Denial and Disagreement

Topoi 34 (1):109-119 (2015)

Authors
Julien Murzi
University of Salzburg
Massimiliano Carrara
University of Padua
Abstract
We cast doubts on the suggestion, recently made by Graham Priest, that glut theorists may express disagreement with the assertion of A by denying A. We show that, if denial is to serve as a means to express disagreement, it must be exclusive, in the sense of being correct only if what is denied is false only. Hence, it can’t be expressed in the glut theorist’s language, essentially for the same reasons why Boolean negation can’t be expressed in such a language either. We then turn to an alternative proposal, recently defended by Beall (in Analysis 73(3):438–445, 2013; Rev Symb Log, 2014), for expressing truth and falsity only, and hence disagreement. According to this, the exclusive semantic status of A, that A is either true or false only, can be conveyed by adding to one’s theory a shrieking rule of the form A & ~A |- \bot, where \bot entails triviality. We argue, however, that the proposal doesn’t work either. The upshot is that glut theorists face a dilemma: they can either express denial, or disagreement, but not both. Along the way, we offer a bilateral logic of exclusive denial for glut theorists—an extension of the logic commonly called LP.
Keywords Disagreement  Dialetheism  Denial  Shrieking  Revenge
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DOI 10.1007/s11245-014-9278-z
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References found in this work BETA

Saving Truth From Paradox.Hartry Field - 2008 - Oxford University Press.
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Citations of this work BETA

Classicality Lost: K3 and LP After the Fall.Matthias Jenny - 2016 - Thought: A Journal of Philosophy 5 (4).
Classicality Lost: K3 and LP After the Fall.Matthias Jenny - 2017 - Thought: A Journal of Philosophy 6 (1):43-53.

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