Adaptive Fregean Set Theory

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 h...

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Veröffentlicht in:Studia logica 2020-10, Vol.108 (5), p.903-939
1. Verfasser: Batens, Diderik
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0039-3215
1572-8730
DOI:10.1007/s11225-019-09882-1