Leibniz Aristotle Individuation

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LEIBNIZ, ARISTOTLE,AND THE PROBLEMOF INDIVIDUATIONBY

RAJA BAHLUL

1. IntroductionFew metaphysical problems can be said to rival the so-called problem ofindividuation when it comes to the number of proffered solutions. Andamong the many solutions scattered throughout the pages of the historyof philosophy, probably no two solutions offer a more seemingly profound or marked contrast than the ones which we find in Leibniz andAristotle.Leibniz, through his famous Principle of the Identity of Indiscernibles(PII), affirms that no two substances are completely alike, that everysubstance has a property, or properties, which no other substance has.Aristotle, on the other hand, neither affirms nor denies this, but for himindividuation is accomplished by each substance having "differentmatter", rather than different properties.In many ways, these two views are worlds apart, for there can hardlybe two sorts of things which are as different as properties and matter are.When we think of properties, we think of that which is universal, shareable, common and abstract. Such is the case of properties and forms aseducated, white, man, which both Socrates and Callias share in commonwith many other things. But when we think of matter, or at least thematter which Socrates is composed of at any one time, we think of thatwhich is spatially circumscribed, particular rather than universal, hereand-now only as opposed to repeatable, concrete rather than abstract.Given all of this, one might think that there is no common ground between Leibniz and Aristotle, that the gap between them is unbridgeable.But appearances can be deceptive. I want to suggest that the twoapproaches which we find in Aristotle and Leibniz are to some extentPacific Philosophical Quanerl y 73 (1992) ()()()...{)()() 0279-0750/92/0300-0000 $00.00Cop}Tight 1992 University of Southern California. Published by Blaclcwell Publishers, 108 CowleyRoad, Oxford OX4 1JF, UK and 238 Main Street, Cambridge, MA 02142, USA.

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186 PACIFIC PHILOSOPHICAL QUARTERLYreconcilable. More precisely, I intend to show that there is a principlewhich is closely related to PII, and which can be viewed as a consequenceof the Aristotelian view of individuation. The new principle is called"The Principle of the Identity of Necessary Similarity" (PINS). In duecourse, it will be explained how this new principle can be looked at as aslight but significant modification of the more familiar PII, and also howit can plausibly be derived from various things which Aristotle ~ a y s aboutmatter.In Section 2, I offer a brief explanation of what I mean by "theproblem of individuation", the problem which I take Aristotle andLeibniz to be concerned with. In Section 3, I describe the Leibnizianview, and dwell on the difficulties which might move one to seek analternative account of individuation. I conclude this section by introducing PINS, a PH-like principle which does not seem to be subject tothe kind of objections that PII faces in connection with the problem ofindividuation. Finally, in Section 4, I discuss Aristotle's view of matteras the principle of individuation, and suggest that PINS can be viewed asa consequence of the Aristotelian position.

2. The Problem of IndividuationTo a large extent, the world presents itself to us in experience as something which consists of an indefinite number of particulars each of whichhas some properties which it shares with other particulars. Universalityand particularity are basic features of the way we experience the world,and both have given rise to basic philosophical problems.

The attempt to understand how a number of different particulars canbe said to be qualitatively similar, even "the same", has come to beknown as the problem of universals. Particularity, on the other hand,has given rise to, not one, but quite a few problems. Only one of these,namely the problem of individuation, concerns us here. But we need tosay precisely what we take this problem to be, since this name has sometimes been applied to other problems as well.There are two such problems which we need to explain and set aside ashaving little or nothing to do with the problem which we take Leibnizand Aristotle to be trying to solve. The first of these two problems has, atvarious times, been called metaphysical, logical, or linguistic, but it canperhaps best be referred to as "the categona1 problem of individuation".It has to do with a contrast that is almost as old as philosophy itself,namely, the c a t e g o r i ~ l contrast between what is individual (particular)and what is universal, between, e.g., Socrates and whiteness. These twocan indeed be spoken of in the same breath as two "things", "entities",or "existents", but, presumably, when all is said and done, they must beUniversity of Southern California 1992


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LEIBNIZ, ARISTOTLE, AND INDIVIDUATION 187assigned to d"ifferent "ontological categories": Socrates is a substance, anindividual, or a particular thing (terms which we shall use interchangeably), whereas whiteness is not.What makes Socrates an individual? In what way does he differ froman attribute, or a property? These questions have been discussed sinceancient times, notably by Aristotle who, in the Categories, draws a distinction between that which is present in, or is predicable of other things,and that which is not. 1 Modern philosophers as well have interestedthemselves in this problem. Thus Frege's well-known distinction between"saturated" and "unsaturated" objects 2 might be seen as an attemptto get at the root of this basic categorial distinction between what isindividual and what is not.Now a philosopher may conceivably call the task of providing anexplanation of this categorial contrast a "problem of individuation". Infact one philosopher, namely Castaneda, seems to think of it as "the"problem of individuation. 3 But however it is referred to, this is a problemto which neither Leibniz's Principle of the Identity of Indiscernibles, norAristotle's matter has any apparent relevance.Another "problem of individuation" which we need to set aside is aplainly epistemological problem that has to do with the question of howwe are able to judge whether an individual x is, or is not, numericallyidentical with an individual y. We may, for example find ourselves in aperceptual situation where we are not certain whether there are, say, twonumerically distinct cats, or one cat plus the visual illusion of anothercat, and hence wonder whether the situation is one that offers "felinemultiplicity". The same epistemological problem will also arise, perhapsmore typically, in situations where we are presented with temporallysuccessive appearances of what may or may not be one and the sameindividual. For example, one meets an individual, x, who bears a strikingresemblance to an individual, y, whom one once met. Is x other than y?This is a problem of reidentification, one that has also come to vex manyphilosophers who worry about "transworld identity", in the context ofmodal statements about what might have been the case. What is in question in all of these cases is the ground(s) on which weare able to count, judge, or regard individuals as one, two, or more.Some philosophers might choose to gloss this as a question about howthings are "individuated", for in order to be (correctly) counted as two,the individuals in question must be two in the first place. Still, whatis primarily in question here is knowledge of numerical diversity, asopposed to the fact of numerical diversity itself. Hence if we want to callthis problem by a special name, we should probably refer to it as "theepistemological problem of individuation".Neither of the two problems which we have just explained and labeledis of any concern to us here. Still, we can use them to clarify the nature of University of Southern California 1992


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188 PACIFIC PHILOSOPHICAL QUARTERLYthe problem which we take Leibniz and Aristotle to be discussing. Forreasons which will presently become apparent, it is appropriate to referto this latter as "the ontological problem of individuation". Its natureemerges more clearly when we compare it with the other two.Like the categorial problem of individuation, the ontological problemis based on a contrast of sorts. But the contrast is not one betweenuniversality and particularity, but rather between (numerical) multiplicityand the lack of it. It is one situation when Socrates is the same individualas Callias, quite another when these are two, rather than one individual.Assuming, however, that they are two, one may wonder whether thisnumerical multiplicity, this relation of otherness in which Socrates andCallias stand with respect to each other, whether this is an ultimate factabout the world, or whether it can somehow be derived in a way thattakes us beyond the individuals themselves. This is a problem that canarise only when there is more than one individual, whereas the categorialproblem will presumably still arise as long as there is at least one individual who exemplifies one universal.The desire to find an explanation for the fact of numerical diversitymakes it appropria te to refer to the present problem as "the ontologicalproblem of individuation". Its ontological character will also serve todistinguish it from the epistemological problem which we have justexplained. In both cases there is indeed concern with numerical distinctness. Furthermore, it is theoretically possible that the same entities maybe employed in solving both problems. But the type of concern withnumerical diversity is not the same. Nor need the criteria for successfulsolution be the same in both cases. That is, we can, and probably do havedifferent requirements for entities that are to function as ontologicalgrounds for Socrates' being distinct from Callias, and those on which wecan rely for purposes of determining whether Socrates is distinct fromCallias. Socrates and Callias consist of different quantities of matter.But these are not identifiable apart from the individuals which theycompose at any one time or other, which means that they are not reallywell-suited for solving the epistemological problem of individuation. Butthis in itself need not impugn their possible use in connection with theontological problem. Similar observations can be made about Leibniz'sproperties. Instead of knowledge of numerical diversity waiting uponknowledge of whether properties are shared, it is often the other wayaround, as Dummett has noted. 5 But, again, this does not by itself meanthat it is wrong to seek a solution for the ontological problem of individuation in terms of the qualitative differences, if any, which numericallydistinct particulars display.Not all philosophers agree that what we have referred to as 'the ontological problem of individuation' is a genuine philosophical problem.Loux, for example, apparently does not. 6 Still, by and large, philos-University of Southern California 1992


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LEIBNIZ, ARISTOTLE, AND INDIVIDUATION 189ophers over the centuries have taken numerical diversity as genuinelyproblematic, and have therefore exerted themselves to find entities andfeatures other than individuals themselves in order to explain numericaldiversity. Leibniz and Aristotle are two such philosophers who havecome to be central figures in two rival, well-established and longenduring traditions of thought about the problem of individuation. Itwill be worth our while to examine their views f rom the standpoint of thepossibility that there might be some common conceptual ground betweenthem. I f this does not lead to the discovery of yet another solution to theproblem of individuation, it will at least increase our appreciation of thenature of the difference between their rival approaches to the problem ofindividuation.

3. The Leibnizian View of IndividuationI f there is any single Leibnizian p r i n c i p ~ e that can more or Jess straightforwardly be associated with what we may call the Leibnizian view ofindividuation, it would have to be Leibniz's famous Principle of theIdentity of Indiscernibles (PII). For to say that completely similar substances have to be one in number, is to invite the suggestion that numerical diversity is established on a foundation of qualitative difference, thatsubstances are made numerically diverse by having different properties.

It is commonly thought that PI I is a consequence of other parts ofLeibniz's philosophy, and Leibniz does indeed offer different argumentsfor PI . Thus in the Discourse on Metaphysics the principle appears to bea consequence of the well-known Predicate-in-Notion doctrine. Here wefind Leibniz saying:In [a substance's) concept are included all the experiences belonging to [the substance],together with all of their circumstances and the entire sequence of exterior events. Fromthese considerations there follows a number of important paradoxes; among others, that itis not true that two substances can resemble each other completely and differ only innumber 7

But in his correspondence with Clarke, Leibniz presents PI I as aconsequence of the Principle of Sufficient Reason. At one point he statesa principle which says that "the nature of things requires that every eventhas beforehand its proper conditions, ... the existence of which makesthe sufficient reason for such an event" 8 Shortly afterwards, he says:I infer from this principle that there are not in nature two real, absolute beings indiscerniblefrom each other, because if there were, God and nature would act without reason in ordering the one otherwise than the other; ... University of Southern California 1992


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190 PACIFIC PHILOSOPHICAL QUARTERLYIt is important to note here that talk of indiscernibility and "exact

similarity" is to be understood in terms of what Leibniz elsewhere refersto as "intrinsic denominations" 10 By this he means what contemporaryphilosophers refer to as purely qualitative properties, properties whichcan have multiple instantiations at one and the same time, and whoseexpression involves no reference to any particulars of any kind The ust>of what one might call "identity properties", I mean properties such asbeing Socrates, being Callias, and the like, will certainly serve to makePII true, indeed trivially true. But, as many contemporary philosophershave pointed out, the price of this would be to rob the proposal thatparticulars are individuated by means of their properties of any philosophical significance which it may otherwise have. 11Leibniz must have understood this very well, with the result that heformulates a rather daring principle. To look at a particular gold ring,for example, and think that there cannot be another one which is "exactlylike" it, is far from obvious, especially when one insists on understandingexact likeness the way Leibniz does. It can only lead one to wonder whatsubstances must in themselves be like for this to be true. Russell's conclusion is that a substance must be, according to Leibniz, nothing buta bundle, or a sum, of properties. "If a substance is only defined by itspredicates-which is essential to the Identity of Indiscernibles, then itwould seem to be identical with those predicates" 12 This view is sharedby C. D. Broad, who claims that the Predicate-in-Notion Principle willnot yield PII "unless we add the assumption that a substance is acomplex whole composed of its predicates (or, rather, the 'modifications'which correspond to those predicates) and containing no other constituents." 13To some philosophers, however, PH's association with the bundlistconception of particulars is reason enough to reject PII. But this is notthe only problem that PII has to face. In order for this principle to be ofany use in solving the problem of individuation, it has to be necessarilytrue. Yet, Leibniz's arguments notwithstanding, this is something thatfew, if any, contemporary philosophers are willing to go along with.That PII has to be necessary if one is to say that particulars are individuated by means of their properties is not difficult to see. Someonewho admits that there can be, in principle, two substances that are twodespite sharing all their properties must find a way to answer the questionof how two such substances would be able to be numerically diverse. Thiscannot be on account of their properties, which are assumed to be thesame. One is therefore tempted to conclude that there must be somethingover and above the properties which accomplishes this, contrary to theintentions of those who would like to believe that numerical diversity isbased on a foundation of qualitative difference.Thus it would seem that the only way we can maintain the Leibnizian University of Southern California 1992


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LEIBNIZ, ARISTOTLE, AND INDIVIDUATION 191view of individuation is to insist that PI I is necessarily true. But it isprecisely here that PI I fails to perform. Those who continue to argue forthis principle generally tend to view it as a "regulative" principle ofempirical inquiry, as opposed to being a metaphysical truth about theworld 14 , while others have gone as far as to argue that recent developments in physics have rendered the principle false or , at best, doubtful. 15But notwithstanding all the methodological arguments in favor of PIIand all the factual arguments against it, there seems to be nothing toimpugn the purely logical or metaphysical possibility that it might havebeen false. For there to be two particulars, each of which is an apple andis red, is certainly possible. To think that this situation can turn frombeing possible to being impossible, as we progressively enrich ou r appleconcepts, is a difficult supposition. Not only is it difficult to see at whatpoint this change is to happen, it is equally difficult to see why it shouldhappen at all. After all, what reason is there to think that the compound-ing of universals upon repeatable universals would give anything bu tmore complex, bu t still repeatable, universals?

The failure of PII to be the necessarily true principle which one wouldneed in order to make a case for the claim that particulars are individuated by means of their properties can lead one to look for an alternativeprinciple of individuation, perhaps even to think that numerical diversityhas nothing whatever to do with qualitative diversity.

But what I want to suggest is that, before we altogether give up on theLeibnizian approach, we should consider the following qualification ofPII, a qualification which seems to yield a more promising principle.Instead of saying that no two substances are completely similar, wewould merely assert that no two substances are necessarily completelysimilar. Or, to pu t it in other words, instead of requiring numericallydiverse substances to be actually different in their qualities, we wouldmerely insist upon their being able to have different qualities.

The difference between these two principles, as well as their essentialsimilarity, will be more easily recognized when both principles arerepresented symbolically. With the predicate variable f ranging overpurely qualitative properties, so-called, PI I can be represented thus:

(PII) (x) (y) [(f) ( fx=fy) ::) x =y] .The new principle, which we shall call "The Principle of the Identityof Necessary Similarity" (PINS) merely adds 0 ('necessarily') to theantecedent of the conditional which PI I embodies.

(PINS) (x) (y) [O(f ) (fx=fy)::) x=y]. University of Southern California 1992


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192 PACIFIC PHILOSOPHICAL QUARTERLYLike PII, PINS allows us to maintain that there is some connectionbetween numerical diversity and qualitative difference. But unlike PII,PINS is compatible with there being two particulars that are completelysimilar, so long as these numerically diverse particulars have in them thepower, or ability to become qualitatively different. Thus PINS is notsubject to the imaginative counterexamples which Max Black 16 andothers have put forward in order to show that PII is not necessary.This is not the only advantage which PINS has over PII. For by introducing this notion of an ability to become qualitatively different, itgives the search for a principle of individuation a chance to bring intoplay other ontological constituents beside properties, thereby avoidingthe bundlist view, which PII seems to lead us into. In other words,PINS seems to be compatible with a nonreductionist explanation of particularity, but one which still manages to leave room for qualitativedifference.There may be more than one method of explaining this "ability todiffer", and thus different accounts of individuation might have some

use for PINS. Aristotle, I believe, offers one such method which seems tofollow naturally from his own account of individuation. It will be worthwhile to explore Aristotle's explanation, as this would serve to establish aconceptual connection between these two well-established, but apparentlyunrelated views of individuation.17

4. Matter and the Ability to DifferThat Aristotle, with his theory of matter as the principle of individuation, might have something to say, or at least imply about PINS, shouldcome as no surprise. For the "primary" substances of the Categories aredistinguished by their ability to change, and, in general, to become otherwise than they are at any one time. Moreover, potentialityand accidentalqualification are central notions in the Metaphysics, where they areclosely linked to the notion of matter. Thus when we say numericallydiverse substances must at least be able to become qualitatively different,which is what PINS states, we are employing notions about which bothLeibniz and Aristotle have something to say.In order to see what Aristotle might have to say about PINS, letus look briefly at PII again. What does the fact that PII is at best acontingent principle tell us about being Socrates, or being Callias, orbeing some particular thing or other? What it tells us, I think, is thatbeing Socrates is not the same thing as being human, white, philo-sophical, etc., for all the purely qualitative properties which Socrateshas. For there can be another particular one who is also human, white,philosophical, etc. Call this other one 'Socrites'. But if being Socrates

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LEIBNIZ, ARISTOTLE, AND INDIVIDUATION 193were the same as being human, white, philosophical, etc., then, by thetransitivity of identity, we must conclude that being Socrates and beingSocrites are the same, which, by assumption, they are not.

What this suggests is that Socrates' being does no t resolve itself intothe mere togetherness of a number of properties, no matter how large thenumber is. What is there to Socrates beyond his properties? According toAristotle,When we have the whole, such-and-such a form in this flesh and these bones, this Callias orSocrates, and they are different in virtue of their matter (for it is different), but the same inform, for their form is indivisible18

It is not likely that Aristotle would object to the idea of Socrates andCalli as being "the same" in color, weight, intelligence and so forth, inaddition to their being "the same" in form. They would still have to be"materially" different, which is what sets them apart as two numericallydiverse individuals.

But what does this material difference have to do with PINS or withthe ability to have qualitatively diff erent properties? There are two thingsthat Aristotle says elsewhere about matter which suggest that, althoughmaterial difference is not the same as qualitative difference, the formernevertheless argues for the possibility of the latter and makes it intelligible. These two things have to do with potentiality and the having ofaccidents.

With regard to the first point, it is well known that Aristotle explainspotentiality and change (which is the actualization of some potency orother) by reference to matter. Speaking of matter in relation to thedifferent kinds of change which he recognized, Aristotle says:Matter, in the proper sense of the term, is to be identified with the substratum which isreceptive of coming-to-be and passing-away [substantial change, that is to say], but thesubstratum of the other kinds of change [place, quality, etc.] is also in a certain sense,matter, because all these substrata are receptive of contraries of some kind 19

And since the individual Socrates "already has in him ultimate individual matter" 20 , we have here the Aristotelian explanation of why it ispossible for Socrates to come-to-be, to pass away, and to undergochange of place, quality, etc. For there is matter in him, and this matter isthe substratum which is "receptive of contraries".

Moreover, Socrates' accidents are also bound up with the materialcomponent in him. In the process of explaining why the pale man is not adifferent species of man, Aristotle says,Contraries which are in the definition make a difference in species, but those which are inthe thing taken with its matter do not make one. And so paleness in a man, or darkness University of Southern California 1992


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194 PACIFIC PHILOSOPHICAL QUARTERLYdoes not make one, nor is there any difference in species between the pale man and the darkman, not even if each of them be denoted by one word. For man is here being considered onhis material side, ... 1

As Chappell puts it, "Matter is a cause for Aristotle, and one of itscausal roles is to account for the accidents which a thing has." 22The picture which begins to emerge in light of these statements is thefollowing. Suppose that there are two material particulars which happento be exactly alike. For example, these could be Black's famous spheres,Castor and Pollux. According to Aristotle, each of these two has its"ultimate individual matter". By virtue of its matter, Pollux has poten-tiality as well as accidents. Say it is (accidentally) green. Having poten-tiality to be otherwise than it is, Pollux will, in some possible world orother, be (let's say) blue. A similar story can be told about Castor. LikePollux, it is (accidentally) green. But it has the potentiality to be other-wise than it is, and so it will, in some possible world or other, be (let'ssay) red.But this still falls short of proving that Castor and Pollux can come todiffer. It could be said that in order for them to differ, it is not enoughthat they should be able to change, nor is it enough that they should havesome accidental properties. After all, what if they were always to act inunison? When Castor becomes red, so does Pollux, and when Polluxdevelops a dent here or there, so does Castor. Can't they carry on likethis in all possible worlds?

I f they do, then we shall have to say that Castor and Pollux are not justcompletely similar, but that they are necessarily so. And this, on theAristotelian view of form and accidents, is tantamount to saying thatthere is something in the nature of entities in question which requiresthem not to differ from each other, even in the slightest respect.Now Castor and Pollux are, say, two iron spheres, or planets, whereasSocrates and Callias are two men. Is there anything in the nature of suchentities, or any other type of entity for that matter, which says that theycannot become ever so slightly different in any respect whatsoever?I shall argue for a negative answer to this question on the basis of one(rather unusual) accidental property which is such that if any one of twoentities, or both came to have it, then they would have to be qualitativelydifferent in some respect or other.The property which I have in mind is the property of being (quali-tatively) unique. It is best introduced by reference to the commonlyaccepted view that PII is logically contingent, but it is possible to arguefor its accidental character by reference to Aristotle's own views.Since PII is logically contingent, let us further assume that it is true ofthe actual world. This would, of course, entail that every particular thatexists has a property, or properties which no other particular has. (It goes University of Southern California 1992


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LEIBNIZ, ARISTOTLE, AND INDIVIDUATION 195without saying that the properties that we are talking about are "purelyqualitative properties", so called). In other words, if PII were true, thenevery particular would be characterized by being unique. Furthermore,such uniqueness might accrue to it by virtue of the exclusive instantiat ionof one simple property, or it could come about as a result of exemplifying a unique-making complex property. For example, there may be manysnub-nosed philosophers other than Socrates, but perhaps no one buthim has the property of being a snub-nosed philosopher who drinkshemlock in jail. Socrates will still be qualitatively unique on account ofexclusively instantiating this complex property, even though he sharesthe simpler components with many other individuals. (R.M. Adams seesno intrinsic difference between purely qualitative simple properties andones compounded from these by what seems like "purity-preserving"logical operations such as negation, conjunction, etc. He refers to allpurely qualitative properties, simple and complex, as "suchnesses". 23)

What is being proposed here is for us to think that there is such aproperty as being unique, which is to be distinguished from all the otherproperties whose (exclusive) possession will entail uniqueness. In thisrespect, being unique is like being colored. A thing has this property byvirtue of being, e.g., red, but to be colored is not the same as being red.Similarly, if no philosopher other than Socrates drinks hemlock in jail,then Socrates has "uniqueness". But to attribute this property to himdoes not imply having drunk hemlock in jail or any unique-makingproperty in particular.

The question which we must face next is the question of whetheruniqueness, in the sense explained above, is a property that Aristotlewould view as an accident. I think the answer must be yes. We can arriveat this conclusion by reflecting on one of the roles which Aristot le assignsto the notion of form, namely the role of explaining how a substantialbeing such as Socrates persists over time, despite the many qualitativechanges which he undergoes, and despite the constant interchange ofmatter with the environment.

While Socrates persists, he persists as the same man, not as the samequantity of matter, the same flesh and bones, or the same snub-nosedantidemocrat. However, being material, he is endowed with potentiality,which means that he is bound to undergo changes of many differentkinds. Now some changes can be viewed as changes which form willallow, others have to be viewed as changes which form will not permit.For example, Socrates' form poses no objection to Socrates' becomingpale (or dark), educated (or ignorant) , single (or married). But it will notpermit Socrates to become a statue, or a machine, or to become atom-sized or planet-sized. There are many such "restrictions" which formimposes on what a thing can or cannot become. Of course, we are notsaying that Socrates' form guarantees him endless persistence; eventually University of Southern California 1992


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196 PACIFIC PHILOSOPHICAL QUARTERLYSocrates dies, and is replaced by ashes or dust. But in the face of suchdrastic changes, the form will "depart", and Socrates, by undergoing"substantial change", simply ceases to exist. Still, the fact remains thatbecoming a pile of ashes is not an "accident" which Socrates is at libertyto acquire or not acquire, as is the case with his being pale, or educated.

The suggestion which I want to make here is to view Socrates' accidents as a proper subset of all the potentialities which attach to him byvirtue of his being a material thing, namely, those potentialities whoseactualization is compatible with persistence of form. Having done thiswe can proceed to inquire whether Socrates' form poses any objectionsto Socrates being (qualitatively) unique. I think the answer must be thatit does not. There is really nothing in the nature of a man (or a cat, or ablade of grass, for that matter) which requires being unique or notunique. Either way Socrates is, he can continue to exist as one and thesame man. To see how implausible it is to think that Socrates' formrequires him to be not unique, consider the following supposition.Suppose then that there is a philosopher who shares all of Socrates'properties, snub nose included. Suppose, furthermore, that this latterphilosopher undergoes surgery and acquires an aquiline nose, thereby (inthis instance, at least) putting an end to Socrates' non-uniqueness.Would Socrates then cease to exist? It seems hardly likely. The type of"change" which Socrates undergoes in this particular example is oftenreferred to as a "Cambridge change", which is to say that it is, in a sense,no change at all. (Socrates does not lift a finger.) But even if Socrateswere to take a more active part to ensure his qualitative uniqueness (sayhe dyes his beard, or grows hair on his head), still this need not put anend to his existence either. He may indeed have many necessary, oressential qualities, but uniqueness does no t seem to be one of them.

We must therefore conclude that uniqueness must be viewed as anaccident, at least as far as Aristotle is concerned. As such, it is somethingthat Socrates or Callias (or both) can come to have. Which means, ofcourse, that they can come to be (qualitatively) different.

I f the above argument is sound, then there is reason to believe thatPINS is a principle that Aristotle might have been willing to accept. No tonly do Aristotle's ideas about matter and form, accidents and poten-tiality hint at such a principle, but (what is more) the principle itselfenables us to see matter in a way that traditional interpretations ofAristotle's view of individuation may have overlooked.

Traditional interpretations usually see matter as a static principle ofnumerical diversity. Ross, for example, explains how matter functions asthe source of plurality by referring to the fact that matter exists in greaterquantities than is needed for the realization of one single instance of thespecies. 24 Here it seems as though matter were being thought of as a hugequantity of dough, from which we can make many loaves of bread, onUniversity of Southern California 1992


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LEIBNIZ, ARISTOTLE, AND INDIVIDUATION 197account of there being more dough than is needed for making one singleloaf of a certain predetermined size. Matter does not seem to be activein any way here-it merely "allows" for there to be more than oneindividual.

But if PINS is a consequence of Aristotle's view, as we have suggested,then it will be legitimate to attribute to matter a dynamic role of bringingabout qualitative differentiation between numerically diverse particulars.To see this we should first remind ourselves that the potentialities whichattach to Socrates by virtue of his being a material thing are only partlygoverned, or regulated by form. What we mean by this is the fact thatSocrates' form does not define a fully detailed life-plan for Socrates. Itdoes not determine whether he is going to become pale (or dark), bearded(or beardless), one-legged (or two-legged).In all of these things, and many others as well, Socrates, to useAristotle's own phrase, is being considered on his "material side" 25Considered as such, Socrates is full of possibilities, some of which, atany one time, are being realized just as others are failing to be realized.On his formal side he does indeed persist in being one and the same man,but on his material side he seems to be in a perpetual state of flux.Viewed in this light, matter ceases to be merely static quantity whichexists in greater amounts than is needed for the realization of one singleinstance of the species, as Ross seems to suggest. One can begin to see itas a perpetual source of instability in the being of substances, somethingby virtue of which these latter are always ready to become otherwise thanthey are, and in ways over which form has no control. Given the fact thatqualitative uniqueness is one of those things over which form has nothingto say, it is plausible to conclude that matter can, and sometimes will,serve to introduce qualitative diversity amongst numerically diverseparticulars.Indiana University-Purdue University at IndianapolisIndianapolis, Indiana

NOTES1 The Basic Works of Aristotle, ed., R. McKeon (New York: Random House, 1941),

2a 11-13.2 See Gottl ob Frege, "On Concept and Object", in Translations From the PhilosophicalWorks ofGottlobFrege, eds., P.T. Geach and Max Black (Oxford: Basil Blackwell, 1952).3 See Hector-Neri Castaneda, "Individuation and Non-Identity: Another Look",American Philosophical Quarterly, 12 (1975), p. 132.4 Cf. Saul Kripke, Naming and Necessity (Oxford: Basil Blackwell, 1980), p. 42.5 Michael Dummett, Frege: Philosophy of Language (London: Duckworth, 1973),

p. 544. University of Southern California 1992


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198 PACIFIC PHILOSOPHICAL QUARTERLY6 SeeM. Loux, "Kinds and the Dilemma of Individuation", Review ofMetaphysics, 27

(1974), p. 777.7 Leibniz, Philosophical Papers and Letters, 2d ed., ed., L.E. Loemker (Dordrecht:D. Reidel Publishing Company, 1969), p. 308.

1 Ibid., p. 698.9 Ibid., p. 699.10 Ibid., p. 643.11 See, for example, D.M. Armstrong, Nominalism and Realism Vol. I (Cambridge:Cambridge University Press, 1978), p. 94 and M. Loux, Substance and Attribute (Dordrecht:D. Reidel Publishing Company, 1978), p. 133.12 Bertrand Russell, A Critical Exposition of the Philosophy of Leibniz (London:

George Allen & Unwin, 1900), p. 59.13 C.D. Broad, Leibniz: An Introduction (Cambridge: Cambridge University Press,1975), p. 40.14 See, for example, Dummett, Frege: Philosophy of Language, pp. 543-4, I. Hacking,"The Identity of Indiscernibles", Journal of Philosophy, 72 (1975), pp. 249-56, and

R. Bahlul, "Ockham's Razor and the Identity of Indiscernibles", Philosophy ResearchArchives, 14 (1988-89) pp. 405-14.15 Cf. A. Cones, "Leibniz's Principle of the Identity of Indiscernibles: A FalsePrinciple", Philosophy of Science, 43 (1976), pp. 491-505, and S. French, "Why thePrinciple of the Identity of Indiscernibles Is Not Contingently True Either", Synthese, 78(1989), pp. 141-66.16 M. Black, "The Identity of Indiscernibles", in Universals and Particulars, ed.,

M. Loux (New York: Doubleday & Co., Inc., 1970), p. 234.17 Elsewhere I have sought to present independent arguments for (PINS). SeeR. Bahlul,"Identity and Necessary Similarity", Canadian Journal o f Philosophy, 22 (1992),pp. 531-46.11 The Basic Works of Aristotle, !034a 5-8.19 Ibid., 320a 2-6.20 Ibid., !035b 31-32.Zl Ibid., 1058b 1-6.22 V. Chappell, "Matter", Journal ofPhilosophy, 70 (1973), p. 686.23 R.M. Adams, "Primi tive Thisness and Primitive Identity", Journal ofPhilosophy, 76(1979), p. 8.24 D. Ross, Aristotle (London: Methuen & Co., Ltd., 1923), p. 170.25 The Basic Works o fAristotle, 1058b 6.

REFERENCESAdams, R.M. "Primitive Thisness and Primitive Identity". Journal of Philosophy, 76(1979), 5-26.Aristotle. The Basic Works of Aristotle. Ed., R. McKeon. New York: Random House,1941.Armstrong, D.M. Nominalism and Realism, Vol. I . Cambridge: Cambridge UniversityPress, 1978.Bahlul, R. "Ockham's Razor and the Identity of Indiscernibles". Philosophy ResearchArchives, 14 (1988-89), 405-14.Bahlul, R. "Identity and Necessary Similarity". Canadian Journal of Philosophy, 22(1992), 531-46.Black, M. "The Identity of Indiscernibles". In Universals and Particulars. Ed., M. Loux.

New York: Doubleday & Co., Inc., 1970. University of Southern California 1992


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LEIBNIZ, ARISTOTLE, AND INDIVIDUATION 199Broad, C.D. Leibniz: An Introduction. Ed., C. Lewy. Cambridge: Cambridge UniversityPress, 1975.Castaneda, H.-N. "Individuation and Non-Identity: Another Look". American Philo-sophical Quarterly, 12 {1975), 131-40.Chappell, V. "Matter." Journal ofPhilosophy, 70 {1973), 679-96.Cortes, A. "Leibniz's Principle of the Identity of Indiscernibles: A False Principle".Philosophy of Science, 43 (1976), 491-505.Dummett, M. Frege: Philosophy ofLanguage. London: Duckworth, 1973.Frege, G. "On Concept and Object". In Translations From the Philosophical Works ofGottlob Frege. Eds., P.T. Geach and M. Black. Oxford: Basil Blackwell, 1952.French, S. "Why the Principle of the Identity of Indiscemibles Is Not Contingently True

Either." Synthese, 78 (1989), 141-66.Hacking, I. "The Identity of Indiscernibles." Journal o f Philosophy, 72 (1975), 249-56.Kripke, S. Naming and Necessity. Oxford: Basil Blackwell, 1980.Leibniz. Philosophical Papers and Letters, 2d ed. Ed., L.E. Loemker. Dordrecht:

D. Reidel Publishing Company, 1969.Loux, M. "Kinds and the Dilemma of Individuation". Review ofMetaphysics, 27 (1974),773-84.Loux, M. Substance and Attribute. Dordrecht: D. Reidel Publishing Company, 1978.Ross, D. Aristotle. London: Methuen & Co., Ltd., 1923.Russell, B. A Critical Exposition of the Philosophy of Leibniz. London: George Allen &

Unwin, 1900.

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