false_vacuum comments on Edward Nelson claims proof of inconsistency in Peano Arithmetic - Less Wrong
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Here's a summary and discussion of the affair, with historical comparison to the Gödel results and their reception (as well as comments from several luminaries, and David Chalmers) on a philosophy of mathematics blog whose authors seem to take the position that the reasons for consensus in the mathematical community are mysterious. (It is admitted that "arguably, it cannot be fully explained as a merely socially imposed kind of consensus, due to homogeneous ‘indoctrination’ by means of mathematical education.") This is a subject that needs to be discussed more on LW, in my opinion.