To set a context for thinking about science-and-miracles, here are excerpts from a page that looks at a wider range of questions about Methodological Naturalism:

      Summary:  The basic theories of science, the "laws of nature," do not explicitly refer to God.  Some scientists, and some students, incorrectly conclude that science is methodologically atheistic.  However, a biblical view of God not only motivates us to do science, but also provides us a philosophical foundation for expecting to find regular patterns of cause and effect in nature.  A scientific understanding in terms of natural laws does not exclude God;  rather, it teaches us about God's governance of creation.  Scientific knowledge is placed in a context of faithfully living for God.
      ... I find the term "methodological atheism" (or "methodological naturalism") to be misleading theologically, philosophically, and historically.  Theologically, it implies God's absence from natural events, which is false.  Philosophically and historically, it implies that the scientific method follows more naturally from the worldview of Naturalism than from other worldviews, which is false. ...

      Science and Miracles (condensed version)
      Another way in which the concept of "methodological naturalism" is misleading is by implying that science must necessarily deny the possibility of miracles.  In this paper I will have to be very brief, although I have written much more extensively on the topic of science and miracles, in the expanded section below.
      As a practical matter, science cannot claim to prove that miracles never happen.  All that science can do, under various circumstances, is say that if the laws of nature keep operating in the way that we understand them to operate, then certain outcomes are likely to happen and other outcome are not.  From an atheistic viewpoint, matter and the laws of nature are all there is.  From a Christian viewpoint, however, the laws of nature were created and are sustained by God, and God can supersede them.  For sound theological reasons, we don't expect God to willy-nilly supersede those natural laws, but the God who made those laws is certainly capable of superseding them on special occasions.  Science can only tell us what will happen if the laws of nature keep operating the way we understand them.  The claim that science disproves miracles, by contrast, is not a scientific claim at all, but a philosophical or religious claim.
      There is a flip side to this.  Science cannot disprove miracles, but as a practical matter, neither can science prove a miracle occurred.  Imagine a surprising event occurs.  Science could tell us is whether or not that event was unexpected in terms of known natural laws.  Science could not, however, tell us whether that unexpected event was caused by supernatural activity, or super-human technology, or some as-yet unknown natural law, or simply some very improbable random occurrence.  Science, by itself, cannot distinguish between those possibilities.  Philosophical and theological arguments weigh in at that point.
      Science makes progress by studying puzzling events and attempting to explain them in terms of known natural laws (or sometimes, in terms of new natural laws which are compatible with older, well-established laws).  When these scientific models are successful, their success does not exclude God.  Instead, it illuminates God's governance of creation.  But science also makes progress when the best possible scientific models, employing known natural mechanisms, are shown to fail — when an event is shown to be unexplained in terms of known natural laws.  Science can do this, and it does do this occasionally.  When this happens, it might indicate that God performed a miracle during that event — but not necessarily.  It might also mean that God brought about that event by some unknown natural laws or processes which we might yet discover.
      If God so choose, God could perform miracles which appear to us to be scientifically puzzling or unexplained events.  It can be tempting for Christians to see scientific puzzles as potential evidence for God's existence and miraculous intervention in the history of the universe.  However, a biblical understanding of God's governance should also warn us from too quickly embracing any particular scientific puzzle as potential evidence of miracles.  Hunting for miracles is not necessarily the most faithful approach to studying God's creation.  Hunting for new scientific explanations, in terms of natural laws which God created and sustains, can be equally God-glorifying — and in many cases may be theologically more defensible.  Every time we solve a new scientific puzzle, we are not taking territory away from God's control; rather, we are learning more about how God typically governs his creation.  Every time we learn a new scientific truth about God's creation and the gifts which He gave it, it should prompt us all the more to worship the Creator.

And from another wide-view page about methodological naturalism, here is an expanded version of the section above:

      Science and Miracles (expanded version)

      When we start talking about science and God, sooner or later we have to address the issue of miracles.  Given that miracles can happen, how should we do science?  Should we do science expecting to find evidence of ongoing miracles everywhere we look?  Or should we utterly exclude the possibility of miracles when we study creation, always looking for explanations exclusively in terms of natural laws?  A biblically informed view of God should warn us against either extreme. Ordinarily, God governs his creation in consistent ways.  God's consistency gives us hope and confidence in our search for universal natural laws.  But God is sovereign over those laws.  God can also surprise us with unusual, unexpected events.

      Is it possible to scientifically prove that a miracle happened?  Or does science rule out any possibility of miracles?  In various discussions I have had, with Christians and non-Christians — especially on the issue of origins of life on earth — I given some thought to this question.  As a Christian, I believe that God can perform miracles, and that if you put such an event under scientific scrutiny, a miracle might appear to be a scientifically unexplainable.  But while I accept the possibility of such miracles, an atheist will reject the possibility of miracles.  Yet we have to work together as scientific colleagues, analyzing the same data.  So how would that work?  What happens when scientists of different religious worldviews encounter a puzzling event?  Here is the answer I have come up with:

      Is it possible to scientifically prove that a miracle happened?  Or does science rule out any possibility of miracles?  A practical understanding of what science can and cannot do should warn us against either extreme.  When faced with a puzzling event, science can neither prove nor disprove that a miracle occurred.  What science can do is this: it can try to understand the physical conditions before, during, and after the event, and it can try to determine what effect known natural laws could have had.  Based upon that knowledge, science can attempt to build an empirical model, using known natural laws, for how the event could have happened.

      Attempts to build empirical models of puzzling events meets with varying kinds of success.  As scientists study the initial conditions, final conditions, and relevant natural laws, they could reach three general types of conclusions:

      1) Explained event.  Sound empirical models predict that known natural laws can account for the event.  (There might still be some puzzling features, but the majority of the event is well understood.)

      It is worth mentioning again the biblical view that scientifically explained events are just as much dependent upon God's governance as scientifically unexplained events.  In addition, even when empirical models successfully explain how an event could happen, that does not necessarily mean that the model correctly describes how the event actually happened.

      Sometimes, "explainable" events occur at special times and places, in ways that have special religious significance to a person or a group of people.  The argument can be made that such "coincidental" events must have some "unexplainable" (supernatural) component.  Science cannot answer that question positively or negatively.  The most that science can do is attempt to determine the relative probability (infrequency) of the event, possibly taking into account known initial conditions.  In determining whether or not a "coincidental" event had a supernatural component, one must go beyond science to consider historical, philosophical, and religious questions.  (e.g. Was the event's timing and location predicted beforehand?  How soundly does the event fit within an established theological framework?  Was there a special revelation accompanying the event?

      2) Partially explained event.  Our empirical models are not sufficiently thorough to explain the event entirely.  However, based upon what we have done so far, we believe that known natural mechanisms are sufficient to account for the event.  We believe that future improvements in knowledge, more elegant models, and more computing power will eventually allow us to prove that the event is "explainable."

      3) Unexplained event.  No known natural laws can account for this event.  In fact, there are empirically sound reasons for ruling out any models in terms of known natural laws.

      (Some objects or events indicate intelligent crafting.  The categories "explained" and "unexplained" become problematic in such cases.  For example, a paleontologist might determine that the breakage patterns on the edges of some stones are unexplainable in terms of ordinary natural laws (at least, not with any significant probability).  However, if hominid bones are found in the same area, the paleontologist might reasonably conclude that the stones were crafted to be tools.  In this model, the intelligent activity of hominids acts as a special kind of "natural mechanism."  A similar argument is made in the search for extraterrestrial intelligence.  If a sufficiently complex repeating radio signal is discovered, the case can be made that no natural mechanism could produce the complex pattern except for the special type of natural mechanism of intelligent activity.  In the debate over biological evolution, some people have pointed to the analogous features between biological life and intelligently crafted objects, thereby arguing that biological life was crafted and assembled by an intelligent agent.  This argument is not strictly speaking scientific.  It is a philosophical argument.  Philosophical arguments have a legitimate role, and sometimes a positive role, in science.  They can be used to persuade, as a starting point for marshaling scientific arguments, and a starting point for formulate testable hypotheses.  The extent to which this philosophical argument is convincing is, obviously, a point of ongoing debate.)

      For any particular event, there may be some debates in the scientific community as to whether it is explained, partially explained, or unexplained.  Even when there are debates, however, it is common for a great majority of scientists to agree.  For example, most scientists would agree that supernovas are "explained" events.  Most would agree that the development of animals from single-celled zygotes into mature adults falls into the category of "partially explained."  A small number scientists argue that the origin of first life on earth is unexplainable in terms of known natural laws; but most scientists argue that it should be considered partially explained.  Most agree that the source of the "Big Bang" is unexplained in terms of known natural laws.

      How do scientists deal with "unexplained" events?  There is usually no consensus.  Individual scientists could reach (at least) five different conclusions about the cause of a scientifically unexplainable event:

      A) An as-yet unknown natural law is responsible for the event.
      B) A supernatural event occurred.  (The event was caused by an intelligent being of an entirely different "reality" than our universe.)
      C) Super-human technology brought about the event.  (The event was caused by intelligent beings who are contained in and limited by our universe, but with superior technology.)
      D) A very improbable event simply happened.
      E) A very improbably event simply happened, but this isn't so surprising because there are many universes and we just happen to live in the one where it happened.

      A search through popular books and articles written by scientists will turn up examples of each of these five types of conclusions.

      Although these five conclusions are, philosophically and religiously, very different from each other, they play virtually identical roles in scientific studies.  Empirical science cannot distinguish between these five possibilities.  Historical, philosophical, and religious arguments are the decisive factors in each scientist's conclusion.

      Although science cannot decide on the best philosophical conclusion for a scientifically "unexplained" event, science does play a vital role in deciding whether an event belongs in the category "partially explained" or "unexplained."  Philosophical and religious arguments can also properly play some role in these debates.  In the boundary areas between "partially explained" and "unexplained" events, scientific data, scientific intuition, philosophical and religious expectations can meet in the same arena.  For example, an atheistic scientist might be motivated to work hard to push an "unexplained" events into the "explained" or "partially explained" category.  This effort might lead her to uncover new natural laws, sooner than scientists who don't share her atheistic philosophy.  Alternatively, a scientist with strong religious reasons for believing that certain events are supernatural can marshal scientific data to show that some events are truly "unexplained" rather than merely "partially explained."  This effort might lead her to uncover flaws in currently-accepted empirical models sooner than scientists who don't share her religious beliefs.

      (Both of these biases could be pushed to the extreme, to the detriment of science.  One could imagine a scientific community so obsessed with finding naturalistic explanations for unexplained events that it wastes vast resources on unproductive pursuits which yield no secondary benefits.  One could also imagine a scientific community so complacent about supernatural explanations (or, for that matter, super-human or many-universes explanations) that it makes virtually no effort to search for new natural explanations for puzzling events.  Fortunately, the present-day scientific community does not seem to fit either extreme.  Moreover, it should be noted that scientists from every philosophical and religious persuasion spend most of their time trying to push events from the "partially explained" category into the "explained" category.)

      Scientific conclusions are tentative.  Events which are deemed "explained" or "unexplained" today could change their status with the discovery of new natural laws or better empirical models.  Ultimately, the development of new empirical models plays a decisive role in determining whether a "partially explained" event is "explained" (if the improved empirical models are successful) or "unexplained" (if the improved empirical models argue convincingly against scenarios involving known natural laws).  While these new empirical models are still being developed, philosophical and religious arguments can play a legitimate role in persuasion and, to some extent, in formulating testable hypotheses. 

      Over the centuries, we have seen many examples of science attempting to construct ever-better empirical models of partially explained events.  In many cases (e.g. supernovas), decades of scientific work have resulted in fairly complete and detailed explanations in terms of known natural laws.  Occasionally science has come to the opposite conclusion — that although some event definitely happened, no known natural laws can account for it (e.g. the cause of the "Big Bang.") Most of the time, modern science gives us incomplete answers.  Most of the time, scientific investigation tells us that some aspects of an event can be understood in terms of known natural laws while other aspects are still puzzling — puzzling, but showing great promise for future discoveries.

      So to those who are eager for science to find evidence for God's miraculous actions in nature, I would say the following: Scientists make progress by building empirical models and by looking for natural laws and natural mechanisms to explain as many aspects as possible of the system they are studying.  Scientists seek to determine precisely which aspects of a system can be explained in terms of known natural mechanisms and which aspects cannot.  By this process, new natural mechanisms are sometimes discovered; old models are refined and sometimes discarded as being inconsistent with the data.

      A great many scientific puzzles remain.  There are many scientific questions, such as the development of the first life on earth, where scientists cannot yet build a model, using known natural mechanisms, which plausibly explains many features of the data.  It can be tempting for Christians to see these scientific puzzles as potential evidence for God's existence and miraculous intervention in the history of the universe.  God is free to act miraculously, free to act in ways different from his ordinary governance of creation.  If God so choose, God could perform miracles which appear to us to be scientifically puzzling or unexplained events.  However, a biblical understanding of God's governance should also warn us from too quickly embracing any particular scientific puzzle as potential evidence of miracles.

      A biblical picture assures us that God governs creation in consistent and orderly ways, and God gives us the gifts we need to study his creation and partially understand it.  Scientists of many religious worldviews can work side-by-side and reach consensus about the natural mechanisms at work in the history and the present functioning of the world.  The fact that Christians and non-Christians can work side-by-side in science should give Christians, not a sense of fear, but a sense of joy and gratitude.  As John Calvin said, "If the Lord has willed that we be helped in physics, dialectic, mathematics, and other like disciplines, by the work and ministry of the ungodly, let us use this assistance.  For if we neglect God's gift freely offered in these arts, we ought to suffer just punishment for our sloth." (Institutes of Christian Religion 1.16.1)

      Science, by itself, does not require one to expect to find natural explanations for every event.  Scientific progress is made by studying puzzling events and attempting to explain them in terms of known natural laws (or sometimes, in terms of new natural laws which are compatible with older, well-established laws).  When these scientific models are successful, their success does not exclude God.  Instead, it illuminates God's governance of creation.  But science also makes progress when the best possible scientific models, employing known natural mechanisms, are shown to fail — when an event is shown to be unexplained in terms of known natural laws.  Science can do this, and it does do this occasionally.  When this happens, it might indicate that God performed a miracle during that event — but not necessarily.  It might also mean that God brought about that event by some unknown natural laws or processes which we might yet discover.

      It is tempting to think that we are more faithful to God if we look for evidence of miracles in every scientific puzzle.  But hunting for miracles is not necessarily the most faithful approach to studying God's creation.  Hunting for new scientific explanations, in terms of natural laws which God created and sustains, can be equally God-glorifying — and in many cases may be theologically more defensible.  Every time we solve a new scientific puzzle, we are not taking territory away from God's control; rather, we are learning more about how God typically governs his creation.  Every time we learn a new scientific truth about God's creation and the gifts which He gave it, it should prompt us all the more to worship the Creator.

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