The inability to agree on the principles that underlie our beliefs is at the root of our political discord. And it can't be solved by voting.
But what counts as “legitimate”? There’s the rub. A legitimate challenge is presumably a rational challenge. Disagreements over epistemic principles [or the assumptions that allow us to accept knowledge as certain] are disagreements over which methods and sources [used to derive knowledge] to trust. And there we have the problem. We can’t decide on what counts as a legitimate reason to doubt my epistemic principles unless we’ve already settled on our principles—and that is the very issue in question. The problem that skepticism about reason raises is not about whether I have good evidence by my principles for my principles. Presumably I do. The problem is whether I can give a more objective defense of them. That is, whether I can give reasons for them that can be appreciated from what Hume called a “common point of view” — reasons that can “move some universal principle of the human frame, and touch a string, to which all mankind have an accord and symphony.”