On consistency and existence in mathematics
Logic
2021-05-03 v2 History and Overview
Abstract
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 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.
Cite
@article{arxiv.2007.10167,
title = {On consistency and existence in mathematics},
author = {Walter Dean},
journal= {arXiv preprint arXiv:2007.10167},
year = {2021}
}
Comments
This is an extended version of a paper delivered to the Aristotelian Society on 15 June 2020 and which has been published in their Proceedings