Denial and Disagreement

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



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Author Profiles

Julien Murzi
University of Salzburg
Massimiliano Carrara
University of Padua

Citations of this work

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Dialetheism.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.

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Individualism and the mental.Tyler Burge - 1979 - Midwest Studies in Philosophy 4 (1):73-122.
In contradiction: a study of the transconsistent.Graham Priest - 2006 - New York: Oxford University Press.
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.
Individualism and the Mental.Tyler Burge - 1979 - In John Heil (ed.), Philosophy of Mind: A Guide and Anthology. Oxford University Press.

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