1. The definition of "Miracle"

The problem I wish to investigate is the relation between science and religion, with a special focus on religion's appeal to miracles. Let us define a "miracle" simply as an event which violates at least one law of nature. I realize that the term is used in other ways. For example, it is sometimes additionally required that miracles be caused by a supernatural being. For our purposes and in the interest of economy, that further requirement can be dispensed with. Alternatively, a miracle is sometimes taken to be any extraordinary event, particularly one that provides someone with a great benefit. That is certainly another use of the term in English, but not relevant to our topic, so let us disregard it. If we employ the definition initially given, that will allow us to focus on a particularly troublesome puzzle in the philosophy of science.
If miracles violate laws of nature, then they could never be explained by appeal to natural law. Note that it needs to be a genuine law of nature that is violated by a miracle, not a manmade generalization erroneously taken as a law of nature. This needs some clarification. By a law of nature I mean a proposition which describes an actual uniformity that obtains in our universe. An example would be the Archimedean Law that a floating body always displaces an amount of fluid the weight of which is equal to its own weight. And an example of a miracle which violates that law would be a man walking on water (thereby displacing an amount of fluid the weight of which would be considerably less than his own bodyweight). In science, events are explained naturalistically (i.e., by appeal to laws of nature), so a miracle would be an event that could never be explained in that way. But if events which cannot at present be explained in that way were to come to be explained naturalistically in the future, then, in retrospect, it would need to be said of them that they were never miracles, although they may at one time have (erroneously) been thought to be that. At the very least, the laws that miracles violate need to be genuine ones.
Consider an example. Centuries ago, it was regarded a law of nature that matter cannot be destroyed. Thus, an event like an atomic explosion, in which matter is destroyed, would at that time have been considered a miracle, for it violates the given law. But subsequent science came to abandon or amend the law in question in such a way that atomic explosions no longer violate natural law. A miracle, then, must be regarded, not as an event which violates current law (which may very well come to be superseded), but an event which violates one or more genuine laws, i.e., ones which can never be superseded by laws of nature which are more accurate and which cohere better with other parts of science.
What would be the status of laws of nature if miracles were actually to occur? First, would they cease to be genuine laws? If we say that a generalization that is violated by some event cannot be a genuine law of nature, then it would follow that miracles are logically impossible. That can be shown as follows:

(1) Miracles, by definition, are events which violate genuine laws of nature.
(2) If a generalization is violated by an event, then it cannot be a genuine law of nature.
(3) Thus, it is impossible for a genuine law of nature to be violated by any event. [from (2)]
(4) Hence, it is impossible for any event to be a miracle. [from (1) & (3)]

I think what we need to do here, to generate our philosophical issue, is to allow that it is at least logically possible for a law of nature to be violated. Let us therefore understand the concept of a law of nature in such a way that step (2) of the above proof is false. It may be that no laws of nature are ever violated, but there is no contradiction in the mere idea of it.
Another issue is that of truth. If a law of nature were to be violated, then could it still be true? One answer that might be given is: Yes, a violated law could still be true because laws of nature are only intended to describe events within the natural realm and miracles are outside the natural realm. Thus, miracles would not then render laws of nature false, for they would not show that the laws fail to correctly describe the natural realm. However, to view the matter in this way, the definition of "miracle" would need to be changed slightly. Instead of saying that miracles violate laws of nature, we would need to say that miracles are outside the natural realm and would violate laws of nature if they were in the natural realm. They would then not actually violate laws of nature, since laws of nature only describe events within the natural realm.
I do not like this way of viewing matters, because it places too much emphasis on the concept of a "natural realm." To work with a definition of "miracles" as events outside the natural realm, we would need some criterion for deciding whether or not an event is inside or outside that realm, and we do not have any such criterion. The result would be that the term "miracle" would be obscure, perhaps even meaningless. Let us, therefore, simply go with our original definition of a miracle as an event which violates a law of nature. That results in the conclusion that if an miracle were to occur, then the law of nature which it violates would be false, since such a law would be a generalization with at least one exception to it. Thus, some laws would be false (namely, the ones violated by miracles) and other laws would be true (namely, those not violated by any miracles). This way of speaking, distinguishing true laws of nature from false ones, may sound rather peculiar, but there seems to be no other meaningful way to permit talk of miracles to enter the discussion. The idea of a law still being useful even though it is false is a familiar one. Newton's Laws, for example, have been superseded in contemporary physics (and thus regarded as false), and yet they are still used in various practical fields. So, to speak of a law as false is not incoherent.
However, there is a problem here. Previously, a distinction was drawn between "genuine laws" and "erroneous (or superseded) laws." How could that distinction still be drawn if we allow that even some of the genuine laws might be false? Let us say that if genuine laws are false, it is only because of isolated counter-instances which cannot be explained or predicted on the basis of any other empirical laws. But when erroneous (or superseded) laws are false, it is because of regular counter-instances which are both explainable and predictable on the basis of other empirical laws. Atomic explosions, for example, occur according to known regularities on the basis of which they could be explained and predicted. Thus, the law that matter cannot be destroyed is an erroneous (or superseded) one. But if a man were to walk on water, although that would make Archimedes' Law false, it would not make it an erroneous law in the given sense. The counter-instance(s) would still be isolated and neither explainable nor predictable on the basis of any other empirical laws. Archimedes' Law could still be a genuine law, though it would no doubt be somewhat suspect under such circumstances.
What would be the result if people walking on water were to become commonplace? Suppose various men were to do it every year, say, on Easter Sunday. Their action could not be explained by Archimedes' Law, since the amount of fluid they displace as they walk on water does not correspond to a force sufficient to keep them from sinking. Some other force would be sought, but suppose that none is ever found and so their actions remain a mystery for science forever. Although such counter-instances to Archimedes' Law would in that case not be isolated events, they would still be miracles if, indeed, the law cannot be replaced by other natural laws which are not violated by the given events. Thus, miracles need not be isolated events, but they do need to be events that violate natural law which are forever unexplainable within the system of science