In my dreams & sensations post, I raised the question of whether sensations were purely subjective things - a question I'd like to pursue further.
Is it possible to have a sensation, yet not be aware of it? I would think not - surely if you're unaware of it, then it's not conscious, and therefore not what I understand 'sensation' to mean. How about the reverse? Could you falsely believe you're experiencing a sensation, when in fact you are not? Again, this seems problematic, unless the word 'sensation' is being used to refer to something beyond subjective conscious experiences, but if so, it's hard to imagine what that something is supposed to be. I'll come back to this in a moment.
How about beliefs? I think I'd take a more objective approach to them. Of course we have a plethora of subconscious beliefs beyond those of which we're aware of at any particular moment. You believe that your 27th paternal great-great-...-grandfather is no longer alive, though you've probably never consciously considered that exact proposition before. But how about once a proposition is made salient - is it possible for you to actively deny a belief that you really have? i.e. Can you believe that P, whilst simultaneously believing that 'I do not believe that P'? That seems trickier. I guess you could go either way, depending on which understanding of 'belief' you're going by:
1) S believes1 that P iff (S would consciously affirm P, were P salient).
2) S believes2 that P iff (S behaves as though P were true).
Those are just rough formulations, of course, but hopefully the general idea is clear enough. We can differentiate between (subjective) belief as affirmation of a proposition, and (objective) belief as an influence on behaviour. You might believe1 that P, yet not believe2 that P, and that is no contradiction (just compare the words and actions of the nominally religious).
I don't think we can divide sensations that way, however, because sensations themselves are just a form of mental event. They only influence our behaviour insofar as they give rise to beliefs. (Your seeing an apple gives rise to your belief that there is an apple, which then - in conjunction with your desires and various other beliefs - causes you to pick it up and eat it.)
Yet, despite what I said earlier, there is a gap between sensation/experience and beliefs. After all, we can imagine a mad scientist or evil demon messing with your mind in such a way that it gives you the false belief that 'I just experienced sensation X'. Thus, it is conceivable that conscious introspection could mislead you, even with regard to your own conscious states and sense data.
I'm not sure what to do about all that. I've almost argued myself into a form of sense-data skepticism. Whether S has experienced sensation X or not is a matter of objective fact, but it seems completely unknowable by anyone, including S himself! What a useless concept that would be! Perhaps we're best to stick with the subjective version: S experienced sensation X iff S believes that this is so. A fairly empty definition then - a somewhat dishonest one, even - but perhaps more practical?
Well, no, I don't like skepticism. Having the belief is (in most cases) pretty good evidence that you did in fact have the sensation. Since we're all forced to be fallibalists about knowledge anyway, there's not really any good reason to deny that we really do know that we've had sensations. It's just that sometimes, we could be mistaken. Sometimes we know, but other times, we only think we know, though in fact we are wrong. And, so far as I can tell, there's no possible way of telling the two apart.
So, I suppose, if Jonathan wants to argue that we're all mistaken when we think we have sensations while dreaming... well, he could just be right. We could also be mistaken that we have them when awake. [That's quite possibly the most insane thought I've ever had.]
P.S. I don't mean to conflate the two hypotheses. As Jonathan points out, there are actually some good reasons to deny that we have sensations whilst dreaming. To deny that we have them even when awake, by contrast, would just be crazy.