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Inconsistent Mathematics (Stanford Encyclopedia of Philosophy)

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Inconsistent mathematics is the study of the mathematical theories that result when classical mathematical axioms are asserted within the framework of a (non-classical) logic which can tolerate the presence of a contradiction without turning every sentence into a theorem. Inconsistent Mathematics began historically with foundational considerations. Frege and Russell proposed to found their mathematics on the naive principle of set theory: to every predicate is a set. But the naive principle leads rapidly to a proof of the existence of the Russell set, the set of all sets not members of themselves, which both is and is not a member of itself. This and other set-theoretic paradoxes noted by Russell and others led to attempts to produce consistent set theories as a foundation for mathematics. Perhaps the best known of these was Zermelo-Fraenkel set theory ZF. But ZF and others such as NBG and the like were in various ways ad hoc, having to include multiple independent principles instead o

--> Inconsistent Mathematics (Stanford Encyclopedia of Philosophy) Stanford Encyclopedia of Philosophy Menu Browse Table of Contents What's New Random Entry Chronological Archives About Editorial Information About the SEP Editorial Board How to Cite the SEP Special Characters Advanced Tools Contact Support SEP Support the SEP PDFs for SEP Friends Make a Donation SEPIA for Libraries Entry Navigation Entry Contents Bibliography Academic Tools Friends PDF Preview Author and Citation Info Back to Top Inconsistent Mathematics First published Tue Jul 2, 1996; substantive revision Wed Nov 30, 2022 In

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