LEIBNIZ, ARISTOTLE, AND THE PROBLEM OF INDIVIDUATION

BY

RAJA BAHLUL

1. Introduction

Few metaphysical problems can be said to rival the so-called problem of individuation when it comes to the number of proffered solutions. And among the many solutions scattered throughout the pages of the history of philosophy, probably no two solutions offer a more seemingly pro­found or marked contrast than the ones which we find in Leibniz and Aristotle.

Leibniz, through his famous Principle of the Identity of Indiscernibles (PII), affirms that no two substances are completely alike, that every substance has a property, or properties, which no other substance has. Aristotle, on the other hand, neither affirms nor denies this, but for him individuation is accomplished by each substance having "different matter", rather than different properties.

In many ways, these two views are worlds apart, for there can hardly be 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 as educated, white, man, which both Socrates and Callias share in common with many other things. But when we think of matter, or at least the matter which Socrates is composed of at any one time, we think of that which 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 two approaches which we find in Aristotle and Leibniz are to some extent

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reconcilable. More precisely, I intend to show that there is a principle which is closely related to PII, and which can be viewed as a consequence of the Aristotelian view of individuation. The new principle is called "The Principle of the Identity of Necessary Similarity" (PINS). In due course, it will be explained how this new principle can be looked at as a slight but significant modification of the more familiar PII, and also how it can plausibly be derived from various things which Aristotle ~ays about matter.

In Section 2, I offer a brief explanation of what I mean by "the problem of individuation", the problem which I take Aristotle and Leibniz to be concerned with. In Section 3, I describe the Leibnizian view, and dwell on the difficulties which might move one to seek an alternative account of individuation. I conclude this section by intro­ducing PINS, a PH-like principle which does not seem to be subject to the kind of objections that PII faces in connection with the problem of individuation. Finally, in Section 4, I discuss Aristotle's view of matter as the principle of individuation, and suggest that PINS can be viewed as a consequence of the Aristotelian position.

2. The Problem of Individuation

To a large extent, the world presents itself to us in experience as some­thing which consists of an indefinite number of particulars each of which has some properties which it shares with other particulars. Universality and 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 can be said to be qualitatively similar, even "the same", has come to be known 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 to say 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 as having little or nothing to do with the problem which we take Leibniz and Aristotle to be trying to solve. The first of these two problems has, at various times, been called metaphysical, logical, or linguistic, but it can perhaps 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 categori~l contrast between what is individual (particular) and what is universal, between, e.g., Socrates and whiteness. These two can indeed be spoken of in the same breath as two "things", "entities", or "existents", but, presumably, when all is said and done, they must be

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assigned to d"ifferent "ontological categories": Socrates is a substance, an individual, 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 from an attribute, or a property? These questions have been discussed since ancient 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 interested themselves in this problem. Thus Frege's well-known distinction between "saturated" and "unsaturated" objects 2 might be seen as an attempt to get at the root of this basic categorial distinction between what is individual and what is not.

Now a philosopher may conceivably call the task of providing an explanation of this categorial contrast a "problem of individuation". In fact one philosopher, namely Castaneda, seems to think of it as "the" problem of individuation. 3 But however it is referred to, this is a problem to which neither Leibniz's Principle of the Identity of Indiscernibles, nor Aristotle's matter has any apparent relevance.

Another "problem of individuation" which we need to set aside is a plainly epistemological problem that has to do with the question of how we are able to judge whether an individual x is, or is not, numerically identical with an individual y. We may, for example find ourselves in a perceptual situation where we are not certain whether there are, say, two numerically distinct cats, or one cat plus the visual illusion of another cat, and hence wonder whether the situation is one that offers "feline multiplicity". The same epistemological problem will also arise, perhaps more typically, in situations where we are presented with temporally successive appearances of what may or may not be one and the same individual. For example, one meets an individual, x, who bears a striking resemblance 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 many philosophers who worry about "transworld identity", in the context of modal statements about what might have been the case. •

What is in question in all of these cases is the ground(s) on which we are able to count, judge, or regard individuals as one, two, or more. Some philosophers might choose to gloss this as a question about how things are "individuated", for in order to be (correctly) counted as two, the individuals in question must be two in the first place. Still, what is primarily in question here is knowledge of numerical diversity, as opposed to the fact of numerical diversity itself. Hence if we want to call this problem by a special name, we should probably refer to it as "the epistemological problem of individuation".

Neither of the two problems which we have just explained and labeled is of any concern to us here. Still, we can use them to clarify the nature of

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the problem which we take Leibniz and Aristotle to be discussing. For reasons which will presently become apparent, it is appropriate to refer to this latter as "the ontological problem of individuation". Its nature emerges more clearly when we compare it with the other two.

Like the categorial problem of individuation, the ontological problem is based on a contrast of sorts. But the contrast is not one between universality and particularity, but rather between (numerical) multiplicity and the lack of it. It is one situation when Socrates is the same individual as Callias, quite another when these are two, rather than one individual. Assuming, however, that they are two, one may wonder whether this numerical multiplicity, this relation of otherness in which Socrates and Calli as stand with respect to each other, whether this is an ultimate fact about the world, or whether it can somehow be derived in a way that takes us beyond the individuals themselves. This is a problem that can arise only when there is more than one individual, whereas the categorial problem 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 diversity makes it appropriate to refer to the present problem as "the ontological problem of individuation". Its ontological character will also serve to distinguish it from the epistemological problem which we have just explained. In both cases there is indeed concern with numerical distinct­ness. Furthermore, it is theoretically possible that the same entities may be employed in solving both problems. But the type of concern with numerical diversity is not the same. Nor need the criteria for successful solution be the same in both cases. That is, we can, and probably do have different requirements for entities that are to function as ontological grounds for Socrates' being distinct from Callias, and those on which we can rely for purposes of determining whether Socrates is distinct from Callias. Socrates and Callias consist of different quantities of matter. But these are not identifiable apart from the individuals which they compose at any one time or other, which means that they are not really well-suited for solving the epistemological problem of individuation. But this in itself need not impugn their possible use in connection with the ontological problem. Similar observations can be made about Leibniz's properties. Instead of knowledge of numerical diversity waiting upon knowledge of whether properties are shared, it is often the other way around, as Dummett has noted. 5 But, again, this does not by itself mean that it is wrong to seek a solution for the ontological problem of individu­ation in terms of the qualitative differences, if any, which numerically distinct 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-

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ophers over the centuries have taken numerical diversity as genuinely problematic, and have therefore exerted themselves to find entities and features other than individuals themselves in order to explain numerical diversity. Leibniz and Aristotle are two such philosophers who have come to be central figures in two rival, well-established and long­enduring traditions of thought about the problem of individuation. It will be worth our while to examine their views from the standpoint of the possibility that there might be some common conceptual ground between them. If this does not lead to the discovery of yet another solution to the problem of individuation, it will at least increase our appreciation of the nature of the difference between their rival approaches to the problem of individuation.

3. The Leibnizian View of Individuation

If there is any single Leibnizian princip~e that can more or Jess straight­forwardly be associated with what we may call the Leibnizian view of individuation, it would have to be Leibniz's famous Principle of the Identity 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, that substances are made numerically diverse by having different properties.

It is commonly thought that PII is a consequence of other parts of Leibniz's philosophy, and Leibniz does indeed offer different arguments for PI I. Thus in the Discourse on Metaphysics the principle appears to be a consequence of the well-known Predicate-in-Notion doctrine. Here we find 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. From these considerations there follows a number of important paradoxes; among others, that it is not true that two substances can resemble each other completely and differ only in number 7•

But in his correspondence with Clarke, Leibniz presents PII as a consequence of the Principle of Sufficient Reason. At one point he states a principle which says that "the nature of things requires that every event has beforehand its proper conditions, ... the existence of which makes the 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 indiscernible from each other, because if there were, God and nature would act without reason in order­ing the one otherwise than the other; ... 9

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It is important to note here that talk of indiscernibility and "exact similarity" is to be understood in terms of what Leibniz elsewhere refers to as "intrinsic denominations" 10• By this he means what contemporary philosophers refer to as purely qualitative properties, properties which can have multiple instantiations at one and the same time, and whose expression involves no reference to any particulars of any kind The ust> of what one might call "identity properties", I mean properties such as being Socrates, being Callias, and the like, will certainly serve to make PII true, indeed trivially true. But, as many contemporary philosophers have pointed out, the price of this would be to rob the proposal that particulars are individuated by means of their properties of any philo­sophical significance which it may otherwise have. 11

Leibniz must have understood this very well, with the result that he formulates a rather daring principle. To look at a particular gold ring, for example, and think that there cannot be another one which is "exactly like" it, is far from obvious, especially when one insists on understanding exact likeness the way Leibniz does. It can only lead one to wonder what substances must in themselves be like for this to be true. Russell's con­clusion is that a substance must be, according to Leibniz, nothing but a bundle, or a sum, of properties. "If a substance is only defined by its predicates-which is essential to the Identity of Indiscernibles, then it would seem to be identical with those predicates" 12• This view is shared by C. D. Broad, who claims that the Predicate-in-Notion Principle will not yield PII "unless we add the assumption that a substance is a complex whole composed of its predicates (or, rather, the 'modifications' which correspond to those predicates) and containing no other con­stituents." 13

To some philosophers, however, PH's association with the bundlist conception of particulars is reason enough to reject PII. But this is not the only problem that PII has to face. In order for this principle to be of any use in solving the problem of individuation, it has to be necessarily true. Yet, Leibniz's arguments notwithstanding, this is something that few, 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. Someone who admits that there can be, in principle, two substances that are two despite sharing all their properties must find a way to answer the question of how two such substances would be able to be numerically diverse. This cannot be on account of their properties, which are assumed to be the same. One is therefore tempted to conclude that there must be something over and above the properties which accomplishes this, contrary to the intentions of those who would like to believe that numerical diversity is based on a foundation of qualitative difference.

Thus it would seem that the only way we can maintain the Leibnizian

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view of individuation is to insist that PII is necessarily true. But it is precisely here that PII fails to perform. Those who continue to argue for this principle generally tend to view it as a "regulative" principle of empirical inquiry, as opposed to being a metaphysical truth about the world 14 , while others have gone as far as to argue that recent develop­ments in physics have rendered the principle false or, at best, doubtful. 15

But notwithstanding all the methodological arguments in favor of PII and all the factual arguments against it, there seems to be nothing to impugn the purely logical or metaphysical possibility that it might have been false. For there to be two particulars, each of which is an apple and is red, is certainly possible. To think that this situation can turn from being possible to being impossible, as we progressively enrich our apple­concepts, is a difficult supposition. Not only is it difficult to see at what point this change is to happen, it is equally difficult to see why it should happen at all. After all, what reason is there to think that the compound­ing of universals upon repeatable universals would give anything but more complex, but still repeatable, universals?

The failure of PII to be the necessarily true principle which one would need 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 alternative principle of individuation, perhaps even to think that numerical diversity has nothing whatever to do with qualitative diversity.

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

The difference between these two principles, as well as their essential similarity, will be more easily recognized when both principles are represented symbolically. With the predicate variable f ranging over purely qualitative properties, so-called, PII can be represented thus:

(PII) (x) (y) [(f) (fx=fy) ::) x = y].

The new principle, which we shall call "The Principle of the Identity of Necessary Similarity" (PINS) merely adds 0 ('necessarily') to the antecedent of the conditional which PII embodies.

(PINS) (x) (y) [O(f) (fx=fy)::) x=y].

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Like PII, PINS allows us to maintain that there is some connection between numerical diversity and qualitative difference. But unlike PII, PINS is compatible with there being two particulars that are completely similar, so long as these numerically diverse particulars have in them the power, or ability to become qualitatively different. Thus PINS is not subject to the imaginative counterexamples which Max Black 16 and others 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, it gives the search for a principle of individuation a chance to bring into play other ontological constituents beside properties, thereby avoiding the 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 qualitative difference.

There may be more than one method of explaining this "ability to differ", and thus different accounts of individuation might have some use for PINS. Aristotle, I believe, offers one such method which seems to follow naturally from his own account of individuation. It will be worth­while to explore Aristotle's explanation, as this would serve to establish a conceptual connection between these two well-established, but apparently unrelated views of individuation. 17

4. Matter and the Ability to Differ

That Aristotle, with his theory of matter as the principle of individu­ation, might have something to say, or at least imply about PINS, should come as no surprise. For the "primary" substances of the Categories are distinguished by their ability to change, and, in general, to become other­wise than they are at any one time. Moreover, potentiality and accidental qualification are central notions in the Metaphysics, where they are closely linked to the notion of matter. Thus when we say numerically diverse substances must at least be able to become qualitatively different, which is what PINS states, we are employing notions about which both Leibniz and Aristotle have something to say.

In order to see what Aristotle might have to say about PINS, let us look briefly at PII again. What does the fact that PII is at best a contingent principle tell us about being Socrates, or being Callias, or being some particular thing or other? What it tells us, I think, is that being Socrates is not the same thing as being human, white, philo­sophical, etc., for all the purely qualitative properties which Socrates has. 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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were the same as being human, white, philosophical, etc., then, by the transitivity of identity, we must conclude that being Socrates and being Socrites are the same, which, by assumption, they are not.

What this suggests is that Socrates' being does not resolve itself into the mere togetherness of a number of properties, no matter how large the number is. What is there to Socrates beyond his properties? According to Aristotle,

When we have the whole, such-and-such a form in this flesh and these bones, this Callias or Socrates, and they are different in virtue of their matter (for it is different), but the same in form, for their form is indivisible 18•

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

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

With regard to the first point, it is well known that Aristotle explains potentiality and change (which is the actualization of some potency or other) by reference to matter. Speaking of matter in relation to the different kinds of change which he recognized, Aristotle says:

Matter, in the proper sense of the term, is to be identified with the substratum which is receptive of coming-to-be and passing-away [substantial change, that is to say], but the substratum 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 is possible for Socrates to come-to-be, to pass away, and to undergo change of place, quality, etc. For there is matter in him, and this matter is the substratum which is "receptive of contraries".

Moreover, Socrates' accidents are also bound up with the material component in him. In the process of explaining why the pale man is not a different species of man, Aristotle says,

Contraries which are in the definition make a difference in species, but those which are in the thing taken with its matter do not make one. And so paleness in a man, or darkness

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does not make one, nor is there any difference in species between the pale man and the dark

man, not even if each of them be denoted by one word. For man is here being considered on his material side, ... 21

As Chappell puts it, "Matter is a cause for Aristotle, and one of its causal roles is to account for the accidents which a thing has." 22

The picture which begins to emerge in light of these statements is the following. Suppose that there are two material particulars which happen to 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 poten­tiality as well as accidents. Say it is (accidentally) green. Having poten­tiality to be otherwise than it is, Pollux will, in some possible world or other, be (let's say) blue. A similar story can be told about Castor. Like Pollux, it is (accidentally) green. But it has the potentiality to be other­wise than it is, and so it will, in some possible world or other, be (let's say) red.

But this still falls short of proving that Castor and Pollux can come to differ. It could be said that in order for them to differ, it is not enough that they should be able to change, nor is it enough that they should have some accidental properties. After all, what if they were always to act in unison? When Castor becomes red, so does Pollux, and when Pollux develops a dent here or there, so does Castor. Can't they carry on like this in all possible worlds?

If they do, then we shall have to say that Castor and Pollux are not just completely similar, but that they are necessarily so. And this, on the Aristotelian view of form and accidents, is tantamount to saying that there is something in the nature of entities in question which requires them not to differ from each other, even in the slightest respect.

Now Castor and Pollux are, say, two iron spheres, or planets, whereas Socrates and Callias are two men. Is there anything in the nature of such entities, or any other type of entity for that matter, which says that they cannot 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 two entities, or both came to have it, then they would have to be qualitatively different in some respect or other.

The property which I have in mind is the property of being (quali­tatively) unique. It is best introduced by reference to the commonly accepted view that PII is logically contingent, but it is possible to argue for its accidental character by reference to Aristotle's own views.

Since PII is logically contingent, let us further assume that it is true of the actual world. This would, of course, entail that every particular that exists has a property, or properties which no other particular has. (It goes

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without saying that the properties that we are talking about are "purely qualitative properties", so called). In other words, if PII were true, then every particular would be characterized by being unique. Furthermore, such uniqueness might accrue to it by virtue of the exclusive instantiation of one simple property, or it could come about as a result of exemplify­ing a unique-making complex property. For example, there may be many snub-nosed philosophers other than Socrates, but perhaps no one but him has the property of being a snub-nosed philosopher who drinks hemlock in jail. Socrates will still be qualitatively unique on account of exclusively instantiating this complex property, even though he shares the simpler components with many other individuals. (R.M. Adams sees no intrinsic difference between purely qualitative simple properties and ones compounded from these by what seems like "purity-preserving" logical operations such as negation, conjunction, etc. He refers to all purely qualitative properties, simple and complex, as "suchnesses". 23)

What is being proposed here is for us to think that there is such a property as being unique, which is to be distinguished from all the other properties whose (exclusive) possession will entail uniqueness. In this respect, being unique is like being colored. A thing has this property by virtue 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 him does not imply having drunk hemlock in jail or any unique-making property in particular.

The question which we must face next is the question of whether uniqueness, in the sense explained above, is a property that Aristotle would view as an accident. I think the answer must be yes. We can arrive at this conclusion by reflecting on one of the roles which Aristotle assigns to the notion of form, namely the role of explaining how a substantial being such as Socrates persists over time, despite the many qualitative changes which he undergoes, and despite the constant interchange of matter with the environment.

While Socrates persists, he persists as the same man, not as the same quantity of matter, the same flesh and bones, or the same snub-nosed antidemocrat. However, being material, he is endowed with potentiality, which means that he is bound to undergo changes of many different kinds. Now some changes can be viewed as changes which form will allow, others have to be viewed as changes which form will not permit. For example, Socrates' form poses no objection to Socrates' becoming pale (or dark), educated (or ignorant), single (or married). But it will not permit Socrates to become a statue, or a machine, or to become atom­sized or planet-sized. There are many such "restrictions" which form imposes on what a thing can or cannot become. Of course, we are not saying that Socrates' form guarantees him endless persistence; eventually

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Socrates dies, and is replaced by ashes or dust. But in the face of such drastic changes, the form will "depart", and Socrates, by undergoing "substantial change", simply ceases to exist. Still, the fact remains that becoming a pile of ashes is not an "accident" which Socrates is at liberty to 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 by virtue of his being a material thing, namely, those potentialities whose actualization is compatible with persistence of form. Having done this we can proceed to inquire whether Socrates' form poses any objections to Socrates being (qualitatively) unique. I think the answer must be that it does not. There is really nothing in the nature of a man (or a cat, or a blade of grass, for that matter) which requires being unique or not unique. Either way Socrates is, he can continue to exist as one and the same man. To see how implausible it is to think that Socrates' form requires 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 latter philosopher undergoes surgery and acquires an aquiline nose, thereby (in this 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 often referred 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 Socrates were to take a more active part to ensure his qualitative uniqueness (say he dyes his beard, or grows hair on his head), still this need not put an end to his existence either. He may indeed have many necessary, or essential qualities, but uniqueness does not seem to be one of them.

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

If the above argument is sound, then there is reason to believe that PINS is a principle that Aristotle might have been willing to accept. Not only do Aristotle's ideas about matter and form, accidents and poten­tiality hint at such a principle, but (what is more) the principle itself enables us to see matter in a way that traditional interpretations of Aristotle's view of individuation may have overlooked.

Traditional interpretations usually see matter as a static principle of numerical diversity. Ross, for example, explains how matter functions as the source of plurality by referring to the fact that matter exists in greater quantities than is needed for the realization of one single instance of the species. 24 Here it seems as though matter were being thought of as a huge quantity of dough, from which we can make many loaves of bread, on

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account of there being more dough than is needed for making one single loaf of a certain predetermined size. Matter does not seem to be active in any way here-it merely "allows" for there to be more than one individual.

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 bringing about qualitative differentiation between numerically diverse particulars. To see this we should first remind ourselves that the potentialities which attach to Socrates by virtue of his being a material thing are only partly governed, or regulated by form. What we mean by this is the fact that Socrates' form does not define a fully detailed life-plan for Socrates. It does 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 use Aristotle's own phrase, is being considered on his "material side" 25 •

Considered as such, Socrates is full of possibilities, some of which, at any 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 which exists in greater amounts than is needed for the realization of one single instance of the species, as Ross seems to suggest. One can begin to see it as a perpetual source of instability in the being of substances, something by virtue of which these latter are always ready to become otherwise than they are, and in ways over which form has no control. Given the fact that qualitative uniqueness is one of those things over which form has nothing to say, it is plausible to conclude that matter can, and sometimes will, serve to introduce qualitative diversity amongst numerically diverse particulars.

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NOTES

1 The Basic Works of Aristotle, ed., R. McKeon (New York: Random House, 1941), 2a 11-13.

2 See Gottlob Frege, "On Concept and Object", in Translations From the Philosophical Works ofGottlob Frege, 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.

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198 PACIFIC PHILOSOPHICAL QUARTERLY

6 SeeM. Loux, "Kinds and the Dilemma of Individuation", Review of Metaphysics, 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 Research Archives, 14 (1988-89) pp. 405-14.

15 Cf. A. Cones, "Leibniz's Principle of the Identity of Indiscernibles: A False Principle", Philosophy of Science, 43 (1976), pp. 491-505, and S. French, "Why the Principle 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 of 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 of Philosophy, 70 (1973), p. 686. 23 R.M. Adams, "Primitive Thisness and Primitive Identity", Journal of Philosophy, 76

(1979), p. 8. 24 D. Ross, Aristotle (London: Methuen & Co., Ltd., 1923), p. 170. 25 The Basic Works of Aristotle, 1058b 6.

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Adams, 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 University Press, 1978.

Bahlul, R. "Ockham's Razor and the Identity of Indiscernibles". Philosophy Research Archives, 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.

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Broad, C.D. Leibniz: An Introduction. Ed., C. Lewy. Cambridge: Cambridge University Press, 1975.

Castaneda, H.-N. "Individuation and Non-Identity: Another Look". American Philo­sophical Quarterly, 12 {1975), 131-40.

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Gottlob 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

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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 &

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