Words often confused us because we fail to press for a definition of the term. Or we can say, words often fail us because we are confused as to their range of meanings. Consider the word proof.
It has muscle, this strong word. It is insistent. “I need proof!” we demand. “There is no proof!” we insist. Or, “You may not believe it, but there is no proof.”
Perhaps this strong word needs to be tamed and not allowed to run so free and reckless across the intellectual landscape. We need to rope in this beast. But what is the range of its meanings?
Proof may mean that we evidence sufficient to warrant absolute certainty. If A=B and B=C, then, A=C. The proof is simply in the understanding of the terms. It could not be otherwise. Even an executive order could not change the conclusion, given the premises.
But few items of our knowledge know of such cognitive assurance. To be sure, we are lost without these kinds of proofs. But there is more to knowing than this. I know full well that my wife is not an alien, but I do not know this in the manner of an absolute proof about which I cannot possibly be mistaken. It is logically possible that she is an alien. However, I have no positive evidence that she is–or that my dog, Sunny, originates from outside the galaxy. The upshot is that most of what we know is defeasible. It could be shown to be wrong. However, we do not need proof in the strongest sense to have knowledge, which is justified true belief.
Proof can also mean “evidence sufficient to convince.” This is a looser sense of the word and is not as commonly used. We might say that we have overwhelming reason to believe P. Thus, it is proven. For example, we have ample evidence that the holocaust occurred. This means that the overwhelming burden of proof is on anyone who would deny it, such as the recent Presidents of Iran.
Now we come to religion. Some trouble the air without wisdom by insisting, “You cannot prove God exists.” By this, they usually mean that you cannot establish the existence of the Christian God in the manner of: if A=B and B=C, then A=C. Perhaps not. Nevertheless, one may reasonably believe in the existence of a personal, infinite, and transcendent being without relying on arguments that confer absolute certainty. The matter—and no small matter it is—concerns whether this being exists and what manner of evidence and reasoning is required to have the knowledge that this is so.
To finish up this epistemicprimer, one may be justified in belief P (about God’s existence or about anything else) without having incontrovertible evidence or total certainty. We rightly believe in the existence of all manner of things without proof in the strongest sense–in teeth, tulips, turnips, and toasters; in planets, insects, parsnips, and posters; in virtues, vices, values, and lobsters; in gravity, levity, tragedy, and comedy. We believe in the past we cannot see, in the future not yet here, and in the “what if” that has never been and will never be. Yes, we do; and all without proof.
Now that this is cleared out of the way, perhaps we can get on with considering arguments for and against the existence of God, not being weighed down by the unnecessarily tonnage of proof.
 Epistemology – Philosophy: The study of knowledge; how we know what we know.