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In Defense of the Law of Noncontradiction

An important philosophical puzzle arises whenever we find a group of philosophically interesting sentences which individually appear to be true but jointly imply a contradiction. It is traditional to suppose that since the sentences in the group are jointly inconsistent, we cannot accept them all. This refusal to accept all the sentences in the group is not just grounded in (a) the problem of accepting the derivable contradiction, but also in (b) the problem that classical logic gives us the means to derive every sentence whatsoever once we have derived a contradiction. But with certain really hard puzzles of this kind, it is difficult to identify even one sentence in the puzzling group to reject. In such cases, there seems to be no good reason or argument for rejecting one of the sentences rather than another. We often find ourselves in the uncomfortable position of having to reject statements that have a strong claim to truth. Paraconsistent logic and dialetheism constitute a fascinating body of doctrines for critically analyzing this kind of philosophical puzzle. Paraconsistent logic removes problem (b), noted above, concerning the presence of contradictions in classical logic. In contrast to classical logic, paraconsistent logic tolerates the derivation of a contradiction without thereby yielding a proof of every sentence. Dialetheism goes one step further, however, and addresses problem (a). It is the doctrine that, in some of these really hard cases, there are indeed true contradictions. Di-