Some time ago I offered an argument for the possibility of reasonable disagreement over philosophical positions. Brian Weatherson at TAR has just posted a paper with an interesting argument for a similar conclusion:
Stuart, I think you conflating two distinct senses in which it might be sensible to judge a theory by "applying it to itself". It seems sensible that theories not be required to justify themselves, as your examples attest. But it also seems sensible to require that they not be inconsistent with themselves, which is what Leiter's on about.
I don't believe checking whether a philosophical theory can be applied to itself is a sensible way to judge it. Most proper theories have quasi-axioms that have to be asserted or taken as true. There is, alas, no inductive proof of the induction hypothesis, yet it underlies all of science.
Conversely, most theories that do justify themselves (such as Freudian analysis, which comes complete with a full justification as to why people do or don't believe it) are very highly suspect.
The philosophical theory "every affirmation I utter is true" is certainly consistent with itself; but I can't avoid feeling that it is somewhat lacking in the credibility department.
The problem seems to me to be that the EW view (at least as presented by Weatherson) is claiming something rather stronger, and less conditional than Aumann's disagreement result, and is consequently easy to dismiss as incoherent. The same incoherence pretty clearly doesn't afflict Aumann's argument. (For one, it applies only between honest Bayesians. Are there any Bayesians who dispute Aumann's result? If not, then there's no relevant disagreement. For two, even if there were, Weatherson's arguments about the stable point wouldn't follow in the case of honest Bayesians. They only work because one party isn't playing by Bayesian rules, and EW (as presented) doesn't seem to care about that.)
Anyway, Robin's right. The extreme view is easy to dismiss, but Weatherson hasn't given us much guidance on the interesting question.
Weatherson rejects an extreme view, that you should give equal weight to the opinions of all "friends," but he doesn't seem to accept the opposite extreme, that you should ignore all their opinions and just go with what the arguments convince you of. So he has not tackled the hard problem: just how much weight should you give to which opinions?