> So, your argument is that methaphysics is based on belief and no logic?

I'm really not sure where you think I said that. And I think it's a false dichotomy in any case. Logical argument has a place in metaphysics but logic requires agreed axioms and those axioms are by definition not amenable to logic.

In general you seem a little bit unclear about the difference between induction and deduction. I'm always a little uncomfortable when people repeatedly use the word "proof" around when defending or defining science. Science doesn't really "prove" anything except in the most causual and colloquial use of the word. Science is always provisional. Proof belongs in mathematics not empirical science.