Grammar and sets

Australasian Journal of Philosophy 84 (1):59 – 73 (2006)
Abstract
'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)
DOI 10.1080/00048400600571711
Options
 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: 27,621
Through your library
References found in this work BETA
Parts of Classes.David Lewis - 1991 - Blackwell.
Logic, Logic, and Logic.George Boolos - 1998 - Harvard University Press.
Realism in Mathematics.Penelope Maddy - 1990 - Oxford University Prress.

View all 22 references / Add more references

Citations of this work BETA
Logic and Grammar.Hartley Slater - 2007 - Ratio 20 (2):206–218.

Add more citations

Similar books and articles
On Realism in Set Theory.Emily Carson - 1996 - Philosophia Mathematica 4 (1):3-17.
What is Required of a Foundation for Mathematics?John Mayberry - 1994 - Philosophia Mathematica 2 (1):16-35.
Sets, Classes, and Categories.F. A. Muller - 2001 - British Journal for the Philosophy of Science 52 (3):539-573.
On Arbitrary Sets and ZFC.José Ferreirós - 2011 - Bulletin of Symbolic Logic 17 (3):361-393.
Sets and Point-Sets: Five Grades of Set-Theoretic Involvement in Geometry.John P. Burgess - 1988 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1988:456 - 463.

Monthly downloads

Added to index

2009-01-28

Total downloads

26 ( #195,864 of 2,169,071 )

Recent downloads (6 months)

1 ( #345,851 of 2,169,071 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums