On consistency and existence in mathematics [article]

Walter Dean
2020 arXiv   pre-print
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 as difficult as it can be but also in which
more » ... rt was correct to maintain that demonstrating existence given consistency is as easy as it can be.
arXiv:2007.10167v1 fatcat:72llgzqmenhivmhgorpdn5xohq