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From The God Delusion:
[Theists] are apt to quote the late Stephen Jay Gould's 'NOMA' — 'non-overlapping magisteria'. Gould claimed that science and true religion never come into conflict because they exist in completely separate dimensions of discourse:
"To say it for all my colleagues and for the umpteenth millionth time (from college bull sessions to learned treatises): science simply cannot (by its legitimate methods) adjudicate the issue of God's possible superintendence of nature. We neither affirm nor deny it; we simply can't comment on it as scientists."
This sounds terrific, right up until you give it a moment's thought. You then realize that the presence of a creative deity in the universe is clearly a scientific hypothesis. Indeed, it is hard to imagine a more momentous hypothesis in all of science. A universe with a god would be a completely different kind of universe from one without, and it would be a scientific difference. God could clinch the matter in his favour at any moment by staging a spectacular demonstration of his powers, one that would satisfy the exacting standards of science. Even the infamous Templeton Foundation recognized that God is a scientific hypothesis — by funding double-blind trials to test whether remote prayer would speed the recovery of heart patients. It didn't, of course, although a control group who knew they had been prayed for tended to get worse (how about a class action suit against the Templeton Foundation?) Despite such well-financed efforts, no evidence for God's existence has yet appeared.
To see the disingenuous hypocrisy of religious people who embrace NOMA, imagine that forensic archeologists, by some unlikely set of circumstances, discovered DNA evidence demonstrating that was born of a virgin mother and had no father. If NOMA enthusiasts were sincere, they should dismiss the archeologists' DNA out of hand: "Irrelevant. Scientific evidence has no bearing on theological questions. Wrong magisterium." Does anyone seriously imagine that they would say anything remotely like that? You can bet your boots that not just the fundamentalists but every professor of theology and every bishop in the land would trumpet the archeological evidence to the skies.
Either had a father or he didn't. The question is a scientific one, and scientific evidence, if any were available, would be used to settle it. The same is true of any miracle — and the deliberate and intentional creation of the universe would have to have been the mother and father of all miracles. Either it happened or it didn't. It is a fact, one way or the other, and in our state of uncertainty we can put a probability on it — an estimate that may change as more information comes in.
Since the god hypothesis is a scientific claim, we can compare it to other scientific claims. It's completely inappropriate to grant god the free pass that theists have bestowed upon him for millenia.
With what's implied in the claim "god exists" and what we know to be true about the universe, the only way the probability of god existing can be greater than ZERO is to abandon intellectual honesty and give god a free pass.