Okay.
Why not? You don't have the free will to choose what you accept as a true? Why can't you accept, as a true, that your cat is a dog? Why can't you believe that?
Yes, you did. You hold the belief that a cat is a cat because you choose to adhere to the proof of identity. It is a choice on your part.
Yes, I can. I might have a medical condition which causes me to perceive colors in that way. I might also choose to deny the proof of identity.
Exactly... This seems like you are open to changing your beliefs about black holes (if convinced that your current beliefs are incorrect). Seems like you have the ability to choose what you believe, and aren't just stuck in believing one way or the other...
Correct. I don't adhere to all common definitions of words; I think that other definitions are much more accurate and better for certain words, fact being one of those words.
You likely meant 'proof' or 'universal truth', as that is what most people mean in most cases of using the word fact...
Dictionaries are not authoritative in any way. They don't define words. -- But yes, you will most likely not find that definition of fact in any dictionary...
That definition comes from Philosophy. What one is doing when they make use of facts is they are assuming a particular thing to be true, regardless of whether it actually is or not... It is a form of shorthand so that people don't have to build an argument for every single little thing that they say... Facts allow for quicker conversation. If a fact is not accepted by all conversing parties, then that fact returns back to being an argument (is no longer a fact). Anything may or may not be a fact, depending upon whether all conversing parties accept that thing as a fact or not...
Reality is experienced differently by each and every one of us, but that doesn't mean that we don't make choices regarding our beliefs... --- I used to believe in amillennialism, but now I believe in a pre-tribulation rapture and a literal millennial reign. In the future, I might believe in something else entirely... I've changed my belief regarding this particular matter, and may do so again...
Sure... I used to reject the Theory of Evolution, but now I believe the theory to be true.