Review of Symbolic Logic 5 (2):269-293 (2012)

Authors
Zach Weber
University of Otago
Abstract
This paper develops a (nontrivial) theory of cardinal numbers from a naive set comprehension principle, in a suitable paraconsistent logic. To underwrite cardinal arithmetic, the axiom of choice is proved. A new proof of Cantor’s theorem is provided, as well as a method for demonstrating the existence of large cardinals by way of a reflection theorem
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DOI 10.1017/s1755020312000019
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References found in this work BETA

Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.
The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Universal Logic.Ross Brady - 2006 - CSLI Publications.

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Citations of this work BETA

Paraconsistent Logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
What If? The Exploration of an Idea.Graham Priest - 2017 - Australasian Journal of Logic 14 (1).
Logical Partisanhood.Jack Woods - 2019 - Philosophical Studies 176 (5):1203-1224.
Dialetheism.Francesco Berto, Graham Priest & Zach Weber - 2008 - Stanford Encyclopedia of Philosophy 2018 (2018).
Against the Iterative Conception of Set.Edward Ferrier - 2019 - Philosophical Studies 176 (10):2681-2703.

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