Research Group
in Analytic Philosophy

Abstract

The concept of truth arguably plays a central role in many areas of philosophical
theorising. Yet, what seems to be one of the most fundamental principles
governing that concept, i.e. the correlation law ‘ ‘P’ is true iff P’, is inconsistent
in 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 rule 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 correlation law (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). I conclude by proving a cut-elimination theorem that
shows the consistency of the theory.