Remarks on naive set theory based on lp

Review of Symbolic Logic 8 (2):279-295 (2015)
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Abstract

Dialetheism is the metaphysical claim that there are true contradictions. And based on this view, Graham Priest and his collaborators have been suggesting solutions to a number of paradoxes. Those paradoxes include Russell’s paradox in naive set theory. For the purpose of dealing with this paradox, Priest is known to have argued against the presence of classical negation in the underlying logic of naive set theory. The aim of the present paper is to challenge this view by showing that there is a way to handle classical negation.

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Citations of this work

Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
There is More to Negation than Modality.Michael De & Hitoshi Omori - 2018 - Journal of Philosophical Logic 47 (2):281-299.
What If? The Exploration of an Idea.Graham Priest - 2017 - Australasian Journal of Logic 14 (1).

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References found in this work

The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
On the theory of inconsistent formal systems.Newton C. A. Costa - 1972 - Recife,: Universidade Federal de Pernambuco, Instituto de Matemática.
Doubt Truth to Be a Liar.Graham Priest - 2007 - Studia Logica 87 (1):129-134.
On the theory of inconsistent formal systems.Newton C. A. da Costa - 1974 - Notre Dame Journal of Formal Logic 15 (4):497-510.

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