Monday, July 18, 2005

Armstrong on Logical Necessity

I'm puzzled by this comment by David Armstrong (A Theory of Universals, p. 42):

If logically equivalent predicates which are not logically empty apply in virtue of the very same universals, and logically equivalent propositions which are not themselves logically necessary are true in virtue of the very same state of affairs, then some de dicto account of logical necessity must be correct. The logical necessity of propositions must, in some way, derive from the words or concepts in which the propositions are expressed. (See also p. 168.)

Why? Wouldn't one way of reacting to Armstrong's claims be to conclude that, in the relevant cases, logical necessity boils down to the (de re) necessity of self-identity between universals states of affairs? (Moreover there are many logical necessities to which Armstrong's comments here seem irrelevant, such as '((A-->B)&A)-->B'. But let's ignore them for now.)

Maybe he'd want to resist this because there are some cases where the identity of the universals in virtue of which two predicates apply does not give rise to a corresponding logical necessity. There are cases of 'contingent identification of properties', according to Armstrong.

But that doesn't seem particularly relevant to a discussion of the source of logical necessity (what it 'derives' from). Why not just say (for instance) that we get logical necessity in cases where the two predicates wear the identity of their corresponding universals on their faces, but we don't get it when this identity is not so obvious?

Presumably Armstrong will say that this means the difference between logically necessary propositions and the rest has something to do with the predicates used (i.e. whether they wear the identity of their corresponding universals on their faces or not) rather than with anything more worldly. That would be right, but it wouldn't establish anything about the source of logical necessity. Armstrong's claim would seem to be that, because we can get a logical truth using one set of predicates then use different predicates corresponding to the same universal and get something which isn't a logical truth, the predicates must be doing (at least some of) the work in generating the logical necessity we had in the first case. But that conclusion doesn't seem to follow.

By analogy, we wouldn't say that any part of the truth of a proposition was 'derived from' the words used to express it, just because if we had used different but co-referential words we wouldn't have got a truth. 'Lois believes that Superman flies' is true but 'Lois believes that Clark Kent flies' isn't - but the truth of the former is not in any way 'derived from' the words we used. It is 'derived' wholly from a fact about Lois's mental state, albeit one we need to use the right words to express.

One thing that might be going on is that 'logical necessities' are simply a priori truths. If that's it, then the distinction between them and cases of 'contingent' (a posteriori) identification of properties is something to do with methods of epistemic access, and of course that is something that could be 'derived from the words or concepts in which propositions are expressed'. On the other hand if we want to admit metaphysical necessity, why not say that this is present in all cases where we have identity of universals, and its source is always the same (the identity of the universals concerned), although in some cases we have a priori access to this identity and in others we don't?

(I am assuming that 'logical necessity' is not a syntactic notion, since if it were it would be trivial that logical necessity is 'in some way derived from the words or concepts in which the propositions are expressed'.)

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