The Barber, Russell's Paradox, Catch-22, God, Contradiction and much more

Wittgenstein speaks of the ‘superstitious dread and veneration by mathematicians in face of a contradiction’ and recommends that, instead of adopting this attitude, people might have wanted to produce a contradiction and ‘would be glad to lead their lives in the neighbourhood of a contradiction’ Gödel thought such remarks ‘nonsense’ and few authors have dissented from that verdict. Perhaps the most striking claim Wittgenstein makes (and defends both early and late) is that contradictions are not false. This paper seeks to defend Wittgenstein’s outrageous view, and to show its relevance to solving a variety of logico-semantical paradoxes.