Truth without contra(di)ction

Review of Symbolic Logic 4 (4):498-535 (2011)
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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 and , 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 . 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 and (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

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Elia Zardini
Complutense University of Madrid

References found in this work

Saving truth from paradox.Hartry H. Field - 2008 - New York: Oxford University Press.
Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Doubt truth to be a liar.Graham Priest - 2006 - New York: Oxford University Press.
Basic proof theory.A. S. Troelstra - 1996 - New York: Cambridge University Press. Edited by Helmut Schwichtenberg.

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