Relative Identity Theory

Perry, "The Same $F$"

In section 3 of the article, he describes examples in which, given the circumstances under which a sentence is true ($R(a,b)$), we can't tell what objects the sentence is about and what predicate is applied to them. That is exactly the same point Quine relies on in "Ontological Relativity": even when we know the circumstances under which a sentence is true, we still can't tell whether it is about rabbits, undetached rabbit parts, or rabbit stages. Quine achieves that by varying what relation word we take to "name" identity. Perry is doing the same thing: he discusses whether to take $R$ (which Perry writes with underlines to indicate spaces) to be identity or not.

Perry is arguing against Geach, and on the side of Aristotle, Frege, Quine, and Kripke: They all agree that there is a single identity relation, but Geach says there is no such thing, only relative identity:

Aristotle, Frege, Quine, and Kripke all agree that $a=b$ makes sense, and is true or false (presuming, of course, that $a$ and $b$ name things. Geach says no, what is true or false is $a=b$ with respect to kind $K$. (Thus, not, $a$ is the same as $b$, but, $a$ is the same man as $b$.)

The example Perry uses is of word types and word tokens (unlike Geach, who uses heralds, personages, and surmen). Who else discussed word types and tokens? Again, Quine (and, probably, Kripke, discussing Quine). What point does use word types and tokens to make? He uses them to illustrate that we not only point out concrete things but abstract ones as well. The reason he wants to do that is to put concrete and abstract things in the same boat. How on earth do we point to types? Quine calls what we do "deferred ostension." We point to the same thing we point to in pointing to tokens and make it clear that what we intend to point out is the type by identifying and reidentifying it. Therefore, for Quine, what we are ostending is only relative to a translation, that is, relative to a choice of what words in the language we take to "name" identity.

Now, we see the close connection with Perry. Depending on whether or not $R$ denotes identity, $a$ either names a type or a token, and we can't tell which.

Geach for several reasons, wants to claim that in each of the cases we are pointing at (or naming with $a$) the very same thing. That would be nice for a reason Perry doesn't mention—in that case ontological relativity is gone. Once we know (choose) what relation is the identity relation, we could tell. Geach needs to block that. How? He disposes with the identity relation altogether. We do, of course, say that things are the same and different, and so Geach needs a replacement for the identity relation. He replaces it with his "relative identity." The price is that there is no way to say what is being named or pointed to outright, only relative to one or another kind. There is no final "type of thing" named. Geach views that as a good thing, in part because that makes our language correctly reporting what Quine has shown us is true anyway. What there is is only carved up into separate things relative to a choice of kind.

As alway, it is helpful in getting the picture to descend from our linguistic heights and say outright what the metaphysical picture suggested is, though it is usually a bad idea to try to stay there, since we get into muddles about language right away. I think the metaphysical picture closest to Geach's is one advocated by Professor Horgan, which he calls blobism: the world is all there really, fundamentally is, but we can choose to carve it up in various ways, using various kinds to establish various relative forms of identity.

How does Geach, according to Perry, argue for relative identity? First, they agree that if any sentence of the form "$a$ is the same $F$ as $b$ but is a different $G$," then relative identity theory wins. The opponents of relative identity theory, since they want to analyze "$a$ is the same $F$ as $b$" as "$a$ is the same as $b$ and is %$F$," just can't allow such a sentence. Thus, Geach gives what he takes to be examples of such sentences. Perry shows that he can neutralize each example in one of the two following ways:

  1. The "$a$" in the first part of the sentence is not used to name the same thing as the "$a$" in the second part of the sentence
  2. At least one of the so-called identity claims isn't actually an identity claim, it is a mere relative identity claim.

Explanation of the second: When I say that the couch and the chair are same color, that isn't really an identity claim at all, they are not said to be the same, only the same relative to color.

Thus, according to Perry, none of Geach's examples need involve identity at all, only relative identity. Geach, of course, agrees.

Perry has shown, let us at least grant for the sake of argument, that all of Geach's examples can be handled using a single notion of identity. But, and, so far as I can see, Perry never confronts the fact, Geach has shown that all identity statements can be handled as relative identity statements. The result is not, as Perry seems to think, a defeat for Geach, but a draw.

Perry takes Geach to give a pragmatic reason why his view is preferable, namely, that it fits with a picture of language as expanding. Perry doesn't think it is an advantage.

-- ShaughanLavine - 04 Feb 2008
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