Mine might not be the most common usage, but I don't think my terminology is messed up spectacularly. At the base of scientific perception is, I aver, faith--no proof exists that compels me to believe what an oscilloscope screen tells me is in any way related to a physical signal, only usage and custom and a continuous stream of accurate results (when the dang thing is tuned right) shore up my belief. This is, at best, strong inductive evidence, not proof.
Striking at the heart of the argument, at the base of logical proof is, I aver, faith in the axioms and predicates, which are, by definition, not proved--ie. taken on faith.
I'm not just being picky. I think the terminology points are of great importance in helping to clarify our thinking. In the case of inductive reasoning, conclusions are based on what is properly labeled "confidence" (not "faith"), which arises from the evidence of previously observed instances involving the same phenomenon. "Faith" is a word used to describe propositions which are accepted notwithstanding zero evidence, which is why I think it's a mistake to use the word "faith" in such a context.
Axioms are also different. We can demonstrate that without a particular axiom (e.g. the validity of sensory evidence), no reasoning can be conducted. This is the kind of logical demonstration which a matter of "pure faith" (e.g. the existence of heaven) is lacking. By being sloppy, and using the word "faith" in contexts where it is inappropriate, we get confused declarations like: "It takes more faith to believe in evolution than in creationism."