Neither 'acceptance' nor 'cognitive feeling' is an entirely mainstream concept. A concern that motivates a lot of my work is that it is procrustean to try to explain all mental phenomena in terms of a select few propositional attitudes. There is little reason to insist that belief and desire must take their traditional place of prominence. The mind is lush, not sparse. The ordinary concept of belief is likely what Ned Block calls a "mongrel concept": a concept that imperfectly picks out various dissimilar cognitive states.
Psychopathologies present us with cases that ordinary folk psychology, with lumpen terms like 'belief', is not well-equipped to describe. They often reveal that mental states and processes which usually coincide can be dissociated from one another. We might need to be revisionary with our ontology of mental states in order to capture these dissociations.
Delusions are a case in point. Others on this blog have discussed how, because delusions act like such strange beliefs, they might well not be beliefs at all. This is non-doxasticism. But then, what would delusions be, if not beliefs? Luckily, we don't need to introduce an ad hoc category. An alternative notion---"acceptance"---can on occasion be spotted lurking throughout philosophy, used to explain phenomena as diverse as voluntary change of mind, self-deception, akrasia, pedagogy, and our understanding of myth and legend. Frankish and Velleman have both suggested that acceptances can help explain delusions. Delusions involve acceptance without belief.
It is easiest to get an grip on the type of acceptance at play in delusions (an imperfect grip, mind you) by considering acceptance as supposition without introspective insight. Over the course of a dinner, we can suppose something for the sake of argument, and then have a discussion as if we believed it. We usually have good introspective insight about when we are merely supposing something rather than believing it. However, what would it look like if we lost this insight? I claim that such a state would look an awful lot like a delusion (though there are differences---delusions are not usually formed voluntarily, for example). In fact, it turns out that many more mundane "beliefs", such as personal, ideological, or religious convictions, also share these features. Lisa Bortolotti has argued in her excellent book on delusions that non-doxasticism is threatened by the fact that delusions do not look very different from more mundane irrational beliefs. But it is not threatened if these other irrational "beliefs" turn out not to be beliefs either.
In a future post, I'll discuss how these pathological acceptances are formed. You can read more about my research interests on my webpage, and feel free to e-mail me with questions if interested. Also be sure to take a look at my iconographic representations of various delusion types!