"God of the Gaps" is a term that atheists often use to describe the nature of theistic belief in a world where science provides increasingly more natural explanations for things that were once explained by God. Perhaps the most striking example of natural explanations replacing theistic ones is the origin of animal species. This was once though to be the work of a divine intelligent creator, but now science has eliminated the need for any "goddidit" explanations. There is a powerful and elegant explanation that does a much better job of answering some of the tough questions associated with the old theistic theory, such as "why are there so many apparent design flaws that are shared among related species?" The theist at best can offer only a hand-waving rationalization, while the evolutionist can give a detailed explanation of how these things occur. And so the natural explanation proves to be superior to the theistic one, which falls by the wayside. And this is what happens in one field of science after another. As science progresses, theistic explanations vanish. Theists who once explained all of nature in terms of godly and supernatural forces are reduced to invoking these explanations for the dwindling number of things that have not yet been fully explained by science.
As scientific knowledge expands into new areas, and more completely fills our understanding of the observable world, the holes or gaps in that knowledge continue to shrink, and along with that, the realm of supernatural explanations is rapidly vanishing too. Theists cling to those ever-shrinking areas where scientific knowledge is still lacking to hang on to their persistent "goddidit" explanations. Their God has been reduced to hiding in the dark shadows where empirical knowledge has yet to penetrate. This God can't reveal itself to human observation, because whenever science examines empirical evidence, the superior explanation for what is observed always turns out to be naturalistic.
This is a matter of considerable embarrassment to theists. They are well aware that theistic explanations are losing ground to science, and they don't have any good response. They turn to explanations that emphasize the hidden aspect of God's works. Instead of claiming that God designed animal species and placed them on the earth as is, they now tout "theistic evolution", which claims that God is still running the show, but in a way that is completely unobservable. Instead of claiming that God cast fire and brimstone at a sinful city, they say God caused a volcanic eruption by fully natural means under his control. The problem with explanations like this is the simple fact that nature alone is sufficient to explain these things, and there is no evidence and no reason to add God into the mix.
Still, they are unwilling to relinquish their deeply-held belief that God is behind it all. To the theist, everything in the observable world is evidence of God. That's nice, but if we're talking about what theory provides the best explanation for the things we observe in our world, then invariably, the naturalistic explanation is superior. Nature is simpler than nature plus God. And nature without guidance answers more questions satisfactorily than nature with God's intelligent guidance. Theists need to face up to the fact that the evidence does not point to any kind of supernatural influence in our world.
Theists have asked if there could be any observable evidence that would convince the naturalist that there must be some kind of supernatural influence at work. The question has been answered many times. For example, Jerry Coyne said this:
There are so many phenomena that would raise the specter of God or other supernatural forces: faith healers could restore lost vision, the cancers of only good people could go into remission, the dead could return to life, we could find meaningful DNA sequences that could have been placed in our genome only by an intelligent agent, angels could appear in the sky. The fact that no such things have ever been scientifically documented gives us added confidence that we are right to stick with natural explanations for nature. And it explains why so many scientists, who have learned to disregard God as an explanation, have also discarded him as a possibility. - CoyneOthers have responded in a similar manner. The common thread in these responses is they they want to see something that is clearly not natural - or to put it another way, something that is clearly supernatural - something that is not consistent with natural laws. Answers like this are never satisfactory to theists, because they know perfectly well that there are no observable supernatural events, and there never will be. The evidence we have in our world simply does not support their supernatural beliefs. And instead of following where the evidence leads, they belittle the naturalist who insists on having evidence to justify belief. They accuse him of scientism. They accuse him of being blind to the truth.
In at least one case, the naturalist who wants to see evidence of the supernatural is accused of using god-of-the-gaps reasoning. Shadow To Light says this about Coyne's answer. It strikes me as bizarre, but if viewed in a simplistic manner, there is a certain logic to it. Mikey says that if Coyne could see something that isn't explained by science, and then attributes that to God, then he is guilty of god-of-the-gaps reasoning. From a scientifically ignorant perspective, that probably sounds like a legitimate complaint. But the scientific ignoramus doesn't understand the implications of Coyne's request for evidence.
To people who have no genuine appreciation for science, naturalism and theism are just two possible ways of explaining things, and you can pick your choice. But one is based on comprehensive observable evidence, and the other is based on belief that has no substantial basis in empirical evidence. People who demand to see evidence of the supernatural before believing it note that everything in the world follows natural laws - everything. And even though those laws may not be fully known to us, it's still true that everything follows natural laws, without exception. Objects that have mass are subject to gravity, and that will always be true, even if we don't yet know everything about gravity. There are no exceptions.
If an ordinary rock starts flying through the air, hovering, and moving through walls without damaging them, there might be three ways of explaining it. First, there might be a supernatural explanation, where the laws of nature are being violated by some supernatural force. Second, there might be some technology that is unknown to us that uses the laws of nature in a mysterious way to cause this event. Third, there might be some as yet unknown law of nature that explains this unusual phenomenon.
Let us dispense with the latter possibility right away. The laws of nature describe regularities in the way things work. This flying rock is not acting in accordance with any kind of regularity. This is a unique behavior. No other rock does this, or has ever done this. It's not compliant with any law of nature - not even one that we have yet to discover, because it doesn't exhibit any kind of regularity. It would be different if we observed this phenomenon from time to time under certain conditions, but that's not the case. This event is unique - never, ever seen before, and different from the regular behavior that we always observe. It is a violation of natural law.
Let us now dispense with the second possibility. Sure, there could be some technology that does this, but under the assumption that mankind currently has no such technology, we still can't explain what is observed. Are there aliens making this happen? Perhaps, but we don't see them, and we have absolutely no reason to think that alien beings are visiting us. All we have for evidence is a rock that does strange things, and no device or any observable thing that causes it.
That leaves us with the only remaining possibility that might make sense. There must be some kind of supernatural influence going on. And why should we think this is the case? Because we have evidence. We have an observable phenomenon that, as best we can tell after eliminating natural explanations, is supernatural. Will scientists try to find a natural explanation for it? You bet they will. But if all such efforts fail, then the only recourse is to explain it as supernatural.
The fact is that everything in our experience so far has been amenable to a naturalistic explanation. Everything does behave according to the regularities of nature, and there has never been a single verifiable exception to this. That's precisely why naturalists believe that naturalism is true. But theists insist that there are supernatural things, yet they can't show us any evidence of it. We just need to see evidence for what we believe. If a frustrated theist like Mikey tells us that our demand to see evidence is just god-of-the-gaps reasoning, he should be reminded that his God of the gaps is not based on any empirical evidence. It is a God that hides in the shadows, refusing to be seen. His accusation is nothing more than a child's retort: "I know you are but what am I?" The gap is between his ears.