T. Parent
Nazarbayev University
Assuming that Q (Robinson arithmetic) is consistent and Church's Thesis is true, the Fixed Point Lemma enables the derivation of a contradiction, in a manner akin to the v-Curry paradox. The derivation could be blocked by excluding certain formulae from the scope of the Lemma, but this would effectively concede that the unrestricted Lemma is false. The resolution of the paradox thus remains an open question.
Keywords Self-Reference and Circularity  Curry's Paradox  Classical Logic  Godel, Kurt  Metamathematics  Incompleteness of Arithmetic
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Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.
An Unsolvable Problem of Elementary Number Theory.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (2):73-74.
Deflating Logical Consequence.Lionel Shapiro - 2011 - Philosophical Quarterly 61 (243):320-342.

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