In any realistic case, the totality of one’s evidence concerning a proposition will be a long and complex story, much of which may be difficult to put into words. This makes it possible that each party to a disagreement has an extra bit of evidence, evidence that has not been shared. You might think that each person’s unshared evidence can justify that person’s beliefs. For example, there is something about the atheist’s total evidence that can justify his belief, and there is something different about the theist’s total evidence that can justify her belief. Of course, not all cases of disagreement need to turn out this way. But perhaps some do, and perhaps this is what the students in my class thought was going on in our class. And, more generally, perhaps this is what people generally think is going on when they conclude that reasonable people can disagree.
Can we say that reasonable disagreement is possible in cases where the parties to the disagreement have 'private evidence'? He says, "It is possible that the private evidence includes the private religious (or nonreligious) experiences one has", but he seems to think that these experiences won't present much of a problem. The idea is that the theist (alleges) she has private evidence for her beliefs and this allows someone with a conciliatory view to say that theist is reasonable in the face of disagreement.
This response will not do. To see why, compare a more straightforward case of regular sight, rather than insight. Suppose you and I are standing by the window looking out on the quad. We think we have comparable vision and we know each other to be honest. I seem to see what looks to me like the dean standing out in the middle of the quad. (Assume that this is not something odd. He’s out there a fair amount.) I believe that the dean is standing on the quad. Meanwhile, you seem to see nothing of the kind there. You think that no one, and thus not the dean, is standing in the middle of the quad. We disagree. Prior to our saying anything, each of us believes reasonably. Then I say something about the dean’s being on the quad, and we find out about our situation. In my view, once that happens, each of us should suspend judgment. We each know that something weird is going on, but we have no idea which of us has the problem. Either I am ‘‘seeing things,’’ or you are missing something. I would not be reasonable in thinking that the problem is in your head, nor would you be reasonable in thinking that the problem is in mine.
I don't think this helps with mystical experience, not if the theist alleges that the object of such experiences chooses who to reveal itself to. It's not as if you can sneak a peak at God, on the theist's view, if you hide behind a bush while God appears to someone else.
Much of Feldman's remarks have to do with feelings of obviousness and insight that the theist and atheist can share, but if these remarks are intended to deal with religious experience, they don't seem to work:
Similarly, I think, even if it is true that the theists and the atheists have private evidence, this does not get us out of the problem. Each may have his or her own special insight or sense of obviousness. But each knows about the other’s insight. Each knows that this insight has evidential force. And now I see no basis for either of them justifying his own belief simply because the one insight happens to occur inside of him. A point about evidence that plays a role here is this: evidence of evidence is evidence.More carefully, evidence that there is evidence for P is evidence for P. Knowing that the other has an insight provides each of them with evidence.
Suppose that evidence that there is evidence for P is evidence for P. Can't P be better supported by the ground level evidence for P than the evidence that such evidence exists? If so, will the atheist really 'share' the theist's evidence when the theist reports a mystical experience?
Suppose we think of evidence as non-inferential knowledge. The theist claims that they know non-inferentially that God is speaking to them. This allegation, if true, means that their evidence rules out the hypothesis that there's no God. I see no reason to think that the theist's report of such an experience gives the atheist evidence that rules out the hypothesis that God exists and no reason to think that the upper limit of evidential support provided by an experience is determined by the degree of support a report of that experience can provide for another. So, I don't think there's anything in these passages that deals with the problem of private evidence understood as a kind of (alleged) mystical experience.
Now, just to be clear, that doesn't mean that the atheist should defer. They shouldn't believe that the kinds of experiences that the theist report are possible. (Should the theist believe they have the kinds of experiences they do? If 'should believe' is cashed out in the way that I think Feldman wants to, I cannot say with much confidence that the theist shouldn't believe that they could have the kinds of mystical experiences they report. (If, however, you shouldn't believe p if p is false or p isn't something you know, that's another matter ...)) The problem is that I don't see how Feldman can use the conciliatory view in the way he seems to want to without either begging the question against the theist who claims to know God directly via mystical experience or assuming something questionable about the kind of justificatory support experience provides.