Define 'incoherent' credences as ones that don't satisfy the probability axioms. There are familar 'Dutch Book' arguments about what's wrong with having incoherent credences. At a reading group meeting today lead by Al Hajek, I became even more convinced than previously that they leave a lot to be desired (at least as they stand). I thought I'd have a shot at something else.
Ideally, it would be nice to formulate a norm of credence which incoherent credences - or rather, credences which you *know* to be incoherent (there needn't be anything irrational about credences which are *in fact* incoherent if you've no reason to think they are) - are in tension with. I thought of this:
NC: You should try to make your credence in p sensitive only to your evidence concerning p.
Now, suppose you notice that you have different credences in p and q and you have credence 1 in (p iff q). Your certainty that (p iff q) will (at least in lots of standard situations) enable you to (properly) treat all your evidence concerning p as evidence concerning q and vice versa. So that you have the same evidence for and against each of them. This means, since your credences in p and q are different, that at least one of those credences must be sensitive to something other than your evidence concerning the relevant proposition. You can see that you have violated a norm of credence.
This seems to me to be a decent explanation of what is wrong with incoherent credences in this sort of case. Is this kind of explanation sufficiently generalizable? I don't know yet. For one thing, I'm not sure how to get this sort of explanation going in situations where you don't have credence 1 in something. But then, I'm also not sure whether you can get clear cases of irrationality in situations where you don't have credence 1 in something. (In the above case, if your credence in (p iff q) wasn't 1, it would be less clear that it was an epistemic mistake to have different credences in p and q.)