This series isn't about showing why theism is wrong. I'm trying to clarify the nature of atheism, by sorting through some confusions about it. It's more a matter of analysis than of criticism.

Just to clarify, I wouldn't equate evidence with proof. Proof deals with necessities and is about the relations between concepts, whereas evidence is empirical and it establishes probabilities. Proof is a priori, whereas evidence is a posteriori or empirical. That's why the evidence is typically mixed for any empirical question, so we have to play the odds or side with what seems most probable.

Proof is technically what you offer in math or logic class when you show your work. You prove a theorem by showing how it follows logically from certain premises. Proof is deductive, whereas the question of whether something exists is inductive and isn't decided just by armchair reasoning or analysis, contrary to philosophical rationalists, Thomists, and confused theists.