Friday, August 13, 2004

Are the Laws of Logic Empirical Generalizations?

Someone on a discussion list recently resurrected the old idea of John Stuart Mill and others that the laws of logic are empirical generalizations from what we do and do not perceive. Thus we never perceive rain and its absence in the same place and at the same time. The temptation is to construe such logic laws as the Law of Non-Contradiction -- ~(p & ~p) -- as generalizations from psychological facts like these. If this is right, then logical laws lack the a priori character and epistemic ‘dignity’ that some of us are wont to see in them. They rest on psychological facts that might have been otherwise.

But now consider this reductio ad absurdum:

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)
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.)
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.