i) Let's begin with some stereotypes. There's the familiar narrative of the boy who's raised in a "fundamentalist church," but loses his faith in Scripture when he goes to college and studies science.
Likewise, secular science regards creationism and intelligent design theory as ad hoc. These aren't driven by the evidence. Rather, they try to find flaws in conventional science, and propose possible alternative explanations which are merely consistent with the evidence.
Moreover, when the evidence runs out or goes against them, they resort to the deus ex machina. Miracles are consistent with anything. Given a miracle, anything can happen.
Although that's a hostile, outsider characterization of creationism and intelligent design theory, there are creationists who, to some extent, have the same misgivings. Take the so-called problem of distant starlight. A popular creationist explanation appeals to mature creation. However, some creation scientists dislike that explanation because it's a miraculous explanation rather than a scientific explanation. They are trained scientists, and they want to defend creationism on scientific grounds.
ii) There's a grain of truth to these objections, but they are one-sided. If, in fact, God-did-it, then to exclude God from the explanation is special pleading. If, in fact, God-did-it, then a naturalistic alternative is ad hoc.
iii) This also goes to the thorny question of what constitutes a scientific explanation. Atheists think divine agency renders an explanation unscientific. And we'd expect atheists to take that position. But I also find similar confusion among some creationists. Both sides are unclear on how to demarcate a scientific explanation from a miraculous explanation.
Atheists like Lewontin take the position that once you allow a divine foot in the door, anything goes. That, however, is a caricature of the miraculous.
The definition of a scientific explanation is bound up with the definition of a miracle. These are correlative questions. Let's consider two potential criteria:
a) Causal continuity.
A presupposition of science is that the same causes yield the same effects. That also supplies a principle of predictability. Given the same cause, the same effect will result.
And that also supplies a basis for interpolations and extrapolations. We infer missing links. We trace the effect back to the cause through a series of intervening processes or events. The principle is symmetrical and reversible. If the same causes entail the same effects, then the same effects entail the same causes.
But that's consistent with miracles. When a given outcome is the result of a miracle, you have a different result because you have a different cause. A cause that bypasses the ordinary chain of cause and effect (on a classic definition of a miracle).
Take a terminal cancer patient who goes into spontaneous remission in answer to prayer. That doesn't subvert medical science. Absent divine intercession, the same causes have the same effects. It simply interjects a new factor, outside the chain of cause and effect, into the transaction. It breaks into the chain of cause and effect, but the chain resumes after divine intercession.
In addition, some miracles result from a continuous chain of physical cause and effect. Take Ahab's "accidental" death by a random arrow (1 Kgs 22). At one level, that was perfectly natural. The end-result of natural means. Yet it was a prearranged event.
b) Physical causation
A presupposition of secular science is that causes are physical. A natural explanation involves physical causes.
This stands in contrast to mental causation. Physical causes are unintelligent forces or processes. Often inanimate.
Because physical causes are unintelligent, they are invariant. They operate automatically, with mechanical regularity–like a programmed result.
From a Christian standpoint, that's often the case, although that's not a matter of principle. In ordinary providence, things normally happen that way. And that also supplies the basis for linear extrapolations and postulated interpolations.
But in the biblical worldview, causation isn't confined to physical causation. In addition, there is mental causation. Personal agents who have the ability to simply will things to happen.
That does introduce an unpredictable element into the equation. This means that in some cases we can't say with confidence how something happened–especially events where there were no human observers. We can't be sure if it happened naturally or supernaturally.
I'd add that there's abundant evidence for miracles, as well as the paranormal. Indeed, this is underreported.
So a Christian isn't guilty of special pleading when he takes this additional factor into consideration. It isn't just a face-saving explanation. Rather, it's making allowance for genuine imponderables. In many cases, that's not something you or he can rationally rule out.