Tuesday, August 31, 2004

Possible Worlds and Question-Begging: A Response to Chappell

Richard Chappell writes:

Don't get me wrong, I think the idea of "possible worlds" can be a useful heuristic. But if they're merely defined by logical possibility, rather than metaphysical possibility, then we should be clear on that. For example, the usually-sharp Maverick Philosopher attempted to refute the idea that laws of logic are empirical generalisations (and hence only contingently true), by equating the laws of logic are possibly false with there is a logically possible world where the laws of logic are false. But of course this is quite blatantly question-begging.

BV: I have no idea what RC is getting at here. Note first that throughout my post logical possibility was at issue. Now, to say that p is logically possibly false is equivalent to saying that there is a logically possible world in which p is false. These are just two different ways of saying the same thing.

Of course if you assume that metaphysical possibility simply is logical possibility, then the laws of logic are necessary and not merely contingent. He reached the conclusion by (implicitly) assuming it as a premise, which is a rather cheap (and unconvincing) move.

BV: This is deeply confused. First, I do not assume that metaphysical and logical possibility are the same. But even if I did, how would it follow that the laws of logic are necessary and not contingent?

I really have no idea what RC is saying. He seems to be saying that I am begging the question by confusing logical with metaphysical possibility. But how?

Here is the reductio ad absurdum argument I gave, with some explanatory material added in red.

1. The laws of logic are empirical generalizations. (Assumption for reductio)
2. Empirical generalizations, if true, are merely contingently true. (By definition of ‘empirical generalization’: empirical generalizations record what happens to be the case, but might not have been the case.) Therefore,
3. The laws of logic, if true, are merely contingently true. (From 1 and 2)

(So far the reasoning is impeccable. Note that that in an RAA type proof, the idea is to prove the negation of the proposition assumed by deriving a contradiction (an absurdity) from it with the help of auxiliary premises whose truth is not in dispute. Thus it should be clear that I am not asserting (1).)

4. If proposition p is contingently true, then it is possible that p be false. (Def. of ‘contingently true.’) Therefore,
5. The laws of logic, if true, are possibly false. (From 3 and 4) Therefore,
6. LNC is possibly false: there are logically possible worlds in which ‘p&~p’ is true. (From 5 and the fact that LNC is a law of logic.)

(It is clear from the context that what is at issue are logical contingency, logical possibility, logical necessity, etc. To save bytes, I left off the qualifier 'logical.' Perhaps this is the source of RC's trouble. Note also that, in (6), the material following the colon is unnecessary, strictly speaking. Thus there was no need for me to bring in worlds at all. And it has been my experience that talk of possible worlds is confusing to people who are unfamiliar with modal logic and its associated metaphysics.)

7. But (6) is absurd (self-contradictory): it amounts to saying that it is logically possible that the very criterion of logical possibility, namely LNC, be false. Corollary: if laws of logic were empirical generalizations, we would be incapable of defining ‘empirical generalization’: this definition requires the notion of what is the case but (logically) might not have been the case.

(Rethinking this, my argument strikes me as logically impeccable. Am I assuming what I need to prove? Not that I can see. What I am arguing, very simply, is that LNC cannot be an empirical generalization since if it were, it would be logically contingent, i.e., logically possible false. But this is absurd since LNC is the criterion of logical possibility. LNC defines what it is to be a logically possible world. Hence a logically possible world in which LNC fails to be true is a world in which a contradiction is true. Hence, by RAA, (1) is false.)