As usual, this is better settled by experiment than by "I just know". My favourite method is holding my nose and seeing if I can still breathe through it. Every time I've tried this while dreaming, I've still been able to breathe, and, unsurprisingly, so far I've never been able to while awake. So if I try that, then whichever way it goes, it's pretty strong evidence. There — now it's science and there's no need to assume "I feel that I know I'm awake" implies "I'm awake".

Of course, if you're the sort of person who never thinks to question your wakefulness while dreaming, then the fact that you've thought of the question at all is good evidence that you're awake. But you need a better experiment than that if you also want to be able to get the right answer while you actually are dreaming.

[Apologies if replying to super-old comments is frowned upon. I'm reading the whole blog from the beginning and occasionally finding that I have things to say.]