On the Alleged Incompleteness of Certain Identity Claims

Canadian Journal of Philosophy

On the Alleged Incompleteness of Certain Identity ClaimsAuthor(s): Jack NelsonSource: Canadian Journal of Philosophy, Vol. 3, No. 1 (Sep., 1973), pp. 105-113Published by: Canadian Journal of PhilosophyStable URL: http://www.jstor.org/stable/40230426 .

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CANADIAN JOURNAL OF PHILOSOPHY Volume III, Number 1, September 1973

On the Alleged Incompleteness of Certain Identity Claims'

JACK NELSON, Temple University

In Mental Acts Professor Peter Geach asserts that " The same' is a fragmentary expression, and has no significance unless we say or mean 'the same X', where 'X' represents a general term . . ."2 In Reference and Generality Geach interjects the following note: "I maintain that it makes no sense to judge whether x and y are 'the same', or whether x remains 'the same', unless we add or understand some general term 'the same F'."3 Here, as in Mental Acts, he goes on to say that not any general term will serve to complete 'the same' constructions; only substantival terms will suffice for this purpose. Finally, in his article, "Identity/'Geach asserts that "When one says 'x is identical with y', this ... is an incomplete expression; it is short for 'x is the same A as y', where 'A' represents some count noun understood from the context of utterance- or else, it is just a vague expression of a half-formed

thought."4 (We should not, incidently, conclude from this last remark that Geach thinks all and only count nouns are substantival terms. In a reply to one of his critics Geach says the foregoing remark about

replacements for 'A' was a 'slip of the pen' and returns to his standard view that being a count noun is a sufficient, but not a necessary, condition for being a substantival term).5

The thesis Geach is expounding in the foregoing passages, the In-

completeness Thesis (IC thesis)- to give it a name, can be interpreted in two quite different ways. When interpreted in the first way the heart of the IC thesis is the claim that all instances of such open sentences as 'x is identical with y', 'x is the same as y', and 'x and y are the same', are in some way literally incomplete. The second interpretation of the IC thesis, which can be flushed out to yield several specific theses,

1 An earlier version of this paper was read at The Western Division Meetings of The American Philosophical Association, May 6, 1971.

2 Peter Thomas Geach, Mental Acts (New York: Humanities Press, 1957), p. 69. 3 Geach, Reference and Generality (Ithaca, New York: Cornell University Press, 1962,

p. 39. 4 Geach, "Identity/' Review of Metaphysics, XXI (1967), p. 31. s Geach, "A Reply," The Review of Metaphysics, XXII (1969), p. 5%.

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emphasizes Geach's use of such phrases as "say or mean/' "add or understand," and "some count noun understood from the context of utterance." (Italics mine). While the first interpretation yields a strong and interesting thesis, that thesis is, as I will show in Part I of this paper, simply false. In Part II I will argue that each of the specific theses

yielded by the second interpretation of the IC thesis is either false or

trivially true, depending upon how the notion of a substantival term is explicated.

I

Geach's claim is clearly not the triviality that the expression 'the same' is incomplete, for this is true of all sentence fragments, just in the sense that they are not well formed sentences. The point must rather be that all sentences of the sort in question are in some way fragmentary or incomplete. Though the syntax/semantics distinction is far from clear, it is also worth noting that Geach's charge that sentences of the sort detailed above are incomplete is apparently not a charge of syntactic incompleteness, at least not insofar as syntactic deviancy coincides with straightforward grammatical deviancy. For while such sentences as 'Charles Dodgson and Lewis Carroll are the same' may be

marginally ungrammatical (and even this is doubtful), this is not true of all the sentences objected to by Geach. 'Tully is the same as Cicero' is not obviously ungrammatical and 'Tully is identical with Cicero' and

'Mary and Bill covet the same thing' are clearly grammatically im-

peccable. Hence inasmuch as Geach is committed to holding that all of the above sentences are incomplete (and we saw on page 105 above that he is so committed), his charge against these sentences must be one of semantic, not syntactic, deviancy, however the notion of semantic deviancy is to be explicated. Note, finally, that the semantic

incompleteness or deviancy in question is certainly not that of simple ambiguity between qualitative and numerical identity: Geach holds that 'a and b are the same thing' is no more complete than is 'a and b are the same'.6

One might argue (though linguists do not, I understand, wish to do so) that 'John is thin and tall' is semantically incomplete in the sense that it does not have determinate truth conditions. Whether that sentence, even made relative to a particular occasion of use, is true or false depends on what standards of thinness and tallness are being applied. John might be tall as pygmies go, but short as basketball players go, and so on. We might now, analogously, see the IC thesis as the thesis that sentences of the type under discussion, e.g., 'a is the same as b', even as made relative to particular occasions of use, are semantically incomplete in the sense of failing to have determinate truth conditions. This, it might be argued, is so just because alternative expansions of those sentences into sentences of a form favored by Geach (e.g., 'x and y are the same F') may have different truth values. Some

6 Geach, Mental Acts, p. 69.

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Certain Identity Claims

x and y might be one and the same F, but distinct G's, where 'F' and 'G' are different substantival terms. This thesis is, of course, just the Geachean thesis that identity is relative.

Historically Geach seems to have reached the position that identity is relative by way of the /C thesis, rather than the other way around. But let this pass, for the only important point is that identity just is not relative. That identity is not relative has been argued at some length in a paper by John Perry entitled "The Same F,"7 and in my own paper "Relative Identity."8 However, it may still be worth here taking space to note at least one incoherency in the relative identity thesis.

Let 'a' and 'b' be individual constants and 'F' and 'G' distinct substantival terms. We will have a case of relative identity if a is an F and a C, and the same F as fa but not the same G as fa (where fa may or

may not be a G). As should be apparent, essential to this or any case of relative identity is the claim that we have an individual, here a, of which two distinct substantival terms, here 'F' and 'G', are correctly predicable, and whose identity conditions vary with the substantival term used to complete identity statements about that individual. It is

precisely the dual predication of distinct substantival terms of this sort that leads to insoluble difficulties.

An example will be useful, and Geach provides one with his account of surmen. According to Geach, surmen are individuals such that all men with the same surname are the same surman. Thus surmen

. . . differ from men just in this respect, that two different ones cannot share the same surname . . . [nonetheless] a surman is in many ways very much like a man,

e.g., he has brains in his skull and a heart in his breast and guts in his belly, for in

these respects two men of the same surname do not differ.9

On Geach's view, then, David and Dwight Eisenhower are distinct men but one and the same surman. I have objected elsewhere that Geach's surmen seem to be classes of men with the same surname, not concrete individuals complete with all the various intestinal accouterments.10 But the more general objection noted above can also be developed with this example.

When presented with David Eisenhower we are clearly presented with a man. Presumably we are also presented with a surman, for David is, ex hypothesis, the same surman as Dwight, which claim

surely entails that David is a surman. fx is the same F as y', where 'F' is a substantival term, must entail 'x is an F\) Now as noted above, to have a case of relative identity the distinct substantival terms in

question must each be truly predicable of one and the same individual. Here '. . . is a man' and '. . . is a surman' must both be true of David

Eisenhower, of one and the same David Eisenhower. And now the difficulties emerge.

We can grant that, when introduced to David Eisenhower, there is

7 John Perry, "The Same F," The Philosophical Review; LXXIX (1970), pp. 181-200. 8 Jack Nelson, "Relative Identity," Nous, IV (1970), pp. 241-260. 9 Geach, "Identity," p. 10.

10 Nelson, "Relative Identity," p. 254.

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a man before us. And we can grant, for purposes of argument, that there is a surman before us, and that they are "both" called 'David Eisen- hower'. But how are we to make sense of the claim that David, the man, is (is identical with) David the surman? If this identity does not hold, then 'man' and 'surman' are not both correctly predicable of one and the same individual, and we do not have a case of relative identity. On the other hand, if identity is relative and the /C thesis true, 'David the man is identical with David the surman' is incomplete, fragmentary.

It will not here do to claim that David the man and David the surman are the same man, or that they are the same surman, for this simply begs the question at issue. We need independent grounds for assenting to the claim that David the man is a surman, David the surman a man. One is here tempted to try to provide such grounds by arguing that because David the man and David the surman are occupying the same place at the same time when they are presented to us, they must be identical, one and the same individual - for no two material objects can occupy the same place at the same time. And since they are identical they must, by Leibniz's Law, have all of their properties in common, including the properties of being a man and of being a surman.

There are a host of mistakes in the foregoing line of reasoning. First, on the thesis that identity is relative, the claim that David the man and David the surman are identical because they occupy the same place at the same time is incomplete. Secondly, the argument relies on Leib- niz's Law (or, more correctly, the Indiscernibility of Identicals Principle), but this Law (or Principle) fails on the assumption that identity is relative. (We cannot conclude from the fact that a and b are the same F, and a a G, that b is a G, far less the same G as a.) Thirdly, the foregoing argument assumes that surmen are material objects, which is hardly clear. Finally, the claim that no two material objects can occupy the same place at the same time has recently come under strong attack. David Wiggins has argued that what is true is merely that no two material objects of the same kind can occupy the same place at the same time.11 And since substantival terms determine substantival kinds, David the man and David the surman clearly cannot be assumed to be objects of the same kind. David Sanford has gone even farther and argued that even Wiggins' restricted claim about the exclusiveness of space occupancy is false - that two material objects of the same kind can occupy the same place at the same time.12

What all of this shows, I suggest, is that on the assumption that identity is relative there is just no way to make sense of the claim that, in the Eisenhower case, we have one individual who is both a man and a surman; that David the man is the same indidivual as David the surman ('individual' is not a substantival term for Geach). And without the above we do not have a case of relative identity, we do not

11 David Wiggins, "On Being in the Same Place at the Same Time/' The Philosophical Review, LXXVII (1968), pp. 90-95.

12 David Sanford, "Locke, Leibniz, and Wiggins on Being in the Same Place at the Same Time," The Philosophical Review, LXXIX (1970), pp. 75-83.

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have one and the same individual whose identity conditions vary with the substantival term used to individuate it. The same problem arises in every purported case of relative identity. Accordingly, a different rationale must be sought for the view that sentences such as 'a and b are identical' are in some way incomplete or fragmentary.

It may seem that a promising place to look for this other rationale is in the fairly common view that there are distinct criteria of identity for distinct kinds of things (where the notion of a kind of thing is explicated by appeal to substantival terms). Just as what consistutes a pygmy's being tall is different from (though related to) what constitutes a basketball player's being tall, so too, it can be argued, what constitutes the identity of persons, e.g., Tully and Cicero, is different from (though related to) what constitutes the identity of other kinds of things, e.g., of numbers (/T+ 4 and If 38 - 2). Different kinds of things have different identity conditions, different criteria of identity. Given this view it may seem a short step to conclude that instances of such open sentences as 'x and y are the same' are incomplete just because such sentences do not tell us what the criteria of identity are for the things whose identity is being asserted.

Geach does hold that every identity claim presupposes, or requires, a criterion of identity, by reference to which the truth of that claim is to be determined. A criterion of identity is, for Geach, "that in accordance with which we ... judge as to the identity."13 And since it is substantival terms which supply criteria of identity, instances of such open sentences as 'x and y are the same', 'x is identical with y', and even 'x and y are the same thing', do not supply the requisite criteria of identity. (Thing', 'object', 'particular', etc. do not count as substantival terms for Geach - they are mere dummy terms, place holders only.) Therefore, Geach's reasoning may be, all instances of such open sentences as the above are semantically incomplete.

Another Geachean thesis is relevant here, namely the thesis that every proper name has a sense, the sense of the substantival term or terms with which its application is associated. According to this thesis 'Julius Caesar', in its most common use, has the sense of 'man', and 'Xantippe', as used as the name of my pet, has the sense of 'cat', and so on.14 This thesis about proper names and the defense of the /C thesis sketched above do not mesh well. For if Geach's view of proper names is correct, then every instance of such open sentences as 'x is identical with y' which replaces 'x' and 'y' with proper names, e.g., 'Tully is identical with Cicero', will carry with it the requisite criteria of identity. In the present example, since 'Tully' and Cicero' both have the sense of 'man', the information conveyed is that that claim is true if and only if Tully and Cicero are the same man.

It cannot here be objected that 'Tully is identical with Cicero' does not itself convey the requisite criterion of identity, and thus is seman-

tically incomplete, because that sentence does not itself tell us in what

13 Geach, Reference and Generality, p. 39. 14 Geach, Reference and Generality, pp. 43-45.

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sense (as the names of what kinds of things) Tully' and 'Cicero' are being used. Parallel reasoning would lead to the conclusion that every sentence is semantically incomplete, since no sentence itself contains an explicit indication of the sense in which each of its component words is being used. It is the context of use that normally makes clear in what sense the component words are being used.

The foregoing is an ad hominem directed at an inconsistency in Geach's views. More important is that from the fact, if it be a fact, that every identity claim presupposes criteria of identity it does not follow that identity claims which do not themselves convey these criteria are semantically incomplete. Geach seems here to have confused the claim that there must be a criterion, or criteria, for such-and-such's being the case with the different, and far stronger, claim that the assertion that such-and-such is the case must itself convey the requisite criterion or criteria- if semantic incompleteness is to be avoided. This latter claim does not follow from the former; indeed it is simply false. Let S be the set of prime numbers. Then being a prime number is the criterion of membership in 5. It does not follow that the sentence '3 is a member of S' is semantically incomplete, though that sentence itself gives no clue as to what the criterion of membership in S is. And someone who does not know what set S is will understand the above sentence in a perfectly clear sense, he will know that it says a certain thing, 3, is a member of a certain set, S. And he will also know the truth conditions for that sentence, in that he will know it is true if and only if 3 is a member of that set. Lack of knowledge of the specific criterion for membership in S, being a prime number, does not count against this understanding.15

II We are, I suggest, now warranted in concluding that there is no

plausible rationale for the view that all instances of such open sentences as we have been considering are literally incomplete, either syntactically or semantically. However, it is possible that I have, so far, misinterpreted Geach's /C thesis. Recall Geach's exact words: '"The same' is a fragmentary expression, and has no significance unless we say or mean 'the same X', . . ." (My italics.) ". . . it makes no sense to judge whether x and y are 'the same', or whether x remains 'the same', unless we add or understand some general term 'the same F\" (My italics.) And " 'x is identical with y' ... is short for 'x is the same A as y;, where 'A' represents some count noun understood from the context of utterance. . ." (My italics.)

By stressing the italicized segments of the above claims it is possible to interpret the IC thesis in several different ways, all of which result

15 A crucial difference between 'John is thin and tall' and 'John is identical with Harry' should here be made explicit. Even after the denotation of 'John' has been fixed the truth conditions of 'John is thin and tall' remain unclear, for John may be both a

pygmy and a basketball player. In other words the predicate x (x is talh is genuinely semantically incomplete. But we do fix the truth conditions of 'John is identical with Harry' by fixing the denotations of 'John' and of 'Harry'. Whatever kinds of things John and Harry may be, they cannot be identical qua one of those kinds but not qua another.

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in weaker theses than that discussed in Part I of this paper. First of all, Geach's position may be just that such sentences as 'a is the same as fa' lack significance, are uninformative, for anyone who is ignorant as to what kind(s) of things a and fa are, who is unable to mentally expand 'the same' into 'the same F'. Such a person may, of course, know the general truth conditions for 'a and b are the same', i.e., know that sentence is true if and only if 'a' and 'b' denote the same thing. But he will not know the specific identity conditions for things of the kind, whatever, it is, of which a and b are instances. For such a person this claim will, accordingly, be of "no significance."

One's first reaction to the above interpretation of the IC thesis is that it makes that thesis very weak. Calling a sentence such as 'a and fa are the same' "incomplete" now seems to be equivalent to saying that that sentence is not as informative as it could be (as 'a and fa are the same F' would be). And this is an uninteresting complaint. More- over, the notion of significance that interpretation appeals to is very vague. What is of significance, in this sense, to one person may not be to another, depending upon what each already knows. And surely there are cases in which being told that a is identical with fa would be

significant, even if one is wholly ignorant as to what kind of things a and fa are. For example, if one friend tells me he will soon give me

something, a, and another that he will soon give me something, b, then the information that a is identical with fa will help me bring my ex-

pectations in line with the future actions of these two benefactors. Further, upon being told that a is identical with b, even in the absence of all other information about a and b, I can conclude that, should I ever come upon a non-repetitive list of things of the kind of which a and fa are a single instance, I will not find both 'a' and V on that list. And this information need not always be of "no significance."

A second weaker interpretation of the IC thesis is also possible. It might be that Geach is claiming, not that certain expressions are

incomplete, or unenlightening, in the absence of certain background information, but just that it is senseless, pointless, or futile, to judge as to the identity of any things unless we know what kind of things they are. That is, perhaps it is Geach's view either that we cannot judge as to the identity of, say, a and b unless we know what kind(s) of

things they are (because one cannot judge as to the identity of a and fa without first individuating a and b, and individuating them requires identifying them as instances of certain kinds of things), or else that in the absence of this knowledge it is unreasonable to hazard a guess as to the identity of a and fa.

Finally, Geach might, in putting forward the IC thesis, be maintaining only that for any true instance of an open sentence such as 'x and y are the same' it is possible to find a true sentence of the form 'x and y are the same F', which utilizes the same individual terms as does the first sentence. This is just the thesis that if any x and any y are identical, then there is a substantival kind (where substantival kinds are determined by substantival terms) of which they are members (and hence the same member).

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The truth or falsity of both of these last weak theses depends, at least in large part, on what sorts of terms are to count as substantival terms. Against the former thesis one might argue that in a weird situation it is possible both to individuate and judge, reasonably, as to the identity of things without being prepared to add that they are 'the same F' for some replacement of 'F' with a substantival term. For

example, it seems possible that I might hear my neighbors, on various occasions, summon, scold, praise, curse, and discuss Xantippe and Rufus, in such a way that it becomes clear that Xantippe is in fact identical with Rufus. And this might happen without its becoming clear what kind of a thing 'Xantippe' and 'Rufus' both name, i.e., whether that thing is a pet, child, or poltergeist, etc.

Against the last of the above weak interpretations of the /C thesis it might be argued that there surely may be things which are of no particular substantival kind (which are not correctly characterized by any substantival term), and hence that that thesis is simply false.

Both of these objections look plausible if we take a fairly naive view as to what kinds of terms are substantival terms, i.e., take 'chair', 'table', 'book', 'person', 'pet', and so on as constituting a fair cross section of substantival terms. But consider also such expressions as

'gift', 'acquisition', 'possession of Jones', 'discovery of Jones', and so on. If these and similar nonrestrictive expressions do qualify as substantival terms it seems probable that both of the last two interpretations of the IC thesis will yield trivially true theses. Whatever else Rufus

(i.e., Xantippe) is, it is surely a topic of my neighbors' conversation. Hence in that example I am not in a position to judge as to the identity of Xantippe and Rufus without also being able to individuate them as instances of the substantival kind determined by the substantival term

'topic of conversation', and also to judge that they are or constitute the same topic of conversation. And however strange or perplexing a

thing may be, it is hard to imagine that it will not be an instance of at least one of the kinds determined by such nonrestrictive expressions as the above.

But are expressions such as those catalogued above substantival terms? It is, perhaps, not entirely clear that one can count topics of conversation, or even possessions of Jones. But neither is it entirely clear that one cannot do so. Moreover we must remember that

supplying a basis for counting- being a count noun - is, on Geach's view, a sufficient, but not a necessary, condition for an expression's being a substantival term.16 Geach seems to hold that a further, or

perhaps more general, sufficient condition for a term, A, being a substantival term is that the expression 'the same A' make sense.17 And 'the same topic of conversation' (as in 'The same topic of conversation kept coming up') and 'the same possession of Jones' (as in 'They both coveted the same possession of Jones'), etc., seem to make perfectly good sense.

16 Geach, Reference and Generality, pp. 39-40. 17 Geach, Reference and Generality, pp. 38-40.

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Perhaps the notion of a substantival term can be further deliniated so as to rule out the above trivializing cases. For example, one might hold that something cannot be a possession of Jones without being some specific kind of possession. But it is hard to see what argument would be advanced for this view, and what notion of kind is being appealed to.

In any event the general conclusion is clear. When given the strong interpretation of Part I of this paper the IC thesis is simply false. The weaker interpretations of Part II seem to make the IC thesis either false, or trivially and uninterestingly true.

December 1971

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On the Alleged Incompleteness of Certain Identity Claims