Can the Classical Logician Avoid the Revenge Paradoxes?

Philosophical Review 124 (3):299-352 (2015)
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Abstract

Most work on the semantic paradoxes within classical logic has centered around what this essay calls “linguistic” accounts of the paradoxes: they attribute to sentences or utterances of sentences some property that is supposed to explain their paradoxical or nonparadoxical status. “No proposition” views are paradigm examples of linguistic theories, although practically all accounts of the paradoxes subscribe to some kind of linguistic theory. This essay shows that linguistic accounts of the paradoxes endorsing classical logic are subject to a particularly acute form of the revenge paradox: that there is no exhaustive classification of sentences into “good” and “bad” such that the T-schema holds when restricted to the “good” sentences unless it is also possible to prove some “bad” sentences. The foundations for an alternative classical nonlinguistic approach is outlined that is not subject to the same kinds of problems. Although revenge paradoxes of different strengths can be formulated, they are found to be indeterminate at higher orders and not inconsistent

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Andrew Bacon
University of Southern California

Citations of this work

The Broadest Necessity.Andrew Bacon - 2018 - Journal of Philosophical Logic 47 (5):733-783.
Generalized Revenge.Julien Murzi & Lorenzo Rossi - 2020 - Australasian Journal of Philosophy 98 (1):153-177.
.Luca Incurvati & Julian J. Schlöder - 2023 - New York: Oxford University Press USA.
Should the Non‐Classical Logician be Embarrassed?Lucas Rosenblatt - 2022 - Philosophy and Phenomenological Research 104 (2):388-407.

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References found in this work

Vagueness.Timothy Williamson - 1996 - New York: Routledge.
The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
Truth.Paul Horwich - 1990 - Oxford, GB: Clarendon Press. Edited by Frank Jackson & Michael Smith.
In contradiction: a study of the transconsistent.Graham Priest - 1987 - New York: Oxford University Press.
Saving truth from paradox.Hartry H. Field - 2008 - New York: Oxford University Press.

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