A self-refutation argument is the claim that some counterintuitive philosophical position undermines itself. Imagine Socrates told someone that he knows that he knows nothing. His respondent could use a self-refutation argument to point out that Socrates cannot take such a position. Either his knowledge about his ignorance provides a counterexample to that proclaimed ignorance, Socrates’ respondent would say, or his ignorance undercuts the proclamation of certainty he made about his overall epistemic state. The respondent would not be informing us about what or how much Socrates does or does not in fact know. He would be telling us instead only what Socrates could or could not manage to maintain.
Castagnoli’s book analyzes with brilliance, incision, sensitivity, and exhaustive depth more than a dozen classes of Ancient Greek and Roman self-refutation arguments. Such arguments took up, among others, the following remarkable positions, in order to “eliminate,” “cancel,” “bracket,” “overturn,” “throw down,” and perform “upside-down, back-to-front reversal on” them.
• Everything is false
• Everything is true
• Contradictions are possible
• All appearances are true
• Everything is flux
• All is one
• There is no free will
• The senses are fundamentally unreliable
• Reason is fundamentally unreliable
• Knowledge is impossible
To repeat, Castagnoli does not concern himself in the first place with whether these positions do undermine themselves. Such a project would require undertaking all the core areas of philosophy. His task is instead to work through the strategies deployed to argue that these positions undermine themselves. Admittedly, this gets pretty close to undertaking all the core areas of philosophy. He reconstructs—with exacting attention to the texts, their logic, and their context—the force and target of these self-refutation arguments. In each case he finds, often against other commentators, that such arguments do not show, or even take themselves to be showing, the falsehood of their target position. They aim rather to defeat their opponents in dialectical exchange. Their limited but (for their purposes) sufficient ambit is to prevent their debating partners from consistently endorsing and successfully defending their propositions.
Besides this argument about the shared (dialectical not metaphysical) goal of all ancient self-refutation arguments, Castagnoli makes an important point about how they differ from one another. Not all self-refuting positions are shown to undermine themselves in the same way. Castagnoli distinguishes between pragmatic, absolute, ad hominem, and operational versions of self-refutation (terms taken up from Mackie, Burnyeat, and Passmore), and argues that knowing which kind is at play is essential for analyzing and diagnosing an argument. Sometimes it is the very act of presenting some position that creates the critical mass for self-undermining. If you assert “assertion is impossible,” it is your asserting itself that makes your position impossible to maintain; your new action—taking yourself to be positing something true, namely a fact about a certain linguistic practice—provides a counterexample to the belief your action articulates. The style of argument that points this out is called pragmatic self-refutation. That you might undermine yourself by speaking about assertion does not by itself, however, instruct us about assertion; the facts about assertion will depend on facts about knowledge, authority, sincerity, and whatever else epistemologists deal with.
Sometimes, however, the action of presenting some position is not what causes the self-undermining. Take Socrates’ knowledge-of-ignorance. It is not Socrates’ assertion that he knows that he knows nothing that causes him to refute himself. For his saying that he knows such-and-such is not an instance of knowing such-and-such, and is not therefore an undermining counterexample. The self-refutation comes rather from the logical inconsistency of his two statements, that he knows, first, and that he knows nothing, second. This style is called absolute self-refutation.
A third kind of self-refutation, “operational,” explains what’s going on in the argument against the Heraclitean proponents of radical flux in the Theaetetus and the Parmenidean proponents of the strong monist view that “all is One” in the Sophist. Both sets of proponents have committed themselves to views that undercut the possibility of the language—and thus thought—anybody would need to present those (or any other) views. This kind of transcendental criticism (“you have removed the preconditions for any philosophical activity whatsoever”) shows up also, according to Castagnoli, when Epictetus charges Epicurus with undercutting a precondition for warning people (having human fellowship) when he warns people against believing in human fellowship.
The fourth kind, ad hominem self-refutation, pertains to times when a speaker admits about his speech something inconsistent with what he takes his speech to be claiming. Imagine if Socrates were to say something like “I speak knowledgeably that I know nothing.” Castagnoli focuses on this kind of self-refutation when analyzing Sextus’ argument against those who assert there is no cause, yet admit they have reasons (= causes) for their assertion.
Castagnoli’s big claim, in summary, is that in the self-refutation arguments he canvasses from the ancient period, the arguer’s immediate aim is not to show that his opponent’s point is wrong, but instead to show that his opponent can’t—for various reasons—show his point to be right. Castagnoli makes little hay, acceptably so, about the importance of his interest in this productive critical gambit. He does highlight in the Introduction, and discusses throughout the text and footnotes, the pervasive contemporary interest in the nature of self-refutation arguments. But there is also a deeper point, that self-refutation arguments have an important position in the history of the practice of philosophy.
Naturally, such arguments don’t always address themselves to the most plausible and thus enduring philosophical positions, since the ones they deal with tend toward extremes and lack of nuance. But, in addition to the fact that many of these extreme theses played signal roles in metaphysics, epistemology, and ethics, these self-refutation arguments have a distinctively philosophical character (i.e., considered from the perspective of the practice of philosophy as such). They don’t subvert theses by appealing to contrary and stronger evidence, or by charging a conclusion with inadequate support, or by challenging the instruments or methods of discovery. They focus instead on the very fact that someone is taking an express stand about something and trying to get someone else to take that stand too. Since philosophical positions are non-evident (in the Skeptical terminology), and because they are concerned what it would be valuable to believe, philosophical positions must be explicitly stated and argued for. In the practice of philosophy neither pointing to phenomena nor avowing intuitions suffices to confirm one’s position. Just as questions of legal standing, though seemingly of merely prefatory or procedural concern to civil litigation, constitute much of the hard judicial decision-making of appellate courts, the questions of assertability or defensibility raised by self-refutation arguments, though they may also seem merely prefatory (“when will we ever get to the heart of the nature of assertability or self-knowledge or whatever?”), constitute much of the hard analysis in the intellectual practice of dialectical debate about important non-evident propositions.
Let me give an example. Castagnoli reconstructs Aristotle’s protreptic argument (“you should do philosophy; but anyway, you can’t avoid it”) at the book’s halfway point (187-196). A traditional reconstruction from the sources is this (p. 189):
(1) p —>p If one must philosophize, one must philosophize
(2) ~p —>p If one must not philosophize, one must philosophize
. .. p In any case, one must philosophize
Castagnoli draws attention to several suspicious features of this reconstruction. First, it has no dialectical context; it is presented as establishing the truth about how one ought to live, not keyed to any particular claim about the necessity of philosophizing. Second, it would seem to expect reduction to (2), a Consequentia Mirabilis -style argument (if the negation of something entails its affirmation, then one can deduce the affirmation); but Castagnoli argues at length that no other ancient self-refutation arguments ever depended on that style. Third, the reconstruction leaves the conditional at (2) wholly unexplained. Fourth, such reconstructions do not follow from Cicero and Alexander of Aphrodisias’ testimony about Aristotle (the testimony Castagnoli argues is most trustworthy), only from later, likely Stoicizing, sources.
Castagnoli goes on to reconstruct the protreptic argument anew:
I suggest that argument might have sounded like this: ‘If your position is that one must philosophise, you are definitely on my side of the barricade, and safe from the snares of Isocrates’ shallow rhetoric; if you contend, on the contrary, that one must not philosophise, you ought to vindicate this crucial choice of lifestyle, in front of me and yourself, by offering reasons for it; but don’t you realise that choosing what to do (and then defending your choices) on the basis of reflection and argument, and not, say, by ballot, is already doing philosophy, and thus you have already jumped over the fence to my side? In any case, therefore, whether you want this or not, you are bound to agree that one must philosophise.’
And he re-symbolizes it like this:
(a) q—>p If
(b) r<—>s ^ s>—>p If
c) q v r Either
. .. p In any case, therefore,
This argumentative strategy had fuller use in the anti-Skeptical arguments against proof, sign, and cause, which Castagnoli develops at length.
Ancient Self-Refutation is an extremely edifying, useful, and serious book of philosophy. Each of Castagnoli’s chapters is full of philosophical freshness, perspicuity, and information, and each must from now on serve as essential reference. It combines philology (about, e.g., wrestling moves and ancient diacritical marks), the history of philosophy, and textual criticism with the most rigorous analysis of arguments and with fulltime engagement with secondary literature. It does this with practically unrelenting focus: there are 137 numbered passages of ancient philosophy to which it gives its attention. The prose is totally clear and helpfully recapitulative, and the formatting excellent (cross-references, section-headings, footnotes, analytic index).1
Let me finish by indicating, at a high level of generality, the content of this book.
1-16 what self-refutation is, vs., e.g., inconsistency, the Liar paradox
17-23 against Mackie’s analysis of the self-refutation argument against “everything is false”
24-30 on “every logos is both true and false” (from Dissoi Logoi)
31-40 on “it is impossible to speak falsely” (from Euthydemus)
40-67 on “man is the measure” (from Theaetetus)
68-94 on denying the principle of non-contradiction (in Aristotle)
95-114 on “every appearance is true” and the Consequentia Mirabilis (in Sextus)
114-20 on “nothing is true” (in Sextus)
121-38 on “truth is imperishable” (in Augustine and his medieval successors)
145-59 on “everything is determined” (in Epicurus)
160-86 on miscellaneous Skeptical peritropai (“reversals”)
187-96 on Aristotle’s protreptic argument
197-204 on the impossibility of being mistaken that one exists (per Augustine) 205-18 on “all is flux” (in Theaetetus)
218-47 on “all is one” and the inexpressible (in Theaetetus)
251-352 that Skeptics avoid the charge of self-refutation
1. I noted no typographical errors except a missing “and” in the heading on p. xiii.