Against a metaphysical understanding of rejection

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 (2014) 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 (mostly) 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.