Grice and Geach on relative identity

Speranza


Identity is not first-order, but only second-order definable, or is it?

Grice was concerned with identity and would often refered to "predicate calculus with identity".

With Myro, Grice developed the Grice-Myro theory of relative identity, notably time-relative identity.

The situation about "=" not being a first-order item provides the basis for Peter Thomas Geach's similarly radical contention that the notion of absolute identity has no application and that there is only relative identity.

Grice possibly felt it odd that he would defend absolute value (in "Conception of Value") but relative identity!

Geach maintains that since no criterion can be given by which a predicate expressing an I-predicate may be determined to express, not merely indiscernibility relative to the language to which it belongs, but also absolute indiscernibility, we should jettison the classical notion of identity.

Geach dismisses the possibility of defining identity in a second-order language on the ground of the paradoxical nature of unrestricted quantification over properties and aims his fire particularly at Quine's proposal that an I-predicate in a first-order theory may always be interpreted as expressing absolute identity (even if such an interpretation is not required).

Geach objects that Quine's suggestion leads to a “Baroque Meinongian ontology” and is inconsistent with Quine's own expressed preference for “desert landscapes”.

Similarly Grice would refer to his ontology not createing a "Meinongian jungle" in his reply to Quine in "Words and Objections".
We may usefully state Geach's thesis using the terminology of absolute and relative equivalence relations.

Let us say that an equivalence relation

R

is absolute iff,, if x stands in it to y, there cannot be some other equivalence relation

S

holding between anything and either x or y, but not holding between x and y.

If an equivalence relation is not absolute it is relative.

Thus, classical identity is an absolute equivalence relation.

Geach's main contention is that any expression for an absolute equivalence relation in any possible language will have the null class as its extension, and so there can be no expression for classical identity in any possible language.

This is the thesis Geach argues against Quine.

Geach also maintains the sortal relativity of identity statements, that “x is the same A as y” does not “split up” into “x is an A and y is an A and x=y”.

More precisely stated, and we owe this to Noonan's clear account in the Stanford Encyclopedia, what Geach denies is that whenever a term “A” is interpretable as a sortal term in a language L (a term which makes (independent) sense following “the same”) the expression (interpretable as) “x is the same A as y” in language L will be satisfied by a pair< x,y> only if the I-predicate of L is satisfied by .

Geach's thesis of the sortal relativity of identity thus neither entails nor is entailed by his thesis of the inexpressibility of identity.

It is the sortal relativity thesis that is the central issue between Geach and Wiggins (1967 and 1980).

Grice was very familiar with Wiggins, since he had used Wiggins's book for a long seminar at Berkeley. Myro was attending -- and actually co-delivering it.

It entails that a relation expressible in the form “x is the same A as y” in a language L, where “A” is a sortal term in L, need not entail indiscernibility even by the resources of L.

Geach's argument against Quine exists in two versions, an earlier and a later.

In its earlier version the argument is merely that following Quine’ suggestion to interpret a language in which some expression is an I-predicate so that the I-predicate expresses classical identity sins against a highly intuitive methodological programme enunciated by Quine himself, namely that as our knowledge expands we should unhesitatingly expand our ideology, our stock of predicables, but should be much more wary about altering our ontology, the interpretation of our bound name variables (1972: 243).

Geach's argument is that in view of the mere possibility of carving out of a language L, in which the relational expressions, E1, E2, E3… are not I-predicates, sub-languages L1, L2, L3… in which these expressions are I-predicates, if Quine's suggested proposal of reinterpretation is possible for each Ln, the user of L will be committed to any number of entities not quantified over in L, namely, for each Ln, those entities for which the I-predicate of Ln (En) gives a criterion of absolute identity.

This will be so because any sentence of L will retain its truth conditions in any Ln to which it belongs, reinterpreted as Quine proposes, but “of course, it is flatly inconsistent to say that as a member of a large theory a sentence retains its truth-conditions but not its ontological commitment” (1973:299).

The crucial premiss of this argument is thus that sameness of truth-conditions entails sameness of ontological commitment.

But this is not true.

The ontological commitments of a theory (according to Quine, whose notion this is) are those entities that must lie within the domain of quantification of the theory if the theory is to be true; or, the entities the predicates of the theory have to be true of if the theory is to be true. A theory is not ontologically committed, we may say, to whatever has to be in the universe for it to be true, but only to whatever has to be in its universe for it to be true. Thus there is no argument from sameness of truth-conditions to sameness of ontological commitments.

The later version of Geach's argument needs a different response.

The difference between the earlier version and the later one is that in the later Geach's claim is not merely that Quine's thesis about possible reinterpretation has a consequence which is unpalatable, but that it leads to an out-and-out logical absurdity, the existence of what he calls “absolute surmen” (entities for which having the same surname constitutes a criterion of absolute identity, ie., entails indiscernibility in all respects).

Because Geach is now making this stronger claim, the objection that his argument depends upon the incorrect assumption that sameness of truth-conditions entails sameness of ontological commitment is no longer relevant.

In order to make out his case Geach has to establish just two points.

First, that there are sentences of English supplemented by the predicate

“is the same surman as”

(explained to mean “is a man and has the same surname as”), which are evidently true and which, considered as sentences of that fragment of English in which “is the same surman as” is an I-predicate, when this is interpreted in the way Quine suggests, can be true only if absolute surmen exist. And secondly, that the existence of absolute surmen is absurd.

But in the end Geach fails to establish these two points.

Quine would say that, for the fragment of English in question, the domain of the variables can be considered to consist of classes of men with the same surname and the predicates interpreted as holding of such classes. Thus, the predicate “is the same surman as” will no longer be true of pairs of men if we adopt Quine's suggestion (I am writing, remember in English, not in the fragment of English under discussion), but rather of pairs of classes of men with the same surname – these then will be Geach's “absolute surmen”.

Now, Geach attempts to rule this out by the argument that “whatever is a surman is by definition a man.” But this argument fails.

The predicate

“is a man”

will also be in the language-fragment in which “is the same surman as” is the I-predicate; and so it, too, will, be reinterpreted, if we follow Quine's suggestion, as holding of classes of men with the same surname. Thus the sentence “Whatever is a surman is a man” will be true in the language fragment interpreted in Quine's way, just as it is in English as a whole.

What will not be true, however, is that whatever the predicate “is a surman” is true of, as it occurs in the language-fragment reinterpreted in Quine’ way, is a thing of which “is a man”, as it occurs in English as a whole, is true of. But Geach has no right to demand that this should be the case. Even so, this demand can be met. For the domain of the interpretation of the language fragment in which “is the same surman as” is the I-predicate can, in fact, be taken to consist of men, namely, to be a class containing exactly one representative man for each class of men with the same surname. Thus, as Geach says, absolute surmen will be just some among men (1973:100).

Geach goes on to say that there will, for example, be just one surman with the surname “Jones”, but if this is an absolute surman, and he is a certain man, then which of the Jones boys is he?

But this question, which is, of course, only answerable using predicates which belong to the part of English not included in the language fragment in which “is the same surman as” is the I-predicate, is not an impossible one to answer. It is merely that the answer will depend upon the particular interpretation that the language fragment has, in fact, been given. Geach is, therefore not entitled to go on, “Surely we have run into an absurdity.”

It thus seems that his argument for the non-existence of absolute identity fails.

Geach's argument for his second thesis, that of the sortal relativity of identity, is that it provides the best solution to a variety of well known puzzles about identity and counting at a time and over time.

The most well known puzzle is that of the cat on the mat, which comes in two versions.

The first version goes like this. (Wiggins 1968 contains the first appearance of this version in present-day philosophical literature; an equivalent puzzle is that of Dion and Theon, see Burke 1995).

Suppose a cat, Tibbles, is sitting on a mat.

Now consider that portion of Tibbles that includes everything except its tail – its “tail complement” – and call it “Tib”. Tib is smaller than Tibbles so they are not identical. But what if we now amputate the cat's tail? (A time-reversed, or “growing”, version can be considered in which a tail is grafted on to a tailless cat; the same responses considered below will be available, but may differ in relative plausibility.) Tibbles and Tib will now coincide. If Tibbles is still a cat, it is hard to see by what criterion one could deny that Tib is a cat. Yet they are distinct individuals, since they have different histories. But there is just one cat on the mat. So they cannot be distinct cats. They must be the same cat, even though they are distinct individuals; and so identity under the sortal concept cat must be a relative identity relation.


The second version goes as follows.

Tibbles is sitting on the mat and is the only cat sitting on the mat. But Tibbles has at least 1,000 hairs. Geach continues: “Now let c be the largest continuous mass of feline tissue on the mat. Then for any of our 1,000 hairs, say hn, there is a proper part cn of c which contains precisely all of c except that hair hn; and every such part cn differs in a describable way both from any other such part say cm, and from c as a whole. Moreover, fuzzy as the concept cat may be, it is clear that not only is c a cat, but also any part cn is a cat: cn would clearly be a cat were the hair hn to be plucked out, and we cannot reasonably suppose that plucking out a hair generates a cat, so cn must already have been a cat.”
The conclusion, of course, is the same as in the previous version of the argument: there is only one cat on the mat so all the distinct entities that qualify as cats must be the same cat.

This version of the argument can be resisted by insisting that the concept of a cat is maximal, i.e. no proper part of a cat is a cat. The first version may be resisted in a variety of ways. Some deny the existence of the tail-complement at all (van Inwagen 1981, Olson 1995); others deny that the tail-complement survives the amputation (Burke 1995). Another possibility is to say that certain of the historical and/or modal predicates possessed by Tibbles and not Tib are essential to being a cat, so that Tib is not (predicatively) a cat Wiggins (1980). Again, it can be accepted that both Tib and Tibbles are cats, but deny that in counting them as one we are counting by identity (even cat identity), rather, we are counting by “almost identity” (Lewis 1993). Another possibility is to accept that both Tib and Tibbles are cats, but deny that they are distinct: rather “Tib” and “Tibbles” are two names of the same cat-stage.

There is, then, no very compelling argument for Geach's sortal relativity thesis to be based on such examples, given the variety of responses available, some of which will be returned to below. On the other hand, no alternative solution to the puzzle of the cat on the mat stands out as clearly superior to the rest, or clearly superior to the sortal relativity thesis as a solution. We should conclude that this component of Geach's position, though not proven, is not refuted either; and, possibly that the linguistic data provide no basis for a decision for or against.

REFERENCES

Geach, P. T.,
Logic Matters, Oxford: Basil Blackwell.
––– Ontological relativity and relative identity, in M.K. Munitz (ed.), Logic and Ontology, New York: New York University Press.
––– Reference and Generality 3rd edition. Ithaca, NY: Cornell University Press.
––– “Replies”, in H. A. Lewis (ed.), Peter Geach: Philosophical encounters, Dordrecht: Kluwer Academic Publishers.
GRICE, H. P. -- The Grice Collection, Bancroft Library.
MYRO, in PGRICE ed Grandy/Warner.
NOONAN, 'Identity', in Stanford Encyclopedia of Philosophy