Review of Symbolic Logic 3 (1):71-92 (2010)

Authors
Zach Weber
University of Otago
Abstract
This paper begins an axiomatic development of naive set theoryin 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
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DOI 10.1017/s1755020309990281
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References found in this work BETA

Universal Logic.Ross Brady - 2006 - CSLI Publications.
Exploring Meinong's Jungle and Beyond.Richard Routley - 1983 - Journal of Philosophy 80 (3):173-179.
Relevant Restricted Quantification.J. C. Beall, Ross T. Brady, A. P. Hazen, Graham Priest & Greg Restall - 2006 - Journal of Philosophical Logic 35 (6):587-598.

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Citations of this work BETA

Paraconsistent Logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
Existence as a Real Property.Francesco Berto - 2012 - Synthèse Library, Springer.
What If? The Exploration of an Idea.Graham Priest - 2017 - Australasian Journal of Logic 14 (1).
Transfinite Cardinals in Paraconsistent Set Theory.Zach Weber - 2012 - Review of Symbolic Logic 5 (2):269-293.
Against the Iterative Conception of Set.Edward Ferrier - 2019 - Philosophical Studies 176 (10):2681-2703.

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