Geach's Relative Identity Theory

We read Perry's paper instead of anything by Geach because Geach is quite hard to understand, and Perry provides a fairly clear account of Geach's theory and the clearest formulation of standard objections to it.

Frege's view, which is the standard view, is that identity is a single, well-determined, logical relation which holds between any object and itself and not between any object and another.

Frege also holds that 'one' is not a well-determined notion. It requires a "concept." Example: when I point at an encyclopedia, it is not clear whether I'm indicating one encyclopedia, 25 volumes, 27,000 pages, millions of words, whatever.

Geach is surprised that Frege doesn't extend the doctrine from "one" to "the same." The same cricket team is not necessarily the same collection of players.

left-handed brother can be analyzed as left-handed and brother.
good bank robber, however, cannot be analyzed as good and bank robber.

Frege thinks that for A to be the same team as B is for A to be a team and for A to be the same as B.

Geach, to the contrary, thinks that "same team," like "good bank robber" doesn't split.

(a) Bull, (b) bull, (c) cow. Three word tokens but two word types. Is (a) the same word as (b)? The question, as posed, has no answer. Frege and Geach agree that it needs to be made more precise in one of the following two ways: Is (a) the same word token as (b)? or Is (a) the same word type as (b)?

Frege thinks that in the two questions, (a) refers to different objects, but the identity relation is unchanged. Geach thinks that in the two questions (a) refers to the same object, and hence that the relation must change. We are, it seems, at the kind of impasse Quine describes in calling attention to the inscrutability of reference. Indeed, on p. 97, Perry dismisses such worries as 'absurd,' on the grounds that they apply to all words, not just the identity predicate. That is not a convincing argument against Geach, it just begs all of the worries about the nature of object talk.

Geach gives an additional argument: we can say, '(a) and (b) are the same type but different tokens of it.' Here we are using one token of '(a)' in both identity statements, forestalling Perry's move of taking one to refer to the type and the other, the token. That isn't a convincing argument on Geach's side. Perry suggests one might read the sentence as '(a) and (b) are different tokens of the same type.' That works. Note the close connection to Quine's notion of deferred ostension.

So far, it seems, we have a standoff: we can always convert a Geachian relative identity sentence into a sentence that meets Fregean standards by proliferating enough objects.

Finally, we get to the meat. Geach says that reading absolute identity into a language forces us to "limit ideology" by "inflating ontology." Adding new predicates to a language (something that happens all the time) will, on the absolute identity picture, force us to discover that we hadn't been talking about anything. Perry, in reply, simply takes 'English' to be a stage of what Geach takes 'English' to be. The familiar Quinian point about rabbits holds: there is nothing that can be said one way that can't be said the other.

At the very end of the article, Perry, it seems to me, provides a decisive argument against his own position and for that of Geach: "he need not have any such intentions, just as when I say "This is brown" with a gesture toward my desk, I need not have decided whether I am referring to the desk or its color" 98.

-- ShaughanLavine - 11 Sep 2008