On 09/01/17 11:50, Graham White wrote:
One (rather trivial) reason why Goedel's Theorem isn't a paradox is because it's true, and there's a good argument for its truth, indeed one that can be formalised, but not in the system that the theorem is about. This differentiates it from paradoxes such as that of the liar, which can't consistently be assigned any truth value.
However, there's something deeper here, which is that most paradoxes go against common sense, so that discovering them is a sort of self-limitation of reason (showing that something which seemed obvious is in fact false). And so was Goedel's theorem: nobody in the Hilbert school seems to have thought seriously that their program could fail, just that they hadn't quite got it right yet. And it says a great deal for Hilbert's personal qualities that he accepted Goedel's theorem when he saw it.
What else could he have done, having read the proof? Paul
(See Wilfried Sieg's wonderful book Hilbert's Programs and Beyond; a must read, in my opinion.)
-- Paul Blain Levy School of Computer Science, University of Birmingham http://www.cs.bham.ac.uk/~pbl [For admin and other information see: http://www.mta.ca/~cat-dist/ ]