How about ethics, anthropology or another branch of the humanities that isn't amenable to the scientific method?
I suppose I'm asking where you draw the line between "distinct from the sciences" and "anti-scientific"?
TBF, all of those can be expressed into binary code and mathematical formulas and mathematical logic, however there does not exist proof that there exist God.
Science requires proving that something exist - not disproving that something that is made up centuries ago does not exist!
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.
Self-organisation to avoid conflict learnt with over millenia of experience in order to survive under a tribe.
Where's the magic in Biology?
Saving our asses as a collective with different and useful roles gave us far more chances to survive than trying to fight for resources alone.