A fellow Mathematician. How Fun! The problem with using empirical datat to “prove” truth is the problem of induction. In science, we begin with specific events and devlope universal rules/laws from those specific events or experiments. Thus we reason from the specific to the universal. The problem with such reasoning will become very clear: Let us say there is a man and he sees a flock of white ducks. It is the only flock of ducks he ever sees. The next day he sees another flock of white ducks. This happens several times a year for this man. He has the same repeated experience. So naturally, he assumes that all ducks are white. You see, through induction he has reasoned that because of his specific experience, the universal law/reality must be that all ducks are white. However, this is wrong. His induction has lead him astray. So, in sense, induction is really one big logical fallacy. Deduction, on the other hand is not prone to this problem because in deductive logic we argue from the universal to the specific. For example, the universal law is that all men are mortal. I am a man. My specific conclusion is that I am then mortal. Good reasoning. Now I do not suggest that we pick or premises to begin our arguments out thing air. That would be nothing more than axiomatic reasoning. But I suggest that we begin the reasoning process with INESCAPABLE premises. For example: The law of noncontradiction. It is impossible to escape such a premise: Something cannot be A and not A at the same time and in the same relationshiop. Even a denial of the law of non-contradiction affirms the law of non-contradiction. If I say that the law of non-contradiction is invalid, I exclude the law non-contradiciton from being valid. But if contradictions can be true, and the law of non-contradiction is false, then it is also true, because the contradictory statement: the law of non-contradiciton is invalid and valdid must also be true. Thus the law of non-contradiction is true. But wait, didn’t we say it was false. But being false, it is true. Hmmmmm. The law of non-contradiction is an inescapable premise. If you affirm it or deny it you end up affirming it. So it is an inescapable premise that is a good place to start the reasoning process from.