Abstract: Why care about logic? Here's a traditional answer (recently defended, for example, by Hartry Field): logic tells us about what patterns of belief are rationally required or forbidden. Now suppose Ada assures me that classical logic is correct, and that I'm rationally required to fully accept p; and Beth tells me that some nonclassical logic is correct, and that I'm rationally required to fully reject p. Modesty suggests I hedge my epistemic bets, and go 50/50 on whether p. But if I do that then both sides condemn me as adopting a rationally forbidden attitude. Can my seemingly reasonable response to uncertainty about logic really be irrational?
Philosophers bump into people like Ada and Beth pretty often, so the question has practical bite for many of us. But it has broader theoretical relevance. `Ada' might be some classically-framed scientific theory; and `Beth' a non-classically framed theory of the same phenomenon. Suppose by ordinary standards our evidence is evenly balanced. If hedging is rationally impermissible, then it looks like there can't be ordinary, rational, evidence-based theory choice between them.
I argue that there are rational requirements on belief of roughly the form that Field (and Bayesians) envisage, but logic isn't baked into them. On the descriptive side, I'll say what these generalized requirements are. And on the evaluative side, I'll argue that the generalized requirements allow us to pinpoint why truth-lovers should care about being rational. The story can't be strengthened to vindicate stronger logical requirements, I'll argue. That gives independent reason to think that my reasonable response to Ada and Beth is also the rational one.