Proving unprovability

Whittle, B. (2017) Proving unprovability. Review of Symbolic Logic, 10(1), pp. 92-115. (doi: 10.1017/S1755020316000216)

Abstract

This paper addresses the question: given some theory T that we accept, is there some natural, generally applicable way of extending T to a theory S that can prove a range of things about what it itself (i.e., S) can prove, including a range of things about what it cannot prove, such as claims to the effect that it cannot prove certain particular sentences (e.g., 0 = 1), or the claim that it is consistent? Typical characterizations of Gödel’s second incompleteness theorem, and its significance, would lead us to believe that the answer is ‘no’. But the present paper explores a positive answer. The general approach is to follow the lead of recent (and not so recent) approaches to truth and the Liar paradox.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Whittle, Bruno
• Authors: Whittle, B.
• College/School: College of Arts & Humanities > School of Humanities > Philosophy
• Journal Name: Review of Symbolic Logic
• Publisher: Cambridge University Press
• ISSN: 1755-0203
• ISSN (Online): 1755-0211
• Published Online: 21 November 2016
• Copyright Holders: Copyright © 2016 Cambridge University Press
• First Published: First published in Review of Symbolic Logic 10(1):92-115
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher