All the mathematics in the world: logical validity and classical set theory

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David Charles McCarty


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.

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McCarty, D. C. (2017). All the mathematics in the world: logical validity and classical set theory. Philosophical Problems in Science (Zagadnienia Filozoficzne W Nauce), (63), 5–29. Retrieved from


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