Ancient Self-Refutation: The Logic and History of the Self-Refutation Argument from Democritus to Augustine by Luca Castagnoli

Abstract

188 PHOENIX intraduisible en grec où l’on parle de sanctuaires communs (koina), même s’il semblerait plus juste d’imputer aux Modernes cet abus de langage attribué à la politique dominatrice des Romains. Il faut être reconnaissant à M. Scott de faire ainsi connaı̂tre à un plus large public les travaux des archéologues et des architectes allemands et français. On retrouve ce même souci de diffusion des connaissances dans le documentaire qu’il a réalisé sur Delphes en 2010, Delphi: Bellybutton of the Ancient World. Universit e de Strasbourg Anne Jacquemin Ancient Self-Refutation: The Logic and History of the Self-Refutation Argument from Democritus to Augustine. By Luca Castagnoli. Cambridge: Cambridge University Press 2010. Pp. xx, 394. Castagnoli meticulously analyzes an impressive array of ancient philosophical arguments , which, in some way or another, undermine themselves. Of course the “self” in “self-refutation” requires and receives careful consideration, as does the question of what it means to “undermine” or “refute.” The central thesis is comparative: ancient self-refutation aims at showing that someone cannot coherently or consistently maintain some (usually revisionist) thesis that he publicly proposes; whereas more modern varieties , in accordance with J. L. Mackie’s influential analysis,1 typically aim at showing that some thesis, regardless of whether it is actually endorsed by anyone, logically entails its contradictory and hence is false (by the notorious Consequentia Mirabilis: (p→¬p) → ¬p). In short, and with some oversimplification: ancient self-refutation is inherently dialectical whereas modern varieties are logical. According to Castagnoli, many commentators have mistakenly assimilated the former to the latter, thereby misrepresenting the logic and the conclusions of those arguments. For example, Socrates’ refutation of Protagoras in the Theaetetus merely shows that one who is willing to propose and defend the Measure Doctrine can be compelled to admit that his view is false. The refutation does not show that the Measure Doctrine is in fact false, but that upholding it is incompatible with the requirements of a dialectical exchange in which one must contradict his opponent. It makes no sense to try to overturn your opponent’s view while maintaining that no one is ever mistaken about anything, i.e., that man is the measure of all things. Aristotle’s elenctic proof of the Principle of Noncontradiction (PNC) in Metaphysics G provides a similar lesson. Castagnoli interprets it, following Wedin,2 as a straightforward modus ponens: some statement “s” signifies, but if “s” signifies then PNC is true (insofar as signification entails some determinate state of affairs), therefore PNC is true. Since in this formulation the targeted thesis, the denial of PNC, does not enter as a premise, it appears not to be an instance of self-refutation. But whether the argument is cast in terms of self-refutation or not, the main point is again dialectical, namely, one who openly rejects the PNC can be compelled either to admit the contradictory of his view or to remain silent and thus be unable to defend himself. In either case, the denial of 1 J. L. Mackie, “Self-Refutation: A Formal Analysis,” Philosophical Quarterly 14 (1964) 193–203. 2 M. V. Wedin, “Some Logical Problems in Metaphysics G,” Oxford Studies in Ancient Philosophy 19 (2000) 113–162. BOOK REVIEWS/COMPTES RENDUS 189 PNC, like Protagoras’ Measure Doctrine is revealed as a dialectical non-starter. The more ambitious project, which is only implicit in Aristotle’s text, is to show that the PNC is in fact true, and not merely a necessary presupposition or commitment we make when engaging in dialectic. Protagoras’ claim that every appearance is true (minus its original relativizers) pops up again in an argument reported by Sextus (M 7.389–390). Insisting on the dialectical context allows us to supply the necessary premise that it appears (to the opponent) that not every appearance is true. It follows that it is true that not every appearance is true; so (obviously) not every appearance is true. If we read these as admissions extracted from the Protagorean, we find once again that he is unable to discharge his dialectical duty: advocating his view bars him from defending himself since he cannot...