School of Historical and Philosophical Studies - Research Publications

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A Paraconsistent Model of Vagueness

Weber, Z (OXFORD UNIV PRESS, 2010-10)
Extensionality and Restriction in Naive Set Theory

Weber, Z (Springer Science and Business Media LLC, 2010-02)
TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY

WEBER, Z (Cambridge University Press (CUP), 2010-03)

This paper begins an axiomatic development of naive set theory—the consequences of a full comprehension principle—in a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead to Cantor’s theorem, the existence of large cardinals, and a counterexample to the continuum hypothesis.