David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
Learn more about PhilPapers
Australasian Journal of Philosophy 84 (1):59 – 73 (2006)
'Philosophy arises through misconceptions of grammar', said Wittgenstein. Few people have believed him, and probably none, therefore, working in the area of the philosophy of mathematics. Yet his assertion is most evidently the case in the philosophy of Set Theory, as this paper demonstrates (see also Rodych 2000). The motivation for twentieth century Set Theory has rested on the belief that everything in Mathematics can be defined in terms of sets [Maddy 1994: 4]. But not only are there notable items which cannot be so defined, including numbers and mereological sums, the very notion of a set, as formalized within this tradition, is based on a series of grammatical confusions.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
David Lewis (1991). Parts of Classes. Blackwell.
Bob Hale (ed.) (2001). The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics. Oxford University Press.
George Boolos (1998). Logic, Logic, and Logic. Harvard University Press.
Penelope Maddy (1990). Realism in Mathematics. Oxford University Prress.
Michael A. E. Dummett (1991). Frege: Philosophy of Mathematics. Harvard University Press.
Citations of this work BETA
Hartley Slater (2007). Logic and Grammar. Ratio 20 (2):206–218.
Similar books and articles
Emily Carson (1996). On Realism in Set Theory. Philosophia Mathematica 4 (1):3-17.
John Mayberry (1994). What is Required of a Foundation for Mathematics? Philosophia Mathematica 2 (1):16-35.
F. A. Muller (2001). Sets, Classes, and Categories. British Journal for the Philosophy of Science 52 (3):539-573.
John J. Ross (2009). Reading Wittgenstein's Philosophical Investigations: A Beginner's Guide. Lexington Books.
Siegfried Gottwald (2006). Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory. Part I: Model-Based and Axiomatic Approaches. [REVIEW] Studia Logica 82 (2):211 - 244.
José Ferreirós (2011). On Arbitrary Sets and ZFC. Bulletin of Symbolic Logic 17 (3):361-393.
Emmon Bach, ACTL Semantics: Compositionality and Morphosemantics: II: Words, Morphemes, Constructions, Interpretations.
John P. Burgess (1988). Sets and Point-Sets: Five Grades of Set-Theoretic Involvement in Geometry. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:456 - 463.
Added to index2009-01-28
Total downloads23 ( #174,748 of 1,934,425 )
Recent downloads (6 months)1 ( #434,193 of 1,934,425 )
How can I increase my downloads?