The question I consider is this:

The Question: Can two people–who are, and realize they are, intellectually virtuous to about the same degree–both be rational in continuing knowingly to disagree after full disclosure (by each to the other of all the relevant evidence they can think of) while at the same time thinking that the other may well be rational too?

I distinguish two kinds of rationality–internal and external–and argue in section 1 that, whichever kind we have in mind, the answer to The Question is ‘yes’ (though that positive answer is less wholehearted in the case of external rationality). Then, in section 2, I briefly make some more general remarks about when discovering a disagreement provides a defeater and when it doesn't. In the final section, I consider an important objection to the answer given in section 1 to The Question.