of those accidents. 39. Unfortunately, the significance of this is obscured even from Aristotle him self in the Organon by the fact that he regularly co ll apses these two very different types of metaphysical connection into a single relation (the said·of relation in the Categories, or type 1 per se belonging in Posterior Analytics). On the other hand, the Metaphysics distinguishes sharp ly between the two relations and focuses especially on the relation between individual and proximate kind.
CHAPTER ), THE CHARACTER OF DEMONSTRATIVE PREMISES I mean here to contrast general epistemology (that is, the phi losophical of the general concepts of knowledge, belief, justification, and so on ) sllch ~s what occurs in the Theaetetus, with special investigations into the nature of specific forms of knowledge and justification. Examples of special epistcmolI.
~nalysis
[ 148 J
Notes to Pages 67 -72 ogy are quire co mmon in Aristotle's works. For insta nce, the Topics is an investigation of dialectical knowledge, the Nicomacbeall Ethics :lI1alyzes the nature of practical know ledge, and (as suggested in my introdu ction ) the I'osterior AlloIytics presents a theory of dem01lStrative (or scientific) knowledge. 2.. White (1972.), 60, Panig (1969). 3. I argue in Fereiohn (1976) that Aristotle's cu ri ous views about the validity of mixed modal syllogisms in the Prior Altolytics (c.g. , at 30:12. 1-2.4 and .W b710) cannot be explained satisfactorily by the suggestion thnt hc is in sensitive to subtle differences in the scope of modal operators. The fact;s that there :.lre other places (c.g., De l11terp,.etatiolle 9.19'12.9 -.U) where he shows himself (l) he quitc sensitive to such mane rs. Mo reover, I argue rhere is a high degree of systema ticiry in Arisrotle's results, which is not accounted for hy the hypothesis that they rest on co nfusion. 4· Hintikka (1957)· 5. This last inference presents some prahl ems in interpretation. On its face, the Aristotelian sentence at 73a2.4, since it conta ins a plural form, t:~ Ql/cryKU'iwv, t"O denote the premises of a demonstration, seems to assert that the necessity of the conclusion of a demonstration requires the necessity of bo th premises. However, Alexander of Aphrodisias tell s us th:lt the modal pri nciple th:a requires th is (namely, the so-ca lled peiorem rule that the concl usion of a modal syllogism can be no stronger than its weakest premise) was developed by Aristotle's successor, Theophrastus. Moreover, it is violated by Aristotle himself at Prior Allofytics 30a15. Hence, either Aristotle has chosen an unfortl1nate W:ly of expressing:J. result that is consistent with his logical theory (ni.1 111 ely tha t the necessity of the co nclusion requires the necessity of at le:lst one premise), or he is here importing some extra logical (perhaps epistemological) re:.lson th,It hath premises of :l demonstrative syllogism must be necessary. Evidence for the latter hypothesis is to be found at Posterior Analytics 74b13ff. 6. Even though Aristotle's discussion in Posterior Allolytics 1.4 - 10 appears to restrict the immediate premises of demonstration only to affirm:ltive stat emen ts, he makes it quite clear in Chapler 15 that his fu ll theory also allows negative premises expressing immediate exclusion relations (79 a.13- _16). The place of such negative predications in the theory of demonstration will he the principal topic of chapter 7. 7. In fact, Aristotle attaches th ese sllhconditiolls to the :.lttrihmes ascribed by such sentences. I represent them as conditions 011 th e relation between subject and predicate for convenience of exposition, since his remarks arc always meant to apply to an atrri bute as apphed to a certa;" slIbjed. 8. Topics I 0 3b8, 109n1o, 12.5<\6, 149b12, 16):1.12. 9. It has been suggested by some writers, e.g. Code (1986) and Lennox (1987 ), that since as a general rule. rhe expression "qua" en) is used hy Aristotle as an imen$ional idiom, the "qua itself" C{"Illdition on c:nholic predications therefore pertains to an intensional rel
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1
Notes to Pages 72 -75
the predicate applies to a certain class of things when they are conceived of or described as falling under the subject term. On such a view, Aristotle might allow that there cou ld be two sciences that study exactly the same genus of things but are nonetheless distinct sciences because one studies them qua Fs and the other stud ies them qua Gs. I certainly do not deny there are many occurrences of 11 in Aristotle that do carry this inten sional mean ing (as, for instance, in his "definition" of KillTjCTt'i at Physics 3.1); and there are dear p recedents for th is use in Plato (e.g., in Reptfblic 1 and 4). What I do deny is that the expression is always used this wa y, and that it is so used in Posterior Analytics 1.4 in particular. For th e intensional reading is at odds with the fact that the rest Aristotle proposes for the cond iti on is given there in exrensional terms: he speaks of the "first subject" (going downward) to possess the attribute, or the "las t differentia" (going upward), whose remova l also removes the attribute, and these ordinals are evidently connected to some sequence of inclusion relations. A key passage on this issue is 74a38- b4 . There Aristotle co ntorts himself so far as ro make bronze a peculiar SO rt of differentia of isosceles triangle just so that he ca n extend the inclusion sequence, plane figure --+ triangle --+ isosceles triangle, one more step to bronze isosceles triangle in order to apply this extensional test. (Hence, I think this passage should be contrasted with Metaphysics Z.8.Io33a2.4-bS, where virtually the same example is emp loyed, but the qua must be taken intensionally.) 10. It is rema rkable that despite the relative clarity of these pronouncements, there are some who would still den y that Aristotle is committed to th e view that all per se predications are necessary. 1 am referring here to views expressed in White (1972.) and Hintikka (1957). I t. The passage also introduces a use of the expression "per accidens" (Karer CTlJI.J..{3e!3r/Ko'i) corresponding to each of the four uses of per se presented and discussed. These uses, which Aristotle says at 73b4,5 and 11 ,1 2. are strictly complementary to the correspondi ng uses of per se, can be igno red unti l chapter 6.
CHAPTER 4, TYPE I PER SE PREDICATION I. This shou ld not be confused with the historica l thesis that the Categories represents a relatively immature stage of Aristotle's thought, whereas the Analytics were written during a later stage of hi s development. My claim is simp ly that, for whatever reason, the Analytics present a more compli ca ted and sophi sticated semantical system than what is found in the Categories. I take this to be compatible both with the "juvenalia" view of the Categories just descri bed, and with what may be called the " primer" view of that work, acco rdin g to which it is seen as a sort of propadeutic, written in full awareness of Aristotle's more subtle views, which he intended to introduce new students to philosophy. As these remarks suggest, I am assu ming here that at least rh e first five chapters of the Categories are Aristo tle's own work, though my conten tions here would not be materially affected if it should turn out that it is an "Aristotelia n" treatise by another hand.
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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 "
Notes to Pages 80- 81 to separate these two alternative views, since Aristotle observes no clear distinction between object language and meta language. 11. Ackri ll (1963 ). 12.. See Owen (1965a). 13. Especially 2al 1-14, 2a2.7-b6, and 3a7-2114. Here again we see Aristotle conflating class membe rship and class inclusion; they appear in the Categories as undifferentiated subtypes of the said-of reo la tion. On this, see Frede (1978). 15. Obviously, the overall intelligibility of the tetrachoromy depends in large part on the proposition that there is a real distinction between Aristotelian substances (entit ies of type [iJ and [iil) and the types of entities that fall into the third and fourth divisions. Whi le this might seem so obvious from a modern point of view th
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Notes fo rages 8 J - 90 19. In particular, there a ppears no way of telling from what he says in the Orgalloll whether he thinks of the higher kinds within his caregorialnetwork in a purely extensional way (as classes of primary suhstances or nonsuhsta nrial particulars), or whether he thinks of them rather as some sort of illlc"siolls (what modern philosophi ca l logicians call " properties") , or whether he th in ks of them in some other way altogether different from both of these. 2.0. Compare Furth (1988), 14. 2. 1. Compa re Owen (196 5b) fo r an intriguing ex planation of how L1lt: " biha rcared" semanti cs of the Categories represents at least on c Aristotelian a ttempt to construct a th eory of predi ca tion immune from defects ch::lrged against Platonic predication in the "Thi rd Man argum ent. " 2.2.. Aristotle did not give up entirely on the project of giving some fu rther explication of inherence relations. I shall argue in chapter Six that th e type 4 per se predi cations discussed at Posterior Alla/ytics IA. 73 b 10- a6, which would have to be classified as exp ress ing the inherence relation in the Categories, are not thought by Aristotle to be fortuitou s. 23. Ackrill (196,), 79-80. 2.4· Co mpare Grene (1963), 58. 25. Notice that this single question is also th e first in the list of most basic questions posed in the mul tiple-questio n method. I shall argue presently that its presence in both methods ha s a n im pact on Ari stotle's choice of term ino logy in Posterior Anoiytics 1. 4. 26. As in my accollnt of the multiple-qu estion medlOd , I alll here preseming an English versi on of the procedure. As before, in Greek a cor rect a nswer co uld very naturally take th e fo rm of a one· or two-word sentence fragment. 2. 7. Th e detail s of this "compa ctness" proof
Lear ( 1980). 2.8. Th is asso rtmenr ill ustrates once Illore that the requiremen ts for member· ship in the initial collection of the single-qllestion method a rc indeed qu ite liheral . It is not even limited to particu lars, as is shown hy the indus ion of items (iii ) and (vi ). In fact each of the di visions in dlC tetrachofO lllY of Ca tegories 2. is represented here. 29. I am not claiming that these are the very chains Ari stotle would havc generated if he had perfo rmed step 2 of the single-questioll method Oil items (i )-(vi), or even that they a rc very close. Th ese ex amples nrc offered merel y to show the formal operation of the method, and not to reOe'er an y suhsta ntive Ari s£Otei ian assumptions about natura l kinds. 30. On the oth er hand, these assumpti ons entail noth ing :l hout the numher of such hi erarchi es required to categorize " everything there is" (7faJl'fu TCr OVTU), and this may be why Aristotle evidently feels free to experiment with his list of categories. } 1. Ackrill (t9 63), 80. ,32.. Ibi d. 33. Ackrill's account, while appealing, does not expla in why this ,alleged shift
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Notes to Pages 91-92 in Aris(Qrle's ways of thinking of the catego ri es should be so sudden as to occur within a mere five lines of text. Apparently recognizing this difficulty, Ackrill closes his brief discussion of Topics 1.9 in the modesttones of a recommendation that the chapter is in need of further stu dy. incidentally, it may be not on ly Aristotle's terminologica l choices but a lso his substantive views that are affected by hi s vaci llating attitude towa rd the construe· tion of the ca tegories. in particular, the retra cho(Qmy of Categories 2., wh ich we saw a bove to depend crucially on the mtelligi bil ity of the substance versus non· substance distinction, is a doctrine that co uld very likely occur to one thinki ng in terms of the multjple·question method, since that method presupposes the ability to pick all[ substance from nonsubstan ces. On the other hand, it would not be so obviolls jf one has in mind the single·question method, to which the substance versus non ·substance di sti nction is nOt essential. 34. More precisely, th e suggestion is that relati on E includes, but eXlends be· yond, the earlier relation. My reason for resisting a simple identification of the two rela ti ons is based on the presence in the Posterior Allalytics of what might be termed "constru ctive" definitions, such as ''Triangle =d f a plane fi gure enclosed by three st ra ight lines," wh ich were apparently in vogue among the p roto~ Euciidean geometries with which Aristotle was p robably conversant. Aristotle may be a llu d~ ing to something like this at 73a 35 -}8 when he says th at line is in the what· i s~i t of triangle, for there is no reason to think that he would be committed in the Categories to holding that line is said of triangle. I thank Mohan Matthen for first pointing out to me the in congruen ce between Aristotle's examples of type 1 per Sf predication at Posterior Analytics 1.4, and a strict genus and differentia conception of definition.
C HAPTER 5, TYPE 2 PER SE PREDI CATION 1. This translarion is from Ackrill (1963)' In an earlier work, Fcrejo hn (1 981 ), I took the presence of both AeyeTul a nd KUT7IYOPStTCU in this pa ssage to indicate ('hat Aristotle is announcing a more complicated principle, which I labeled "vi· ca rio us predication," in volving both the said·of relation and the generi c pred ica. tion rclation. I thank Montgomery Furth and Michael Frede for convincing me this is just an illusion created by the fact that Aristotl e often uses the two verbs interchangeably. 2.. See chapter 5, note 6 below. 3- Notice that on the suggestion in cha pter 4 that relation E of the Posterior Analytics is the descendant of the sai d ~of rela tion in the Categories, it becomes very easy (Q see why Aristo tle assigns the properties of transitivity and participa· tioll to the ancesto r relation. For it should be immedi ately obvious that the tela· tiOIl that orders term s into the hie rarchical Structures generated by the single· queSTion method descrihed in chapter 4 is tran sitive. And if it is understood th at a defini ti on is a Aoyor; signi fying the what~is·it, it fo llows directly from transitivity
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Notes to Pages 93 -97 that the definition of any predicate th:lt belongs in the what-is-it of given suhject will itself belong-in fact, belong pcr sc-to that subject. This las t is not to impl y that the other so rt of type 1 per se predications (those:: that correspond to the constructive d efinition s menri o ned in cha pter 4, note 34 ) satisfy either of these condi tions. 4. On thi s, see cha pter I above. 5. PriorAllalytics 21a26, 49b5, Top ics I Olh39-102:1I, 1.',oa'l9, 14 2.112.- 6, 147bJ 3- 15, 1 4 9 al -2 ,b.~-5· 6. This is fo llowed immediately (at 1 a2.8- 34) by the ohse rvation thnt there a re some special cases, e.g., that of wh iteness (TO Af:tn
Categories. 8. Ack rill (196)), 85 - 87. 9. Metaph ysics 7.1 2. I03 7 b8 - I038aJ5 . 10 . Dancy (1975) and Kung (r9 77). I I. Thi s is reinforced by the usual placement of the ToPics:1s earli er th;'ln Categories, for that wou ld make it very easy to underSf
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Notes to Pages 99-105 J 4. This, incidentally, is the view shared by Arisrotle's ancient commentaro rs: see J. Philoponus, [n Analytica Posteriora, f.I6 (Brandis 204a48 -b3), and Them istius, In Altalytica Posteriora, f.3 (Brandis 2.04a39 - 40). 15. It is adm ittedly peculiar to find Aristotle using the nominal expression allTlKeiILev{X in an adverb ial sense without the addition of a preposition. But however strange this may seem, the occurrence of this expression opposite the famil iar (.brA.w, in an '11 . . . '11 ... construction leaves little doubt that he is doing just that. The text may suffer from some defect in the manuscript tradition (perhaps the omission of a KaTO ), but if so th e defect is now hidden, since no ne of the important manu scripts va ry from this reading. 16. This vi ew is co rroborated by Philoponus, f.x6b (Brand is 204b1 )-1 8). 17. The n'otion of absolute necessity here is apparently unconnected with that discussed in chapter 2. of Patzig (1969). 18. But cf. the "essentializing addendum to Categories 5" in Furth (1988) and chapter 4, note x6 above on that subject. 19. The central argument of chapter 7 below is that both writers perceive and react to what they see as serious co nceptua l difficulties with the employment of negative predicates in insufficiently restricted contexts, as would be required, for instance, to state that everything whatever (including living things) is either odd or not odd. 20. These will of cou rse include differentiae, but may not be limited to them. Aristotle docs not seem sure about what to do with pairs such as (male, female ), on which see Metaphysics 10.9.Ios8a2.9 -b26. 21. It might be objected here th at on thi s interpretation the argumen t doesn't really establish the necessity of opposites, since STRONG MLEM itsel f implies that any opposite is possessed necessarily by its subjects. While this objection has force , it should no t be thought to convict Aristotle (on this interpretation) of outfight circularity. Rather, the argument should be understood as makin g epistemological headway oy showing how the necessity implicit in what might be termed the "essenrialistic bifurcation" of a division by opposites distributes to the connections between those attributes taken separately and their respective subjects. Hence, the argument should not be viewed as a demonstration of the necess ity of type ;z. per se pred ica ti ons on the basis of their non modal properti es, but rather as proceeding from the assumption that a certa in genus contains a necessa ry partition to the concl usion that each of its members necessaril y possesses o ne or the other of the pair of opposites that jointly effect that partition. 2.2. Barnes ( 197S) , 115. 23. Barnes doesn't actually distinguish the stronger and weaker interpretations of MLEM , but he presumably prefers the weaker. 24· Barnes (1975), 11 5. Aristotle's aim in the Prior Analytics 1. ) 1 passages cited (46bJ -I9, 30-35) is essentially polemica l and anti-Platon ic. His point, which is reiterated at Pos terior Analytics 2.5.9 1b 35 - 92.3 5. is that the propo nent of the method of divis ion errs in supposing that he can move by logical means
ra
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Notes to rages 106-107 directly from, say, (i) All men are either mortal o r im mo rta l, to (ii) All men are mortal. The mi stake here, accord ing to Aristot le, li es in the f;'lct that the choke of mortality ove r im morta lity (or neith er) as a d istin guishing fe;lture of Illen is left unsupported, so th at this reasonin g simp ly assu mes th e truth of (ii) and therefo re begs the question (46b l 2.. 18, 33), whereas (ii ) C:l n and sho uld he proved by syllogistic means (46a .16 - 39 ). Whar Aristo tl e docs /lot say, a nd w hoa Ba rnes tri es LO rcad into thesc passages, is that these means will necess:l rily incorpor:lte th e use of (i) o r some other disjunctive predi cation :IS a sy ll ogistic premise. Sim il :l rl y, the schematic arguments in Prio r Analytics 1.46 and 2..2.2. to which Barnes po ints (5 Ib39-4 I , 52.334 - 37, 68a3- 16) arc ce rtain ly not presented in exp licit syllogis tic form and seem to be among the inference p:atterns that Aristotle regards as genuinely deductive but nor syllogistic in char:H.:ter (eL 4 7;l2. .l - 2. .'i ). 2.5· Compare Bonin (r870), 9bS 3 - 5 5. On e interesting seconda ry result of the extremely compellin g argument in Frede ( 1978) in slippon of Owen's " m:l ximal ly specific" interpretation of nonsubstnnti:l l pnrticlIlars (d. Owen ( 1965:11 " nd chapter 4, note I 7 above) is that even the indefin ite sentences of the Catego ries, where Aristotle is not co ncerned with th e genera l sentence forms of the sy llogistic, should be interpreted as pani cul" f statements. In pani cul;lr, rrede's main argumem relies pardy on the co rrect observatiun that th e indefini te scntt!'llce, "White inheres in body," a t CAtegories s.2.rq 1-3 2.lll llst he understood as :lsse r(in g that some bod ies ue white. 2.6. This mistake is di scussed in chapter 2. in co nnecrion with the interpreta tio n of w hat 1 ca ll "referential universal s." 2.7. Of course, this need not be a prope r suhset, since w here " Every S is P" is true, th e singula r propositio ns th"t make its consequence, "Some S is P" trlle are the very ones that underli e the truth of the universal statement itself. This is the rea son onc ca nnot move fro m "Some S is P" to "SomeS is not P" in Aristoteliilll iogic. Geach ( 1962.) attempts ro un dermine the intel ligibilit y ()f rhis mode of interpretation by as king how it would treat a falsI' statement of th e for m "Some S is P," and rejecting ou t of hand the response that it would then Ilot he abollt ;l ll Y S at all. Th e reason behi nd this rejecti o n is presllm:l bl y the Russclli a n ide;l (pressed again st Frcge in "On Denoting") that determining rhe referelHs o( the terms in :I sentence shou ld properly be prior to, :1n d certai nl y not dependen t upon ,;l determination of the sentence's truth-value. If so, it is cl1rious th ;tt Ceacl! sho uld rely o n this cons ideration. gi ven that he himself takes p:lins to po int out that th e sort of " reference" involved is nor il1tel1ded (or spc:l ker) rderence, but a I1lllch "thin ner," who ll y semanti c relario n (7, 8). Accord ing to Geach, indeed, it iS:ln ent irely nonpsycho logica l notion acco rding to which the refe rents of thc sl1bject of:l sentence are just those thin gs rhe facts abou t whi ch l1l:lkc th e sentence true. Only by slipping back into th ink ing about intended reference does one fi nd it probl ematic that reference sho uld be posterio r to tru th-va lue. 2.8. It is important here to record a poin t that precisely In "tches o ne made in the earli er di scussio n of the referentia l un ive rsal in chapter 2., namely that the ( 157 (
Notes to Pages 108 - 110 transparency of the referential particular versions of (7b) and (8 b) does not entail that they ate each synonymous with conjunctions of singular statements (about the odd a nd even numbers respectively). To recall th at earlier discussion (especia ll y chapter 2, note 12), it would be entirely possible to know that a referential particular was true without knowing exactly which singul ar propositions made it true, even though the replacement of any of those proposi tions with different ones would result in the sentence being about a different group of individual s. So, for exampl e, various covert departmental com ings and goings could alter the reference of my uttera nce of "Some o( my coll eagues are in," through different occasions, and these altera tions would change the content of my knowledge of its truth , even though its truth-value would remain unch anged so long as th e departmenl was not empty. I think it is failure to recognize this possibility that ultimatel y leads Geach to deny the intelligibility of referentia l pa rticulars. 29. Since the rea son ing at 73b 22 - 24 involves equating the properties signified by not odd and eve" , it also is concerned wit h the necessity of such sentences as (7C) So me numbers are not odd, an d (8c) Some numbers are not even. How exactly such predications fi gure in Aristotle's theory of dem onstration is the main topic of chapter 7.
CHAPTER 6, TYPE 3 PER ACCIDENS AND TYPE 4 PE R SE PREDICATION I. Th is translation will be observed not to make obvious sense as it stands, since the referent of irs subject is obscure. The usual and accepted manner of rectifying this, employed by both Mure (1928) and Tredennick (19 38), is to supply a grammatical subject in English by inserting the catc h ~ ali noun thing after th e adjective white, so that the translation reads (I ') The white thi"g is a man. In view of Aristotle's subseq uent rema rks at 81b27. it does a ppear that this device produces a n English translation that comes cl ose in meaning to the o ri ginal Greek sentence. But at the sa me time, it docs so by obscuring th e reason Aristotle finds sentences like (I) interesting. For sentence (1 '), unlike (1), is not an intercategorial predi cation with a nonsubstanrial subjecr. Its supplied grammatical subject, " thin g," is a very general sorral noun that co mes dose in meaning to Aristotle's own "substance" (owla). Hence, ( 1 ') would he classified as homocategorial by Aristotle, and therefo re not of the type that interests him at 8 ,h24- 27. For thi s reason, I prefer the somewhat awkward translation of ( I ) given here, which at least has the virtue of reAecting the relevant categorial features of the original G reek. For it is quite usual in Greek to form a complete gram matica l sub ject simply by prefacing a neuter adjectival form with an appropriate definite article, and there is no need to supply a grammatica l sub ject by the use of placeholding nou ns or pronouns. Hence, for Aristotle the only signifying expression that occurs in the subject part of ( f ) is the ad jective white. And since this exp ression signifi es a nonsubsta ll ce. this sentence is indeed an intercatego rial predicati on with a no nsubstantial subject.
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Notes to Pages 110-121 2. We are of course not talking abollt perfect context-independence, which would be tantamount to some sort of natural sign itic:ltion theory. 3. Incidentally, the absence of context-dependent semantica l relations in Aristotle's Organon also explains why he is sometimes tempted w ndd ro his onrology what are referred [0 in Matth ews (1982) as "kooky objects," such :IS "cu ltured Mikkalos," who is said at Prior Allalytics 47b .W - .H8 to perish w hen Mikblos becomes un cultured. For if Arisrotle hnd no way to say that the expression "cu ltured Mikk a los" tempora rily refers to Mikkalos, it is easy to see w hy he might be inclined co invent this peculiar temporn ry entity as the signiticatllm of the co m ~ bined expressio n. 4. Per accidens, that is, in a ll three o f the other senses expl il"nted in Posterior Allaiylics 1.4. In terms of the Categories semanti cs discussed in chapter 4, A a nd B must both inhere in S. 5. This sudden change of sub ject might not be <,u t of th e ordinary if Aristot le were engaged at 7.,\a .~ 5 - bT 6 in reporting the :l ctllalusages (If the expressions per se and per accidens current am o ng his comempora ries. However, all the avail:tble evidence indicates that he is contrivin g. and not just reporting, these uses. 6. Compare Physics 2. I and chapter 3 above. 7. The point of these passages should not be overrated. There is 110 evid~n(:e for the claim that the Cntegor;es rega rds a ll true inherence-predications ;'I S fortuitous (and so as outside the domain of sc ien ce). What we learn from th e De irzterpretatione 9 passage is that Aristotle recogniz.es some de;lt-cllt installl.:es of inherence-predicati o ns as fortuit o us, and that he provides no me:!Il S in the Categories to distinguish these from others that are not (if there :!re allY such ). 8. See my discussioll in chapter 2 of th e place of d efiniti ons in demonstration. 9. Especia lly in Book I. On this see Barnes ( 1969). 10. Bonitz (1870), T77<15)-54. t I. Cohen (197 1). 12. Mure (192 8 ). 13. Here it is important to distinguish sharply hetween genera lity :1n d universali ty. Characterizing the subjecrs of bTl. TO 1TOI\.1i predications as geneml (a s opposed to restricted) is nOt the sa me
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Notes to Pages 12 1- 12 7 "Thunder always fo ll ows li ghtning." And while correlations involving o bj ects and their properties are not usuall y ex pressed chis way, they might be. $0, for in stance, one might say "A man is always an animal," meaning simply chat all men are anima ls. If the sa me holds for Greek, then what Aristotle intends when he says that necessary truths are aei is that they are strictly universal. J 5. It seems that Aristotle's inclusion of this sort of example in Posterior A"alytics 1. ) I (where hi s general aim is to show how expl anations involving all three of the Physics' four "causes" that are present in the Analytics ca n be cast into the fo rm of demonstrati ve syll ogisms) leads him for the first time to think of hi s highly related concepts of cause an d explanation primaril y in terms of causal (in the modern sense) relations between events, instead of logica l relations between terms. Th is in turn leads him in Posterior Analytics 2. T T to begin asking " Humean" questions abom the temporal relations between causes and their effects. 16. On this pecul iar exp ression, whi ch is evidenrly a counterparr [Q the expression the what-is- it in the Posterior Allaiytics, see Kosman (forthcoming). 17. I believe the same point would be expressed in the language of Posterior Allalytics ) .4 by sayi ng th at grammatica l ca pacity belongs to man not only KaTer 1TctJJ rO~, bur also auro (on which see chapter 3 above). Thi s point is co ntested by Code ('98 6). 18. Perhaps these are connected through the concept of rationality. 19_ Aristotle actuall y lists and discusses three types of pro pria besides the per se variety at Topics 128b' 5[f. These he descri bes as " tempo rary" (1TOTe), " relarive" (7TP0>; i repov), and "permanent" (ae l ). The special characteristics that distinguish these three types have no relevance to the present di scussion, and wi ll be ignored here. 2 0. Th is passage is discussed at length in chapter I above. 2. 1. See also De Anima 1.1,4°2.38 - 13. 22. Lennox (1987) does an excellent job of distinguish ing this late ral form of demonstration (which he labels " A-expl anations") from the two vertica l types set out above (which Lenn ox does not distinguish from each other, but refers to in differentl y as " B-explanations"). However, I believe he miSinterprets Ari stotle's arguments in Posterior Analytics 1.24 , that demonstrations tha r are " universa l" (ril>; Ka8oAov) are "better" (/Jehi wII; 85a15 ), or " mo re compelling" (KVptWripa; 86323), than those th at arc "particul ar" (rils- /-LSp0s-), to imply some preference on Aristotle's part for A-explanations over B-explana tions. In fact, the main poim of this chapter is really no more th em an echo of Posterior Analytics 1.4 and 5: proving that a given attribute (in Aristotl e's ex·ample having angles equal to two right angles) belongs to a certai n kind (isosceles triangle) , when the attribute in question also belongs necessarily to a wider kind (in this case, triangle), is epistemologi calty inferior to (an d indeed depends upon) a "universa l" proof that th e attribute belongs to the whole of th at wider kind. Thi s, I take it, is just a restatement of the requirement of Posterior Alfafytics 1. 4 that i:l complete demonstration must rest exclusively on prem ises that are extensiona lly immediate (or aliTo, as
n
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Notes to Pages 128 - 132
thal express ion was exp lained in chapter 3 above). This does not affect wh.\[ I see as Lennox's correct and very important insight that Aristotle's Iolter hiologica l works (most especially, the Historia Anillltllillll1) display (I pronounced preference for lateral explanations involving coextensive properties and toliiffercnriae. 2.3. Mute (192.8 ). 2.4. This modei is appl ied to Aristotle's Physics in chapter, of Waterlow (I 9g2.). 2.5. This assumprion is entailed by a principle adhered to in the Orgallml (e.g., at Topics 1.15.I07b I 9 - z6), bur perhaps dropped in the biological works, that differemiating characteristics can apply only hnmonYlllously (usll,llly analogously) across natural kinds. 2.6. If this is substantially correc t, there remains the question of why Aristotle himself does no t draw this connec ti on expl ici tly, and why for that matter he does virtually nothing to indi cate he is even aware that the two types of st~ltements are superficially unlike one another. This I believe is just one of many symptoms of the fact that the theory of demonstration as a whole is intended to app ly eql13lly well both to natural sciences like biology and exact sciences like geometry (where by "equa lly" I mean that Aristotle is not willing to treat one of these types as paradigmatically demonstrluive, and the other as a ticgencrMe type). For R1Ti 1'0 1TO.\V truths, wh ile quite freque nt in natlltai sl.:ienccs, ha ve no place at all in mathematics, whereas Aristotle's usual examples indicate th'lt predi cations of per se propria are closely associated in his mind with mathematical proofs. Hence. I suggest' that because his general policy is to stress the similarities between rhe two kinds of science (if, indeed, he even recognizes them as two distinct kinds in any important sense) and to underplay their differen ces, he is reluctant to att,lCh Illu ch importance to what he regards as a stlpern.c i:ll difference between the two sorts of predica tion. 27. As was argued in chapter 2, these must be gelluine I}r(·dictltio/ls. i.e., referential universals. and not just Platonistic mean ing assumptions.
CHAPTER 7, DEMONSTRATION AND NEGATION J. By "negative predications," I am referring here Jnd helow to sentences stating that their subjects do not have the properties denoted hy their respective predicates. That is, they arc to be understood as involving the "illternal" neg:ltion of a predicate, or perhaps of the copu la. No contentions in thi s paper would be affected materially by making a finer distin ction. clcarly rc..:ugnizeJ hy Aristotle in De Interpretatiolle 1 0 and Prior Allalytics I -46, between neg,lting a preJi c:ne and negating the attachment of a predicate to a suhject. Unth of these nre to be contrasted sharply with delli(l/s, or what have sometill1CS heen Gllled "senten ce negations," which involve the "external" negation of some affirmative sentence (o r proposition ). 2. I tha nk James Lennox for this example.
I
161
I
Notes to Pages 132 - 135 3. Plato's views about this problem and his ways of dealing with it in the So~ phist are discussed in some deta il in Ferejohn (1989)· 4. Moravcsik (1962 and 1973 ) tries to resi st understanding Plato's objections to such divisions as having any essentia l connection with the use of negative con~ cepts or expressions, insisting instead that the distinction relied lipan in these pas~ sages is simply that between natural and artificial delineations. This view, which is compelled by Moravcsik's wider interpretation of the Sophist, is undermined by his own admission (1962,72) that the mOSt natural interpretation of States~ man 262D-E is the one be rejects. 5. Alexander, ;'1 Metaphysic.a 8r, .~-4. Though Aristotle's worries about the meaning of negative predicates arise during a critical discussion of the Platonic Ideas, one may assume they apply mutatis mutandi to his own theory of predication on which Aristotelian universals arc taken as the denotations of general terms. 6. There is some evidence to suggest that this view is shared by Alexander: "For 'not-man' is true of the horse and the dog, and of everything else besides the man, both existent and non-existent (i5VTWV Te Kat /.LTJ OVTWV). For it applies to both wood and stone, to both centaur and chimera, to what is utterly insubstantial, to what nowise nohow is (TOi) /.LT/Sa/.Lf} ILT/Sa/-Lw,> OVTO'»" (In Metaphysica 80.17ff. alt.). 7. The absolute extreme of this sort of case is one where the background field is taken as all subjects of discourse, including nonexistents; d. De Il1terpretatione 2, and Peri [deon 80. 17ft 8. Lee (1972) incorrectly assumes thar all varieties of meaning deficiency are "infectious" in th e sense that any such defect of a part of a compound expression will necessarily be visited upon the whole. Hence: "each determinate Part of Oth erness is opposed to some determinate Form and ... its determinacy really is that of the Form to which it is directed .. ," (284-85, note 25, emphasis in original). In fact, given a constant background set, the determinacy of a negative term is inversely related to that of its affirmative com ponent. I believe this confusion is ultimately rooted in Lee's overplaying of the knowledge analogy at 257C- D to the extent that he has Plato holding that each part of difference derives not just its determinate nature (and consequently its name worthiness) but also its very existence from its correlated Form together with the Form of Difference (much as one might hold that arithmeric owes its existence to the faculty of knowledge and the field of numbers). This leads Lee to construe the not-beautiful as a sort of secondorder intension which is somehow constructed out of, or as Lee puts it, "constituted by," the interweaving of Beauty and Difference (286) . To the contrary, I maintain that the not-beautiful is simply the class of independently existing Forms that share the distinction of be ing different from and opposed to Beauty. If asked whether this interpretation of Plato is intensional or extensional, I would reply that the question is misdirected. It is most certainly not intensional in the sense employed by Lee (293) ; it insists that every term (positive or negative) signifies some Form or class of Forms and not some mysterious "specific negative inten· sian" (293) . Yet my interpretation is intensional insofar as Forms themselves are [ 162
I
Notes to Pages 136 -137
class ified as intensiona l entities, and insofar as it recogn izes th at Pl ato wou ld never endorse a nomi nal istic ana lysis of "Socrates is not heautiful," on wh ich the sentence merely places Socrates outside the class of beautiful things. 9. De Il1 terpretariol1e 2. , 6a."\0-.13 , and ~.16b12-T6. Compnre alst) D(' 111 terpretatioue 1 0, 12., and 14, passim, with Prior Analyties 1.46, pnssi m. 10. The specific co ndi ti on fo r termhood mention ed at De /Ilt erl"ctarion<' 2.16a28 -30 is that an expression must " become a [genu in el sy mhol" (yr. V'11Ta t uVJL{3o'Aov), that is, something more than the " in articul ate noi ses" (aypaJLI.taTOt .parbot) of beasts (329 ), and this seems quite clearly to he a condi tion on mean ingfulness. Conseq uently, it is a reasonable in ference that Aristo tle 's grounds for disquali fy ing indefinite expressions as nouns
Notes to Page 135 hibiting app li cations of so-ca lled non logica l axioms across different genera, even though these principles do nor generally involve negative predication. For example, his insistence that the principle "Equa ls taken from equa ls yield equals," can only be used in restrined demonstrative contexts (e.g., as perta ining to equal numbers, or to lines of equal length) ca n be seen to reflect a concern that, if the term equal were taken to denote anything whatever in the ca tegory of Quantity, it would be too wide to possess a determ inate meaning.
I
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Bibliography
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1969. "Aristorle's T heory of DClllonsrr;nioll ." Plmmesis 14: 1 2...' - 5 2. I, Sciellce. Edited hy j. B:lrnes, M. Schofi eld, and R. Sorabj i. London, 1975. - - - . 1981. " Proof nnd the Syllogism" in Aristotle 011 ScienCe': The POS/('rior Allalytics. Proceedings of the Eight" S)'mposium Arisrolcliwl1I. Edited hy Barnes,
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E. Berti. Padua and New York. Barnes, J., trans. 1975. Aristotle's Posterior Analytics (rransJ:uion ;lI1J notes). Oxford. Bonitz, H. 1870. Index Aristote/iCII s. Berl in. Burnycat. M. 1970. "The Material
- - - . 1981. "A ri stotle on Unders randill~ Knowledge." In Arisloth· (II/ S('jl'lIce: The Posterior Allalytics. Proceedillgs of t/J,' Eighth S),I11/JOS IlII1l AriSlo //?hCWfl. Edi ted by E. Berti. P;,du;, an d New York. Chern iss, H . 1944. Aristotle's CriticislII o{ P/"tO ,1110 tin' Amell·my. Baltimore. Code, A. 1986. "Arisrorle's Treatment of
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Co hen, S. M. 1971. "Socrates on the Definition of Pie l),: !-:lI lhYf1!Jm l oA- l iB." jOllntai of the History of PbilosopbY9: 1- 1.1. Reprinted ill S()cr.ltcS: Critical Essa)'s. Ed ited hy G. VI:"Istos. G;uden City. 1971 , 151'1-76. Dancy, R. 1975. "On Some of Arisrorle's First T houghts Ahout Su hst;l nee. '" Pbilosophica/ Rel,jelt' R4: HR-7J.
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menta tion." Archiv fur Geschichte der Philosophie 40 . - - -. Unp ublished. "Anstotle on Snubness and the Definition of Composites." Fine, G. 1979. "Knowledge and Logos in the TIJeaetelus." Philosophical Review RR: 367-97' Frede, M. 1978. "Individuen bei Ari stoteles." Alltike and Abelldland. Reprinted in Essays;n Ancient Philosophy, Mi nneapolis, 1987. Furth, M. 1988. Substance, Form , and Psyche: All Aristotelean Metaphysics. Camhridge. Geach, P. T. 1962.. RefereHce alld Generality: All Examiltation of Some J.1edieval alld Modem Theories. !!haca. Grene, M. 1963. A Portrait of Aristotle. Ch icago. Hin tik ka, J. 1957 · "Necessity, Universali ty, and Time in Arisrotle." A;atus 20: 65 - 90 . - - - . '971. "On the Ingredients of an Aristotel ian Science." NOlls 6(1): 55 - 69.
Time alld Necessity: Studies in Aristotle's Theory of Modality. Oxford. Irwin, T. 1988. Al'istotle's First Pri" ciples. Ox rord. J
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Kung,]. 1977. "A ri stotle on Essence and Exp laniltioll ." Phi/osolJhiall Stl/dies 3 l: )6 ,- 8) . Lea r, ]. J 980. Aristotle's Logical Theory. C"lInbrid~e. Lee, E. N. 1972. "PI:lfo on Not-Bei ng in rhe Sophist." Philosophical RelJiew ~h: 26 7-3 0 4. Lennox, ]. 1987. " Divide and Exp lain: The Posterior Alla/yt;cs in Prnctice." In Philosophical Issues ill A ristotle's Biology. Edited by A. Gotthelf nn d J. Lennox . Lesher, j. 19 7 _~. "The Meaning of N UllS in the Posterior AlUriyti(s. " I'ImJllt!sis [8. Luka siewicz, J. 1957. Aristotle's Syllogistic (rolll the Stalldf1 0illt of Modem Logic. 2d edition . Oxford. Mansion, S. 1976 . Le jllgelllel1t d'cxistt'H((, (hez Aristo({'. !.d edition. LOInaill. - - -.1 981 . " La Sign ifi cation de l'Univcrs:l\ rI':lpres An . Post. rio" [n Aristotle 011 Science: The Posterior Altl1lytics . Proaetiings of the t:ighth Symposium Ar;stoteliwm. Ed ited by E. Berti. P;ldu:l :lntl New Yo rk . Manhews, G. 1982. " Accidental Unities." In Ll1l1gl/dgeall/f Logos . Edired by M, N ussba um and M. Schofield, Cambri dge. Mignucci, M. 1981. " Hos Epi To Polu er Necessn ;re dans L1 Conception Aris(Oteli cienne de In Scie nce." In A ristotle 011 Sciellfl'; Th e Posterior Amz/ylics. Proceedings of the Eighth SymposiulJI AristotcliClfm . Edi ted hy E. Berti. Padua a nd New York. Modrak, 0.198 7. Aristotle: The Power of Perception. Chi cago. M oore, G. E. 1936. " Is Ex istence a Predic:ne?" Proceedillgs of the Aris/otl'l;all Society 1936. Reprinted in L ogic ,l1Id t l1llglldge. 2-d scrie!'. Edited hy A. Flew. Oxford 1955. Moravcsi k, J. 1962. " Being nnd Men ning in [he Sophist." Acta Philoso" hi(t'l FelllIiea 14 : 23-78 . - - - . 1967. "A ristotle's Theory of C:ltcgori es." III Aristot!f': Critied ! ESSdYS. Edi ted by J. Moravcsi k. Garden City, [96 7, - -- . [97)· "The Anatomy of Plato's Divisions." In f-:xegesis dlul Argument: Swdies i1l Greek Philosophy Prescl1ted to Gregory Vlastos. 1'Imml'sis SltPP!. vol. T. Edited hy E. Lee, A. MOllrelaros, and A. Rorty. Mure, G. R. C. [928. Aristotle: PasteriOl' Ailidytics. Oxfo rd . Nehama s, A. 1983 ... EpislC1I1P nnd Logos in Plato's Later Th o ught." Archill ftlr Geschichte der I'IJilnsop IJie 65: I 1- .,6. Owen, G. E. L. 1961. "Tithellai Tn PIJdiI10me/1a. " In A ,·istlJlt, 1'1 Il!s PmMI!1IIes de la Methode. Edited by S. Mansion, LOUY:l in . Reprinted in Aristotle: Critical Essays. Edited by J. Moravcsik. Garden City. 1967; a nd Articles 011 Aristotle, vol. [, Sciellce. Ed ited by J. Barnes, M. Schofield, and R. So r:lh ji. London, 1975. - --. 1 965~· " In herence." Phrollesis 10: 97 -1 05. - - - . 1965b. "The Pla to nism of Arisrotle." Proacdillgs of t/'" iJ ritish A cademy 5 1: 125-50,
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Bibliography Panig, G. 1969. Aristotle's Theory of the Syllogism. Dordrecht. Quine, W. 1960. Word and Object. Cambridge, Mass. Robe rts, J. ] 982.. "Being, Not-Being, and Fal sity in Plato's Sophist." Ph.D. dissertation , Unive rsity of Pittsburgh. Ross, W. D. ' 9 49 . Aristotle's Prior alld Posterior Allalytics. Oxford. Russell, B. '905. "On Denoti ng." Mi"d 14: 479 -93' Smith, R. 1982.. "The Syllogism in Posterior Analytics I." ArcfJiv fur Geschichte del' Phi/osophie 64: 113- :;5. - - - . 1986. " Immediate Propositions and Aristotle's Proof Theory." Ancient Philosophy 6: 47 - 68. Solmsen, F. '929. Die Ell twicklllllg ner Aristotelisehell Logik I/Ild Rhetorik. Berlin. Sorabji, R. 1980. Necessity, Cause, alld Blame: Perspectives 011 Aristotle 's The ory. Ith aca. Treclenni ck, H., trans. 19 .~8. Aristorle's Posterior Allalyties. Loeb Classica l Library. Cambridge, Mass., and London. Waterlow, S. 1982.. Nature Challge and Agency in Aristotle's Physics. Oxford. White, N. 1972.. "O rigins of Aristotle's Essemial ism." Review of Metaphysics 2..6: 57- R5-
I 168 J
Index
pedagogical interpretation of "ostt!-
Academy: influence on Aristotle's views, 4, 19, 81
Accidents: no science of, 1481138 Ackrill,j. L, 151112, 15 1 114. 15I!l .~ , 15411 I; on linguistic method in Categories, 77, So, 1.~21/11; on constructioll of categories, 84 - 90, 15.1111..,; on inherence, 152111 7; on expression "what-is-it," t5'>1I .~I, 15.111 .) 2, t .~.l 541133; on differentiae, I .S jlIS A(firmations, 15 1116, 1S T117 Alexander of Aphrodisias: Oil negative forms, 1.14, I3~, 136, 16211S; on peiorem rule, 14 9115 An3 lyticity objection, 57-6 1 Antisyllogisticism. 18, 14111 .) , 14 1114 Aporetic surveys : in method of s;J\'ing the phenomen;J, 54 Atomic sentences, 7 8, l.'i I 1/6, 151117 B3rb3ra (syllogistic mood ), 2.0, 24, 29,
J I,
J _~ I, 1 37
Barnes. Jon3than, t .1911 I; 011 de re vs. merely universal knowledge, 42 - 4 .1, 146 1'9,1461110; on necessity of type 2 per se predication. 104-7, 15 6 11 22, 156112}, 1.' 16- 571124; o n chronology of Allalytics, 140117, '40- 4111.'1;
r ior AII"fylirs, 140 - 41I1J, 14 1114, 1 " .\ /II -I; on obll'..::tive vs. subjective in telli~ib il i t y, 14,1I1.l; on 111:Hhent<1tica l v~. n:l[ur:ll sciences, 159/1') Basic assumptions of science, ' 7- I R; ba ckground :l .~Slll11r t i(ll1s, .,2- ,,7; of meaIlin~s, .~9 - 4', 44 - 49, S2-.~7, 'i7- 6 1 "!lrt':l U5t' of il~elf" (fit' mIni) characterization oi type 4 pet St"" pn:di.:::uion, I l!l - 19
Bonin, H., ' 57/12 .~, IS91110 BlIn1YC;1t, Myles: Oil inrerrd,ltloll:11 model of justificatioll. -I 9-'i0, '47'127 , I "R 1129; OIl Pt'd;Jgll~k;11 illterpft't:ltioI1 of POS/criOf AII,Ilyfirs, 14 I 114
Call1t'stres (syll(l~istic mood). r ,6 "Capaci t y" (,''i';''lf/.Lt<;), Y.~. IlCCllrrCIH COIldition, 46 - 47,1471117 C negorit·s. doctrine o f, 75-7S; methods for constr ucting, R4 - R9; hier:lrchica l branching structure of, RII, I J7, 154 ~ 5 11 .> C,tq,:ori<'s, p laceillellt of,
I 169 1
1 -';.'i 11 l I
I
~Olll, ' 55 "7,
Index "Catholic" (Ka-lIo'\ov) pr~dication, 68-72.; three conditions on, 69 Causal conn~ction5: role in demonstrative science, 9.117; conveyed by " for-the-most-parr" premises, 120-2.3 C;:'Iusal po wer:", 129 "Cause" (arno/l): shown in demonstration, 17.65-66; of conclusion in premises, 2.0-21; four types, 1601115; of events, 1601f 15 Celarent (syl logistic mood), 2.4, 3 1, 131, 13 6 -37
Ch ains: generated in single-question method, 86-91, I 53'1l.9 "Chance" ('I] niX1): distinguished from necessity, I 16; distinguished from "for-the-most-parr" and " by nature," 12.0-2.1
Cherniss, Harold, 142.116, qU17, 1441141 Chronology of Allalylics, 140117. 14 0 -4 111 3 Code, Alan. '49-50119, 1601117 Cohen, S. M., 159111 I Common axioms, 18; principle of noncontradiction, 6, 36, 4S , 145'14 .'j; law of excluded middle (LEM ), 36-37, 137, 1451'4 3; non-logical, 144-4 51'42., ' 4~1I4J, 16)-64 11 15
"Compactness" proof in Posterior AII,JIylics 1.1 9-22., 14'1122., 143'12.7, 15.1 112 7
C.om partmental ization of demonstrative science, I ~ 5- .1 8 Composite substances. 15 Sill) "Constructive" definitions. ' .~411 .14, 'H -H " 3
Context-de pendent semantic relations. I TO-II
Context-i ndependent semantic relations,
55-57; as mere theses, 40; apprehension of, 44-51; vs. immediate premises, 52- 53; demonstrability of, 56-57, 1481136; per genus etdifferemia, 94 - 95,145"4,155'11); "constructive," 154 IIH. t 54- 55 113 "Demonstration" (u7Toolat"l'5"): as explanation, 2.,16 - 17,2.1, 51,65 -66, 139114, 14 2.- 4 .~ 11 1 3; two stages of, 6, 19-)2.; framing stage of, 6, 19-P, 41,57 ,60; and systematiciry, 7, 49 - 5 I, 51; products of, 51 - 52. only of what is necessary, 66 - 68; affirmative vs. negative, 13 I - 3 2.; universal vs. particular, 160- 61112.2 Denials, 151 1/6, Ip1l7. 16 1111 Dichotomous division, [ 43 112.6, 144"4 I Differentiae : role in demonstration, 8-9; problem of. 94-98,147-48112.8; not qualities, 96-97; what-is-it of, 96 - 97; one-to-one with species, 143"2.5; classifications of, 1551112 Disjunctive predications: inappropriate for demonstration , 104 -5, 142.1110, 15 6 -57 11 2.4
Distribution of necessity over disjun ction, fallacy of, 105 Division, Aristotelian, 20- 32; as method of using definitions to obtain immediate premises, 6,19,2., - 2.4,2.9-32., 41,60; rules for correct ordering of terms, 24 - 2.6; rules fo r preventing omissions of terms, 2.6-28 . See also Framing stage of demonstration Division. Platonic, 5-6, 48; Aristotle's criticism of, 19 -20, 142.11 7. 142118, 156-571124; as method of generating definitions, 22-23; Speusi ppus's version vs. Plato's version, 142117
1I0- 1I,I S9 "2.
"Convertihle" predica tions. 70-72.,
Empiricist conception of necessary fruth,
'4 3 11 2 3, 14 8I1H
Correct ordering of terms: rules for, 24- 26
Dancy, Russell, I S5 IIlO De re knowledge: vs. merely universal, ) 8 --'9,5 2.- 57,59-6 1; tra nspa rency of, 42-44,14 6119, 14611f0. 14611I1,
58- 60 " Endoxa" (iv8o{a): in philosoph ical method,54-n Epistemological conservatism, pri nciple of (Ee), 67-68 Epistemology: general vs. speCial, 14 8 - 49 111
Equivocity: and philosophical method,
14 6111 2.
"Definitions" (OpOl): merely universal, 6-7; real vs. nominal, 35, 40 , 51..-5.1,
H - 55
Essential properties, 8; distinguished from propria, 12.) , 1<13"2. 3; distin-
I 170 I
Index guished from accident., 1 properties.
t ,'iOIl 10: Oil
14 3 11 1 9
,~.l - .l,'i.
cxi~tence
:lsslIlllptio!ls.
14 (,1/1 \; 011 St:ttus of definitions, 40- 41, ,~!.- ,U, 14(,I/R: "Irkt syllogi~ticism, ' 40-4 I Ill, ' <1 ' 114; un
Excluded middle, law of (LEM ), ,1 6- ,1 7, 101, 137: mod.,1 versions (MLEM l, 102. -8, 1~6-1.1
" I,
the verb "to he," 1 4~ "5: (In COl1lmOI1 axiOlllS, 145" 4 ,1 ; (111 necessity and rime, 159-6011 14 H umean cun ception of Ca!ls:tlity, 16011 r 5
Existence: of subject-maner assumed in demonstrative science, 6, )2.- ,1 5: of atrri butes proved by demonSlr:trive science, 32.-3), 51-52.; singular vs, genera l, 4)- 44 , '461110, 146111; Exp lan:\tion: g.ivcn by demo nstration, l,
Imma nent re"lism, 4H . S9-lio, 1'1 7"26 Immedi.,te demon~ r ra r ivt, prem ises: dis( in ~l1ish cd from starting points, ~-7, 18, 41, 14411l9; method for notainlllg, 1J - 2S, 29-.12; :md the "QIl ;1 iaelf" condition, 7 1-72 Indefinite statements. ('9-70, 10(;,
16- 17. :U . St. 65-66, t.>9"4. I42.-H 1113: o bj ective vs, subjective. 11,142. - 43" T 3
"Far-fetched explanations" (Ta I(a(t l.I1Tep(3oA Til' eiPTJlLi,/('l.), 1,,6 -.17 Ferejohn, Michael, 1 :t9 " 3, I J9-40115, 140116,149"3. IH'II, 155'11 ,; .
I ,pillS
I n d ~finile
terms, 9, I,H, " Indu..:tion" (F.7I'[(ywyrj), 47- 4 R lnheren..:e, 79-8\, Ip1l17. Inl/1.~ Inquiry: not suhjcci of I'osft:rior A'IIf-
162.113, 16)1114
Fine, Gail. 14 7 "2. 7 " For-the-most·parl" (irri TO 1ToAul conneclions: role in demonstr:uion, 9: statistical vs. causa l interpretation, 119 -2.2.; and type .. pe r se predic:ttion. 12.1.-2.}: as displised propri:t-pred ic.,tions, 128-30; genet:tlity of, 15911 1,1 Forms (Ideas), Platonic, 48 , 16211,'i,
lyrics,
1.19114
IlHelli~il1il i ty:
hy 1l3tttre vs. in rdation to us. 142.-'0" 1 \ Intercategori:tl prclti..:arinns with nOIlsu bst:l nti.,1 SUbjct'IS, 109- I ,~, I ~HIII Interrelational ml,dd of j llsti~c:tt i ol1, 49-P., t47-4 HII !.R « l llrc rwt':lV ; n~" ( ml~1T,\f) I('lj )
162.- 6 3 118
Foundationalist theory of justification, 4- 6 ,17- 19,14 0111 Framing stage of demonstr.,tion: procedure for collecting immed iate premises. 6, 19 .2 ,-2.4. 29-P , 41, p, 60: .,ml systemat icity, 7: rules fo r correct ordering of terms, 2 4-26 : rules for prevenring omissions of terms, 26-28 Frede, Michael, 15211 [ 4, I Hill; on inherence, 1 5 2 111 7; on problem of differentiae, 155 " 7; on indefinite statements. , 57112..'i Furth, Montgomery, I S.l"20, ' S411 1; on predication in Categories. 78-79. ' j 1 11 8; on substance vs. nonsubsl ance. 15211 15,152 111 6, '561118; on namelogos ap plic:uion, 155 11 6
of ,~el1tel1ti:l1
elements. 76. 7ft. r ~ I 1/6 «llHllition" (l'O j,,;-), 47, '4 7 11 2.1 Irwin, Tert'llct'. t 40 111.
Kahn, Charles: '4 ,'i- 461/5: 147 112 J
011 0 11
the vcril "In he," illlll itiol1, 147111R,
Kneale, WilIi:lIll. 14('" 14 "Knowll." dge" (i1TUrrrilLlI): demonstrative, I ; as facul l)" ~ t:lte (I f soul. or infonmuiona l iteTll. I. I '\}-4011~: si mplici ter, 1, , 6, 4 2.. 49-<;0, ~1.: (If universals, 6; rtt't'J(ist~nt. ; (, - I 7. 44 - 4R, 48 -<; I . (,,; tie re vs. Illerely univers.,l. ,\ R - .\9,
G~ach, Peler, 157 // 17, q 7-5811l8
Gotthelf,Al1a n, 155 I1t1 Grene. Marjorie. 15,' 11Z.4
-1 9-5 0
"Kooky objec[s." H intikka,J33kko, '.19 "1 , IHIIF,
KO ~IIl:1n.
1 ~9111
L A.. 147'1:!.1, 160111(,
K IIIl~,Jll:lll, 1 5 ,~" ' 0
14411 33. 1441134. I44 "H. 14 9114,
I
17 1
I
Index lear,jonalhan, '4 .\1122., 15)1127 Lee, E. N., 162-63118 Lennox , james, 149- 50n9, 160-6 11122, 16111 2.
Lesher, J;']mes, 14 711 2} Logic of gene ral terms: Aristotelian 'IS . Post-Fregean, 4.' - 44, 106 -7 , 1461110,
133- .U. 1561119; distinguished from denials,161111 Nehamas. Alexander. '47112.7 Noncontradiction, principle of. 6, 3 6 -45, 14 51'43 Nonexistent subjects, 162.11 6, 162.117 Nonsubsrantial particulars, 81, 152.11 17, 1521118,157112.5
14 61112. 1471116
Logos: necessary for knowledge, 49- 50; inl!'! rrational model, 49- 5 I, 52,
Nonsubstantia l subjecls, 109 -15, IS8111 "One-oyer-many" principle, 1 H Opposites: necessity of. 101-8. 1561115, 1561l u ; principle of, 102. -4. 107 Owen, G. E. L : on Aristotle's philosophical method, 54, 1481134; on origin of said-of vs. inherence distinction, 1521112.; on inherence, I) 2.111 7. 157112. .~; on theory of predication in Categories, 153112.1
147 - 4 81128
Luka siewicz, );']n, 148113 7 Mansion, Suza nne, 14811.1 7 Mathem:l!ics: vs. natural science, 117, T2.4, 1.44"\8, 1<14-4 5 1142, '5411\4, 159119. 16 11126 ; and propria, 12.4
M3tter-form analysis of substances, la, ISS /II 3
Manllen , Mohan, 15411\4 Mauhew ~. Gareth, 15911\ Meaning assu mptions of science. Sec Basic asslimptions of sci!'!nce Memory, 47 MellO (Plaw), 16, ,l8, 46,1471/ 19 MenD's Paradox, 16 , 41,4.\,46 Middle term s of syllogisms, 18 Mignucci, "-'brio: 0/1 "(or-the-most-p3tt" predic
Namewonhiness of klllds, 133 "Nature" (dnicTl"), 8. 12.9 Nece\sity : of scientific prem ises. 7-8, 22, 66 -68; analytic 'Is. essentialistic, 61. 100 - t , 14811-'9; and eternality, 67 - 68, 159-6011 14; of per se predications, 72-74, 99-108; absolute, 100- 1 ; in the manner of opposites, tOI -II, 15611l5, 1 56 112.1
Negative predication: in demonstration, 9. 1} 1-)2.. 136-38, 143'121, 144"30, 149116; necessary for division, 112. -3.\ ; problems with,
Parmenides. 9, I} 5 Participation condition on said-of relation, 92-94, 95-96, 154 -55 11} Patilig, Gunther. 149112, 1561117 Pedagogica l interpretation of Posterior Allalytics, 139"4, 140-41113; criti-
dud, 141114 Per Sf affections, 15Pfl} Per se predication, 8, Jl.-H, 66, 72.-74; type 1, 82.-91; type 2, 96-108; necessity of, 99- 108; no type }, 10 9- 15; type 4, liS -3D Perception: as capacity for grasping definitions, 46; of universals. 47,59 Philebus (Plato), 1 .1 2 Philoponus,john, 156/114. 1561116 Philosophical method, Aristotelian: use of li nguistic data, 4; "sav ing the phenomena," 54-55; and equivoCLty of terms, 54-55 Platonism: influence on Aristolle's theory of demonstration, }- 4; differences from Aristotelianism. 48 Platon istic' universal StatementS, 44, 59-60
Porphyry, tree of, 88 Posterior Analytics: natu re of work, I -}; reputation for disorganization, 15 -16, 14 0 11I
Potentiality vs. actuality distinction, 14 7 /1 2.0
I 172
J
Jlldex Single-qlle~tion method for t:(lIlstructinf,
Predic~t ion, theory of. 4; in Posterior
AlIol)'tics. 8. 76- ' 1.9 pusim; in C'/egor;es. 8. 78-83, 15tll6, 1",1-51."10 Pr;m~ry pr~mises. See Immedi:lte demonstrative premises "Prim:lry substance" (wpWnll oVa-un). 80-8 1 Priority of dernonstratjv~ premises. 2.0- 1.1. 66. 14 1.- 4 .1 '11 .1 "Propria" (l'ot.Gt'): role in demonstration. 9, 12 3-28; distillg\l i sh~d from essential properri~s. 1203; convertible. 12 .1 - 24. 14 J "2 .'I: frequent in mathe· mati cal sci~nces, 124; per sc vs. accidental. 1.14-15; tempor;l r~.. relative. 3nd permanent. 1601119
(n
"QlI:l itself" o:ilT(i) (Oruiition Oil c:ltho· lic p redic:ltiotl. 69. 70-72.; and con\·erribiliry. 70-7.t; extension;11 3nd intensional interpretations of. 149-50Jl9. 1601l t 7. 160-6 1J1.t J. Quine, W. V. 0 .• I pllq
Realism: Plat01l;C vs. imm3nent. 48. 59-60 " Recol lection" (al,ctlJ.V1'}CTt<;). Platonic theory of, 16.46 , 1.1]1119 Reference. varieties of. I5]II.t7 Referential particular statements, 10(. - 8, 15]112], q7- .~811z.8
ReferentJa llmiversal statements, 6, 44, 107-8; distingllished from Platonis[1c lmiversal statements. 44. 50, 60 Republic (Plato). 16, t49-50119 Robens, Je:l!1. 14~ -46 I1S Ross, W. D., 15, l .l911 1; on ch ronolo~y o f Allal)'tics, t 4 I II); o n common axioms. 145 11 4' Said-of rclation: distinguished from inl1erence, 79-83; inrra-catcgorial conditions on. 8.\-91; properties of. 92.-9.\. 154-551'.\ Science: development of concept. 2. See "Iso "Knowledge" (i1TtO"TYj~1J) "Seconda ry substances" (ll£1in:pat ovuiat): in Colegories.lh. 15.1" 19 Semantic fragmenta rion, 9. r \ 1- .\8. 16 .1 11 10, t631l1J
Signification relal ion. I 1 1
t:ate~ories.
116-119. I ~ 11/2.(;. I q 1I.t1l. I SV'.t9 Smith. Robin: 0 11 foulld;ltion;)lism. '4 °1/2.; on clmmol'lgy uf A""i),li(s. '4°117: and antisrlltlf,istit:ism. 14 0 -4 111 3 "Snl1hness." ' .~511 1 \ Solrnscn. Frlcd rit:h . 1 ",, 0-4 I 111 SOII/JiM (Pbtu). 9. 94, ' .1 1.- .1." "P·1I7. I 62.IIJ
Sorah;i. Richard, '41111 .17 SpellsipplIS. '4l11 7. 1441141 "$tartin~ poims·· «(~JlX(~i) of dl'1ll0Ilstr;l· tio n. ~, 17- I H; di .~ t i ngllishrd from imlllt'di;ltl' demonstrative premi ses. 6. 7. IR - 19.41. 144112.9; 11Ol1SlIbst:lIltive bat·kgrolilld ilssumpt ions. ,2.- \7; me,llling ;IS.~lI tl1rri(lm. 19 - 4 ' .44 - 41). ~2.- .p. 57-6 1 St"teSI/I,lI/ (Pbto), ')4, 1\ l-
q. 162.114 Subject·gclills of ;, d('l1IuIIstr;uive sl"ience. 10 • .\.t- .16. t .P-:;S. 144"l l Sl1bordinate sc1rnt:es, 16.; 11' 4 Subsrance. II I ; vs. IItIl1Sllh!>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 The7. 14 8 -49 111 Thcmi~tius. 15611 14 Th~ophrastus, '49115 Tr ;lIl~itiv ity of said ·of rei;,titJIl, (,.t. I H -5S II .\
TreJennit:k, Hugh. 1-1 7"17. I ~KIII Undcrrestricred CI'l\lplelllt'nl.~. 1 \ .~ - \ II Unity of dehnit;oll. ' 4'''4 , 1.17-.II'I/2.R
[ 173 [
Index 89-9J; and type I per se predication, 90-9 r; central to single-question method, 9I; of differentiae, 96-97 White, Nicholas. 149n1., 1501110
Univers
I
174 J
