The word ‘miracle’ has had a long etymological history; interestingly its everyday usage has now returned to that of the Latin root miraculum. When we talk about the German economic miracle or a miracle stain remover, we are not suggesting supernatural causes, but only that these things are ‘objects of wonder’, which is exactly the meaning of the Latin. The miracles of Jesus, to take the most well known example, are of course qualitatively different (some would argue that the Gospel miracles were either allegorical or psychosomatic, however I am not here arguing for any particular interpretation of religious texts, but rather investigating miracles in the sense understood by the orthodox theology of Semitic religions). It is difficult to pin down in words precisely what this qualitative difference is, and this is because of the changing interpretations of two millennia. The Oxford English Dictionary defines this sort of miracle as: ‘an extraordinary event attributed to some supernatural agency’. But ‘extraordinary’ doesn’t quite capture the difference between an impressively flourishing economy and Lazarus being raised from the dead. The word ‘miracle’ has been defined in many different ways, I intend to look at a few of those best suited to philosophic investigation. We shall see that any definition of ‘miracle’ is closely linked to our definition of what a ‘law of nature’ is. Here then are some definitions of a miracle:

1]  ‘[something] done by divine power apart from the order generally followed by things’ - St. Thomas Aquinas [1]
2] ‘[something whose production exceeds] the power of visible & corporeal nature only’ - Pope Benedict XIV [2]
3] ‘an event involving the suspension of natural law’ - Alastair McKinnon [p49]
4] ‘a transgression of a law of nature by a particular volition of the Deity, or by the interposition of some invisible agent’ - David Hume [3]
5] [differentiates between] ‘the contingency concept and the violation concept’
 - R.F.Holland [p56]
6] ‘a non-repeatable counter-instance [to a natural law]’ - Richard Swinburne [p78]
7] ‘an exception to the natural order of things caused by the power of God’
 - Richard Purtill [p192]

    The first two definitions are in terms of the scholastic Aristotelian philosophy. Aristotle’s physics, based on observation and teleological thinking, assigned natures to all objects which prescribed what they would do when left to themselves. The actions of an agent could cause an object to move in ways outside its nature (violent motion) according to the power of the agent. The distinction between Aquinas’ and Benedicts’ definitions is that Benedict allows any non-corporeal being to work miracles, whereas Aquinas reserves this for God alone. In the world view of these philosophers a supernatural miracle is no different in type from a man throwing a stone up in the air, both are causing objects to act outside of their natures, the difference is only one of magnitude. Of course there were other philosophical standpoints in the Ancient world, such as the atheistic atomism of Epicurus, in which miracle have no place. The understanding of the majority of the population, in so much as it relates to philosophy, probably inclined towards an Aristotelian viewpoint which see purpose in nature. A first century Jew therefore would understand reports of miracles as signs of God at work, the only possible alternative might be that suggested about Jesus by the teachers of the law in Mark.3.22, that the power at work in the miracles was that of the Devil instead. The options open to our Jew, or indeed to a Roman hearing good reports of the Emperor Vespasian’s miraculous healings in Alexandria [4], were only which supernatural being might have caused these miracles; there was no reason to suggest that somehow miracles weren’t possible and therefore reject the reports immediately; indeed I can imagine no grounds on which to base such a suggestion within their world view (which I am suggesting would be along the lines of Aristotle’s physics). However, in our 20th Century Western society, it would be considered perfectly reasonable for someone with theistic beliefs to deny the possibility of the miraculous.
    Just as we need to look at a first century Jew’s world view to understand his reaction to miracles, we must look at our own basic world view in order to understand and evaluate arguments concerning miracles. The general change in paradigm from a physics of ‘natures’ to one of more general ‘laws of nature’ happened as scientist began to find mathematical relationships which seemed to describe and even predict the motions of planets, projectiles and gradually more and more of the world. Initially these scientists conducted their research in an almost religious manner, believing that they were beginning to read the language in which God had made the universe ordered and understandable. During The Enlightenment science and religion increasingly began to clash and divide, partly because the Church had taken Aristotle’s philosophy on board as part of its dogma. This schism between religion and science led to a new questioning of miracles, events which appear to challenge the order and understandability of the universe revealed by scientific method.
    The third definition of miracle given, talks of a miracle as a suspension of a natural law; McKinnon defines natural laws as ‘highly generalised shorthand description of how things do in fact happen’ [p49]. These definitions lead to a powerful form of argument that miracles are not just physically impossible, but that the very concept of a miracle is self-contradictory, since substituting in the definition of natural law, leads to a miracle being ‘an event involving the suspension of how things do in fact happen’, which is clearly inconsistent. Furthermore, if the natural laws we use do not describe a miraculous event then they are inadequate, and we must formulate new laws which do describe the miracle; once this has been done, there is nothing special about the event designated ‘miracle’, it is merely one of many events described by our natural laws. R.F.Holland expresses this argument well: ‘laws of nature can be formulated or reformulated to cope with any eventuality, and would-be miracles are transformed automatically into natural occurrences the moment science gets back on track to them’ [p59].
    Is it possible to salvage anything, in the face of these objections to miracles? R.F.Holland, in the fifth definition given, splits the concept of a miracle in two. Clearly his contingency concept, referring to extraordinary coincidences seemingly in answer to prayer or need, is still valid. If someone wishes to believe that a set of coincidences were brought about by God without violating physical laws, then it is difficult to produce an argument which could shake this believe, short of an attempt to disprove the existence of God. A certain amount of stage managing seems necessary on God’s part to bring about the coincidences. Subtle tweaks here and there might not be detectable, but inevitably they must involve violation of natural laws, and McKinnon’s definition has made this logically impossible. Events, however, depend not only on natural laws but also on initial conditions, and study of deterministic chaos in the past few decades has reveal just how dependent non-linear systems are to small changes in their initial states. For a theist, even one rejecting violation miracles, God presumably still gets to choose the initial conditions, and therefore could conceivably choose them to bring about the required coincidences. This explanation of course brings us into the theology of predetermination and God’s foreknowledge, which is clearly beyond the scope of this essay, however the point remains that initial conditions could explain contingency miracles.
    Strangely, R.F.Holland also holds on to the violation concept of miracles. He gives an example of a horse which we know from observation is receiving no nourishment and yet continues to flourish as if well fed. A self-sustaining horse is, he claims, conceptually impossible for us and yet at the same time empirically certain because we have been carefully studying it. Instead of rejecting the concept that horses need food to survive which has served well for every other horse in history and continues to serve well for other horses, Holland thinks ‘that the price is too high and it would be better to be left with the inconsistency’ [p64]. Holland applies this principle more widely, and concludes that Jesus turning water into wine in John.2.9 could logically be true. I don’t think Holland’s argument is wholly convincing, but his decision to hold on to a useful concept is understandable. If we suddenly come across an apple which fall up off a tree instead of down, (as well as being extremely surprised!) we would be loath to reject our concept of gravity which has worked so well and continues to work for all things we experience except this one apple. The reason why we feel this way, I think, is that the meaning of natural law differs slightly from our current definition. Natural laws are formulated by a process of observation and experimentation, Ockham’s razor is the principle by which scientists choose the simplest known formula compatible with experiments, the laws are always corrigible if further experiments are more in favour of a different formula. Einstein’s relativity theory has replaced Newtonian gravity as the preferred natural law because every experiment sensitive to the differences in the theories supports Einstein; the theory accurately predicts the results of the experiments. With relativity the theory came before experiments showed that Newtonian gravity was inadequate, however with quantum mechanics, theory was developed in response to classical mechanics failure to correctly predict experimental results (such as black-body radiation). The formulators of quantum theory had good reason to reject classical mechanics and search for a new theory to match their results. Would they be equally justified in searching for new theories in response to Holland’s horse, Jesus turning water into wine or an up-falling apple? The difference between the situations is that which both black-body radiation and an up-falling apple are counter-instances to established theories, the former is a repeatable experimental phenomena while the later is a singular event. Richard Swinburne terms such an event ‘a non-repeatable counter-instance’ [p78]. The problem is that natural laws (or to be more precise our theories modelling natural laws) seem to ‘describe what happens in a regular and predictable way. When what happens is entirely irregular and unpredictable, its occurrence is not something describable by natural laws’ [p78]. Swinburne points out that if we could reformulate our laws to include this strange occurrence then, since natural laws predict as well as describe (in fact their descriptive power is really one of predicting the past) they would predict instances of this occurrence given a similar situation - but then the event would be regular and predictable in contradiction to our definition of it! Whether irregular and unpredictable things do occur is a matter for experience, but they do not appear to be in any way logically impossible. Perhaps we should like everything to be predictable, and hence define natural laws as McKinnon does, however that is not within the scope of science to prove or disprove, since the problem is in fact that of science’s scope.
    A few more definitions of natural law help to clarify these ideas. ‘A formula…[such] that virtually invariably its predictions are true and that any exceptions to its operation cannot be accounted for by another formula which could be taken as a law’ [Swinburne, p80]. ‘The laws of nature, we must say, describe the ways in which the world - including, or course, human beings - works when left to itself, when not interfered with’ [J.L.Mackie, p87]. Non-repeatable counter-instance, outside the scope of these laws, could logically occur. These counter-instances need not in fact be due to God, or any other spiritual being, they could be totally without reason. If this were the case, then our universe would not be completely the place of order and understandability we think it to be, but one tainted with some degree of chaos. Miracles, counter-instances due to a personal being, are not such a challenge to an ordered world view since they would at least be the products of reason and within the realms of explanation (if personal explanations are valid), though only in a religious sense. To conclude this section, the arguments which at first seemed so shattering to belief in miracles have faded away after careful scrutiny of our definitions of miracle and natural law. All that has been shown is that a miracle can be a coherent and consistent logical concept; whether we can ever have sufficient evidence to justifiably believe a miracle has taken place is another matter, which will now be considered [5]. Ironically, much of the understanding of natural laws above, which has helped restore miracles as logical concepts, has its roots in the empiricism of David Hume. Hume’s causality is one in which cause and effect are frequently seen in conjunction, but nothing can be said about whether they are connected. Natural laws therefore do not have the same sort of nomological necessity, and therefore it is much easier to think in terms of counter-instances to them. The irony is that Hume argued very forcibly against the believability of miracles, and section X of his Enquiry Concerning Human Understanding forms the starting point for all philosophic discussion of this topic.
    I shall first clearly outline Hume’s argument against the believability of miracles, and then consider its validity. The argument begins with the basic axiom of his philosophic method, ‘though experience be our only guide in reasoning concerning matters of fact; it must be acknowledged, that this guide is not infallible… a wise man, therefore, proportions his belief to the evidence’ [para 87]. In line with this method, he proceeds to consider the process of weighing up the evidence of human testimony. ‘Evidence, derived from witnesses and human testimony… is regarded either as a proof or a probability according as the conjunction between any particular kind of report and any kind of object has been found to be constant or variable’ [para 88]. This criteria may seem strange, but Hume is just being consistent with his views on causation; he must further assert that experience shows that men have at least some inclination towards correct and truthful testimony, in order to allow this sort of evidence any value at all. Next he must consider in what sort of ways this evidence might conflict: ‘This contrariety of evidence, in the present case, may be derived from several different causes; from the opposition of contrary testimony; from the character or number of the witnesses; from the manner of their delivering their testimony; or from a union of these circumstances. We entertain a suspicion concerning any matter of fact, when the witnesses contradict each other; when they are but few, or of a doubtful character; when they have an interest in what they affirm; when they deliver their testimony with hesitation, or on the contrary, with too violent asseverations.’ These certainly are important considerations when judging human testimony. Moving towards the subject of miracles, Hume claims that ‘the evidence, resulting from the testimony, admits of a diminution, greater or less, in proportion as the fact is more or less unusual’ [para 89]. He is now ready to unleash the full force of his objection: ‘it is a miracle, that a dead man should come to life; because that has never been observed in any age or country. There must, therefore, be a uniform experience against every miraculous event, otherwise the event would not merit that appellation. And as a uniform experience amounts to a proof, there is here a direct and full proof, from the nature of the fact, against the existence of any miracle; nor can such a proof be destroyed, or the miracle rendered credible, but by an opposite proof, which is superior’ [para 90, my underlining]. In short, ‘no testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous’ [para 91]. In part II, Hume continues with four reasons why a miracle has never been established on sufficient evidence.
     Firstly he claims that no miracle has ever been performed in a public manner in an important part of the world (meaning, I guess, Western Europe) and been backed up by sufficient good and intelligent witnesses with reason not to lie - which are the criteria needed to give full assurance of the testimony.
     Secondly, ‘the passion of surprise and wonder, arising from miracles, being an agreeable emotion, gives a sensible tendency towards the belief of those events, from which it is derived’ [para 93]. Furthermore people might be tempted to knowingly lie concerning a miracle to support their religious position or from pure self-interest, and ‘the many instances of forged miracles… ought reasonably to beget a suspicion against all revelations of this kind’ [para 93].
     Thirdly he claims that miracles are ‘observed chiefly among ignorant and barbarous nations… [since] fools are industrious in propagating the imposture’ [para 94].
     Fourthly he notes that miracles are claimed by the adherents of many religions to support their dogma, and therefore they invalidate each other since ‘in matters of religion, whatever is different is contrary’ [para 95].
    What response is there to these powerful arguments? To begin with, the (im)probability of miracles occurring depends very much on one’s basic world view. As shall be expanded below, Hume offers no advise to someone who thinks they have personally experienced a miracle, and this must be deliberate: he thought this would never happen because his world view already excluded miracles. Equally, to a theist, ‘the incredibility of miracles… is not in itself greater than the event, call it either probable or improbable, of the two following propositions being true: namely, first that a future state of existence should be destined by God, for his human creation; and secondly, that, being so destined, he should acquaint them with it… In describing the improbability of miracles, [Hume] suppresses all those circumstances of extenuation, which result from our knowledge of the existence, power and disposition, of the Deity’ [William Paley, p43]. Richard Swinburne draws a useful analogy which helps clarify the importance of background belief: ‘If we have already good grounds for believing that there is a gorilla loose in snowy mountains, we require less by way of evidence of footprints to show that he has visited a particular place’ [p151].
     An important criticism is that part of Hume’s argument seems to be circular, when he moves from assuming ‘uniform’ experience against miracles to a general proof against their existence. Richard Purtill suggests that for Hume ‘to argue for the conclusion that miracles do not happen by assuming that miracles, under whatever description, don’t happen, is just to argue in a circle or beg the question’ [p191].  Even if we allow this assumption of uniform experience, Hume’s own causation produces problems, because without the concept of necessary connection, ‘the inductive argument from the observation “All so far observed As have been Bs” to the generalisation “All As are Bs” is far from secure, and it would be most misleading to call this a proof’ [J.L.Mackie, p91]. Indeed all that Hume’s ‘uniform experience’ amounts to is no more than a merely numerical universal conjunction, and Antony Flew recognises that ‘any attempt to use our knowledge, or presumed knowledge, of such a merely numerical universal proposition as an evidential canon by which to justify the outright rejection of any testimony to the occurrence of a falsifying exception would be a preposterous piece of question begging’ [p97].
    In response to Hume’s list of four reasons to discredit miracle testimonies: the first point seems to be that no precedence has been set by at least one miracle which is easily acceptable - but this is open to debate, and some of the miracles that Hume mentions later on, such as that of the tomb of Abbé, might be good candidates. The second point makes good sense, though Hume does exaggerate; clearly religion fraudulence seems to have taken place in the past, and so it is reasonable to be suspicious of any witnesses and accept only the most credible ones. Hume’s third point is a little harsh and intellectually snobbish, though again it is valid to a degree; there are, however, conceivable reasons why miracles might be more frequent among less advanced peoples, such as their having more pressing need and more fervent prayer than the more advanced and more comfortable nations. The final point is an interesting one, but not rigorous enough, since it requires a number of assumptions:
    that a miracle validates completely all the dogma of the group in   whose context it occurs;
    that only a single God works miracles;
    that evidence for the miracles is equal in the different religious  traditions.
The first assumption only seems valid for certain sorts of miracles, such as the duel of Elijah and the priests of Baal in 1Kings.18, or the resurrection of Jesus. The second assumption is not necessary, and even monotheistic religions allow a Devil with power to affect the world, and hence work miracles in the context of rival religions to trick people (the classic angle of light disguise). It remains to be proven that the third assumption is valid, and certainly many religions, Islam being a prime example, do not have a miracle tradition like Judaism and Christianity, and few have anything like the level documented evidence.
    In conclusion, David Hume’s arguments contain circularity and unsupported assumptions, and so are not convincing. However, many of the points he raises should rightly cause us to be suspicious of testimonies, and particularly religious testimony. Conspicuous in its absence from Hume is any discussion of the part played by direct experience (say our memories) and physical traces (such as seven baskets of bread crumbs), which might reasonable have bearing on our analysis of an event. Even these types of evidence are not certain sources of knowledge, since we may be fooled or construct false memories.
    Miracles, at least in view of the definitions suggested in this essay, are logically possible. There might in fact be reason to believe that a miracle had taken place, though it does not seem possible to construct a simple formula to deduce this from any set of evidence. In reality we must juggle all the various strands of evidence, including testimony, personal experience and physical traces; our personal world view, and the rigidity of our adherence to it, must rightly have a powerful effect on our eventual conclusions. For this reason, two intelligent people, given the same set of evidence, could arrive at opposite positions regarding the miraculous nature of an event, yet at the same time equally reasonable positions of belief.
    Answering the question posed in the title of this essay: a miracle is an unpredictable (at least scientifically) exception to nature as it is described most of the time by mathematical laws, brought about by the power of a supernatural being. A miracle is a coherent and possible concept and it could be perfectly rational to believe that some particular miracle had taken place, though often people believe in miracles blindly and irrationally.
 
Footnotes
1. Summa Contra Gentiles 3.101.1
2. Quoted on page 3 of Miracles, ed. R.Swinburne, Macmillan, 1989 (most of my quotations are from this anthology and shall be given in the form ‘[p3]’ - Its quite an easy read and worth getting out, the editor is a lecturer here at Oxford, and is supposed to be the last major philosopher of religion who still believes in God - he could probably do with our prayers! )
3. In the footnote to paragraph 90 of The Enquiry into Human Understanding (all further quotations from this book shall be given in the form ‘[para 90]’)
4. In Tacitus, The Histories, 4.81
5. I offer this only as a footnote, since I think the arguments given in favour of the logical possibility of miracles are valid. However, even if one finds reason to reject this reasoning, and deny the possibility of violation miracles, there may still be some room for God to interact directly in the world, if the laws of nature by statistical not universal. This is the case in quantum mechanics, which even bends fundamental laws such as the conservation of momentum according to the Heisenberg uncertainty principle. Suppose Jesus was stepping out onto the water: God could arrange the motions and positions of all the particles in the universe which might influence this situation (those for whom that event is contained within their light cones) such that there is no additional net force down on Jesus, and thus he could walk across the water. Each particle would have an extremely small probability to be in the state God arranged, and the combination of the independent probabilities of all these particles would amount to an incredibly small probability, however if the universe has a very long future, God could still balance the probability books eventually!