Review of Symbolic Logic 1 (1):81-96 (2008)

Luca Incurvati
University of Amsterdam
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.
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DOI 10.1017/s1755020308080088
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References found in this work BETA

The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
Truth and Other Enigmas.Michael Dummett - 1981 - Philosophical Quarterly 31 (122):47-67.
Platonism and Anti-Platonism in Mathematics.Matthew McGrath - 2001 - Philosophy and Phenomenological Research 63 (1):239-242.
Frege: Philosophy of Mathematics. [REVIEW]Charles Parsons - 1996 - Philosophical Review 105 (4):540.
Constructive Set Theory.John Myhill - 1975 - Journal of Symbolic Logic 40 (3):347-382.

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Numbers and Everything.Gonçalo Santos - 2013 - Philosophia Mathematica 21 (3):297-308.

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