Scientists are confronted with things the sciences can’t explain all the time – why do research on something that’s been all figured out? Most of the things that aren’t explained are passed over without notice, but every now and again one finds some non-explained things that cause persons to wonder if we shouldn’t explain them by appealing to God (e.g. the “fine tuning” of the constants in the Standard Model, the low-entropy of the early universe… I’ve even seen fine tuning arguments based on the fact that ice floats). This sense that the absence of a physical law is of theological significance hits some more than others – for some the thought is like a daydream that they would feel strange to say out loud and for others it’s a hardened axiom that we could only fail to acknowledge if we were under the grip of a malevolent, materialist ideology. To someone who sees these problems as interesting research areas, and even chances to win Nobel prizes, such theological speculation is infuriating or at least inappropriate.
It seems that the two responses are mutually exclusive and exhaust all options: either the cause is natural or above nature. But it is possible for both approaches to the problem to be substantially correct. Human knowledge, especially as extended in the sciences, is infinite, and so we can always expect both that we will find a scientific answer to a scientific question while at the same time knowing that to complete this process once and for all would involve a contradiction. Science is infinite but (or therefore) not possibly complete, and so it must relate to the unknown-that-must-be-explained as necessarily explained by a natural cause but never in such a way as to move closer to a totality. The Naturalist is thus right that the universe is causally closed in the sense that there will never be some phenomena that will not eventually be reducible to a natural cause, but this happens precisely because a complete science is a contradiction and so the very ability we have to always find a natural cause also guarantees that this search cannot terminate in a complete explanation. Infinite causes and descriptions are not all possible causes and descriptions.
And so the experimental sciences have an infinity-paradox of their own in that any given phenomena can be explained by a natural cause while (necessarily) not all can be. When we deny the finitude of the ignorance that is gradually driven out by the advance of the sciences, then the “God in the gaps” ceases to be a fallacy, for even an infinite advance of the sciences cannot exhaust that which must be explained in relation to some cause.