On Numerical Sameness / Identity / “Absolute” Identity

I’ve been reading some stuff about identity and relative identity lately, in the process of writing something on relative identity versions of trinitarianism. This post is to share some good finds.

In his excellent entry “Relative Identity“ veteran logican and philosopher of language Harry Deutsch says about the best that can be said for relative identity theories – that maybe, arguably, they solve or help to solve various metaphysical problems. See his sections 2 and 4 for these. His section 5 is a penetrating analysis of Geach’s very hard to follow arguments.

Deutsch’s point of view is very different from that held by most philosophers. For this, see chapter 1 of Colin McGinn’s Logical Properties. (NDPR review.) This is more or less  the “orthodox” view that most philosophers hold, atheist or theist, trinitarian or not. I largely agree with it, except for its Platonic aspect. I uphold the logic of identity as McGinn understands it, but do not want to commit to the existence of abstracta like relations. I think the truthmaker of a sentence like “Dubya just is George Bush” is going to be a concrete object, the ex-president himself. In this, I’m in the minority; most philosophers find abstracta indispensible.

Another place one can start is Harold Noonan‘s excellent “Identity” entry. He’s an excellent philosopher, and the piece has many virtues; in particular, see his section 2 on Leibniz’s Law vs. substitutivity principles.

The best thing I’ve ever read on identity and relative identity is John Hawthorne’s chapter “Identity” in The Oxford Handbook of Metaphysics. A version is available to scribd users here.

• This piece is very rich, and defies easy summary.
• A basic point is that “identity” in a basic, unanalyzable concept, and so we ought not worry about circular definition. Geach’s failure to recognize this is a core problem with his whole project. (p. 122)
• Hawthorne’s section 3.1 brings out the many problems facing Geach’s project. His conclusion: “In sum: it is no mere artefact of philosophical fashion that Geach’s relative identity approach has few adherents.” (p. 123) You’ll have to read the piece to see why.
• Another basic, crucial point, I would paraphrase as follows. (p. 100) We all understand “something is cold and fizzy”. The shows that we have a concept of identity; if that sentence is true, the cold thing just is the fizzy thing. Contrast with the sentence: “something is cold, and something is fizzy.” That we have this concept of identity, of course, doesn’t imply that we understand identity-logic, or have any theoretical opinions on the subject at all.
• Hawthorne’s main point is that “Puzzles that are articulated using the word ‘identity’ are not puzzles about the identity relation itself.” (p. 99) When I think about the many metaphysical treatments I’ve read recently of the puzzles Deutsch discusses, I think this is an emerging consensus. There are always other moves to be made, and all sorts of weird metaphysical doctrines to be brought into play. But the emerging consensus is that identity is to be held constant; the concept of identity is common coin in these disputes, just as is, say, the assumptions that modus ponens is valid, or that no contradiction is true.
• By the examples he gives, it is plain that Hawthorne is well aware that evaluating Trinity and Incarnation theories necessitate careful thinking about identity, but he doesn’t ever entry the fray. (But he almost does – see p. 120 fn. 38.)

Be forewarned; there are pervasive confusions about numerical sameness among Christian theologians nowadays, in particular about personal identity (the relation being the same self as). This is largely due, I think, to uncritical reliance on poorly done philosophy. This is not due to any intrinsic difference between the fields or any commitment intrinsic to Christianity, as there are and have been theologians who are thoroughly clear-headed about identity. The solution is to digest well done philosophy, so as to be able to make clear distinctions and to reason surefootedly; that’s the reason for this post. Don’t give in to the temptation to foolishly heap scorn on “absolute” identity or on Leibniz’s Law, as if they were mere speculations, and things to which you yourself are not committed.