Synthese

pp 1–17

Capturing naive validity in the Cut-free approach

S.I. : Substructural Approaches to Paradox

DOI: 10.1007/s11229-016-1199-5

Cite this article as:
Barrio, E., Rosenblatt, L. & Tajer, D. Synthese (2016). doi:10.1007/s11229-016-1199-5
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Abstract

Rejecting the Cut rule has been proposed as a strategy to avoid both the usual semantic paradoxes and the so-called v-Curry paradox. In this paper we consider if a Cut-free theory is capable of accurately representing its own notion of validity. We claim that the standard rules governing the validity predicate are too weak for this purpose and we show that although it is possible to strengthen these rules, the most obvious way of doing so brings with it a serious problem: an internalized version of Cut can be proved for a Curry-like sentence. We also evaluate a number of possible ways of escaping this difficulty.

Keywords

Validity Paradoxes Strict-tolerant logic Substructural logics Cut 

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Conicet - University of Buenos AiresCiudad Autónoma de Buenos AiresArgentina

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