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ON ADOPTING KRIPKE SEMANTICS IN SET THEORY

Published online by Cambridge University Press:  01 June 2008

LUCA INCURVATI
LUCA INCURVATI*
Affiliation:
University of Cambridge
*
*DEPARTMENT OF PHILOSOPHY, ST. JOHN'S COLLEGE, CAMBRIDGE UNIVERSITY, CAMBRIDGE CB3 9DA, UK. E-mail: [email protected]
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Abstract

Several philosophers have argued that the logic of set theory should be intuitionistic on the grounds that the open-endedness of the set concept demands the adoption of a nonclassical semantics. This paper examines to what extent adopting such a semantics has revisionary consequences for the logic of our set-theoretic reasoning. It is shown that in the context of the axioms of standard set theory, an intuitionistic semantics sanctions a classical logic. A Kripke semantics in the context of a weaker axiomatization is then considered. It is argued that this semantics vindicates an intuitionistic logic only insofar as certain constraints are put on its interpretation. Wider morals are drawn about the restrictions that this places on the shape of arguments for an intuitionistic revision of the logic of set theory.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 1 , Issue 1 , June 2008 , pp. 81 - 96
Copyright
Copyright © Association for Symbolic Logic 2008

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