(Meta)inferential levels of entailment beyond the Tarskian paradigm

Synthese 198 (S22):5265-5289 (2019)

Abstract

In this paper we discuss the extent to which the very existence of substructural logics puts the Tarskian conception of logical systems in jeopardy. In order to do this, we highlight the importance of the presence of different levels of entailment in a given logic, looking not only at inferences between collections of formulae but also at inferences between collections of inferences—and more. We discuss appropriate refinements or modifications of the usual Tarskian identity criterion for logical systems, and propose an alternative of our own. After that, we consider a number of objections to our account and evaluate a substantially different approach to the same problem.

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Author Profiles

Eduardo Alejandro Barrio
Universidad de Buenos Aires (UBA)
Federico Pailos
Universidad de Buenos Aires (UBA)
Damian Szmuc
Universidad de Buenos Aires (UBA)

References found in this work

Introduction to Metamathematics.Stephen Cole Kleene - 1952 - Princeton, NJ, USA: North Holland.
The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.

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