Every method of “proof” available to us is a human-devised system, based on formulations of logic we are able to comprehend. It might surprise you to know that many such systems exist: for example, constructive logic (where proof is given by a truth witness), and classical logic (where proof may depend on axioms we hold always to be true).

If proof is a system of human construction, it can only establish proof for questions posable within that system. That is, it can only answer questions within its own sphere. The reason we can prove “1 + 2 = 2 + 1” is because we know the definition of “+” and the meaning of the symbols “1” and “2”. Without that knowledge — if “+” is left undefined, for example — it becomes unprovable.

Therefore, since any deity is, by definition, beyond human understanding, any proof system we devise cannot apply to it, either positively or negatively. We just can’t know, exactly because we don’t know.

I think Wittgenstein stated it quite succinctly when he wrote: “The limits of my language means the limits of my world.”