Non-contradiction: Oh Yeah and So What?

The logical Law of Non-contradiction – that a proposition cannot be both true and false – enjoys a special, perhaps uniquely privileged, status in philosophy. Most philosophers think that finding a contradiction – the assertion of both P and not-P – in one's reasoning is the best possible evidence that something has gone wrong, the ultimate refutation of a position. But why should this be so? What reason do we have to believe it? In this paper, I address these questions.