On Self-Defeating Skeptical Arguments

Usually, self-defeating arguments are bad. If say "Trust me, you shouldn't trust anyone", my claim (you shouldn't trust anyone), if true, undermines the basis I've offered in support (that you should trust me). Whoops!

In skeptical arguments, however, self-defeat can sometimes be a feature rather than a bug. Michel de Montaigne compared skeptical arguments to laxatives. Self-defeating skeptical arguments are like rhubarb. They flush out your other opinions first and themselves last.

Let's consider two types of self-defeat:

In propositional self-defeat, the argument for proposition P relies on a premise inconsistent with P.

In methodological self-defeat, one relies on a certain method to reach the conclusion P, but that very conclusion implies that the method employed shouldn't be relied upon.

My opening example is most naturally read as methodologically self-defeating: the conclusion P ("you shouldn't trust anyone") implies that the method employed (trusting my advice) shouldn't be relied upon.

Since methods (other than logical deduction itself) can typically be characterized propositionally then loaded into a deduction, we can model most types of methodological self-defeat propositionally. In the first paragraph, maybe, I invited my interlocutor to accept the following argument (with P1 as shared background knowledge):

P1 (Trust Principle). If x is trustworthy and if x says P, then P.
P2. I am trustworthy.
P3. I say no one is trustworthy.
C. Therefore, no one is trustworthy.

C implies the falsity of P2, on which the reasoning essentially relies. (There are surely versions of the Trust Principle which better capture what is involved in trust, but you get the idea.)

Of course, there is one species of argument in which a contradiction between the premises and the conclusion is exactly what you're aiming for: reductio ad absurdum. In a reductio, you aim to prove P by temporarily assuming not-P and then showing how a contradiction follows from that assumption. Since any proposition that implies a contradiction must be false, you can then conclude that it's not the case the not-P, i.e., that it is the case that P.

We can treat self-defeating skeptical arguments as reductios. In Farewell to Reason, Paul Feyerabend is clear that he intends a structure of this sort.[1] His critics, he says, complain that there's something self-defeating in using philosophical reasoning to show that philosophical reasoning shouldn't be relied upon. Not at all, he replies! It's a reductio. If philosophical reasoning can be relied upon, then [according to Feyerabend's various arguments] it can't be relied upon. We must conclude, then, that philosophical reasoning can't be relied upon. (Note that although "philosophical reasoning can't be relied upon" is the P at the end of the reductio, we don't accept it because it follows from the assumptions but rather because it is the negation of the opening assumption.) The ancient skeptic Sextus Empiricus (who inspired Montaigne) appears sometimes to take basically the same approach.

Similarly, in my skeptical work on introspection, I have relied on introspective reports to argue that introspective reports are untrustworthy. Like Feyerabend's argument, it's a methodological self-defeat argument that can be formulated as a reductio. If introspection is a reliable method, then various contradictions follow. Therefore, introspection is not a reliable method.

You know who drives me bananas sometimes? G.E. Moore. It's annoyance at him (and some others) that inspires this post.

Here is a crucial turn in one of Moore's arguments against dream skepticism. (According to dream skepticism, for all you know you might be dreaming right now.)

So far as I can see, one premiss which [the dream skeptic] would certainly use would be this: "Some at least of the sensory experiences which you are having now are similar in important respects to dream-images which actually have occurred in dreams." This seems a very harmless premiss, and I am quite willing to admit that it is true. But I think there is a very serious objection to the procedure of using it as a premiss in favour of the derived conclusion. For a philosopher who does use it as a premiss, is, I think, in fact implying, though he does not expressly say, that he himself knows it to be true. He is implying therefore that he himself knows that dreams have occurred.... But can he consistently combine this proposition that he knows that dreams have occurred, with his conclusion that he does not know that he is not dreaming?... If he is dreaming, it may be that he is only dreaming that dreams have occurred... ("Certainty", p. 270 in the linked reprint).

Moore is of course complaining here of self-defeat. But if the dream skeptic's argument is a reductio, self-contradiction is the aim and the intermediate claims needn't be known.

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ETA 11:57 a.m.: I see from various comments in social media that that last sentence was too cryptic. Two clarifications.

First, although the intermediate claims needn't be known, everything in the reductio needs to be solid except insofar as it depends on not-P. Otherwise, it's not necessarily not-P to blame for the contradiction.

Second, here's a schematic example of one possible dream-skeptical reductio: Assume for the reductio that I know I'm not currently dreaming. If so, then I know X and Y about dreams. If X and Y are true about dreams, then I don't know I'm not currently dreaming.

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[1] I'm relying on my memory of Feyerabend from years ago. Due to the COVID shutdowns, I don't currently have access to the books in my office.