Dissonant cases of belief are, I think, "antecedently unclear cases" of the sort I discussed in this post on pragmatic metaphysics. The philosophical concept of belief is sufficiently vague or open-textured that we can choose whether to embrace an account of belief that counts dissonant cases as cases of belief, as intellectualism would do, or whether instead to embrace an account that counts them as cases of failure to believe or as in-between cases that aren't quite classifiable either as believing or as failing to believe.
I offer the following pragmatic grounds for rejecting intellectualism in favor of a broad-based view. My argument has a trunk and three branches.
The trunk argument.
Belief is one of the most central and important concepts in all of philosophy. It is central to philosophy of mind: Belief is the most commonly discussed of the "propositional attitudes". It is central to philosophy of action, where it's standard to regard actions as arising from the interaction of beliefs, desires, and intentions. It is central to epistemology, much of which concerns the conditions under which beliefs are justified or count as knowledge. A concept this important to philosophical thinking should be reserved for the most important thing in the vicinity that can plausibly answer to it. The most important thing in the vicinity is not our patterns of intellectual endorsement. It is our overall patterns of action and reaction. What we say matters, but what we do in general, how we live our lives through the world -- that matters even more.
Consider a case of implicit classism. Daniel, for example, sincerely says that the working poor deserve equal respect, but in fact for the most part he treats them disrespectfully and doesn't find it jarring when others do so. If we, as philosophers, choose describe Daniel as believing what he intellectually endorses, then we implicitly convey the idea that Daniel's patterns of intellectual endorsement are what matter most to philosophy: Daniel has the attitude that stands at the center of so much of epistemology, philosophy of action, and philosophy of mind. If we instead describe Daniel as a mixed-up, in-betweenish, or even failing to believe what he intellectually endorses, we do not implicitly convey that intellectualist idea.
Too intellectualist a view invites us to adopt noxiously comfortable opinions about ourselves. Suppose our implicit classist Daniel asks himself, "Do I believe that the working poor deserve equal respect?" He notices that he is inclined sincerely to judge that they deserve equal respect. Embracing intellectualism about belief, he concludes that he does believe they deserve equal respect. He can say to himself, then, that he has the attitude that philosophers care about most – belief. Maybe he lacks something else. He lacks "alief" maybe, or the right habits, or something. But based on how philosophers usually talk, you'd think that's kind of secondary. Daniel can comfortably assume that he has the most important thing straightened out. But of course he doesn't.
Intellectualist philosophers can deny that Daniel does have the most important thing straightened out. They can say that how Daniel treats people matters more than what he intellectually endorses. But if so, their choice of language mismatches their priorities. If they want to say that the central issue of concern in philosophy is, or should be, how you act in general, then the most effective way to encourage others to join them in that thought is to build the importance of one's general patterns of action right into the foundational terms of the discipline.
Too intellectualist a view hides our splintering dispositions. Here's another, maybe deeper, reason Daniel might find himself too comfortable: He might not even think to look at his overall patterns of behavior in evaluating what his attitude is toward the working poor. In Branch 1, I assumed that Daniel knew that his spontaneous reactions were out of line, and he only devalued those spontaneous reactions, not thinking of them as central to the question of whether he believed. But how would he come to know that his spontaneous reactions are out of line? If he's a somewhat reflective, self-critical person, he might just happen to notice that fact about himself. But an intellectualist view of the attitudes doesn’t encourage him to notice that about himself. It encourages Daniel, instead, to determine what his belief is by introspection of or reflection upon what he is disposed to sincerely say or accept.
In contrast, a broad-based view of belief encourages Daniel to cast his eye more widely in thinking about what he believes. In doing so, he might learn something important. The broad-based approach brings our non-intellectual side forward into view while the intellectualist approach tends to hide that non-intellectual side. Or at least it does so to the extent we are talking specifically about belief -- which is of course a large part of what philosophers do in fact actually talk about in philosophy of mind, philosophy of action, and epistemology.
Another way in which intellectualism hides our splintering dispositions is this: Suppose Suleyma has the same intellectual inclinations as Daniel but unlike Daniel her whole dispositional structure is egalitarian. She really does, and quite thoroughly, have as much respect for the custodian as for the wealthy business-owner. An intellectualist approach treats Daniel and Suleyma as the same in any domain where what matters is what one believes. They both count as believers, so now let's talk about how belief couples with desire to beget intentions, let's talk about whether their beliefs are justified, let's talk about what set of worlds makes their beliefs true -- for all these purposes, they are modeled in the same way. The difference between them is obscured, unless additional effort is made to bring it to light.
You might think Daniel's and Suleyma's differences don't matter too much. They're worth hiding or eliding away or disregarding unless for some reason those differences become important. If that's your view, then an intellectualist approach to belief is for you. If on the other hand, you think their differences are crucially important in a way that ought to disallow treating them as equivalent in matters of belief, then an intellectualist view is not for you. Of course, the differences matter for some purposes and not so much for other purposes. The question is whether on balance it's better to put those differences in the foreground or to tuck them away as a nuance.
Too intellectualist a view risks downgrading our responsibility. It's a common idea in philosophy that we are responsible for our beliefs. We don't choose our beliefs in any straightforward way, but if our beliefs don't align with the best evidence available to us we are epistemically blameworthy for that failure of alignment. In contrast, our habits, spontaneous reactions, that sort of thing -- those are not in our control, at least not directly, and we are less blameworthy for them. My true self, my "real" attitude, the being I most fundamentally am, the locus of my freedom and responsibility -- that's constituted by the aspects of myself that I consciously endorse upon reflection. You can see how the intellectualist view of belief fits nicely with this.
I think that view is almost exactly backwards. Our intellectual endorsements, when they don't align with our lived behavior, count for little. They still count for something, but what matters more is how we spontaneously live our way through the world, how we actually treat the people we are with, the actual practical choices we make. That is the "real" us. And if Daniel says, however sincerely, that he is an egalitarian, but he doesn't live that way, I don't want to call him a straight-up egalitarian. I don't want to excuse him by saying that his inegalitarian reactions are mere uncontrollable habit and not the real him. It's easy to talk. It's hard to change your life. I don't want to let you off the hook for it in that way, and I don't want to let myself off the hook. I don't want to say that I really believe and I am somehow kind of alienated from all my unlovely habits and reactions. It's more appropriately condemnatory to say that my attitude, my belief state, is actually pretty mixed up.
It's hard to live up to all the wonderful values and aspirations we intellectually endorse. I am stunned by the breadth and diversity of our failures. What we sincerely say we believe about ourselves and the people around us and how we actually spontaneously react to people and what we actually choose and do -- so often they are so far out of line with each other! So I think we've got to have quite a lot of forgiveness and sympathy for our failures. My empirical, normative, pragmatic conjecture is this: In an appropriate context of forgiveness and sympathy, the best way to frankly confront our regular failure to live up to our verbally espoused attitudes is to avoid placing intellectual endorsements too close to the center of philosophy.