(De)motivating gluts

Jonas Becker Arenhart, Ederson Safra Melo


Semantic paradoxes, like the Liar Paradox, are one of the best-known motivations for the dialetheists' claim that there are true contradictions. Liar-like arguments arise in natural language and dialetheists argue that the Liar sentence is true and false, i.e., it bears a glut as its truth-value. However, in a recent paper, JC Beall (2015) argued that, by parallel reasoning, one should also be led from the resources of natural language to triviality by the use of validity paradoxes (Curry-style paradoxes involving a pre-theoretical notion of validity). Priest (2016) answers Beall's challenge based on a typical move against Curry paradoxes: we avoid triviality by avoiding structural contraction, which is one of the steps in the derivation of triviality. We shall argue that this strategy poses some further difficulties for the dialetheist: i) it is hard for a dialetheist to motivate restriction of structural contraction; ii) structural contraction, if properly motivated, on the other hand, may lead one to avoid the Liar paradox too, and thus, the main motivation for the existence of gluts seems threatened; iii) the asymmetry in the treatment of paradoxes (take the Liar at face value, avoid the Curry) raises difficulties for the desideratum that pre-theoretical concepts should play a prominent role in motivating dialetheism.


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