Against a Metaphysical Understanding of Rejection

Principia: An International Journal of Epistemology 22 (1):189-202 (2018)
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Abstract

In this article, we defend that incorporating a rejection operator into a paraconsistent language involves fully specifying its inferential characteristics within the logic. To do this, we examine a recent proposal by Berto for a paraconsistent rejection, which — according to him — avoids paradox, even when introduced into a language that contains self-reference and a transparent truth predicate. We will show that this proposal is inadequate because it is too incomplete. We argue that the reason it avoids trouble is that the inferential characteristics of the new operator are left unspecified, exporting the task of specifying them to metaphysicians. Additionally, we show that when completing this proposal with some plausible rules for the rejection operator, paradoxes do arise. Finally, we draw some more general implications from the study of this example.

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References found in this work

In contradiction: a study of the transconsistent.Graham Priest - 2006 - New York: Oxford University Press.
Doubt truth to be a liar.Graham Priest - 2006 - New York: Oxford University Press.
Paraconsistent Logic: Consistency, Contradiction and Negation.Walter Carnielli & Marcelo Esteban Coniglio - 2016 - Basel, Switzerland: Springer International Publishing. Edited by Marcelo Esteban Coniglio.
Spandrels of truth.Jc Beall - 2010 - Bulletin of Symbolic Logic 16 (2):284-286.
On the theory of inconsistent formal systems.Newton C. A. da Costa - 1974 - Notre Dame Journal of Formal Logic 15 (4):497-510.

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