Richard Feldman and Earl Conee in "Evidentialism" wants to argue for something called evidentialism. Because I am kind of tired of the logicist formulations, I'll just put it simply. Evidentialism for Feldman and Conee is when your belief "is determined by the quality of [your] evidence for the belief." The better the evidence, the better reason you have for you belief. Furthermore, they think you should believe things for which you have adequate evidence for.
We hold the general view that one epistemically ought to have the doxastic attitudes that fit one's evidence. We think that being epistemically obligatory is equivalent to being epistemically justified.So having good reasons for your belief is the same, according to Feldman and Conee, as believing what you ought to believe according to the best evidence. You shouldn't just try your best, though. And trying your best is not enough to make it the case that you have good reasons for your belief. You also have to have good evidence, plain and simple.
One of the big contenders against this view is reliabilism. Reliabilism is the view that "epistemically justified beliefs are the ones that result from belief-forming processes that reliably lead to true beliefs." In other words, according to reliabilism, you have good reasons for your belief when whatever cognitive processes or processes related to your mind and the world make your beliefs true. Feldman and Conee think that this view is so broad that you could actually accept this and accept evidentialism as the proper way to fill it out.
About this debate: My view is that both of these do not account for good reasons to belief. Think about mathematics, for example. If evidentialism is true, your beliefs about conceptual truths like mathematics, or logic, have good reasons supporting them if there is good evidence for the belief. But what good evidence is there? How could you give 'good reasons' for your beliefs like, for example, that the sum of 2 and 2 is 4? Do we even need to appeal to evidence? Surely there are math proofs but for day to day activities we seem to think that we could have this belief without having good evidence supporting claims like these.
If reliabilism is true, then claims about mathematics and logic must have the proper belief-forming processes. What could could even count as such, though? What is the appropriate chain of reasoning that gets you to those beliefs? I don't think there are any.
My point is that there is no good broad account of good reasons for belief that could or would not be formulated relative to the domains which one would ask for such criteria. And there is no catch-all 'good reasons' category for everyday experience, per se, because the world of everyday experience is not a domain; a domain is a formal field of study, an idealized or conceptualized part of the world.
So anyway, I don't think this is sufficient, and I don't like the debate very much.