What If? The Exploration of an Idea

Graham Priest
CUNY Graduate Center
A crucial question here is what, exactly, the conditional in the naive truth/set comprehension principles is. In 'Logic of Paradox', I outlined two options. One is to take it to be the material conditional of the extensional paraconsistent logic LP. Call this "Strategy 1". LP is a relatively weak logic, however. In particular, the material conditional does not detach. The other strategy is to take it to be some detachable conditional. Call this "Strategy 2". The aim of the present essay is to investigate Stragey 1. It is not to advocate it. The work is simply an extended exploration of the strategy, its strengths, its weaknesses, and the various dierent ways in which it may be implemented. In the first part of the paper I will set up the appropriate background details. In the second, I will look at the strategy as it applies to the semantic paradoxes. In the third I will look at how it applies to the set-theoretic paradoxes.
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DOI 10.26686/ajl.v14i1.4028
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References found in this work BETA

Saving Truth From Paradox.Hartry Field - 2008 - Oxford University Press.
Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Spandrels of Truth.Jc Beall - 2010 - Bulletin of Symbolic Logic 16 (2):284-286.
An Introduction to Non-Classical Logic: From If to Is.Graham Priest - 2008 - Bulletin of Symbolic Logic 14 (4):544-545.

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Citations of this work BETA

Old Wine in New Bottles: Some Comments on Beall.Graham Priest - 2016 - Australasian Journal of Logic 13 (5).
Paradoxical Propositions.Graham Priest - 2018 - Philosophical Issues 28 (1):300-307.
Enthymematic Classical Recapture1.Henrique Antunes - forthcoming - Logic Journal of the IGPL.

View all 7 citations / Add more citations

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