A Hierarchy of Classical and Paraconsistent Logics

Journal of Philosophical Logic 49 (1):93-120 (2020)
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In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of strict-tolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely classical. We will claim that a logic is to be identified with an infinite sequence of consequence relations holding between increasingly complex relata: formulae, inferences, metainferences, and so on. As a result, the present proposal allows not only to differentiate Classical Logic from ST, but also from other systems sharing with it their valid metainferences. Finally, we show how these results have interesting consequences for some topics in the philosophical logic literature, among them for the debate around Logical Pluralism. The reason being that the discussion concerning this topic is usually carried out employing a rivalry criterion for logics that will need to be modified in light of the present investigation, according to which two logics can be non-identical even if they share the same valid inferences.

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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)

Citations of this work

Limits of Abductivism About Logic.Ulf Hlobil - 2020 - Philosophy and Phenomenological Research 103 (2):320-340.
Classical Logic and the Strict Tolerant Hierarchy.Chris Scambler - 2020 - Journal of Philosophical Logic 49 (2):351-370.
Metainferential duality.Bruno Da Ré, Federico Pailos, Damian Szmuc & Paula Teijeiro - 2020 - Journal of Applied Non-Classical Logics 30 (4):312-334.

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References found in this work

Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
Tolerant, Classical, Strict.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2012 - Journal of Philosophical Logic 41 (2):347-385.

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