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When Curry met Abel
Logic Journal of the IGPL ( IF 0.6 ) Pub Date : 2020-07-16 , DOI: 10.1093/jigpal/jzaa006
Manuel Eduardo Tapia-Navarro 1 , Luis Estrada-González 1
Affiliation  

Based on his Inclosure Schema and the Principle of Uniform Solution (PUS), Priest has argued that Curry’s paradox belongs to a different family of paradoxes than the Liar. Pleitz (2015, The Logica Yearbook 2014, pp. 233–248) 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.

中文翻译:

当库里遇见亚伯

基于他的封闭模式和统一解决方案原理(PUS),Priest认为库里的悖论与骗子属于不同的悖论家族。Pleitz(2015,The Logica Yearbook 2014,pp。233–248)认为Curry的悖论与其他悖论具有相同的结构,并提出了一种方案,其中“封闭模式”是一个特例,他批评了Priest的立场,指出了应用PUS表示使用了无法验证收缩的超一致性逻辑,但是这种逻辑很难被视为统一的。在本文中,我们将提出进一步的理由来捍卫普莱兹的论点,即库里的悖论与其余的自指自反悖论属于同一家族,并使用条件是广义否定的思想。然而,我们不会跟随普莱兹(Pleitz)考虑以超常一致的精神对悖论采取统一的解决方案表示怀疑。我们将论证,超一致性策略可以看作是限制分离策略的特例,而后者则统一地阻止了所有涉及结缔性的自我指称悖论,包括库里的。
更新日期:2020-07-16
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