When asked to prove that God does not exist, we encounter a fundamental problem in logic and epistemology. The challenge lies in proving a universal negative, especially when dealing with entities defined as transcendent or beyond the physical universe. This is similar to asking someone to prove that invisible unicorns do not exist anywhere in the universe.
The fundamental issue lies in the different domains of inquiry. Empirical science operates within the realm of observable phenomena, testable hypotheses, and measurable evidence. However, many theological concepts of God are defined as transcendent - existing beyond physical observation, outside space and time, and by definition non-empirical. This creates an unbridgeable gap where scientific methods simply cannot address transcendent claims.
This brings us to the burden of proof problem. In logic, the burden of proof lies with the person making the claim, not with the skeptic. While positive claims like 'God exists' require evidence from the claimant, demanding proof that 'God does not exist' creates an impossible standard. We cannot prove the non-existence of something defined as undetectable. Absence of evidence is not evidence of absence, but it is rational to withhold belief until sufficient evidence is provided.
It's crucial to distinguish between arguments against belief and definitive proofs of non-existence. While there are compelling arguments like the problem of evil, logical contradictions in certain definitions, lack of empirical evidence, and Occam's razor, these challenge specific concepts of God rather than proving the impossibility of all possible definitions. These arguments can justify rational skepticism and provide grounds for withholding belief, but they cannot provide the absolute proof that was originally requested.
To summarize what we've learned: Proving that God does not exist is logically impossible because it requires proving a universal negative about a transcendent entity. The burden of proof lies with those making positive claims, not skeptics. While rational arguments can justify withholding belief, they cannot provide the absolute proof of non-existence that was originally requested. This is a fundamental limitation of logic and epistemology, not a failure of reasoning.