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

Synthese 135 (3):379 - 399 (2003)
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.
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
Categories (categorize this paper)
Reprint years 2004
DOI 10.1023/A:1023542621122
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 25,711
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Deflating skolem.F. A. Muller - 2005 - Synthese 143 (3):223-253.

Add more citations

Similar books and articles
A Model Theoretic Semantics for Quantum Logic.E. -W. Stachow - 1980 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:272 - 280.
Plural Quantification and the Iterative Concept of Set.Stephen Pollard - 1985 - Philosophy Research Archives 11:579-587.
Distance Semantics for Belief Revision.Daniel Lehmann, Menachem Magidor & Karl Schlechta - 2001 - Journal of Symbolic Logic 66 (1):295-317.
Second-Order Logic and Foundations of Mathematics.Jouko Vaananen - 2001 - Bulletin of Symbolic Logic 7 (4):504-520.
Naïve Set Theory is Innocent!A. Weir - 1998 - Mind 107 (428):763-798.
Kripke Bundle Semantics and C-Set Semantics.Eiko Isoda - 1997 - Studia Logica 58 (3):395-401.

Monthly downloads

Added to index


Total downloads

30 ( #164,128 of 2,146,235 )

Recent downloads (6 months)

12 ( #56,498 of 2,146,235 )

How can I increase my downloads?

My notes
Sign in to use this feature

There  are no threads in this forum
Nothing in this forum yet.

Other forums