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I think Modernism is Aristotelian. I understand exactly where you are coming from and I don't think Gödel thought of himself as a post modern (I think he was a royalist politically) The effect of his proof was by my definition the definition of post-modernism.
The history of mathematics has a pre-Gödel Hilbert or modern period and a Post-Gödel or postmodern period perfect. :) [edit] I don't think that Gödel should be included in the nothing means anything crowd.
and I do agree that mathematics is or should be immune to the stupidities of the worst manifestations of post-modernism is other fields.