Truth Through Proof: A Formalist Foundation for Mathematics

by Alan Weir

Overview

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 Godel 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.

Product Details

ISBN-13:	9780199541492
Publisher:	Oxford University Press
Publication date:	12/09/2010
Pages:	296
Product dimensions:	6.30(w) x 9.30(h) x 1.00(d)

About the Author

Alan Weir is Head of the Department of Philosophy at the University of Glasgow. His main research interests have been in philosophy of logic and mathematics, but he has also written on philosophy of language, epistemology and the theory of perception.

Table of Contents

Introduction1. Metaphysics2. Ontological Reduction3. Neo-formalism4. Objections and Comparisons5. Applying Mathematics6. Proof Set in Concrete7. Idealisation Naturalised8. LogicConclusionAppendix