One must argue first, cogently, for the existence of the God of traditional theism (hereafter TT--omnipotent, omnibenevolent, eternal, unique) before one can argue that a particular miracle has happened.
A corollary to this is:
A miracle cannot be an argument for TT, which must have been already established, but rather is evidence only for more particular versions of TT--e.g., for Christianity as an extension of Judaism.
I have been fascinated for quite some time with this position, ever since a spin-off of it emerged in Alvin Plantinga's confused discussion of the so-called Principle of Dwindling Probabilities. In the most recent exchange between Esteemed Husband and I, on the one hand, and Plantinga, on the other (in Philosophia Christi), Plantinga was still treating the prior probability of theism (before taking into account the specific evidence for a miracle) as if it were the posterior probability (after taking into account that evidence), and then using the Theorem on Total Probability to argue that an agnostic can never come to believe that, say, the resurrection of Jesus has occurred. The idea from Plantinga was that the agnostic's probability (notice the ambiguity on whether it is the prior or posterior) of approximately .5 for TT will constitute an upper bound on the probability of the more specific proposition that God raised Jesus from the dead, the probability of which must be lower than the .5 probability of TT. But of course the agnostic's prior probability for TT doesn't constitute an upper bound on the posterior probability either of the resurrection or of TT, both of which could, in principle, be as close to 1.0 as you like on the basis of evidence not already conditioned on by the agnostic. And if the agnostic refuses to take into account strong evidence for a miracle that he hasn't previously taken into account, treating his .5 probability as immovable even on the basis of new evidence, then he is simply being irrationally stubborn, and this has nothing to do with probability theory but only with the potential irrationality of agnostics.
Plantinga's argument for the position that a miracle cannot be an argument for theism is a particularly sophisticated one, although it embodies a plain mistake in probability. We cite several vaguer versions in the section called "Hume's Maxim and Worldview Worries" in our article on the resurrection. The assumption behind those versions appears to be that there is such a thing as a prior probability for theism "too low" to be overcome by historical evidence, so that one must cross some prior probabilistic "threshold" before giving an argument for miracles. Sometimes this is expressed by saying that one cannot argue to God from miracles but can only argue from God to miracles.
A particularly surprising statement of the position that context is everything even comes from a philosopher known for his Bayesian analysis of theistic questions, J. L. Mackie.
[W]e should distinguish two different contexts in which an alleged miracle might be discussed. One possible context would be where the parties in debate already both accept some general theistic doctrines, and the point at issue is whether a miracle has occurred which would enhance the authority of a specific sect or teacher. In this context supernatural intervention, though prima facie unlikely on any particular occasion, is, generally speaking, on the cards:...But it is a very different matter if the context is that of fundamental debate about the truth of theism itself. Here one party to the debate is initially at least agnostic, and does not yet concede that there is a supernatural power at all. From this point of view the intrinsic improbability of a genuine miracle . . . is very great, and one or other of the alternative explanations...will always be much more likely – that is, either that the alleged event is not miraculous, or that it did not occur, that the testimony is faulty in some way.This entails that it is pretty well impossible that reported miracles should provide a worthwhile argument for theism addressed to those who are initially inclined to atheism or even to agnosticism. . . . Not only are such reports unable to carry any rational conviction on their own, but also they are unable even to contribute independently to the kind of accumulation or battery of arguments referred to in the Introduction.To this extent Hume is right, despite the inaccuracies we have found in his statement of the case(Miracle of Theism, p. 27, emphasis added).
This position, however, is simply incorrect if taken to be (as it is intended to be) an in-principle argument. While it is of course true in specific cases that a particular prior probability is too low to be overcome by a particular set of evidence, there is no such thing as a "slippery" prior. In principle, any finite low prior probability can be overcome by sufficiently strong non-deductive evidence. One might argue that in fact all of the evidence we have for some particular miracle, such as Jesus' resurrection, is too weak to overcome the prior probability of theism without natural theology arguments, but this claim (which I think is probably false) would not be an in-principle argument in any event.
Another approach to all of this is that of my esteemed blog colleague Ed Feser, when he implies in this excellent post that, since natural theology arguments are so strong, they naturally precede arguments for specific miracles. After all, if you can metaphysically prove TT, why would you start out first with a merely probabilistic argument for a miracle? And once you have given such a metaphysical proof, why would you bother saying that the argument for a miracle was an argument for the existence of God, which had already been proved?
Ed reiterates this position briefly in a comment apropos of the investigation of Catholic miracles:
Re: Lourdes, yes, but that's because God's existence is already assumed on independent grounds. It's not an argument for God's existence. The claim isn't "This sure looks like a miracle; so, probably God exists." It's rather "We already know God exists; and given that plus the specific evidence at hand, this looks like it is probably a case where He has caused a miracle." In general, A-T writers tend to approach the question of miracles only after establishing God's existence (e.g. as part of an apologetic for Christianity specifically) rather than using miracles as themselves an argument for God's existence.
One way of looking at this position, which Ed does not spell out, is a sort of diminishing returns view. If you have an absolute proof for TT, then what is there for probabilistic arguments to add to TT? It has a probability of 1.0. Or even if we allow (as I think we should) for some slippage if you aren't absolutely certain that you got all the steps of your metaphysical proof right, the probability for you will still be fairly close to 1 given high confidence in what purports to be an absolute proof, so there will be diminishing returns from additional arguments from miracles for TT. It would be like a billionaire digging for changing in his couch. Hence, the arguments from miracles should be seen as arguments for something else, something with a lower prior probability "going into" the evaluation of their evidence--e.g., the probability that God is a Trinity, that Jesus was God, etc.
(I had hoped to deal with these issues in the article I'm currently working on on history and theism for a Routledge volume on theism, but space constraints made that impossible, so I'm taking the lazy way and doing it in a blog post. The nice thing about a blog post is that you can put digressive comments like this in parentheses right in the middle when you can't find anywhere else to put them, while not being too bothered by your writers' conscience for doing so. But I digress...)
One immediate answer to the "change in the couch" objection is that it is simply true, as a matter of logic, that an argument that supports the occurrence of a miracle is an argument that supports the existence of the one who did the miracle. This is evident from the fact that "God performed a miracle" entails "God exists," so evidence that makes it probable that God performed a miracle makes it probable that God exists. Perhaps this won't seem interesting, but I think it's rather interesting. In other words, you can't say, "This shouldn't be seen as an argument that God exists" when it is a logically necessary fact that it must be an argument for the proposition that God exists. It's rather like saying that an argument for "Lydia went to the store" shouldn't be seen as an argument for "Lydia exists." It just is an argument for "Lydia exists" whether it "should" be or not, since the proposition that Lydia did something entails the simpler proposition that Lydia exists. (The question of whether I can have my own personal probability for "Lydia exists" raised by that argument, given that, as a good Cartesian, I really do have a probability of 1.0 for "I exist" is complicated and gets into issues like opacity and what I would mean by "Lydia" in such a proposition and so forth.)
Second, I'm afraid that there are some people who are unable to see the force of the metaphysical proofs of TT. Here I include myself, particularly when it comes to Divine goodness. I've really tried, but the interconvertibility of the transcendentals just is over my head. That's not to say that I don't think any natural theology arguments are any good. The ones that seem to me most cogent thus far are something like a Kalam cosmological argument and the argument from mind. But those don't get you to a full TT, whereas the existence of the God preached by Jesus does.
Now, this may well be a limitation on my part. But if I can't see the full force of the a priori arguments for TT, there are no doubt a lot of other people who can't, either. And the prior probability for TT for some person like me, before taking miracles (including evidence of fulfilled prophecy) into account, will therefore be a good deal lower than it is for the convinced Thomist.
Here we enter muddy waters, epistemologically. For if the Thomistic arguments really do work, but I just can't see it, then my probability distribution in that case is, to that extent, incorrect and incoherent. No doubt all of us have areas of incoherence in our probability distributions, especially when it comes to deductive logic and our own failure of logical omniscience. I am strongly inclined to think that such problems in distributions do not necessarily metastasize throughout the whole distribution. That is to say, one could still see correctly the impact of some further piece of evidence even if one were putting it together with a logically incorrect prior. But the fact remains that for people in my situation, or even people who know even less natural theology than I do, the historical evidence for miracles is certainly not going to be a "change in the couch" matter.