One Step is Enough

Journal of Philosophical Logic:1-27 (forthcoming)
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Abstract

The recent development and exploration of mixed metainferential logics is a breakthrough in our understanding of nontransitive and nonreflexive logics. Moreover, this exploration poses a new challenge to theorists like me, who have appealed to similarities to classical logic in defending the logic ST, since some mixed metainferential logics seem to bear even more similarities to classical logic than ST does. There is a whole ST-based hierarchy, of which ST itself is only the first step, that seems to become more and more classical at each level. I think this seeming is misleading: for certain purposes, anyhow, metainferential hierarchies give us no reason to move on from ST. ST is indeed only the first step on a grand metainferential adventure; but one step is enough. This paper aims to explain and defend that claim. Along the way, I take the opportunity also to develop some formal tools and results for thinking about metainferential logics more generally.

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David Ripley
Monash University

Citations of this work

Inferential Constants.Camillo Fiore, Federico Pailos & Mariela Rubin - forthcoming - Journal of Philosophical Logic: 1 - 26.
On the Metainferential Solution to the Semantic Paradoxes.Rea Golan - forthcoming - Journal of Philosophical Logic:1-24.
Vague connectives.Paula Teijeiro - forthcoming - Philosophical Studies:1-20.

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Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
Vagueness.Timothy Williamson - 1995 - British Journal for the Philosophy of Science 46 (4):589-601.

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