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The open-endedness of the set concept and the semantics of set theory

A. C. Paseau

pp. 379-399

Abstract

Some philosophers have argued that the open-endedness of the set concept has revisionary consequences for the semantics and logic of set theory. I consider (several variants of) an argument for this claim, premissed on the view that quantification in mathematics cannot outrun our conceptual abilities. The argument urges a non-standard semantics for set theory that allegedly sanctions a non-classical logic. I show that the views about quantification the argument relies on turn out to sanction a classical semantics and logic after all. More generally, this article constitutes a case study in whether the need to account for conceptual progress can ever motivate a revision of semantics or logic. I end by expressing skepticism about the prospects of a so-called non-proof-based justification for this kind of revisionism about set theory.

Publication details

Published in:

(2003) Synthese 135 (3).

Pages: 379-399

DOI: 10.1023/A:1023542621122

Full citation:

Paseau A. C. (2003) „The open-endedness of the set concept and the semantics of set theory“. Synthese 135 (3), 379–399.