The Cut‐Free Approach and the Admissibility‐Curry

The Cut‐Free Approach and the Admissibility‐Curry 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Thought: A Journal of Philosophy Wiley

The Cut‐Free Approach and the Admissibility‐Curry

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Publisher
Wiley
Copyright
© 2018 The Thought Trust and Wiley Periodicals, Inc.
ISSN
2161-2234
eISSN
2161-2234
D.O.I.
10.1002/tht3.267
Publisher site
See Article on Publisher Site

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.

Journal

Thought: A Journal of PhilosophyWiley

Published: Jan 1, 2018

Keywords: ; ; ; ;

References

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