(1) If someone is aware that there is an undecided dispute about ?Q, then he ought not to accept or reject any proposed answer to ?Q.1
(2) On every issue ?Q, there has been (or might be) disagreement.
(3) If a disagreement is to be decided, we need a yardstick (a criterion, a standard) to decide it.
(4) On any question of the form “Is Y appropriate for ?Q?” there is undecided disagreement.
(5) If we are to use a yardstick Y for issue ?Q, we must (a) believe that Y is appropriate to ?Q and (b) be justified in believing that Y is appropriate for ?Q.
(6) Hence, there is no Y and no ?Q for which we're justified in holding that Y is appropriate to ?Q. (1, 4)
(7) Hence, for no Y and no ?Q may we use Y for ?Q. (5, 6)
(8) Hence, no issue is decided. (2, 3, 7)
(9) Hence, we should suspend judgment on every issue ?Q. (1, 8)
It entails radical skepticism about the world.
I'll start my defense of the argument by summarizing Barnes on it.
Premises (1), (2), and (3)
Barnes first lays out definitions for attitude and dispute. He says that someone takes an attitude to a question ?Q if he either accepts some proposition as the answer to ?Q, rejects some proposition as the answer to ?Q, or suspends judgment over ?Q; and that two people dispute the answer to a ?Q whenever they take conflicting attitudes to it.
He also distinguishes historical decisions and rational decisions. Historical decisions concern the attitudes people take towards an issue; in contrast, rational decisions concern only the arguments for and against the issue. The dispute over the authenticity of the Magna Moralia is historically decided when everyone involved takes the same attitude towards its authenticity; it's rationally decided only when an argument determines the text's authenticity one way or the other. I'll use “decision” to mean “rational decision” in this post.
Barnes then argues for (1). Suppose (1) false. Then I could be aware of the dispute over the Magna Moralia's authenticity, decide for or against that authenticity, and still maintain that the dispute is undecided. But that is absurd. If it's rational or warranted for me to decide against the text's authenticity, then whatever warrants my decision also decides the dispute over the text's authenticity; if the dispute is undecided, then it must be irrational or unwarranted for me to decide against the text's authenticity. There is therefore good reason to accept (1): it's incoherent to both decide a dispute and maintain that it's undecided.
Next, Barnes points out that even if we reject (2), there has, as an empirical fact, been disagreement over almost everything interesting or important. In other words, he points out that even if (2) fails something close enough succeeds.
He then argues for (3). He argues (i) if we didn't need a criterion to rationally decide an issue ?Q, we would be able to rationally decide it by arbitrarily deciding it; (ii) we can't rationally decide something by arbitrarily deciding it; hence (iii), we need a criterion to rationally decide ?Q. In short, he argues that we need criteria to rationally decide questions because rationally deciding (at least in part) means deciding based on criteria.
He thinks the foregoing entails (1), (2), and (3).
Premise (4) and (5)
Next, Barnes suggests that Sextus means for us to take (4) as an empirical premise. He, however, doesn't think it's clear that it succeeds as such. (He would if we were talking about historically undecided disagreement, but not rationally undecided disagreement.) He ultimately concedes that (4) needs the support of other Pyrrhonian modes to stand2.
He then argues that it's unclear whether (5) succeeds. Suppose, for instance, that someone uses the law of non-contradiction to resolve a dispute. Does he also need to hold a belief in its appropriateness to the dispute to be justified in using it? Barnes doesn't think it clear that he does. In brief, he thinks that it's unclear whether (5) succeeds because non-skeptics may be able to reject (5a).
He thinks the foregoing suggests that it's unclear whether (4) or (5) succeed.
But, Barnes adds, the skeptic isn't finished yet. For even if it turns out that the non-skeptic is right, it's still the case that if he ever stops and (to return to the last example) reflects on the law of non-contradiction and comes to a conclusion other than belief in its suitableness to the dispute, he can no longer be justified (or at least no longer feel justified) in using it to resolve the dispute. A modified version of the argument therefore succeeds for any yardstick the non-skeptic reflects on and doesn't come to believe appropriate.3
Barnes thinks that (1), (2), and (3) are well-supported, (4) requires the support of other Pyrrhonian modes, and (5) remains poorly supported even with other modes. He doesn't think that the argument is probative.4
In a future post, I'll put on the mantle of the Pyrrhonist and try to show that the argument is probative.
1Barnes calls (1) the principle of disagreement.
2A “mode” is an argument-form.
3Barnes promises that this “form of reflection […] will turn out to be the final cunning thought in the Pyrrhonian philosophy”.
4There is one further consequence of the argument worth flagging—that of self-refutation. I have nothing to say about this charge here, except that a proper defense against it will take us straight to the heart of the Pyrrhonian way of life.