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p. 11015. Maybe it is true—but you can’t prove it!locked

  • Graham Priest

Abstract

‘Maybe it is true—but you can’t prove it!’ first considers David Hilbert’s Program in the Foundations of Mathematics, which was to prove that mathematics was consistent. Hilbert’s ambitious proposal required all of mathematics to be axiomatized. The existence of such an axiom-system was disproved by the Austrian mathematician Kurt Gödel (1906–78). What Gödel showed was that such an axiom system cannot be provided even for the fragment of mathematics that concerns natural numbers, let alone the rest of it. Gödel’s result has been held to have many other philosophical consequences, concerning the nature of numbers, our knowledge of them, and even the nature of the human mind.

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