Assertion, Denial, Accepting, Rejecting, Symmetry and Paradox

May 2015

“Assertion, Denial, Accepting, Rejecting, Symmetry and Paradox,” pages 310-321 in Foundations of Logical Consequence, edited by Colin R. Caret and Ole T. Hjortland, Oxford University Press, 2015

Proponents of a dialethic or “truth-value glut” response to the paradoxes of self-reference argue that “truth-value gap” analyses of the paradoxes fall foul of the extended liar paradox: “this sentence is not true.” If we pay attention to the role of assertion and denial and the behaviour of negation in both “gap” and “glut” analyses, we see that the situation with these approaches has a pleasing symmetry: gap approaches take some denials to not be expressible by negation, and glut approaches take some negations to not express denials. But in the light of this symmetry, considerations against a gap view point to parallel considerations against a glut view. Those who find some reason to prefer one view over another (and this is almost everyone) must find some reason to break this symmetry.

This short paper was written for presentation at AAP2004. After very many revisions, it’s finally going to be published in an edited collection from members and friends of the Arché project on Foundations of Logical Consequence.

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You are welcome to download and read this document. I welcome feedback on it. Please check the final published version if you wish to cite it. Thanks.


I’m Greg Restall, and this is my personal website. I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the Director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology I like thinking about – and helping other people think about – logic and philosophy and the many different ways they can inform each other.


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