ayers - individuals without sortals

7/27/2019 Ayers - Individuals Without Sortals

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Canadian Journal of Philosophy

Individuals without SortalsAuthor(s): Michael R. AyersSource: Canadian Journal of Philosophy, Vol. 4, No. 1 (Sep., 1974), pp. 113-148Published by: Canadian Journal of PhilosophyStable URL: http://www.jstor.org/stable/40230490 .

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CANADIAN JOURNAL OF PHILOSOPHYVolume IV, Number 7, September 1974

Individuals W i t h o u t S o r t a l sMICHAEL R. AYERS, Wadham College, Oxford

Consideration of the counting and reidentification of particulars leadsnaturally enough to the orthodox doctrine that, Mon pain of indefiniteness,"1 anidentity statement in some way involves or presupposes a general term or"covering concept1': i.e., that the principium individuationis or criterion ofidentity implied depends upon the kind of thing in question. Thus it is said thatan auditor understands the question whether A is the same as B only in so far ashe knows, however informally or implicitly, the answer to the supplementaryquestion, 'The same what?"It is true that there are disputes.2 Some hold that the "covering concept"completes, in each proposition, the incomplete concept of identity, determining,as it were, the kind of sameness involved; while others strongly deny thatidentity itself is an incomplete concept, preferring to locate the function of thecovering concept within the acts of reference necessary to any identitystatement. On the latter view, simply in order to have something definite inmind, we must know what kind of thing it is essentially. It is perhaps somethingof an oversimplification, but a suggestive one, to say that the dispute concernsthe question whether or not the sentence "A is the same man as B" can beexplicated by the sentence "The man A is identical with the man B." My ownpresent concern, however, is with the possibility that this sort of dispute overliessome common assumption itself deserving critical examination.Now it is, I believe, indisputable that if a speaker indicates something, e.g.demonstratively, then in order fpr other people to catch his reference, and tounderstand what he is indicating,' they must know, at some level of generality,

1 David Wiggins, Identity and Spatio-Temporal Continuity (Oxford, 1967), p. 27.2 Represented, e.g., by Geach on the one side and Quine on the other: vid. P. T.Geach, "Identity," Review of Metaphysics, XXI (1967); and W. V. O. Quine, Froma Logical Point of View (2nd ed.; New York, 1961), pp. 67f.; cf. John Perry, "TheSame F," Philosophical Review, LXXIX (1970).

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Michael R. Ayerswhat kind of thing he is intending to indicate. They must certainly know whatcategory of thing it is: whether it is an event, a physical object, a quality orwhatever. It is, with unimportant exceptions, impossible to think aboutsomething without knowing that much about it. But does the knowledgenecessary for identification extend further in this direction? Must it be knownnot only that the object of reference is an event or process, but that it isspecifically an explosion, a cricket-match or a fit of anger? The plausibility andpopularity of the view that such further knowledge is indeed necessary stems, asI have said, partly from the topic of identity through time and partly from thenature of number. If someone says no more than "It will be over in one hour'stime," he would naturally be taken to speak of an event or process, but it will beimpossible to know whether his assertion is true unless we know more: e.g. thathe was referring to the bombardment rather than to the battle or .to the war.Likewise we cannot count events merely, we must know what sort of event tocount.

Yet is what is true of the identification of events also true of theidentification of physical objects or "things" in the narrow sense? If we can showthat it is not, and I believe that we can, then a direct, refreshingly "logical"rather than "epistemological" route is opened up towards the theory that rightlyenjoys some popularity, namely that there is something central and fundamentalabout this category of individuals, the "primary substances." For theirindividuality would then appear peculiarly "absolute" and independent ofhuman concepts or ways of looking at the world.Philosophers who would contemplate such a prospect with equanimitymight be called "realists," and their opponents "conceptualists." This, at anyrate, is the dichotomy that I shall adopt for convenience, although admittedly itdoes less than justice to the possibilities. There could, for example, bequasi-Kantian conceptual ists who allowed an ineluctable primacy to the categoryof physical object in "our conceptual scheme." I shall return, very briefly, to themetaphysical issue, but for the most part my concern will be with theindependently important suggestion that much that is regularly alleged about theindividuating function of "sortal" concepts is completely false.Adopting, then, a "realist" tone of voice, let me first say that physicalobjects are natural unities or natural structures which come into existence,continue to exist and cease to exist quite independently of any conceptualizingon bur part.3 The principle of unity in each case is causal: it is a proper object ofnatural science, and may be known or unknown to human beings, who arethemselves perhaps the most remarkable examples of such unities. Lessremarkable are coherent lumps of metal, stone, hardened mud and so on; and

3 Neither here nor elsewhere am I attempting to define the category of physicalobject.

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Individuals without Sortalssimple cohesion, however it is to be explained in each case, is an importantnatural principle of unity. For this rather primitive kind of thing, ceasing to existcharacteristically consists in breaking into pieces, and continuing to exist, in notdoing so. There is nothing "ideal" about such unities, as a man will discoverwhen a heavy and relatively indissoluble one drops on his toe. If it remains thereimmovably, it does so with an ungentle disregard for his conceptual scheme.A fact that has been known or guessed for a very long time is that manysuch unities or things depend for their continuing existence on the continuousutilization, dissipation and replacement of the stuff that composes them, just alittle like a bonfire and very remotely like a river. This consideration seems tohave worried some early thinkers, especially on top of some purely logicalperplexities about change in general, or a thing's becoming what it is not. Butsoon, if not immediately, the worry found resolution in the reflection that theindependent reality of the logos of the whole, and the continuity of thisprinciple of unity, is not cast in doubt by the process-like character of itsoperation. This line of thought, while valuable, proved also dangerous. For thepresent let it stand.

Identification, we are often told, presupposes classification. Yet when aman is presented with some quite strange thing, a simple creature, say, or itsskeleton, or a crystal, or an amorphous but coherent lump of some unknownsubstance, he does not need a preformed concept, none at least less general orprimitive than "thing," in order to decide, become aware or guess that he isconfronted by a thing with some sort of synchronic unity. Nor need there be,simultaneous with this realization, any relevant conceptualization orclassification of the thing as a member of a specific kind. Consequently thereneed be no such general concept or sortal in terms of which a judgment aboutthe object must be expressed or understood- "Here is a queer thing" is notelliptical. By the same token the man can be aware of the continuity of the thingover a period of observation, its diachronic unity, without bothering his headabout what sort or species of thing he has picked up and is carrying about in hishand. He may not even know whether the object is animate or inanimate. It is acorollary that he need not know, prior to further observation, what alterationthis thing is liable to undergo or is capable of surviving. In such a state ofignorance he would be rash to emulate Linnaeus, and before trying his hand atclassification he had better wait and see what the object does, or perhapsactively conduct experiments upon it. Yet according to the clearest advice of theconceptualist or "Same what?" theory, our observer cannot even regard it as athing, or at any rate as a thing capable of continuity, except under some sortalconcept that will automatically determine what is essential to it and what not,and under what conditions it will cease to exist.

It may be helpful to remove a common source of misunderstanding. I donot particularly wish to deny that in order to identify or be aware of someobject before him a man must be aware of it as possessing certain recognizable

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Michael R. Ayersproperties over and above its position in space. In this trivial sense specific"conceptual ization" and classification may be involved in identification. Let ussuppose that a man identifies something in his neighbourhood as this small,round, fluffy, yellow thing that squeaks when pushed. The significant point isthat the content of this adequate identifying description of a chick does nottouch the basis of its unity and continuity, which may be quite unknown. Everyproperty that figures in an initial and adequate identification of the thing(except, as Descartes saw, its occupancy of space) may presently pass from it tothe surprise, perhaps, of the observer, without giving the least ground for thejudgment that the object thus identified has ceased to exist. It is a fact about theworld (reflected, no doubt, in our concept chick) that the possessors of theseparticular observable properties do not in general keep them until the end oftheir existence, but lose them when they become hens. If, after such a transition,we are sentimentally inclined to talk as if the chick itself no longer exists, thepretended existential discontinuity might well be described as "ideal." Thecontinuity, by contrast, is real.What I am here denying appears to be expressed very admirably, if withoutevident justification, by David Wiggins in his recent book, when, after remarkingthat "we cannot single out bare space-occupying matter," he writes, "How wedo our singling out determines both what we single out, and (which is the samething) the principle of individuation of what we single out, and (again the samething) the conditions of existence of what we have singled out.1'4A serious objection to conceptualism, therefore, is that the life-histories ofnatural things have to be discovered, often gradually and with difficulty, and socannot be supposed to be determined by an observer's conceptual scheme. Theobjection would sometimes, I think, meet with a pragmatist or instrumentalistinterpretation of such discovery. On this interpretation experience may in someunexplained way lead us to drop some part of our conceptual scheme as not"pragmatically acceptable": e.g., a part incorporating the distinction betweenmaggots and houseflies as a specific difference on a level with the differencebetween sheep and goats. In order to think the continuity that, on the ordinaryway of talking, was discovered between maggot and insect, we must do so (theargument continues) under a new covering concept of (e.g.) fly such that a fly isfirst a larva, then a pupa, then an adult fly. In the circumstances of ourexperience, it will be said, the new scheme will strike us as "natural," and theso-called discovery of a continuity can be seen to consist in the discovery thatthe fresh suit of conceptual clothes is indeed "pragmatically acceptable." By thisor some equally elaborate story reality can be kept at a proper distance. Yet itmust be remarked that as an account of the observation of continuity it has noindependent plausibility whatsoever, and so is vulnerable to the charge that it is

4 Wiggins, op. eft., p. 42.

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Individuals without Sortalsmerely doctrinaire.5A very much more attractive view is that no observer who becomesacquainted with what goes on from pupation to emergence could rationally takeit to involve the cessation of the existence of a maggot or indeed of any thingwhatsoever from any conceivable point of view. For, on the assumption that heis not simply mistaken about the general character of the underlying causalprocess (as he might have been had he observed the emergence of an ichneumonwasp from a parasitized pupa), he has witnessed a continuity and nothing else. Itis a trivial, indeed tautologous point that at the same time he must suppose thathe is observing a thing of such a kind as can survive the observed metamorphosis.What is important is that the recognition of the fact of continuity is logicallyindependent of the possession of sortal concepts, whereas the formation of thesortal concept is at least psychologically dependent, in normal cases, upon therecognition of continuity. It should not come as a surprise that a fact that can beindependently recognized can be independently stated.Why then is it so popularly supposed that the judgment of continuity insuch cases is either relative to a preconceived sortal or else essentially involvesthe formation of a sortal concept as a more or less arbitrary, even if also more orless "natural" procedure, as if it were possible to define or conceptualize thingsand their continuity into and out of existence?6 Part of the answer lies, I believe,in supposed analogies with other kinds of case, and traditional but questionableassumptions about the best description of the latter. The cases that dominate theliterature need to be re-examined.

Problems and ParadoxesProponents of the conceptualist or "sortalist" theory of continuity haverecently become clear that they fall into two camps, and the mutual criticismdoes useful damage. The view that is perhaps the more difficult to maintain,although neither is easy, holds it possible (or so it seems at first) that A shouldbe the same g as B and yet not be the same fas B. We seem to be encouraged tothink in terms of /"-samenessand ^-sameness, f-continuity and ^-continuity, thenature of each being determined by the concepts f and g: thus, it is possible that

5 A not dissimilar account, which no longer has its author's approval, is given byWiggins, ibid., pp. 59 and 69f .

6 Recourse to a Fregean notion of objectivity will not avoid the point of thischaracterization: cf. "The objectivity of the North Sea is not affected by the factthat it is a matter of our arbitrary choice which part of all the water on the earth'ssurface we mark off and elect to call the 'North Sea'." (G. Frege: The Foundationsof Arithmetic, trans. J. L. Austin [Oxford, 1968].) For the point is precisely thatthe spatial and temporal limits of a physical object are not a matter for our arbitrarychoice.

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Michael R. Ayersb0th A = B and A * B

g f_Let us consider a case: a bottle A is melted down and recast as a jampot,B. A is the same piece of glass as B, but not the same bottle as B.

Schema 1f 1 1the bottle = the jampotbottle

A = i = , ( = = B.the piece of = the piece of *glass piece of glass glass

Now if such a case is to support the view in question, it cannot merely bebecause "A is the same piece of glass as B" expresses a truth while "A is thesame bottle as B" does not. For the latter may be false or otherwiseunacceptable simply because B is not a bottle. The contrast would then illustrateone restriction on the use of expressions of the form "the same f* (i.e. bothterms must be fs7) but could hardly supply a reason for believing that suchexpressions are always either used or presupposed. The argument thereforerequires that A is positively discontinuous with, or other than, B under theconcept bottle, on the same level as it is continuous with, or the same as B underthe concept piece of glass. That is to say, we must suppose that A ceases to existunder the former concept yet continues to exist under the latter. We are notasked to believe that a bottle has ceased to exist while a piece of glass continuesto exist; for the bottle continues to exist under the concept piece of glass, whilethe piece of glass has ceased to exist, under the concept bottle. It is acompensation, perhaps, that the bottle, and so the piece of glass, can lookforward to coming into existence, under the concept Jampot The jampot itselfdoes not, of course, simply come into existence. It was previously in existence,after all, under the concept bottle, and for longer, and more recently, under theconcept piece of glass. Indeed, had the piece of glass been made into a newbottle, an individual would have gone out of existence and come into existenceunder the same concept.These excesses could be avoided, it may seem, if we jettison substitutivity;e.g., if we say that, even though the bottle and the piece of glass are the sameindividual thing, A, yet the piece of glass can continue to exist while the bottledoes not. This supposition, however, appears merely unintelligible, since, given

7 Another is that the individual must be supposed to have been an f throughout anyrelevant lapse of time.

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Individuals without Sortalsthe identity, what else are we given if not that the piece of glass can itself bereferred to as "the bottle"? Moreover, the whole account leaves us wonderingwhy covering concepts are required for diachronic identities, when they must besupposed unnecessary for synchronic identities.A different kind of example is favoured by Peter Geach in his defense ofthis view. If I talk to the Prime Minister before and after an election, I shall betalking to the same official but perhaps to a different man on the two occasions.If I write down the letter A twice, then what I write the second time is the sametype-letter but not the same token-letter as what I wrote the first time.8 Now insome such cases, perhaps, two sorts of continuity may seem to be involved. Butone is not spatio-temporal continuity, and the real subject is not a concreteindividual. In fact no sort of continuity is implicit in "is the same official as,"not even the continuity of a conventional role, since the title might have been inabeyance. But .certainly it is an abstract particular, the office held, not suchindividuals as Wilson and Heath, that can most reasonably be regarded as thetrue subject of any identity here. That is to say, "Heath is the same man asWilson" entails "Heath is Wilson" tout court, whereas "Heath is the same officialas Wilson (was)" entails no such thing, but means merely that Heath holds thesame office that Wilson held. We may note that there is a perfectly good sense inwhich "Heath is the same official as Wilson" is false, and a perfectly good sensein which, simply because they are different individuals, it is false that in talkingto both I have talked to the same official twice- just as it is false that (in onenatural sense) I have talked to the same Prime Minister twice. A rather disastroustheory of proper names can attempt to disguise these differences by assertingthat proper names too are sortal-relative, and that "Wilson" and "Heath" happento be relative to the sortal man, while another name, say "P.M.," might berelative to the sortal Prime Minister or official. Thus in the glass bottle example,the individual that is both a bottle and a piece of glass could only be referred toas "A" under one sortal or the other. But the disguise is as thin as the theory,and there is no more temporal continuity of the kind on which an identityjudgment could be founded between individual successive prime ministers thanthere is spatial continuity between contemporary heads of state, even when theyare shaking hands. The case of token-word and type-word merits similartreatment. No covering concept can make two separate marks on papernumerically the same individual, whether it is space and time or only space thatseparates them. The true subject of the identity, the type-word, is an abstractentity, beyond destruction, as the marks on paper can never be.

Perhaps it is the efficacy of this resolution of such cases, which we canunderstand by distinguishing categorially different subjects of the two identity

8 Cf. Geach, Reference and Generality (Ithaca, N. Y., 1962), p. 157 and p. 10.9 Further criticism of Geach appears in Perry, op. cit.

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Michael R. Ayersstatements, that encourages opponents of Geach's view in their belief that adistinction between subjects will be an equally effective treatment of the firsttype of case that we considered, in the example of the glass bottle. But that casewas different in that both the alleged continuity and the discontinuity werespatio-temporal: a bottle is as straightforwardly a concrete individual, anon-abstract, material particular, as is a piece of glass. Thus the distinctionbetween subjects here produces the paradox, as Locke might have put it, of twobodies in the same place at the same time. The move that is made can berepresented as follows:Schema 2A = the bottle = the jampot = B

A' = the piece of glass = the piece of glass = B'Substitutivity and transitivity are preserved, but at what cost! We are assuredthat it is not paradoxical to distinguish the bottle from the piece of glass becauseit is better to do so than to accept the alternative: there is no multiplication ofentities beyond necessity, simply because it is necessary to multiply them, oneon top of the other.10 We shall find that there is no such compulsion, but nowlet us notice some odd implications of the doctrine. It might appear, first, that ifI point at an object and say "That is a bottle," what I say is either tautologousor false or not what it seems. For if "that" refers to the piece of glass, theproposition is false, and if to the bottle, the proposition is, so to speak,tautologous. Otherwise we must say that the true predicate is not "is a bottle"but something else, e.g. "constitutes a bottle," which is even at first blush aqueer and undesirable complication. It seems to me to be virtually a datum forany theory of reference that it is possible to refer to certain pieces of marble asstatues, and vice versa. Moreover, in such a case, the statue is marble andman-shaped, but so is the piece of marble; so not only are there supposed to betwo objects in the same place, there are two marble and man-shaped objects inthe same place, so that the definite description, "the marble, man-shaped objectover there" must be supposed an ambiguous or indefinite mode of reference.The only non-ambiguous mode of reference must involve a sortal concept. Thisconsequence is well in line with explicit pronouncements of proponents of thedoctrine,1 1 but seems to me quite contrary to ordinary intuitions aboutreference.

10 a. ibid., pp. 198t.1 1 See footnote 4, above.120



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Individuals without SortalsAn attempt is made to soften the paradox of numerically distinct objects

occupying precisely the same space* and the issue can be said to hang upon itssuccess. It is admitted that there is indeed an intimate relation between suchi r\objects, although it is not identity, or not strict identity. Some ingenuity hasgone into the effort to tell us what this relationship is, but the results aredisappointing. According to Wiggins, it is correct to say that the statue is a pieceof marble, but the "is" is not the "is" of predication but the "is" ofconstitution, meaning "is made of," "is constituted by," and so on. Yet thisexplanation would only look adequate on the unnatural and question-beggingassumption that the statement "The statue is composed of a single piece ofmarble" does not by itself entail the straightforward predication, "The statue isa single piece of marble."Furthermore the relation seems symmetrical, whereas a piece of marblecan hardly be composed of a statue. It has therefore been argued that, strictlyspeaking, it is the relation "is composed of the same matter as." Yet this move,believed by Sydney Shoemaker to be an improvement on Wiggins* account,merely renders it more obviously paradoxical. For it is not so much occupancyof the same space on its own that seems in such cases incompatible withnumerical diversity, but the having of all matter or parts in common. It is anattractive doctrine of Aquinas that the principle of individuation of physicalthings is "matter subject to dimension," a doctrine that finds an echo in one ofthe least questionable aspects of Goodman's "Calculus of Individuals," hisaccount of identity: roughly, a and b are identical if there is exact overlap, i.e. ifevery part of each is a part of the other.14 In the face of this tradition, andcommon sense, to offer is composed of the same matter as as an alternative tostrict identity is palpably question-begging, being at least as paradoxical as theoriginal unadorned assertion that spatial position does not after allindividuate.1 5

12 S. Shoemaker, in "Wiggins on Identity," Philosophical Review, LXXIX (1970), 531,says that in ordinary language the relation can be expressed by "are one and thesame thing" although it is not identity, merely "especially easy to confuse withidentity"!

13 Ibid.14 Nelson Goodman, The Structure of Appearance (Cambridge, Mass., 1951), pp.42-55.15 Perhaps more so: the claim that space-occupancy individuates has been contested

(admittedly without much relevance to the present issue) by an appeal to thealleged logical possibility of one object's passing through another. Such a possibilitywould not entail the possibility that every part of each should become a part of theother and yet diversity be maintained. (Moreover it is arguable that the passage of Athrough B is only logically possible on the supposition that at some level each hasparts that do not occupy the same space as parts of the other: e.g., atoms.)

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Michael R. AyersAnother account is popular with some. If a piece of clay is moulded intothe form of a man, and is then returned to a formless lump, it exists, so it is said,both before and after the image. It therefore cannot, so it is argued, be identicalwith the image. We are now invited to regard the image as a "temporal part" or

"stage" of the piece of clay. The overlapping of different things thus seemsharmless enough, like the overlapping of a man and his own leg. Theintroduction of the concept of a momentary stage constitutes a refinement ofthe theory. It has some apparent utility in preventing the part-whole relationfrom becoming potentially mutual. For, in the ancient example, there mightseem to be no less reason to claim that the river is a temporal part of the mass ofwater than that the mass of water is a temporal part of the river, a possibilityclearly obnoxious to part-whole logic. It is therefore said that the river and themass of water that at some time composes it, share a momentary part. Thus theintimate relation between image and piece of clay consists in the fact thatconsecutive "stages" of the one are identical with consecutive "stages" of theother.1 6 They share temporal parts in such a way, in this particular case, that allthe parts of the image are parts of the piece of clay but not vice versa. Quine, inhis presentation of the theory, implies that what determines that any particularstage is a part of this, that or the other thing will be human conceptualization,whether verbalized or of some less formal kind.

The notion of "momentary stages" is as artificial as the notion of theplanes or points that may be said by some to make up real three-dimensionalobjects. Simply for this reason they cannot be taken seriously as candidates forthe status of parts. Like mathematical points, they cannot be ostensivelyidentified. Yet even if we overlook their peculiar transitoriness (necessary as it isto their apparent philosophical utility), there are other objections to suchtemporal "parts." Even temporally extended "parts" are still mysteriouslyinseparable and not subject to rearrangement: a thing cannot be cut temporallyin half. Much more importantly, to pretend that there are any discontinuitiesbetween these entities that require bridging, and so can be bridged, by somehuman conceptual scheme is to indulge in precisely the kind of idealization inrelation to discontinuity that the realist would very properly contrast with realdiscontinuity. In this respect a momentary stage is no different from afive-minute stage. The invention of a concept of a five-minute man, and aninsistence that the life history of each of us consists in a succession of brieflyexisting five-minute men, is an empty business that provides no analogue for thereal destruction of a real man. This kind of five-minute man (i.e., not theunfortunate possible creature that genuinely has a life-span of only five minutes)has a causal unity that continues unaffected when his time is up. The same goesfor a momentary "man-stage," for even this entity, if it has a synchronic unity,

16 Cf. Quine, op. cit., pp. 65f., and Perry, op. cit., p. 199.122



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Individuals without Sortalshas precisely that of a man. In fact we cannot separate, even in thought, thesynchronic from the diachronic unity of a thing, as cohesion sufficientlydemonstrates: there is no sense in talk of momentary cohesion. There is no morewarrant for the theory that a human conceptual scheme can define the temporallimits of a thing's existence than for the view that it can determine a thing'sspatial extent.Some shrink from neither opinion. Discussing Hume, Terence Penelhumtells us that identity "depends entirely on what concepts we are using .... If weheard a continuous sound we would say it was one sound and not several; but itis not hard to imagine some situation in which we would be interested incounting the number of seconds of sound, in which case we would say therewere, for example, ten of them."17 This claim is interestingly ambivalent.Counting units of time is undeniably different from counting sounds, and theanswer to the question "How many units of time did the sound last?" obviouslypresupposes some determinate unit-concept such as second. Yet, from thecontext, Penelhum must want us to conclude that it is our concepts whichimpose unity or diversity on the phenomenon and, indeed, on anything at all;consequently he must be making a claim of the same character as Berkeley'sassertion that number is relative because "the same extension is one, or three, orthirty-six, according as the mind views it with reference to a yard, a foot or aninch."1"8 But if it were so easy to impugn the real unity or number of a thing itwould be as possible as it would be convenient for a man to view the boulder onhis foot as a heap of pebbles.

Perhaps this foray against high conceptualism is an unnecessary digression.For, as generally happens with such technical devjces, the postulation of"momentary parts" merely complicates without resolving the difficulty beforeus. It seems a reasonable first assumption that all statues stand in the samerelation (whatever it is) to the particular pieces of clay that compose them. Letus then imagine that a particular statue and its overlapping piece of clay happento come into existence at the same time, being built up by the handful, and alsohappen to be demolished together. As in the earlier example, during the timethat both exist there is nothing that is a spatial part of either that is not part ofthe other; but in this case, there is equally nothing that is a temporal part ofeither that is not a temporal part of the other. Part-whole logic, certainly asnormally applied to events and processes, here requires identity. Thus it canhardly come to the assistance of the "division of subjects" thesis with which,indeed, it is incompatible.In other words, the argument for the division theory that appeals to the

17 "Hume on Personal Identity," Philosophical Review, LXIV (1955). Cf. p.below, on measurement.18 Principles of Human Knowledge,, Part I, 12.

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Michael R. Ayersnotion of a "stage" should lead to the conclusion, not that the relation betweena statue and the piece of clay composing it is not identity, but that we cannotknow whether or not it is identity unless we happen to know how each beganand will cease to exist. We shall even be able, given our powers of demolition,actively to determine as we choose whether some particular statue should beidentical with or diverse from the piece of clay that composes it. Lastly, unlesswe do happen to know whether the relation between statue and piece of clay isidentity, we shall not know whether it is possible to refer to the statue as "thatpiece of clay" and vice versa. These frills on the division theory hold littlepromise of an attractive account of reference, and do nothing to render thetheory itself less paradoxical.

Realist Solutions(i) It remains to offer a more realistic explanation of the examples onwhich the conceptualist case commonly rests. The general form of thisexplanation is simple. We need only insist that, where there is diachronicidentity, there cannot also be diachronic diversity. Thus we have to choose, notarbitrarily, but according to the facts of each case, between the two possibilities

illustrated as follows:Schema 3

the bottle the jampotA = = = B

the piece of the piece ofglass glassSchema 4the bottle the jampot

A - = * Bthe piece of the piece ofglass glass

Disregarding a complication that will be discussed later, we can say thatthe relevant facts in this particular example lie in what happens in the process ofremanufacture. For example, can we regard a molten lump of glass as a unifiedthing, with an internal principle of unity? If not, then the piece of glass isdestroyed with the bottle, and Schema 4 applies. Otherwise Schema 3 is124



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Individuals without Sortalsapplicable. This is a question about which I neither need nor intend to bedecisive. For if there are cases on this borderline, their existence is no solace tothose who advocate Schema 1 or Schema 2. It is also important to see that thequestion of continuity is quite independent of the concept piece of glass. It isquite possible that, if we decide for continuity, we shall also be prepared to saythat the molten glass constitutes a piece of glass. But perhaps we shall not, andlinguistic overtones may incline us to talk of a lump or blob rather than apieceof molten glass. The issue of continuity is not directly affected. The sort ofcircumstances that would settle this issue, however, might be as follows. If wehappened to know that, at some stage in the process, the glass had solidified inthe form of a large number of separate globules, then B would perhaps be a newpiece of glass, different from A, although made from the same material. As fewwould deny, two things existing at different times can be composed of the samemolecules or same stuff without being the same thing. Pieces of glass seem noexception. A piece of#glass is destroyed by being split up into many pieces, butthe stuff of which it was composed is not thereby destroyed, even if it isscattered to the ends of the earth.

To avoid misunderstanding, it must be repeated that the difference here isnot between two sortals, same glass and same piece of glass, but between thecategory of stuff and the category of thing. For A and B to be composed of thesame stuff some sort of real spatio-temporal continuity is requisite: perhaps therequirement is fulfilled if every part of B (say, a set of dining chairs) onceexisted as a part of A (say, a particular tree); or perhaps the reverse relation isalso requisite. But there is certainly not required the sort of continuity thatwould be necessary for A and B to be the same thing. For the latter is thecontinuity of a causal unity such as is in any case lacking when one term is a setof chairs.

(ii) The discussion of a traditional and crucial example has often beenseriously affected by a failure to get precisely this point clear. We are asked byLocke to accept that

an oak growing from a plant to a great tree, and then lopped, is still the same oak;and a colt grown up to a horse, sometimes fat, sometimes lean, is all the while thesame horse, though in both these cases there is a manifest change of the parts, so thattruly they are not either of them the same masses of matter. The reason whereof isthat, in these two cases of a mass of matter and a living body, identity is not appliedto the same thing.

19 Essay Concerning Human Understanding, Book II, Chapter XXVII, 3. NoticeLocke's inconsistent adoption (at any rate, verbal) of both the modern forms of theconceptualist theory. Which of them he would have preferred is not entirely clearfrom the Essay.

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Michael R. AyersMany others since Locke have smuggled in the stuff/thing distinction as if itwere a case of. different thing-sortals or (as his procedure might as well bedescribed) have tried to say about the continuity of a thing what could only betrue of the continuous composition of a thing by the same stuff.The term mass of matter is, in my view, best regarded as analogous to athing-sortal like piece of giass, denoting something that can be demolished orbroken up. A colt is indeed such a thing, but unified and organized, while alive,on such principles that its stuff is continuously being replaced. That is to say,the mass of matter is itself organized in this way, and thus, as much as the colt,survives replacement of parts. Its matter is gradually replaced, but it is not itselfreplaced by a different mass of matter. This, since the mass of matter and thecolt are the same thing, is not surprising. Hence Locke is mistaken when hestates that the removal or addition of one atom is enough to bring to an end theexistence of a mass of matter. Nothing ceases to exist, except possibly the colt'sproperty of being composed of a particular number of atoms, and similarnon-substantial entities.

This rebuttal of Locke's contention (bringing the case under Schema 3,above) is often in my experience greeted with indignation as an artifice or trick.It is, on the contrary, the exposure of a particularly misleading artifice. As theanalogy with the expression "piece of glass" confirms, my understanding of theexpression "mass of matter" is at least the most natural. Let us, however,consider some rival interpretations.

First, we might quite intelligibly take mass of matter to mean somethinglike set of partic/es, in which case its destruction must involve annihilationperhaps of all, but at least of one of these particles; for mere dispersal, howeverradical, would be not merely insufficient but irrelevant. On this reading, thesense in which one mass of matter is replaced by another would be entirelyparasitic on the assumption of a continuous unity or real thing which acts as thetheatre, so to speak, of such a change of cast. Thus the expressions "mass ofmatter" and "matter" become virtually interchangeable, and the Lockean claimreduces to the truism that a thing can survive the dispersal of the matter that, atsome previous time, composed it. No argument for the "softalist" thesis canpossibly emerge from this alone.Other ways of conceiving of a mass of matter are all, it seems to me,attempts to combine incompatible features of different categories of question.Locke himself requires that what he calls a mass of atoms should be causally"united together," i.e. like a thing, and he even uses the term bodyinterchangeably, in his argument, with the term mass of atoms. Yet he merelydisregards the continuity of this unity or body when he stipulates that the masswill not survive the subtraction of a single atom. (He even overtly conflates therelation "is the same mass of particles as" with the relation "is a mass of thesame particles as.")20 Thus his concept of a mass or (in this context only) bodyis as artificial, and as misleading, as that of a "man-stage." For suppose that we

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Individuals without Sortalsdefine a man-mass as any Lockean "mass of particles" constituted or united as aman is at any moment of his life. The continuity of a man can thus be said toconsist in a sequence of briefly-existent, temporally discontinuous man-masses,each replacing a previous one. This is nothing more than an eccentric and verymisleading way of saying what has never been denied since Heraclitus, that thematter or parts of a man are continually being replaced. It is a misleading storybecause it suggests what is false, that a complex, structured, unified individualthing is every moment going out of existence and another taking its place; butalso because it is mistakenly offered in support of the false general theory thatcontinuity is always relative to a sortal concept or, as one powerful tradition hasit, is a matter of words.One sometimes meets with another proposal, that the concept mass ofmatter be treated as equivalent to the concept of a set of parts in close localconjunction, whether or not "united together." It is then said that under such aconcept there can be discontinuity while under another concept, e.g. horse,there is continuity. It is thought unimportant that the proposed concept isartificial (only roughly corresponding to heap or collection) since if any work isprovided for Schema A or Schema B, by whatever device, the sortalist thesisappears to find support. Perhaps the point of the suggestion is better illustratedby a different sort of case, involving continuity rather than discontinuity undersuch an artificial concept.(iii) Borrowing an example, therefore (and more than the example), fromWiggins, let us imagine that a jug is destroyed by being smashed, while the"collection of parts" or "collection of china bits" that constituted it remains inexistence. Now the smashing will destroy the mass of matter on the Lockeaninterpretation as well as on my own, although on neither interpretation is thematter or stuff itself destroyed. Locke's masses are always very fragile, whilethese "collections" appear, in such cases, to be rather robust. They must not betoo robust, however, or their continuity will collapse into mere survival ofmatter.22 Let us then suppose that "collections," unlike matter, can bedestroyed by local dispersal. Can they be destroyed by a second tap with ahammer? On the assumption that to destroy all the members of a collection is todestroy the collection, then if each china bit breaks into more bits, it seems that

20 The details of Locke's discussion are very interesting, as is the relation between hisaccount of identity and his philosophy of science and notion of substance. Thequestion why Locke, a metaphysical Realist, should adopt a conceptualist view ofidentity can be answered (and the structure of that view be understood) only in thelight of a careful examination of his distinction between real and nominal essences,his discussion of the question whether individuals have essences, his doctrine, moresubtle than might appear, that species are the work of the understanding, etc.

21 Op. cit.y Part I, 1.6. The argument here criticised is not, of course, that of Wiggins.22 A requirement noted by Wiggins, ibid., p. 10.

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Michael R. Ayersat least one collection of bits has been destroyed, and perhaps indefinitely many,as it is not difficult to see. On this view, give me a jug and you also give meindefinitely many overlapping collections of pieces. Break my jug and you breakindefinitely many of these, although indefinitely many remain unbroken.Collections now appear individually less robust than at first sight, their strengthlying rather in numbers. Another difficulty might be seen in the claim that thejug is even one collection of china bits. It seems an odd thing to say about anunbroken jug. The most promising line of defense might thus appear to be to fallback, like Locke, on the atomic theory, thinking in terms of particles rather thanparts. Must we not admit that the collection of particles can survive thedestruction of the jug, and is therefore a different thing?It is worth giving a realist's answer to all this, because it may help toclarify his position. First, a "collection" is not a different thing from the jugsimply because it is not a thing at all, in the required sense: in this sense, nothingis a thing that is not an objectively discrete unity or structure. That is why,contrary to a common philosophical belief, neither the counting of things northe determination of their beginnings and endings is arbitrary, or relative to ourconceptual scheme, or a matter of words, or a mere reflection of humaninterests. But the limits of a "collection," on the proposed artificial definition,are intrinsically arbitrary, and counting "collections of particles" an impossibleand absurd enterprise. If a cock stands on a dunghill, the particles of its feetform as genuine a "collection" with the particles of the dunghill as they do withthe particles of its legs or body. It is thus easy to see how many questions arebegged in the argument about the jug. One is left wondering, for example, whythe particles of air in the jug or between the fragments are not included.

(iv) What does happen to a statue when a vandal beats it out of shape, if itis not destroyed1. And what is a sculptor bringing about when he beats a piece ofmetal into shape, if he is not creating a statue? In so far as these questions do notanswer themselves, a suitable reply to the first is that a piece of metal is ceasingto be a statue, and to the second, that a piece of metal is coming to be a statue.We can talk of destruction and creation if we like, for such talk can be fairlyunserious, or at least detachable from considerations of substantial continuity. Ican create an eyesore by cutting down a tree or destroy an aesthetic whole bypainting my house red, white and blue. We could say that what the vandal isdestroying is a shape or form. None of this gives any grounds for arguing thatone thing, the statue, ceases to exist, while another thing, the piece of metal,continues existing. Paperweights are physical objects, and it is possible to makepaperweights by scratching patterns on pebbles, but this is not a way of makingphysical objects. It is a way of making certain physical objects intopaperweights. A pebble can become a saleable paperweight without changing atall, to revive a point made by Robert Boyle against teleology.This kind of case illustrates a further fundamental mistake in theAristotelian form of realism, one that regrettably paved the way for

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Individuals without Sortalsconceptualism. Aristotle reasonably explained individual continuity by referenceto the form, conceived of as a causal principle of unity; but he reified thisprinciple, as if the embodied form could cease to exist while the still unifiedmatter remained as an accidentally cohering, second-class thing. On the contrary,the individual statue can survive the destruction of its form, although not as astatue, or not as a statue of that form.

(v) By the same token, it is wrong to say that the individual man or personceases to exist at death. Very violent death apart, death is existed through. Theindividual becomes dead. "Our bodies last longer than we do" is a false dogma.This fact is independent of the question whether to call the corpse a man or aperson. Even if a dead person were not really a person, this would show that anindividual can cease to be a person, not that a person is an individual that ceasesto exist at death. So, too, if a small infant is not to be granted the full status of aperson, it does not follow that the individual who later comes to be regarded as aperson, and who comes to refer to himself as "I," has not existed since birth or,for that matter, since the formation of the zygote. The concept person will notconveniently solve the moral problem of abortion.

(vi) Other aspects of the so-called problem of "personal identity1' are toocomplex for discussion now. The division of subjects thesis will be able to drawon much of what makes substance-dualism plausible. If, however, we assume theinvalidity of any notion of the psychological continuity of an individual that isor might be independent of all spatio-temporal continuity, the peculiar difficultyfor an opponent of the conceptualist thesis seems to lie in the logical possibilityof surgical replacement and exchange of parts as radical as any that artifactsundergo. The individuality of a person seems so tied up with his personality andcognitive powers, including his memories, that on the supposition that it becamepossible to transfer some part of a man, say the brain, as the bearer of thesecharacteristics into a suitably evacuated body, it becomes not whollyunattractive to conclude that a resultant living individual would be the sameperson, but not the same body or perhaps even the same man as the original. Onthis view the person, alone logically capable of such migration, is never the samething as the man or body, although for much of the time all three have a head,two arms, a trunk, and so on, for the while or throughout their existence havingall parts in perfect unison, yet managing somehow to exist apart.

23 Cf. ibid., Part IV. I should perhaps just indicate a line of response to the argumentthat the body is a different thing from the man or person because bodies cannotproperly be said to think or have sensations. I take it that "body" no more denotesa thing distinct from the person than does "mind" (although minds, unlike people,cannot naturally be said to be six feet tall). As distinctions between substances, Ibelieve that these distinctions should be taken no more seriously than, e.g., adivision between "my better self" and "my worse self," each of which pseudo-selveswill necessarily have properties the other lacks. Because such terms are related as itwere to "aspects" of a thing, they cannot be freely used to denote the thing in all

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Michael R. AyersA number of replies suggest themselves, and I am not entirely sure which isbest. I do not much like one possibility, which is to treat the person, the

thinking thing, as a part, the neural core, of the living body or man. On thisview, a person does not have bones, skin and so on, and could in principlesurvive the destruction of the whole body in the same unparadoxical way as canan arm or finger.24An alternative is to deoy that the individual would have survived, carriedover with the transplanted brain. This response seems appropriate to somestories which concentrate exclusively on continuity of "memory" as thepurported guarantee of a particular life history. For if a recipient'smemory-beliefs were affected by the transfer of, say, a small amount of brain oreven brain-fluid, it would be quite unjustified to conclude that the recipient wasthe same conscious, rational being, or person, as the original donor. Thestorehouse of the mind is not the whole mind, and the same could be true at thephysiological level. Yet, given the prospect of surgery on a large enough scale, itmay still seem that the brain-donor can look forward to a genuine, if unnaturaland temporarily "disembodied" extension to his existence, while thebody-donor is less fortunate.A more promising argument starts from the premise that a living humanbeing is not just a coherent lump of stuff. Thus far the difference between merecoherence and more complex natural principles of unity has been mentionedonly in connection with the power of some individuals to survive even rapid andconstant replacement of matter. But the distinction can have anothersignificance. If a lump of clay is divided in half, there is no reason for identifyingone half rather than the other with the original individual, and so no reason forthinking that that individual has survived. If, on the other hand, an animal issimilarly divided, but so that only one half, because of its structure, can live,there is sufficient reason for regarding this part as the surviving individual. This isso even if the living part is smaller, even considerably smaller, than theremainder, which is now to be regarded as a former part of that individual.Now the causal unity of a man is demonstrated not simply in coherence,nor in the life of the parts, but in the unified powers of sentience, intelligence,intentional action and so on. Conceivably it could be the case that, while anypart may be kept "alive" in a sense, only one part could be the bearer of this

contexts. Yet there is much to be said for the tough line that, really, my better selfsometimes behaves badly and, indeed, that it bears all properties in common withmy worse self, for the reason that there are not really two selves or persons but onlyone. Such ontological pedantry, however, may seem to lose the point of the faconde parler. Similarly the body/person distinction has point, although a good enoughreason for asserting that, after all, the body does think is that there are not twothings but only one.24 Cf. W. Sellars, "The Identity Approach to the Mind-Body Problem," Review of

Metaphysics, XVIII (1965), IV.130



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Individuals without Sortalsunified higher form of life in separation from the rest of what used to be thebody (not, note, "from the body")- In that case, it would perhaps be correct tosay of certain individuals- whether or not we are prepared to call themthroughout their existence "human beings," "men," "bodies," "persons" orwhatever else- that they are capable of survival through dire transformationsindeed, rather as some lowly animals might be capable of surviving as minutenuclei temporarily deprived of the much greater quantity of surroundingprotoplasm that previously helped to compose them. The realist need not assertthat it would be correct to say this. He may regard the issue as open or even asirremediably borderline. All that is necessary for his case is that the issue is bestunderstood as a question- hypothetical, of course- about the continuity of anindividual thing. What answer we give to this question is quite independent ofwhat we may say about the concepts man, body, person and so on. In order tobelieve that there would be continuity, it is quite unnecessary to hold that thebrain in the surgeon's hands would rightly be called a "body," a "man" or a"person." To see this we need only remember that it is unnecessary to callmoths "caterpillars" or caterpillars "moths" in order to recognize that a moth isthe same individual as a previously identified caterpillar. It may be thatour sortal concepts reflect our beliefs about continuity, but our beliefs aboutcontinuity need not reflect our sortal concepts.

(vii) If a single thread of wool, measuring one hundred yards from end toend, is knitted into a sweater measuring two feet from shoulder to waistband,and if the sweater and the piece of wool are one and the same thing, how long isthat thing? Nothing, it seems, can be both one hundred yards long and yet onlytwo feet long. Moreover, it is simply false to say, in ordinary language, eitherthat the sweater is one hundred yards long or that the woollen thread is two feetlong.25 I have admitted that a rejection of the broad principle of thesubstitutivity of identicals is immediately incoherent. Must I not therefore admitthat the sweater and the woollen thread are two different physical objects, notone?

First, the concept of numerical identity can be approached not onlythrough the principle of substitutivity but through the notion of number itself.For the present I shall only draw attention to a certain kind of error in counting,namely that of counting the same thing twice. Even if it were accepted thatcounting objects always presupposes some sortal, it would surely be clear thatthe class of objects to be counted could be designated by two sortals rather thanone. Thus we may count members of the single class of the tables and chairs in acertain room, or all the bureaux and chests of drawers. There is a piece offurniture called a chair-table, the back or top of which is hinged. If only tablesare being counted, a chair-table would very properly be counted; and so too if

25 No doubt a fact related to the point of footnote 23, above.

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Michael R. Ayersonly chairs are being counted. But if chairs and tables are to be counted, while achair-table might be included with even less hesitation, it should, of course,count for only one. For it is one and the same object that is both a chair and atable. Now the same goes for garments and hanks of wool. There is nothingunintelligible in the order to count, indiscriminately, all the garments togetherwith all the hanks of wool over twenty feet long in a room: if anything is agarment or such a woollen thread, it is to be counted. Yet only a philosophertenacious of a theory would proceed to count a sweater and the woollen threadof which it is constituted as two items. For we know very well what it is tocount the same thing twice. Thus to distinguish, in this case, between the "is" ofidentity and the "is" of constitution seems to drive a wedge between numericalidentity and number, which may be just as bad as a denial of substitutivity.The argument that the sweater and the piece of wool are different lengths,and so must be distinct, is not as damaging as it may seem if only because itwould prove too much. If a piece of wool temporarily forms a loop or coil, or aworm wriggles itself into a mat, then the loop of wool or the worm-mat hasdimensions that it would be misleading to attribute to the piece of wool or theworm except qua loop or qua mat. Thus, in our case of the sweater, there issomething which is both a woollen thread and a sweater, and which qua thread isone hundred yards long and qua sweater, two feet long. A sweater is a physicalobject, but so is a loop of wool. If the former is unravelled into a single length ofwool, there is no more reason for saying that a physical object has ceased to existthan if the latter is made straight. If it is insisted that surely a sweater has ceasedto exist, for after all there was a sweater and it is no longer the case that there isa sweater, the unanswerable retort is that this logic can be exactly paralleled inthe case of the loop of wool, so that we could be forced to admit that anindividual ceases to exist at every moment that another individual changes itsposture or, indeed, gains or loses any property at all. Such a multiplication ofentities is neither necessary nor useful.The more important issue that arises in this and previous examplescould be expressed in the abstract question whether the same matter could besubject to more than one principle of unity simultaneously, or unified by morethan one "form." It is tempting to think that the present example is anillustration of just such a possibility, since a sweater can be regarded as a unityindependently of whether it consists of one or more pieces of wool. Thus itmight be thought that in unravelling the sweater we remove or destroy oneprinciple of unity and by cutting the thread we remove a second. Each operationis possible without the other, and s6 each principle of unity seems independentof the other. The better and more realistic view, however, is that if a sweaterconsists of a single thread, then this means only that the different parts of thewool hang together in more than one way, and so have a unity that is moredifficult to destroy than otherwise would be the case. Roughly, the unity orstructure of a sweater knitted from a hundred separate threads is destroyed by132



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Individuals without Sortalsunravelling, the unity of a single thread by cutting; while the unity of a sweaterknitted from a single thread survives either operation but not both. Thus noserious doubt is cast on that apparently essential ingredient of a realist theory ofthe identity of physical objects, the principle that the same matter cannot besubject to more than one principle of unity at the same time: i.e., cannotcompose more than one individual simultaneously.Complications and Implications

The objections considered so far can, I think, be met without questioningor modifying the simple lines of my "realist" approach. The objections that Ishall now consider can also, I believe, be answered, but may stimulate rathermore self-searching. My suggestions are intended as exploratory, rather than asdefinitive answers to difficult and complex problems.(i) The planks of a ship are gradually replaced, one by one, until none ofthe originals remain. The old planks are preserved, and finally reconstituted as aship. Which of the two ships is the original ship? Two problems about continuityare involved in this traditional riddle. Can a thing survive such radical repair, andis a reconstituted thing the same as the original?One of the more interesting and extravagant conceptualist explanationsruns as follows. What we should say depends on the concept we use. If by shipwe mean something that can survive repairs but cannot survive dismemberment,and by ship^ we mean something that, like a tent, can survive dismantling, thenwe can agree that there are two perfectly good continuities but no paradox. Forthere are two continuant things of equal status, a ship and a shipj, originallyoccupying the same place (and matter) but coming to occupy different places.The realist, on the other hand, might start with the question whether thereis a unified material whole that survives continuously. First, the grammaticalstatus of the word "tent" does not ensure that every tent is as much one thing asis a stone: the average tent is at best a carefully constructed heap of wood andcanvas, and at its worst a functionally related set of items half of which havebeen left at home. It can at least be argued, then, that the "reconstituted" ship isnot really the same individual thing as the original.What about the "repaired" ship? Here too the realist may pause, perhapseven over its synchronic unity, a matter of pegs and nails, but at least over itscontinuity. The case is not after all very much like the metabolism of an animal.The replacement is at a grosser level, the parts remain clearly defined and are inthemselves unchanged by incorporation in the whole, and the agency is external.But whatever his conclusion (and it is again important to note that thisconclusion may be that the case is a borderline case of substantial continuity)my realist's position is not obviously at risk. His claim is that the questionwhether there is continuity of a genuine whole or thing makes sense as it stands,and does not and cannot arise as the question whether the concept ship or someother concept allows for this or that eventuality.

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Michael R. AyersYet such an approach seems to leave too much room for counter attack.There is, it must surely be admitted, something exaggerated in the suggestionthat a man who takes a chair to pieces and then puts it together again has made anew and different thing or whole- although the same difficulty faces one who

says that he has made a new chair. A related question concerns the notion of acategory. I have talked of a class of identity statements involving the category ofsubstance or thing, and I tried to explicate, although not, of course, to define,the concept of a thing by means of such expressions as "structure" and "naturalunity." Yet a tent, a family and a stamp collection, which may seem to besubstances, i.e. possible subjects or terms of this class of identity statements, arenot obviously "structures" or "natural unities" in the required sense. Howshould such difficulties be met?

A possible line of response would be to allow that when we stray into therealm of functional terms or others that so obviously reflect human interests orconventions, we may find ourselves conferring conventional continuities, orcontinuities "for all practical purposes," just as we can confer an other thannatural unity on what is not really one thing. For all practical and aestheticpurposes, the monolithic temples of Abu Simbel were not destroyed when theywere moved piecemeal, but preserved. A sculpture generally is one thing, but itcan also be five bits of bronze on the lawn with a unity only in the eye of thebeholder or the intention of the sculptor. There is nothing wrong with talking, inthese cases, of continuity or unity. There is equally nothing wrong, in the quitedifferent case of a truly conventional, purely onomastic distinction, in sayingthat the Missouri and the lower Mississippi, or the Cam and the Granta, are"different rivers." But the realist may reasonably claim that it is a quiteunjustified leap to argue from such usages to the conclusion that all unity and allcontinuity is arbitrary or relative to human concepts. If there were no naturalobjects there would be no conventional objects either.Such a response preserves the essential metaphysics of realism, butapparently at the expense of allowing something very much like theconceptualist logic. That is to say, it becomes possible to argue that unless weknow how an identity statement is to be understood, i.e. whether it is concernedwith the continuity of a natural object as such or, on the other hand, with aconventional continuity from some specifically human point of view, we cannotdetermine the import and truth-conditions of the statement. This concessionlooks a good deal less portentous than the full-blown theory that identity oridentification is always relative to such sortal concepts as man, rock, ship and soon, but it still seems objectionable because it apparently leads to the sameparadoxes as that theory: whether such a paradox as that the temple wasidentical for a time with the monolith, the destruction of which it survived; or asthe alternative paradox that the temple was at no time identical with themonolith with which for a time it shared all matter in common.

Another line of thought, however, starts with the reflection that

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Individuals without Sortalsdifficulties such as those over temporary disintegration can at least be imaginedto occur as a result of some natural process. If a biological individual came topieces before our eyes, and the pieces then organically recombined, it would beplausible to argue that we have the same individual, which existed for a time inpieces. Thus the consideration that it happens to concern an artifact, or that"ship" is a functional term, is not after all the source, or only source, of thefamous riddle, and so cannot be relied on for its solution. It is important toothat not any disintegration can be survived. Had the original Portland Vase beenground to fine powder from which a vase of the same structure was thenfabricated, there should, I think, be no hesitation in denying'identity. Rational*doubt seems to arise when it can be thought that the fragments preserve the"form" of the vase: so that the vase still exists, although in pieces. Thepreservation of the form can be regarded as a matter of causality rather thansomething relative to human interests or conventions. Human agency may ormay not be involved, but even if it is, the question can arise as to how much theunified structure or form of the original object has directly contributed to thatof the reconstructed object. In the case of the vase ground to powder, theanswer is, hardly at all. Thus a realist could allow, as a solution to the riddle ofthe temple, that both temple and monolith survive as one although rebuilt, nolonger a monolith and, for that matter, more of a tourist attraction than atemple.(ii) The identity of packs of cards, families, troops, stamp collections,flocks, crowds and, perhaps, bundles and heaps (of bricks, if not of tar) is aseparate topic of some importance. These concepts are what Locke calls"collective ideas of substances." Collective substances are different fromindividual substances, despite the fact that they occupy space and have a certainunity bestowed by a variety of principles, some natural, some conventional- bloodrelationship, a common owner, a shared history, a joint use, even barecontiguity. As a physical object can survive the replacement of its parts, so agroup continuity is possible as something partly independent of the continuityof its members. Yet groups are not individuals, for every group is essentiallycomposed of individuals as members or units. From this point of view a swarmof bees is more like the set of bees than it is like a bee.

Perhaps the chief difficulty in the proposition that groups differcategorially from things derives from the possibility that a group should eithercompose or be composed of a single individual. It might then seem to be thatindividual, as occupying the same space and having all parts in common with it.If Jones is the only living member of the Jones family, then where Jones stands,his family stands. Yet when he marries and has children, he no longer composesthe Jones family, which may survive him as it existed before him. The notion oftemporary identity is an absurdity: should we then hold that two distinct,concrete individual things stand in the same place at the same time? For if Jonesalone constitutes his family, how can the latter be any less a concrete objectthan he is?

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Michael R. AyersThe answer must, I think, be that the family composed of Jones is nomore a thing in the categorial sense than is the family composed of a hundred

far-flung members. We might even deny, not unreasonably, that one man canmake a family, one brick, a heap of bricks, or one stamp, a stamp collection.Blood relationship unites a family, but it cannot unite Jones. To be a member isto be a part, and it is at least plausible that nothing can be a part of somethingelse no larger than itself. But this denial is unnecessary, since members are apeculiar sort of parts, in that they are logically atomic parts or units. Jones'finger is a part of Jones, but it is not a part of the Jones family. Removing itmakes Jones smaller, but does not make his family smaller. This unparadoxicalcounterexample ot the transitivity of the part-whole relationship yieldssomething of the special character of the category of "collective substance." Italso demonstrates that, whether or not Jones can by himself constitute the Jonesfamily, he and his family never have parts in common, and so are never identical.Groups are made up of their members, but are not made of them.The case in which a group composes, rather than is composed of, anindividual is very different. The logical difference between a family and a man isevident partly because the principle of unity is of an evidently different kind,historical or social rather than structural. But, as we have already seen, it ispossible for what is prima facie a "collective substance" to be conceived of ashaving precisely the same principle of unity as an individual substance: forexample the united mass of molecules that constitutes a horse. Not surprisingly,only in such a case can a collective substance be identical with an individualsubstance, and then it virtually ceases to be, logically speaking, a mere collectionor group. It is conceived of as having parts smaller than its members, so that notonly is every part of the mass of molecules a part of the horse, but every part ofthe horse is a part of the mass of molecules. It is thus questionable whether"mass" here functions as a true collective noun. The size of a mass, so conceived,is its extent, not the number of molecules in it; whereas to say that one herd ofhorses is larger or smaller than another is normally to make a numericalcomparison. It is true that we might naturally describe a swarm of bees as gettinglarger without knowing or caring whether this is because the bees are gettingbigger, farther apart or more numerous. A swarm of bees is fairly thing-like in itsappearance. But from the premise that a swarm can excusably be mistaken for asingle thing, it does not follow that it is excusable to mistake the concept swarmfor a thing-concept. We call a "swarm" only what we recognize as a mere groupof individuals, having a numerical magnitude. A true group can no more beidentical with an individual than many things can be identical with one thing.Just as we can identify an individual without knowing what sort of thing itis, so we can in principle identify a group of individuals without knowingprecisely how they are related. Just as we can recognize a unified object withoutbeing able to explain the source of its unity, so we can sometimes reasonablyascribe coherence to a group of objects without understanding the nature of itscoherence, or even the nature of its members. Collective sortals such as crowd,136



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Individuals without Sortalsflock, constellation, troop or pack are more definite in one or both of theserespects. Others, such as pair, quire and (perhaps) cricket team, convey thenumerical magnitude of the group. Hence "This pair of shoes is larger than that"cannot mean "numerically larger," and in fact means no more than that theseshoes, which make up a pair, are larger than those, which do the same.

Counting Physical ObjectsThe contention that physical objects can be counted as such, i.e., withoutexplicit or presupposed sortals, is in need of defense if only because itcontradicts what is commonly taken to be evident from a few simpleillustrations. These examples generally derive from Frege, although the favouredinterpretation of them is by no means essential to Frege's own programme,which is to prove that numbers are not physical properties, but rather "objects"that "belong" to "concepts." His destructive aim is fully achieved not only byhis illustrations, but even by his reflection that if number were essentially aphysical or phenomenal property then only the physical or phenomenal could becounted. At the same time, whatever the strength or weakness of his positiveaccount of number, the claim that physical objects can be counted as such can

be rephrased in terms of his theory, as the claim that such a concept as "physicalobject in this box" can have a finite number. It may be that Frege commitshimself to the proposition that the "decision" to regard things through themedium of any particular concept is "arbitrary" or at best "natural," and itseems that he would extend such an attitude towards the concept of a physicalobject or individual substance. But that mistake, as I think it, is another matter.It is perhaps not often that the specific claim about the counting ofphysical objects is distinguished from a wider claim about counting objects ofthought in general. This is as we might expect when the significance of thedistinction between sortal and categorial concepts is overlooked. But- thefollowing passage may seem unequivocal:If I give someone a stone with the words: Find the weight of this, I have given himprecisely the object he is to investigate. But if I place a pile of playing cards in hishands with the words: Find the Number of these, this does not tell him whether Iwish to know the number of cards, or of complete packs of cards, or even say ofhonour cards at skat. To have given him the pile in his hands is not yet to have givenhim completely the object he is to investigate; I must add some further word-cards,or packs, or honours.26It is only necessary, however, to recognize as we have the insubstantialnature of groups 7 in order to see that the argument is overstretched when it is

26 Op. cit, p. 28.137



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Michael R. Ayerssuggested that a man cannot simply count the objects that he has been given. Itis significant that the judgment that these 104 objects constitute two packs ofcards must be based on knowledge of card-games and the conventions for thecomposition of packs, whereas the judgment that there are 104 objects isindependent of any such knowledge. It would doubtless be natural enough forone quite ignorant of cards to conclude from their appearance that they are allobjects of the same sort, yet in the case of chess-pieces, for example, one mightfail to draw even this conclusion, without detriment to the possibility ofcounting them. Thus such examples prove nothing to our point. It may be that"I can say with equal truth both It is a copse' and 'It is five trees', or both'Here are four companies' and 'Here are 5000 men'."28 But the individualsubstances, trees and men, are here merely paired with collective substances,from which the concept of an individual substance would itself providesufficient distinction. As for the question whether just the honour cards are tobe counted, it would arise no more than the question whether just the honourcards are to be weighed. In any case, it would be no less successfully answeredby the word "object" or "thing" than by the word "card."

Frege associates his arguments with a reasonable theoretical point aboutcounting: every number coherently arrived at must possess a definite "unit." Wemust know what we are counting. But this does not justify his approval ofSpinoza:

We only think of things in terms of number after they have first been reduced to acommon genus. For example, a man who holds in his hand a sesterce and a dollar willnot think of the number two unless he can cover his sesterce and his dollar with oneand the same name, viz., piece of silver, or coin; then he can affirm that he has twopieces of silver, or two coins. 9

Now this example lacks all plausibility, except what it can borrow fromthe general principle that it is wrongly supposed to illustrate. For it is obviouslypossible to count the objects in a man's hand without knowing that they are allsilver or all coins. This is because a physical object is, as such, a satisfactory unit.

There is a certain unclarity in Frege's account of units. His approval ofSpinoza and talk of "generic concepts" suggests simply a belief in the need for asortal to constitute the unit. Elsewhere, however, he seems to assume that hisown theory that number belongs to concepts is just a way of expressing orallowing for the necessity of a unit. Yet if we count the coins in a box, theFregean "concept" to which the resultant number "belongs" is not coin, but

27 Frege criticizes Mill for believing that "two and one pair are the same thing" (ibid.,p. 33) but fails to grasp that the notion of a pair of boots is at least parasitic on thatof a number of boots, i.e., is a group concept.28 Ibid., p. 59.29 Ibid., p. 62.

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Individuals without Sortalssomething like coin in this box. It is possible, however, to regard coin as the"unit,'1 while taking in this box to limit the scope of the operation. Thedifference between counting the coins in one box and counting the coins in twowould be regarded as a difference not in unit, i.e. in the kind of objects counted,but in

ayers - individuals without sortals

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