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It has become a standard line to claim that science and religion are separate magisteria that despite occasional bursts of contention can peacefully coexist sort of like the USA and USSR during the Cold War. In this view science always assumes that it is investigating natural causes, because supernaturalism is not subject to investigation. Both opinions are quite wrong, it not being at all hard to disprove the supposed compatibility of science and paranormalism, or the alleged inability of science to test supernaturalist claims. Contending that science and religion should respect each another is like saying astronomy and astrology should get along with one another, or that physicists and psychics should respect the other -- after all, the latter are prone to citing the quantum mechanics developed by the former to justify belief in ESP. Can you imagine astrology being the subject of a university department in the same manner as there are divinity departments and even colleges? (Actually astrology is taught in some Indian universities, which only goes to prove the point.) Although it can be argued that the existence of the supernatural can never be totally falsified for the same reason I cannot prove there is not an invisible elephant in your room, many if not most acknowledge that modern science has thoroughly discredited the existence of ghosts (that a third or more Americans believe in), speaking to the dead, fairies (that Conan [Sherlock Holmes author] Doyle believed were about the reveal themselves to the world during the fairy craze of the early 1900s), astrology, psychic powers and a host of paranormal beliefs (Gallup finds that three quarters of Americans believe in something paranormal). So exactly why are the gods less subject to scientific investigation and refutation or confirmation?
Of course they are not free from scientific examination. For example, if astronomers showed that the universe was just a few thousand light years across, and geologists found that our planet was just a few thousand years old, and paleontologists discovered that all creatures great and small were present from the get go, then there would be no choice but to conclude that some form of super powerful intelligence had created it all just like the Bible says. Or if articulated elephant skeletons were found in 260 million year old Permian sediments, then it could only be concluded that some form of intelligence rather than natural evolution was running the big show.
Instead science has found not the slightest evidence of the existence of supernatural creator in the same manner it has failed to uncover good reason to conclude ghosts or poltergeists exist. This leaves theists with two, desperate, alternatives. One is to claim that science has in fact disproven natural evolution via Intelligent Design Theory. Because ID is nothing more than the god of the gaps pseudoscience that is creationism even most theists don't go for it. That leaves most religious supernaturalists including believing scientists, Francis Collins most prominent among them, resorting to the equally bogus argument that since you can't absolutely falsify the existence of supernatural beings that believing in gods is just fine even though in doing so they are sinking to the same silly and pseudoscientific tactic used by supporters of ghosts and psychic powers.
Since it is egregiously evident that scientific methodology can be used to investigate many religious claims, then why the widespread denial of the fact? For science-friendly theists the reason to push the fallacy is obvious; if they don't opt for the delusion then advanced science threatens to ruin their faith-based paranormalism. For science-oriented nontheists the reason to at least go along with the misapprehension is also obvious; many just don't want to upset all the theists if they don't have to, all the more so because the godly voters and politicians have a lot of control over governmental science funding. Why stir up trouble?
A basic problem with faith-based belief is that it is at worse obstinate opinion held despite the facts to the contrary, and even at best is wildly speculative opinion that is no better than other discredited forms of improbable supernaturalism. Science-based conclusions are superior because science tries to objectively go wherever the data and analysis indicates the reality lies. That's how science has shown that a myriad of diseases are caused by microbes, that the earth is a sphere orbiting a star in a colossal universe, that evolution has occurred over deep time, that it is not possible for a moral creator to exist, and that the most atheistic democratic nations and regions are the most successful (the last two items being subjects of this series).
