Philosophia Mathematica (forthcoming)

Authors
Øystein Linnebo
University of Oslo
Salvatore Florio
University of Birmingham
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.
Keywords plural logic  set theory  paradox  Cantor  Gödel
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DOI 10.1093/philmat/nkaa020
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References found in this work BETA

Plural Predication.Thomas McKay - 2006 - Oxford University Press.
The Potential Hierarchy of Sets.Øystein Linnebo - 2013 - Review of Symbolic Logic 6 (2):205-228.

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