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Super Special Seminar Walter Dean (Warwick) On consistency and existence in mathematics
´¡²ú²õ³Ù°ù²¹³¦³Ù:Ìý Following the publication of his Foundations of Geometry in 1899, David Hilbert engaged in a well-known debate with Frege which concerned (amongst other things) the question of whether the consistency of a set of axioms entails the existence of a model in which they are satisfied.  I will consider this dimension of the so-called Frege-Hilbert controversy in light of the subsequent work in logic and philosophy which it inspired. I will argue for the following claims: i) the controversy both anticipated Gödel’s completeness theorem and shaped its reception (in which Bernays played a central role); ii) Frege was right to maintain that consistency checking is as difficult as it can be; ii) Hilbert was also right to maintain that given consistency,Ìý demonstrating the existence of a model is as easy as it can be.