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

Journal article

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. © 2003 Kluwer Academic Publishers.

Authors: Paseau, A

• Publication status: Published
• Journal: SYNTHESE
• Volume: 135
• Issue: 3
• Pages: 379-399
• Publication date: 2003-06-01
• DOI: 10.1023/A:1023542621122
• EISSN: 1573-0964
• ISSN: 0039-7857
• Language: English