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PROVING UNPROVABILITY

Published online by Cambridge University Press:  21 November 2016

BRUNO WHITTLE
BRUNO WHITTLE*
Affiliation:
Department of Philosophy, University of Glasgow
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF GLASGOW GLASGOW G12 8QQ, UK E-mail: [email protected]
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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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 1 , March 2017 , pp. 92 - 115
Copyright
Copyright © Association for Symbolic Logic 2016 

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