If God is going to interact with the physical world, as is claimed when he performs miracles, he could then be detected by science. But if there is no physical way to detect God, then how could we possibly know about Him outside the want or desire for this to be true?
The first thing to note is the claim that God ‘interacts’ in the physical world. The classical theist rejects this on grounds that God is continually acting in the world by divine conservation. There is no contingent thing that exists at any time which is not given its act of existence by God. And this conclusion is demonstrated from metaphysical inquiry, reasoning from the sensible to the supersensible. God is not necessarily doing more in the world when a miraculous event occurs then He is at any other time.
The second thing to note is the claim that, if a miracle is performed, it could be detected by science. The rationale here seems to be that miracles occur in the physical world and anything that happens in the physical world is reducible to scientific observation. I think this misses the mark for several reasons. First, miracles are by nature infrequently occurring and unique. There is no intrinsic repeatability or controlled environment with which miracles could be studied with the rigors demanded by science to the extent that the claimant would be satisfied. Further, even if they could be, what would be observed in a laboratory miracle situation is simply the effect. The cause of a miracle is supernatural, as this is just what a miracle is. Thus, while the effect (miracle) is observed, the cause is not. Science comes up with a blank as to the cause of the miracle because the cause of the miracles is not within the realm of inquiry.
At this point, the skeptic thinks the theist is simply offering a gap argument along the lines of “I do not know the cause of X, therefore God must be the cause of X.” And then usually something like the scientific revolution is shown in contrast beliefs across the world to illuminate the foolishness of people thinking God or gods cause certain phenomena when certain phenomena are perfectly explainable by science. It is not demons possessing a person to make them sick, they simply have a virus. And so forth.
But the skeptic must be in tune with the claim the theist is actually making about miracles. The theist is not making a gap argument when he says miracles are possible, and at least some miracles have occurred. The theist is stating that, in certain instances, God acts in particular ways, sometimes through particular individuals, for particular reasons. If God exists, then He is constantly acting in the world by upholding every single existing thing in it. And, if God exists, it is the case that His effects are known and visible; and these effects may be known and visible in ways that are non-normative.
What seems to underlie the above claim against miracles is an a priori commitment to scientism. This is the belief that only the physical scientific disciplines can deliver true knowledge about the world. Much has been written on this subject, and I will not rehash this issue right now. The only thing that I will say is that the claim of scientism is not often defended in the philosophy of religion by atheists/agnostics. Some philosophers of science might defend variations of this position, but, in its purist sense, scientism hearkens back to strands of logical positivism, a la Carnap, Ayer, and friends which are notoriously difficult to defend.
The skeptical claim against miracles we are considering also begs the question against the theist and possibly creates a straw-man. The argument seems to imply “if God exists, He should be detectable by science. God is not detectable by science. Therefore, God does not exist.” But the theist makes the explicit claim that God is not physical. Since the domain of science, at least the ‘hard’ sciences advocated by the skeptic (note the implicit emphasis on empirical observation, testing, etc.), is physical, there is a complete disconnect from what the theist is arguing. Here the skeptic essentially denies God’s existence because God is non-physical. But the very nature of God is non-physical, and this is indeed what the theist claims. Nothing the theist says should lead one to think that God should be detectable by scientific methodology employed in the physical sciences.
There is not much to say regarding the claim about knowing God by our desire for Him to be real. This claim has been played out from Marx to Freud. And the conflation of metaphysical and epistemological claims is palpable. I tend to condense this down to the claim that God only has cognitional being or is a being of reason. This is to say that God exists in the same way hobbits and Star Wars characters do; they exist in the mind of existent beings but do not have their own independent acts of existence. Thus the skeptic claims that God only exists in the minds of theists, by their own acts of will or desire. And the only supposed way out of this conundrum for the theist would be if God was subject to verification of the physical sciences.
But the theist claims that God is Existence, is Pure Act, Being Itself. And this is a distinctly metaphysical claim. It is impossible that God exist within the existential act of another being. It is God who gives the act of existence to the finite being who discursively reasons from effect to cause.