Jump to ContentJump to Main Navigation
Truth Through ProofA Formalist Foundation for Mathematics$
Users without a subscription are not able to see the full content.

Alan Weir

Print publication date: 2010

Print ISBN-13: 9780199541492

Published to Oxford Scholarship Online: January 2011

DOI: 10.1093/acprof:oso/9780199541492.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 21 August 2019

Neo-formalism

Neo-formalism

Chapter:
(p.68) 3 Neo-formalism
Source:
Truth Through Proof
Author(s):

Alan Weir (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199541492.003.0004

After discussing historical formalism, a revised version, ‘neo-formalism’, is introduced, utilizing the informational/metaphysical content distinction. Mathematical utterances effect truth-valued assertions, made true or false by the existence of proofs and disproofs though this content is not part of the informational content. Mathematical assertions are made in a non-representational mode, formal rather than projective. A simple illustration, using decimal arithmetic, is given and distinctions drawn between the purely formal game level, the content level, where utterances are truth-valued, and the metatheory which explains how the content level sentences are made true or false by the existence of proofs. The question of how the language can be extended to accommodate logical complexity is raised, a Basic Semantics for logical operators given, and problems in ensuring a good mesh between a semantics of proof and the meaning which logical terms have outside formal contexts highlighted.

Keywords:   formalism, game formalism, neo-formalism, assertion, proof, truth, semantics

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .