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

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 ...

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Publication status:
Published

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Publisher copy:
10.1023/A:1023542621122

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Institution:
University of Oxford
Department:
Oxford, HUM, Philosophy, Philosophy Postholders
Role:
Author
Journal:
SYNTHESE
Volume:
135
Issue:
3
Pages:
379-399
Publication date:
2003-06-05
DOI:
EISSN:
1573-0964
ISSN:
0039-7857
URN:
uuid:af8decec-2863-40eb-9813-291b2b253f21
Source identifiers:
143253
Local pid:
pubs:143253
Language:
English

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