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Aristotle on the Principle of Non-Contradiction

Published online by Cambridge University Press:  01 January 2020

S. Marc Cohen
S. Marc Cohen*
Affiliation:
University of Washington, Seattle, WA98195, U.S.A.
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Extract

Not the least among the many puzzling features of the fourth book of Aristotle's Metaphysics is his discussion of the Principle of Non-Contradiction (hereafter ‘PNC’). Even leaving aside the obvious difficulty of determining what his arguments succeed in showing about PNC, we face the more fundamental problem of figuring out what he takes them to show. For he proceeds in such a way as to suggest that he is not always completely clear about what he is up to.

Aristotle seems to be offering arguments in support of PNC. Yet to do so would be to try to demonstrate something he considers indemonstrable, to prove a first principle, to treat an ultimate explanans as also an explanandum – and to try to explain it. These maneuvers fly in the face of the teachings of the Organon, which allow no room for a demonstration, or proof (apodeixis), of PNC.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 16 , Issue 3 , September 1986 , pp. 359 - 370
Copyright
Copyright © The Authors 1986

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References

1 ‘Aristotle's Discovery of Metaphysics,’ Review of Metaphysics 31 (1977) 210-29

2 ‘Aristotle on the Law of Contradiction,’ in Barnes, Schofield, and Sorabji, eds., Articles on Aristotle,vol. 3, Metaphysics (London: Duckworth 1979) 50-62

3 Aristotle's Metaphysics, BooksГ , Δ, and E (Oxford: Clarendon Press 1971) 93-105, W.D. Ross (Aristotle's Metaphysics, vol. 1 [Oxford: Clarendon Press 1924]265-8) likewise finds seven ‘proofs’ inГ 4, although his divisions of the text differ slightly from Kirwan's. In the present discussion I follow Kirwan's divisions.

4 Properly speaking, 3. does not express the indubitability of PNC, but merely its universal acceptance; the correct formulation should be modalized. This complication is irrelevant for present purposes and has therefore been ignored.

5 I have found this example useful in discussions of Plato's refutation of Protagoras in the Theaetetus. I thank Alan Code for pointing out to me its application to the present case.

6 More precisely, with respect to each proposition, I believe that, if I believe it, it is true:

(∀p)[I believe that (I believe that p⊃ it is true that p)]. (This is an acceptable generalization because there is no proposition with respect to which I believe both that I believe it and that it is false.) But the importation of the quantifier into the belief-context yields a falsehood, since I do not take myself to be an infallible believer, i.e.,

I do not believe that (∀p)(I believe that p⊃ it is true that p).

7 Dancy, R.M. Sense and Contradiction: A Study in Aristotle (Dordrecht: D. Reidel 1975), 4CrossRefGoogle Scholar