In determining whether a miracle took place, we should not begin our inquiry by presupposing it did or didn't -- for the same reason that you should not do so in any inquiry. If you begin by presupposing your conclusion (whether it be "X happened" or "X didn't happen"), you're making a circular argument, which is invalid. Of course if you start with your conclusion you're going to end up with your conclusion. The whole thing would be question-begging. Thus when making any investigation we should begin from an agnostic perspective; X may have happened and it may not have. This is the only way to let the evidence decide.
This agnosticism is only methodological. It's not necessary or desirable to evacuate whatever beliefs you have about something in order to investigate it. It's simply a matter of putting the beliefs you have to the side for the sake of the investigation. Moreover, by "agnosticism" I'm not referring to the usual sense of this term -- namely whether or not God exists -- but rather to openness regarding the issue under investigation. Of course, here I am talking about agnosticism regarding the possibility of miracles, and this would obviously have some relevance to the existence of God. But this would merely be a particular application of agnosticism: we should be agnostic about whether miracles take place prior to our investigation, and since a miracle is an act of God, it would also mean agnosticism as to whether God acts in the world. We should keep open the possibility that he does not (perhaps because he doesn't exist) as well as that he does, and let the evidence decide.
Assessing an explanation, whether it be historical or scientific, proceeds according to "inference to the best explanation", what Peirce called "abduction". Thus, a miraculous explanation should be preferred to its naturalistic alternatives when it is the best explanation. There's a massive literature on inference to the best explanation, but suffice it to say that it is the method by which all of science, as well as history, operates. We can't dismiss it without having to give up all of science with it -- the significance of this being that the most common objection to miracles is that it allegedly contradicts the scientific view of the world.
Many object to this by claiming that if we allow possible miraculous explanations then there's no justifiable stopping point. Anything could be explained by contriving some miracle to account for it. In the first post I contested this by pointing to a very obvious test, one of the tests used in inference to the best explanation: whether an explanation is ad hoc or contrived. To illustrate, the implausibility of conspiracy theories is at least partially due to their ad hoc nature; they posit all sorts of fanciful connections between insignificant events while ignoring more relevant events that don't fit the narrative.
The problem with ad hoc hypotheses is that they're contrived. Virtually any claim could be defended by such tactics. So, for example, Marxists insist that the only type of cause of historical change is economic factors. They use economics in an ad hoc way, plugging all the holes in our knowledge, and "explaining" any possible historical change by it. But of course their misuse of this doesn't allow us to conclude that economics does not play a role in historical change. Just because someone uses something in an ad hoc fashion doesn't mean that we can dismiss it in its entirety.
Now it's generally assumed that supernatural explanations are ad hoc by definition, but this is simply false. I showed this in the first post by contrasting two explanations of the evidence surrounding Jesus' alleged resurrection: the miraculous hypothesis that Jesus actually rose from the dead and the naturalistic hypothesis that Jesus had an evil twin. Obviously the evil twin theory is more ad hoc than the resurrection theory, even though it's naturalistic. Thus supernatural explanations are not automatically ad hoc -- some fit the facts very well. Just as we can't dismiss economics as a motive force in history because some people do so in an ad hoc way, so we can't dismiss miraculous explanations because some people do so in an ad hoc way.
Everyone acknowledges that some claims of miracles are more bizarre, more ad hoc, more implausible, harder to believe, or whatever, than others. C. S. Lewis makes this point in chapter 13 of Miracles:
Whatever men may say, no one really thinks that the Christian doctrine of the Resurrection is exactly on the same level with some pious tittle-tattle about how Mother Egarée Louise miraculously found her second best thimble by the aid of St. Anthony. The religious and the irreligious are really quite agreed on the point. The whoop of delight with which the sceptic would unearth the story of the thimble, and the "rosy pudency" with which the Christian would keep it in the background, both tell the same tale.
So, for example, a supernatural explanation that did not have any empirical effects would be ad hoc and should be rejected. Some people seem to think that a miracle, by definition, has no empirical effect, and thus can have no empirical evidence to support it, but again, this is obviously false. For example, if the claim is that a man dead for three days was resurrected, some obvious empirical effects would be that the grave or tomb is empty, or that people saw him alive, then dead, then alive again. We can certainly have evidence of these effects, and if the miraculous explanation is the best explanation of them, we then have evidence of a miracle.
The same objection can be put a different way: miracles are not predictable, and therefore no moment is more privileged than another with respect to them. Thus, we could appeal to a miracle for any and all historical explanations. But this objection would apply equally to naturalistic events that are rare or unique. No moment is more privileged than another with respect to meteor strikes, for example. So when should we appeal to a meteor strike as a historical explanation? Obviously when we have specific reasons for suggesting a meteor strike took place -- that is, when it's not ad hoc. The fact that meteor strikes, rogue waves, and many natural phenomena are unpredictable does not justify us in excluding them as explanations unless we begin by assuming that they never happen. But if we make such an assumption, no amount of evidence could ever convince us that they have happened, because we have begged the question against them. We have concluded they don't happen because we started by assuming that they don't happen. But obviously, the fact that this event
was unpredicted does not mean that we can't offer it as an explanation of what happened afterwards.
This applies equally to miracles. We are justified in considering a miraculous explanation when we have specific reasons for suggesting a miracle took place. If we don't have specific reasons for suggesting it, it would be ad hoc.
It might be objected further that we can have corroborative evidence from other fields for rare natural events. There are a few problems with this though. a) It could easily not be the case. There are plenty of occurrences of "falling stars" throughout history that we only know via historical testimony. b) Corroborating evidence from another field could certainly be helpful if the historical evidence is inconclusive. But if it's not, if the historical evidence is sufficient, it's not needed in order to draw a conclusion. c) If miracles have empirical effects, as I've argued, then theoretically we could have evidence of those effects from more than one field.
In going over all these points in the comments to the first post, a continued objection was that we can't say beforehand what a miracle would look like. As I've already argued, however, this is obviously false: if the claim is that a dead man was resurrected we have some very obvious ideas what it would entail (an empty tomb, post-mortem appearances, etc.).
What this objection is asking is what limitations or predictions can we make about miracles a priori. But we can't assess limitations or make predictions a priori about natural events either: our knowledge of the natural world is based on our experience of it a posteriori. We can't determine the likelihood of a meteor strike or predict what one would look like until we have some a posteriori experience of them. If it's suggested that we could make some judgments based on the nature of matter, that just pushes it one step back: we can't make a priori judgments about matter, we can only make a posteriori judgments about matter based on our experience of it. Thus, in claiming that miracles be predictable, the objector is making a demand that natural events would not be able to meet. In fact he is holding the supernatural to a standard that nothing could ever meet, and then using that as a justification for not considering the possibility that miracles have actually taken place.
In other words, it doesn't really matter what the facts are or what the evidence says. These critics reject any miraculous explanation in such a way that they can get the same answer without having to look at the evidence. A priori.
Update (15 Feb 2010): See also part 1, part 3, part 4, and part 5.