Gödel Without Tears, slowly, 2

This very short second chapter ‘The First Theorem, two versions’ makes a key distinction between the semantic and syntactic flavours of the incompleteness theorem. That distinction is already there in Gödel 1931; but if I recall rightly, it was Andrzej Mostowski in his short book twenty-one years later who first brings it out really clearly and explicitly. The chapter also makes another key point: we should really talk, not of an incompleteness theorem (after all, mere incompleteness in itself might be boringly repairable) but of an incompletability theorem.

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