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Topoi

, Volume 34, Issue 1, pp 109–119 | Cite as

Denial and Disagreement

  • Julien Murzi
  • Massimiliano Carrara
Article

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 \(A \wedge \lnot A \vdash \bot \), 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 \(\mathsf {LP}\).

Keywords

Disagreement Dialetheism Denial Shrieking  Revenge 

Notes

Acknowledgments

The first author is grateful to the British Academy, the Alexander von Humboldt Foundation, the School of European Culture and languages at the University of Kent, and the University of Padua for generous financial support during the time this paper was written. We wish to thank Salvatore Florio, Graham Priest, and the audience of a workshop at the University of Padua for helpful feedback and discussion, and Jc Beall, Pablo Cobreros, Dave Ripley, and two referees for very helpful comments on earlier drafts. Special thanks to Enrico Martino for many enjoyable conversations on denial, dialetheism and semantic paradox.

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of European Culture and LanguageUniversity of KentCanterbury, Kent UK
  2. 2.Munich Center for Mathematical PhilosophyLudwig-Maximilians UniversitätMunich Germany
  3. 3.Section of Philosophy, FISPPA DepartmentUniversity of Padua PaduaItaly

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