All the mathematics in the world: logical validity and classical set theory
All the mathematics in the world: logical validity and classical set theory
Author(s): David Charles McCartySubject(s): Philosophy, Logic, Special Branches of Philosophy
Published by: Copernicus Center Press
Keywords: ustification of deduction; set validity; class validity; general validity; intuitionism; topological models
Summary/Abstract: A recognizable topological model construction shows that any consistent principles of classical set theory, including the validity of the law of the excluded third, together with a standard class theory, do not suffice to demonstrate the general validity of the law of the excluded third. This result calls into question the classical mathematician's ability to offer solid justifications for the logical principles he or she favors.
Journal: Zagadnienia Filozoficzne w Nauce
- Issue Year: 2017
- Issue No: 63
- Page Range: 5-29
- Page Count: 25
- Language: English
