Adaptive Fregean Set Theory

Studia Logica 108 (5):903-939 (2020)
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Abstract

This paper defines provably non-trivial theories that characterize Frege’s notion of a set, taking into account that the notion is inconsistent. By choosing an adaptive underlying logic, consistent sets behave classically notwithstanding the presence of inconsistent sets. Some of the theories have a full-blown presumably consistent set theory T as a subtheory, provided T is indeed consistent. An unexpected feature is the presence of classical negation within the language.

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Diderik Batens
University of Ghent

Citations of this work

Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

Transfinite numbers in paraconsistent set theory.Zach Weber - 2010 - Review of Symbolic Logic 3 (1):71-92.
A universal logic approach to adaptive logics.Diderik Batens - 2007 - Logica Universalis 1 (1):221-242.
Transfinite Cardinals in Paraconsistent Set Theory.Zach Weber - 2012 - Review of Symbolic Logic 5 (2):269-293.
Minimally inconsistent LP.Graham Priest - 1991 - Studia Logica 50 (2):321 - 331.
A semantical Analysis of the Calculi C n.Newton C. A. Da Costa & E. H. Alves - 1977 - Notre Dame Journal Fo Formal Logic 18 (4):621-630.

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