Άδύνατον and material exclusion 1

Australasian Journal of Philosophy 86 (2):165 – 190 (2008)
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Abstract

Philosophical dialetheism, whose main exponent is Graham Priest, claims that some contradictions hold, are true, and it is rational to accept and assert them. Such a position is naturally portrayed as a challenge to the Law of Non-Contradiction (LNC). But all the classic formulations of the LNC are, in a sense, not questioned by a typical dialetheist, since she is (cheerfully) required to accept them by her own theory. The goal of this paper is to develop a formulation of the Law which appears to be unquestionable, in the sense that the Priestian dialetheist is committed to accept it without also accepting something inconsistent with it, on pain of trivialism—that is to say, on pain of lapsing into the position according to which everything is the case. This will be achieved via (a) a discussion of Priest's dialetheic treatment of the notions of rejection and denial; and (b) the characterization of a negation via the primitive intuition of content exclusion. Such a result will not constitute a cheap victory for the friends of consistency. We may just learn that different things have been historically conflated under the label of 'Law of Non-Contradiction'; that dialetheists rightly attack some formulations of the Law, and orthodox logicians and philosophers have been mistaken in assimilating them to the indisputable one.

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Franz Berto
University of St. Andrews

Citations of this work

Negation on the Australian Plan.Francesco Berto & Greg Restall - 2019 - Journal of Philosophical Logic 48 (6):1119-1144.
A Modality Called ‘Negation’.Francesco Berto - 2015 - Mind 124 (495):761-793.
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A Survey of Logical Realism.Tuomas E. Tahko - 2021 - Synthese 198 (5):4775-4790.
Conjunctive paraconsistency.Franca D’Agostini - 2021 - Synthese 199 (3-4):6845-6874.

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References found in this work

Change in View: Principles of Reasoning.Gilbert Harman - 1986 - Cambridge, MA, USA: MIT Press.
In Contradiction: A Study of the Transconsistent.Graham Priest - 1987 - Dordrecht, Netherland: Oxford University Press.
Assertion.Peter Geach - 1965 - Philosophical Review 74 (4):449-465.

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