What obligates George to believe B in these circumstances is not merely his belief that "if A then B" and also that "A," but rather modus ponens itself. And it is not his belief in modus ponens that obligates him to believe B, for that [...] is irrelevant. What obligates him to believe B is that, if he does not reason in accordance with modus ponens, he will not have a mind at all.It seems to me that the first and third sentences quoted here make different claims, one consequentialist in form and one absolutist.
The consequentialist claim is that if you don't reason in accordance with modus ponens then you will not be reasoning at all, so you had better reason that way or lose your mind. Illogical thought is not thought at all. But someone might not care about this, so the "obligation" looks problematic.
The absolutist claim is that modus ponens itself obligates George to believe B. That is, it tells him to do so. (It doesn't make him do so.)
This all reminds me of Wittgenstein's Lecture on Ethics, in which he contrasts someone who plays tennis badly but does not care to play better with someone who behaves morally badly and does not care to behave better. The former is understandable, but the latter is not. His attitude is unacceptable, that is to say. So Wittgenstein's view seems to be that moral obligation obligates in roughly the same way that modus ponens obligates, i.e. it tells you what to do. It does not force you to do it, though, and it does not threaten you with any dire consequence if you disobey. If it did, then your obedience would be self-interested, not moral. That is, if the force of moral obligation consisted in the fact that dire consequences awaited the disobedient, then there would be no moral obligation at all, only questions of self-interest. But telling someone what to do (without any threat attached) is not obligating them in any clear sense. Hence Kant's odd idea that we command ourselves, and Wittgenstein's suggestion that talk of moral obligation is nonsense.
What would the moral parallel be to the consequentialist claim about modus ponens? You must not behave immorally or else you will not be moral? That isn't much of a threat, or reason to change your ways. Korsgaard might want to argue that you risk losing yourself in some way, but a) do you really?, b) must you care about this?, and c) is this the reason why immorality is bad?