Wittgenstein vs. Turing on consistency and contradictions in mathematics
Professor (emeritus) Mark Steiner, Hebrew University of Jerusalem, gives a talk that is of interest both to philosophers and mathematicians.
In 1939, Wittgenstein gave a series of lectures on the Foundations of Mathematics, which Turing attended. During these lectures, Wittgenstein scoffed at what he regarded as the "superstitious" fear by mathematicians of inconsistency, and their search for consistency proofs of mathematical theories. Here he was met by stiff opposition by Turing, who argued, among other things, that "bridges would fall down" if engineering were based on a "hidden" contradiction. I will explicate this altercation and attempt to say who won the debate.