On Williamson's new Quinean argument against nonclassical logic

Australasian Journal of Logic 16 (7):202-230 (2019)
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Abstract

In "Semantic paradoxes and abductive methodology", Williamson presents a new Quinean argument based on central ingredients of common pragmatism about theory choice (including logical theory, as is common). What makes it new is that, in addition to avoiding Quine's unfortunate charge of mere terminological squabble, Williamson's argument explicitly rejects at least for purposes of the argument Quine's key conservatism premise. In this paper I do two things. First, I argue that Williamson's new Quinean argument implicitly relies on Quine's conservatism principle. Second, by way of answering his charges against nonclassical logic I directly defend a particular subclassical account of logical consequence.

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Jc Beall
University of Notre Dame

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The logic of paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Anti-exceptionalism about logic.Ole Thomassen Hjortland - 2017 - Philosophical Studies 174 (3):631-658.
Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
[no title].Gilbert Harman - 2008 - Cambridge University Press.
How a computer should think.Nuel Belnap - 1977 - In Gilbert Ryle, Contemporary aspects of philosophy. Boston: Oriel Press.

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