Sorry for the confusion, but I think you do have a burden of proof. To assert your claim that people got it wrong and your new definition is the right one, you have to slog through all the ancient and medieval philosophers' work, to be certain that your revised definition really captures what they were talking about, whatever misconceptions they had aside, and you have to be sure that there isn't something else that is valid, which their definition encompasses but yours does not.
Otherwise, and this is the key point, you can't assert that your version of it is really a correction,
as opposed to something similar but also something else entirely.
Additionally, it's as if you wanted to redefine God as, say, the Big Bang. Doing that doesn't get you anywhere, and moreover things remain mired in the superstitious. It seems a bizarre and needless thing to do.
I think there is some aspect in the irrational usage according to #2 that could be valid but which is not captured by your rationalization in #1, or I might not care as much. Ancient and medieval philosophers got a lot wrong, but they were still, by and large, just as intelligent
as we are.