A positive mystery P is something that is intelligible (an epistemological feature of it) but not necessitated—which is an ontological feature of P. That means that, in principle at least, P is explicable in a way that is complete for purposes of the appropriate sort of explanation but is not exhaustively explicable, as if P were explicable-in-principle in a way that would show that P had to be so rather than not. Obviously, what all that means in turn depends crucially on how the concept of explanation is itself deployed. I shall deploy it by way of arguing that miracles, properly so-called and if any, are cases of the positively mysterious. Having done that, I shall argue that Scott's critique misses the point of the Vatican's miracle-vetting process.
When discussing the miraculous, there are two main questions to answer at the outset, or at least to get as clear as we can get about them: (1) What does it mean to call some event a miracle? (2) When may we count some event as a miracle in that sense? Answering (1) leads us toward what analytical philosophers call the "intension," or the conceptual content, of the term 'miracle'; whereas (2) is about how to decide when to count some event as falling under the concept of miracle, as belonging to the "extension" of the concept. Now, since the occasion for this whole discussion is the Vatican's process of miracle-vetting, it must be stipulated that the relevant concept of the miraculous is craftbound. We're not using the term 'miracle' in just any old way in which it can be and has been intelligibly used; rather, we're following (or trying to follow) the Catholic Church's traditional use of it, which is an irreducibly theological one. It would be idle to criticize the Vatican for not answering (2) aright if we are not using the same concept of the miraculous that the Vatican is using for the purpose in question.
One part, but only one part, of the relevant concept of the miraculous is that miracles are "supernatural." Thus, calling a given event a miracle means, among other things, that it is "beyond the order of all created nature," to use one of Aquinas' definitions. To affirm that a miracle is a supernatural event in that sense entails, among other things, that no proposed scientific explanation of the event, if any, could be adequate as an explanation. In such a case, we do not merely happen to lack a scientific explanation in the present; rather, no such explanation would be appropriate to the subject matter and thus useful as an explanation. This is the sense in which I can agree with Scott that "empirical evidence is completely irrelevant to the question of the miraculous in general." If we're using the term 'empirical evidence' just to mean the sort of evidence that natural scientists as such can and do count as evidence, then no such evidence could suffice, even in principle, to establish that such-and-such an event is a miracle—for one cannot use the methods of natural science to establish that anything is actually supernatural. Nor can one legitimately infer just from the absence of a scientific explanation that some empirically observable phenomenon is miraculous. That's also why I don't like the Intelligent-Design movement any more than Scott does: from the fact that we cannot now explain certain features of living things without recourse to intelligent design by a (presumably) supernatural being, it does not follow that we could not do so even in principle. Where Scott and I differ is in the conclusions we draw about how to identify events as miraculous.
He concludes, in effect, that the sort of thing the Vatican does in vetting alleged miracles of healing is wrongheaded. If "empirical evidence is completely irrelevant to the question of the miraculous," then neither the presence nor the absence of associated, empirically observable phenomena is relevant to deciding whether some medically inexplicable cure is miraculous, and the Vatican must therefore be wrong to consult scientists when assessing reports of miracles of healing for their credibility. But that cannot be the right conclusion to draw.
For one thing, it does not because it cannot apply to any and all miracles, and thus to "the miraculous" merely as such. Consider, e.g., that miracle without which, St. Paul says, our "faith is in vain." If Jesus rose bodily from the dead, then the empty tomb could be observed as such and, according to New Testament, was in fact so observed. That is a very much an "empirical" phenomenon—which is why the Shroud of Turin could be the very burial cloth in which Jesus' body was wrapped when it underwent that miraculous transformation entailed by what we call "the Resurrection." But of course, natural science cannot establish that that's what the Shroud is; all natural science can do is rule out some natural explanations and entertain others as (possible) hypotheses. To see the empty tomb or the Shroud as miraculous, the eyes of faith are required. But it must not be said that any and all observable facts are irrelevant to deciding whether to count some event as a miracle. All that can be said is that, if there are miracles that manifest themselves in what's observable, then those observables cannot be adequately explained by the investigatory methods of natural science, and instead require the eyes of faith for adequate explanation. Hence even though, for reasons I've stated, the absence of scientific explanation for certain alleged cures is something to expect if those cures are miraculous, it neither follows nor is true that "empirical" facts, in the sense of "observable" facts, are simply "irrelevant" to identifying some events as miraculous.
All this suggests what I believe ought to be obvious: it is not enough, for purposes of identifying some observable event as a miracle in the relevant sense, to say that it is somehow beyond the order of nature. Things we can observe from within nature must be relevant, and relevant in a certain way. What's relevant here is not just the mere fact that we can observe the event from within nature. It's not even just that certain particular, observable features of the event itself are relevant. What's equally and crucially relevant is the spiritual context in which the event occurs.
Thus, in deciding whether a given medically unexplained cure is miraculous, the Congregation for the Causes of Saints does not merely note the absence of a medical explanation for what has been observed as fact. It verifies, by reasonable means, that the cure occurred some identifiable time after the proposed saint's intercession was invoked in faith for the purpose. In this sort of case, that is the spiritual context in which the event must have occurred in order to be counted as a miracle in the relevant sense. And so, in addition to being supernatural in the general, ontological sense I've already specified, the miracle must be supernatural in an epistemological sense: it must be seen as such by the eyes of faith. Since that is how miracles are presented in Scripture and Tradition, as well as by the experience of the faithful, I see no need to defend my claim beyond noting its status in those sources.
To answer the question I labeled above as (1), therefore, we should say that a miracle is a event "beyond the order" of nature that is seen as such by the eyes of faith, in such a way as to signify God's love and power to those with eyes to see. That's what it means to call an event a miracle in the relevant, craftbound sense; that's the intension of the relevant concept of the miraculous. To answer the question I labeled above as (2), therefore, we should say that we "may" count, and thus are justified in counting, an observable event E as a miracle in the relevant sense when it can be shown (a) that there is no scientific explanation for it, and (b) that it occurs in a spiritual context suggesting that no such explanation would be of the appropriate sort for E. That's what gives us the extension of the concept of the miraculous.
Now if all that is so, then regarding some event E as a miracle in the relevant sense is not merely to classify E. It is to classify E in such a way as to imply that only a certain sort of explanation would be appropriate to E and, at the same time, to actually adumbrate such an explanation. No such explanation, of course, could show that E had to occur given what is said to explain it. Miracles in the relevant sense are not mechanical or even stochastic outcomes of the laws of nature working on initial conditions; nor are such miracles magic, as if invoking God or the saints could automatically make them happen. They are extraordinary and gratuitous manifestations of divine love and power. But they don't just happen for no reason: they happen either in response to acts of faith or to elicit such acts. So, miracles are indeed explicable to a degree and to the eyes of faith. But the way they're explicable does not and, indeed, cannot show that they have to happen given what explains them. The explanations, at least in principle, are as complete as the nature of the explananda permits, but not exhaustive. Miracles in the relevant sense are thus intelligible but not necessitated. They are what I call "positive" mysteries.
Now if that's what miracles in general are, then Scott's critique of the Vatican's miracle-vetting process simply misses the point. If the concept of the miraculous as I've been limning it even roughly corresponds to the concept the Vatican is following, then we should expect the CCS to verify the absence of scientific explanations for certain cures as part of its vetting process. For miracles in the relevant sense just aren't the sort of thing, ontologically speaking, to which scientific explanation would be appropriate. Of course it does not follow, from the mere absence of a plausible scientific explanation for it, that a given cure is miraculous in the relevant sense. All that follows is that, if the cure is miraculous in the relevant sense, then no such explanation could be relevant even if offered. Thus the absence of such an explanation is, itself, one kind of evidence needed in order to be justified in claiming that some event proposed as a miracle in the relevant sense is, in fact, such a miracle. It is not sufficient evidence by itself, but it is necessary.