Truth Through Proof: A Formalist Foundation for Mathematics

OUP Oxford (2010)
Abstract
Truth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Classic formalists claimed implausibly that mathematical utterances are truth-valueless moves in a game. Alan Weir aims to develop a more satisfactory successor to game formalism utilising a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance. This framework allows for sentences whose truth-conditions are not representational, which are made true or false by conditions residing in the circumstances of utterances but not transparently in the sense. Applications to projectivism and fiction pave the way for the claim that mathematical utterances are made true or false by the existence of concrete proofs or refutations, though these truth-making conditions form no part of their sense or informational content. The position is compared with rivals, an account of the applicability of mathematics developed, and a new account of the nature of idealisation proffered in which it is argued that the finitistic limitations Gödel placed on proofs are without rational justification. Finally a non-classical logical system is provided in which excluded middle fails, yet enough logical power remains to recapture the results of standard mathematics.
Keywords Mathematics Philosophy  Logic, Symbolic and mathematical  Metaphysics
Categories (categorize this paper)
Call number QA8.4.W45 2010
ISBN(s) 9780199541492  
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
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 11,412
External links
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

No references found.

Citations of this work BETA
David Bain (2007). The Location of Pains. Philosophical Papers 36 (2):171-205.
Similar books and articles
M. Redhead (2004). Mathematics and the Mind. British Journal for the Philosophy of Science 55 (4):731-737.
Dale Jacquette (2006). Applied Mathematics in the Sciences. Croatian Journal of Philosophy 6 (2):237-267.
Analytics

Monthly downloads

Added to index

2012-01-31

Total downloads

4 ( #259,269 of 1,103,045 )

Recent downloads (6 months)

3 ( #120,820 of 1,103,045 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Start a new thread
Order:
There  are no threads in this forum
Nothing in this forum yet.