The Cut‐Free Approach and the Admissibility‐Curry

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Abstract
The perhaps most important criticism of the nontransitive approach to semantic paradoxes is that it cannot truthfully express exactly which metarules preserve validity. I argue that this criticism overlooks that the admissibility of metarules cannot be expressed in any logic that allows us to formulate validity-Curry sentences and that is formulated in a classical metalanguage. Hence, the criticism applies to all approaches that do their metatheory in classical logic. If we do the metatheory of nontransitive logics in a nontransitive logic, however, there is no reason to think that the argument behind the criticism goes through. In general, asking a logic to express its own admissible metarules may not be a good idea.
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Archival date: 2018-02-13
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References found in this work BETA
Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
Two Flavors of Curry's Paradox.Beall, Jc & Murzi, Julien
Tolerant, Classical, Strict.Cobreros, Pablo; Egré, Paul; Ripley, David & van Rooij, Robert
Reaching Transparent Truth.Cobreros, Pablo; Égré, Paul; Ripley, David & van Rooij, Robert

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