Jump to ContentJump to Main Navigation
Mathematics as a Science of Patterns$
Users without a subscription are not able to see the full content.

Michael D. Resnik

Print publication date: 1999

Print ISBN-13: 9780198250142

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198250142.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 08 July 2020

The Local Conception of Mathematical Evidence: Proof, Computation, and Logic

The Local Conception of Mathematical Evidence: Proof, Computation, and Logic

(p.137) 8 The Local Conception of Mathematical Evidence: Proof, Computation, and Logic
Mathematics as a Science of Patterns

Michael D. Resnik (Contributor Webpage)

Oxford University Press

The fact that mathematics is ordinarily practised as an autonomous science with its own, peculiar type of evidence constituted mainly by deductive reasoning (proofs and computations) is often taken as evidence that mathematics and science have specifically different evidential supports and specifically different subject matters. I argue against this conclusion by first analysing deductive proofs, and the type of evidence that is usually required for axioms, and claiming that most of the evidence for the most elementary and fundamental parts of mathematics is empirical. I then appeal to the role of computation to argue that non‐deductive inference from empirical premises is part of the contemporary methodology of mathematics, and so some of our proofs turn out not to be purely logical deductions. Finally, I discuss the relation between mathematics and logic and argue against logical realism by denying that statements attributing logical properties or relations are true independently of our holding them to be true, our psychology, our linguistic and inferential conventions, or other facts about human beings. In the end, both mathematics and logic turn out to be a priori only in the sense that some mathematical and logical truths are obtained through deductive proofs, and for pragmatic reasons, are insulated from experience; but neither mathematics nor logic are a priori in the sense of being immune to empirical revision.

Keywords:   a priori, axioms, computation, deduction, deductive reasoning, empirical, inference, logic, logical realism, mathematics, proof, revision

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 .