" Our conceptual schemes change (e.g., classical mechanics to quantum mechanics). How do you explain that? "
I think you are looking at the problem from the wrong perspective. It somebody tells me they discovered that one apple plus one apple does not equal two apples, I'll die before I take him seriously. The important issue here is that even if the person is actually capable of putting together one apple, then another apple, and end up with three apples, I can still object that what he's doing is not addition.
I say wrong perspective because you seem to think the solution to the conflict between conceptual schemes and reality has something to do with reality, and it's clear to me that reality has nothing to do with it. For instance, you seem to think quantum mechanics proved classical mechanics wrong, but in fact quantum mechanics could not have been discovered if classical mechanics had never been invented. What really happened was that classical mechanics always contained a paradox, but it took a couple of centuries for the paradox to become obvious.
So my explanation as to why conceptual schemes change is bifold. First, not all of them change; schemes that are perfectly self-consistent, such as the scheme for adding apples, will never change. Second, schemes that embody a subtle paradox will only last as long as the paradox remain undetected.
" Also, you move from possibility to fact, on what basis?? "
That's actually an interesting question. How do possibilities move to fact? How did the possibility that it was going to rain today become the fact that it rained today? Knowledge seems to be the key. The best I can say is that I know it is a fact, but it's very hard to explain why.