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

Authors
Diderik Batens
University of Ghent
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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DOI 10.1007/s11225-019-09882-1
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References found in this work BETA

A Universal Logic Approach to Adaptive Logics.Diderik Batens - 2007 - Logica Universalis 1 (1):221-242.
Transfinite Numbers in Paraconsistent Set Theory.Zach Weber - 2010 - Review of Symbolic Logic 3 (1):71-92.
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.

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