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arXiv:2007.10167 [math.LO]AbstractReferencesReviewsResources

On consistency and existence in mathematics

Walter Dean

Published 2020-07-20Version 1

This paper engages the question Does the consistency of a set of axioms entail the existence of a model in which they are satisfied? within the frame of the Frege-Hilbert controversy. The question is related historically to the formulation, proof, and reception of G\"odel's Completeness Theorem. Tools from mathematical logic are then used to argue that there are precise senses in which Frege was correct to maintain that demonstrating consistency is \textsl{as difficult as it can be} but also in which Hilbert was correct to maintain that demonstrating existence given consistency is as easy as it can be.

Comments: This is an expanded version of a paper delivered to the Aristotelian Society on 15 June 2020 and which will be published in Volume CXX, No. 3 (2020) of their Proceedings
Categories: math.LO
Subjects: 03-03, 03C35
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