The approach Jaynes takes in the opening chapters Probability: The Logic of Science based on Cox's theorem was very persuasive to me and the few others I've mentioned it to. The basic idea is to start with a few criteria that just seem like common sense that everyone should agree are desirable in a reasoning system. Then Jaynes shows that probability theory is the only possible system that fulfills these criteria.

Is there a similar approach that can be used to argue to rationality in general? I like to appeal to universiality. Different subjects should be governed by the same rules. And science and rationality have been enormously successful, so why shouldn't it be applied universally. Unfortunately, this approach can easily be abused. Can we formulate a good approach of this sort that isn't just leading people to say what we want?