Need anything follow from a contradiction?

Inquiry: An Interdisciplinary Journal of Philosophy 65 (3):278-297 (2022)
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Abstract

ABSTRACT Classical and intuitionistic logic both validate Ex Contradictione Quodlibet, according to which any proposition whatsoever follows from a contradiction. Many philosophers have found ECQ counter-intuitive, but criticisms of the principle have almost universally been directed from a position of support for relevance or other orthodox paraconsistent logics, according to which some, but not necessarily all, propositions follow from a contradiction. This paper draws attention to the historically significant view that nothing whatsoever follows from a contradiction – Ex Contradictione Nihil. It addresses the key arguments – model-theoretic, proof-theoretic, meaning theoretic and holist – deployed by proponents of ECQ against their standard opponents, and shows that each can be defeated from a position of support for ECN. In the course of answering these arguments, some understanding is developed of possible motivations for ECN and a solid case is built that ECN deserves further investigation.

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Simon Hewitt
University of Leeds

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References found in this work

Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
The logical basis of metaphysics.Michael Dummett - 1991 - Cambridge, Mass.: Harvard University Press.
Remarks on the foundations of mathematics.Ludwig Wittgenstein - 1956 - Oxford [Eng.]: Blackwell. Edited by G. E. M. Anscombe, Rush Rhees & G. H. von Wright.
Spandrels of truth.J. C. Beall - 2009 - New York: Oxford University Press.

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