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TRUTH WITHOUT CONTRA(DI)CTION

Published online by Cambridge University Press:  07 November 2011

ELIA ZARDINI
ELIA ZARDINI*
Affiliation:
Instituto de Investigaciones Filosóficas, Universidad Nacional Autónoma de México, and Northern Institute of Philosophy, University of Aberdeen
*
*INSTITUTO DE INVESTIGACIONES FILOSÓFICAS, UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO, MEXICO CITY, 04510, MEXICO, NORTHERN INSTITUTE OF PHILOSOPHY, UNIVERSITY OF ABERDEEN, ABERDEEN, AB24 3UB, UK. E-mail: elia.zardini@abdn.ac.uk
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Abstract

The concept of truth arguably plays a central role in many areas of philosophical theorizing. Yet, what seems to be one of the most fundamental principles governing that concept, i.e. the equivalence between ‘ ‘P’ is true’ and ‘P’, is inconsistent in full classical logic, as shown by the semantic paradoxes. I propose a new solution to those paradoxes, based on a principled revision of classical logic. Technically, the key idea consists in the rejection of the unrestricted validity of the structural principle of contraction. I first motivate philosophically this idea with the metaphysical picture of the states-of-affairs expressed by paradoxical sentences as being distinctively “unstable”. I then proceed to demonstrate that the theory of truth resulting from this metaphysical picture is, in many philosophically interesting respects, surprisingly stronger than most other theories of truth endorsing the equivalence between ‘ ‘P’ is true’ and ‘P’ (for example, the theory vindicates the validity of the traditional laws of excluded middle and of non-contradiction, and also vindicates the traditional constraint of truth preservation on logical consequence). I conclude by proving a cutelimination theorem that shows the consistency of the theory.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 4 , December 2011 , pp. 498 - 535
Copyright
Copyright © Association for Symbolic Logic 2011

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