Critical plural logic

Salvatore Florio, Øystein Linnebo

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Abstract

What is the relation between some things and the set of these things? Mathematical practice does not provide a univocal answer. On the one hand, it relies on ordinary plural talk, which is implicitly committed to a traditional form of plural logic. On the other hand, mathematical practice favors a liberal view of definitions which entails that traditional plural logic must be restricted. We explore this predicament and develop a "critical" alternative to traditional plural logic.
Original languageEnglish
Pages (from-to)172–203
Number of pages32
JournalPhilosophia Mathematica
Volume28
Issue number2
DOIs
Publication statusPublished - 24 Jul 2020

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