Topics Logic

Question For what I've seen until now, logical laws are always assumed to be necessarily true (in the "all possible worlds" sense), but is it possible that this necessity is weaker? Is it possible that our logical capabilities are adaptations to physical regularities of the actual world and are still evolving, together with our minds? If our logical capabilities are tracking our evolution, then the Necessity of Logic laws could be only Physical, instead of Metaphysical, and there could be possible worlds where the Physics would constrain Logic differently. This (I think) would also have implications regarding the Ontological commitment of Logic: instead of assuming that there is none, it would be possible, even likely, that the physical existents of the World would appear in our logical theories. Has anyone put forward sustained arguments for/against this?

Accepted:
March 5, 2009

Comments

People have talked about this. One oft-cited paper is Hilary Putnam's 1968 paper "Is Logic Empirical?" (Reprinted in his Mathematics, Matter and Method as "The Logic of Quantum Mechanics.") Putnam's arguments were of a "web of belief" sort: our beliefs form a web with some more central than others, but all are revisable. Quantum mechanics, Putnam thought, has given us the same sorts of reasons to revise our logical opinions as relativity gave us to revise our geometrical opinions. A large literature (to which I made some contributions) followed in the wake of Putnam's paper.

The issues here resist easy summary. In an unpublished talk, Saul Kripke offered some trenchant criticisms of Putnam's approach. My own view is that many of Kripke's criticisms can be met, but the upshot is not exactly that logic is empirical in the way Putnam believed. Rather, it could be, for all Kripke has shown, that there are logical relations found in some worlds that may be absent in others. If that's right, it would still be part of logic that these relations are possible. It would, however, be an empirical question whether they hold in this world.