I was reading this (older) post on the Law of Non-Contradiction over at Philosophy, et cetera. Is it really the case that it is not rational to question LNC? One might think that (P v -P) is an analytic truth. Indeed, I think that it is. But this is true only if one is operating within the confines of a two-valued logic. If one takes a many-valued logic then -(P & -P) is not analytic at all! So then the issue is whether or not classical two-valued logic is The One True Logic or not. How would we know this? I take it that someone like Richard would say that classical logic is what a maximally rational ideal agent would subscribe to. But how could we possibly know what kind of logic such an agent would subscribe to?
In an earlier post (Why Does 1+1=2?) I argued that there is nothing that could possibly decide between whether or not mathematics is an empirical science or an a priori one. The same seems true of logic. The basic laws of logic only seem rational to us because of the kind of experience that we have in this world filled with ‘medium sized dry-goods’ and this means that coherence as a criterion of truth is only valuable because of the world we live in and the kind of experience that we have. So the fact that the LNC seems to us to be denied at our own peril cannot possibly be evidence that it cannot be denied. We have no way of knowing whether it is actually ideally rational or not, since what we can concive of is limited to the kind of experience that we have.