Logic Journal of the IGPL 28 (6):1233-1242 (2020)

Authors
Manuel Tapia
National Autonomous University of Mexico
Luis Estrada-González
National Autonomous University of Mexico
Abstract
Based on his Inclosure Schema and the Principle of Uniform Solution, Priest has argued that Curry’s paradox belongs to a different family of paradoxes than the Liar. Pleitz argued that Curry’s paradox shares the same structure as the other paradoxes and proposed a scheme of which the Inclosure Schema is a particular case and he criticizes Priest’s position by pointing out that applying the PUS implies the use of a paraconsistent logic that does not validate Contraction, but that this can hardly seen as uniform. In this paper, we will develop some further reasons to defend Pleitz’ thesis that Curry’s paradox belongs to the same family as the rest of the self-referential paradoxes & using the idea that conditionals are generalized negations. However, we will not follow Pleitz in considering doubtful that there is a uniform solution for the paradoxes in a paraconsistent spirit. We will argue that the paraconsistent strategies can be seen as special cases of the strategy of restricting Detachment and that the latter uniformly blocks all the connective-involving self-referential paradoxes, including Curry’s.
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DOI 10.1093/jigpal/jzaa006
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References found in this work BETA

Mathematical Logic as Based on the Theory of Types.Bertrand Russell - 1908 - American Journal of Mathematics 30 (3):222-262.
On Some Difficulties in the Theory of Transfinite Numbers and Order Types.Bertrand Russell - 1906 - Proceedings of the London Mathematical Society 4 (14):29-53.
A Modality Called ‘Negation’.Francesco Berto - 2015 - Mind 124 (495):761-793.
Beyond the Limits of Thought.Graham Priest - 1995 - Philosophy 71 (276):308-310.

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