On consistency and existence in mathematics

Por • 21 ene, 2021 • Sección: Leyes

Walter Dean

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 Gödel’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.

arXiv:2007.10167v1 [math.LO]
Logic (math.LO); History and Overview (math.HO)

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