Studia Logica 94 (1):87-104 (2010)

Zach Weber
University of Otago
The naive set theory problem is to begin with a full comprehension axiom, and to find a logic strong enough to prove theorems, but weak enough not to prove everything. This paper considers the sub-problem of expressing extensional identity and the subset relation in paraconsistent, relevant solutions, in light of a recent proposal from Beall, Brady, Hazen, Priest and Restall [4]. The main result is that the proposal, in the context of an independently motivated formalization of naive set theory, leads to triviality.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
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DOI 10.1007/s11225-010-9225-y
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References found in this work BETA

Paraconsistent Logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
Transfinite Numbers in Paraconsistent Set Theory.Zach Weber - 2010 - Review of Symbolic Logic 3 (1):71-92.
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.
Relevance Logic.Michael Dunn & Greg Restall - 2002 - In D. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic. Kluwer Academic Publishers.
Άδύνατον and Material Exclusion 1.Francesco Berto - 2008 - Australasian Journal of Philosophy 86 (2):165 – 190.

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Citations of this work BETA

Transfinite Numbers in Paraconsistent Set Theory.Zach Weber - 2010 - Review of Symbolic Logic 3 (1):71-92.
Absolute Contradiction, Dialetheism, and Revenge.Francesco Berto - 2014 - Review of Symbolic Logic 7 (2):193-207.
Transfinite Cardinals in Paraconsistent Set Theory.Zach Weber - 2012 - Review of Symbolic Logic 5 (2):269-293.

View all 15 citations / Add more citations

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