Mill on miracles

J. S. Mill was a brilliant atheist who wrote a sustained attack on Christianity (Three Essays on Religion). I'd like to comment on his attempted attack on miracles. 

Taking the question from the very beginning; it is evidently impossible to maintain that if a supernatural fact really occurs, proof of its occurrence cannot be accessible to the human faculties. The evidence of our senses could prove this as it can prove other things. To put the most extreme case: suppose that I actually saw and heard a Being, either of the human form, or of some form previously unknown to me, commanding a world to exist, and a new world actually starting into existence and commencing a movement through space, at his command. There can be no doubt that this evidence would convert the creation of worlds from a speculation into a fact of experience. It may be said, I could not know that so singular an appearance was anything more than a hallucination of my senses. True; but the same doubt exists at first respecting every unsuspected and surprising fact which comes to light in our physical researches. That our senses have been deceived, is a possibility which has to be met and dealt with, and we do deal with it by several means. If we repeat the experiment, and again with the same result; if at the time of the observation the impressions of our senses are in all other respects the same as usual, rendering the supposition of their being morbidly affected in this one particular, extremely improbable; above all, if other people’s senses confirm the testimony of our own; we conclude, with reason, that we may trust our senses. Indeed our senses are all that we have to trust to. We depend on them for the ultimate premises even of our reasonings. There is no other appeal against their decision than an appeal from the senses without precautions to the senses with all due precautions. When the evidence, on which an opinion rests, is equal to that upon which the whole conduct and safety of our lives is founded, we need ask no further. Objections which apply equally to all evidence are valid against none. They only prove abstract fallibility.

That's well taken. 

But the evidence of miracles, at least to Protestant Christians, is not, in our own day, of this cogent description. It is not the evidence of our senses, but of witnesses, and even this not at firsthand, but resting on the attestation of books and traditions. 

i) Although differentiating between the evidence of our senses and the evidence of witnesses is a valid distinction, his dichotomy between witnesses and attestation of books and traditions is a false anthesis. That's the nature of most recorded testimonial evidence, which has its origin in oral history. 

ii) Moreover, he assumes that 19C Protestants had no firsthand experience of miracles. How would he be in any position to know that? He was raised in an irreligious household. As an adult, he didn't move in evangelical circles. He avoided the settings in which miracles, if they occur, are more likely to occur. There's a circular, self-reinforcing quality to infidelity, where unbelievers associate with other unbelievers, so that their social circle deliberately excludes the company where answered prayer, if it happens, would fall under their purview. 

iii) Nowadays, we also have lab tests and medical scans that show a patient's before and after condition. That's different from either firsthand observation of a miracle or testimony to a miracle. You could pull someone's records and see the results for yourself. 

And even in the case of the original eyewitnesses, the supernatural facts asserted on their alleged testimony, are not of the transcendant character supposed in our example, about the nature of which, or the impossibility of their having had a natural origin, there could be little room for doubt. On the contrary, the recorded miracles are, in the first place, generally such as it would have been extremely difficult to verify as matters of fact, and in the next place, are hardly ever beyond the possibility of having been brought about by human means or by the spontaneous agencies of nature. It is to cases of this kind that Hume’s argument against the credibility of miracles was meant to apply.

That denial is conspicuous for the utter lack of specific examples. He doesn't say what recorded miracles he's alluding to, how they'd have been extremely difficult to verify as matters of fact, or hardly ever beyond the possibility of having been brought about by human means or by the spontaneous agencies of nature. So his denial is a vacuous abstraction. 

His argument is: The evidence of miracles consists of testimony. The ground of our reliance on testimony is our experience that certain conditions being supposed, testimony is generally veracious. But the same experience tells us that even under the best conditions testimony is frequently either intentionally or unintentionally, false. When, therefore, the fact to which testimony is produced is one the happening of which would be more at variance with experience than the falsehood of testimony, we ought not to believe it. And this rule all prudent persons observe in the conduct of life. Those who do not, are sure to suffer for their credulity.

At variance with experience? As in no one's experience? 

Now a miracle (the argument goes on to say) is, in the highest possible degree, contradictory to experience: for if it were not contradictory to experience it would not be a miracle. The very reason for its being regarded as a miracle is that it is a breach of a law of nature, that is, of an otherwise invariable and inviolable uniformity in the succession of natural events. There is, therefore, the very strongest reason for disbelieving it, that experience can give for disbelieving anything. But the mendacity or error of witnesses, even though numerous and of fair character, is quite within the bounds of even common experience. That supposition, therefore, ought to be preferred.

There are two apparently weak points in this argument. One is, that the evidence of experience to which its appeal is made is only negative evidence, which is not so conclusive as positive; since facts of which there had been no previous experience are often discovered, and proved by positive experience to be true. 

That's well-taken. 

The other seemingly vulnerable point is this. The argument has the appearance of assuming that the testimony of experience against miracles is undeviating and indubitable, as it would be if the whole question was about the probability of future miracles, none having taken place in the past; whereas the very thing asserted on the other side is that there have been miracles, and that the testimony of experience is not wholly on the negative side. All the evidence alleged in favour of any miracle ought to be reckoned as counterevidence in refutation of the ground on which it is asserted that miracles ought to be disbelieved. The question can only be stated fairly as depending on a balance of evidence: a certain amount of positive evidence in favour of miracles, and a negative presumption from the general course of human experience against them.

That's well-taken. 

In order to support the argument under this double correction, it has to be shown that the negative presumption against a miracle is very much stronger than that against a merely new and surprising fact. This, however, is evidently the case. A new physical discovery even if it consists in the defeating of a well established law of nature, is but the discovery of another law previously unknown. There is nothing in this but what is familiar to our experience: we were aware that we did not know all the laws of nature, and we were aware that one such law is liable to be counteracted by others. The new phenomenon, when brought to light, is found still to depend on law; it is always exactly reproduced when the same circumstances are repeated. Its occurrence, therefore, is within the limits of variation in experience, which experience itself discloses. But a miracle, in the very fact of being a miracle, declares itself to be a supersession not of one natural law by another, but of the law which includes all others, which experience shows to be universal for all phenomena, viz., that they depend on some law; that they are always the same when there are the same phenomenal antecedents, and neither take place in the absence of their phenomenal causes, nor ever fail to take place when the phenomenal conditions are all present.

i) I don't know what Mill means by natural law. On one definition, a natural law is merely descriptive. It doesn't do anything. Laws aren't causes. 

Is he using "natural law" as a synonym for a universal natural force or process? If so, it's not self-evident that miracles per se are inconsistent with universal forces or processes, although some may be. 

ii) In any event, natural laws simply mean the same causes produce the same effects. If, however, a miracle involves the temporary introduction of a new cause, then that wasn't covered by a natural law. It's not inconsistent with natural laws, since they only deal with events covered by the same kind of causation. 

It is evident that this argument against belief in miracles had very little to rest upon until a comparatively modern stage in the progress of science. A few generations ago the universal dependence of phenomena on invariable laws was not only not recognized by mankind in general but could not be regarded by the instructed as a scientifically established truth. There were many phenomena which seemed quite irregular in their course, without dependence on any known antecedents: and though, no doubt, a certain regularity in the occurrence of the most familiar phenomena must always have been recognized, yet, even in these, the exceptions which were constantly occurring had not yet, by an investigation and generalization of the circumstances of their occurrence, been reconciled with the general rule. The heavenly bodies were from of old the most conspicuous types of regular and unvarying order: yet even among them comets were a phenomenon apparently originating without any law, and eclipses, one which seemed to take place in violation of law. Accordingly both comets and eclipses long continued to be regarded as of a miraculous nature, intended as signs and omens of human fortunes. It would have been impossible in those days to prove to any one that this supposition was antecedently improbable. It seemed more conformable to appearances than the hypothesis of an unknown law.

To the contrary, many biblical miracles were regarded as astounding to the original audience because they run counter to ordinary providence. 

Now, however, when, in the progress of science, all phenomena have been shown, by indisputable evidence, to be amenable to law, and even in the cases in which those laws have not yet been exactly ascertained, delay in ascertaining them is fully accounted for by the special difficulties of the subject; the defenders of miracles have adapted their argument to this altered state of things, by maintaining that a miracle need not necessarily be a violation of law. It may, they say, take place in fulfilment of a more recondite law, to us unknown.

Critics of the Bible don't really believe that. They reject biblical miracles because they think those are naturally impossible. Indeed, that's why they reject Bible history. 

If by this it be only meant that the Divine Being, in the exercise of his power of interfering with and suspending his own laws, guides himself by some general principle or rule of action, this, of course, cannot be disproved, and is in itself the most probable supposition. But if the argument means that a miracle may be the fulfilment of a law in the same sense in which the ordinary events of Nature are fulfilments of laws, it seems to indicate an imperfect conception of what is meant by a law, and of what constitutes a miracle.

When we say that an ordinary physical fact always takes place according to some invariable law, we mean that it is connected by uniform sequence or coexistence with some definite set of physical antecedents; that whenever that set is exactly reproduced the same phenomenon will take place, unless counteracted by the similar laws of some other physical antecedents; 

For some reason, Mill's entire discussion is framed in terms of natural law. However, it's unnecessary for a counteracting natural law to produce the exception. A counteracting cause or agent will suffice. 

and that whenever it does take place, it would always be found that its special set of antecedents (or one of its sets if it has more than one) has preexisted. Now, an event which takes place in this manner, is not a miracle. To make it a miracle it must be produced by a direct volition, without the use of means; or at least, of any means which if simply repeated would produce it. To constitute a miracle a phenomenon must take place without having been preceded by any antecedent phenomenal conditions sufficient again to reproduce it; or a phenomenon for the production of which the antecedent conditions existed, must be arrested or prevented without the intervention of any phenomenal antecedents which would arrest or prevent it in a future case. The test of a miracle is: Were there present in the case such external conditions, such second causes we may call them, that whenever these conditions or causes reappear the event will be reproduced? If there were, it is not a miracle; if there were not, it is a miracle, but it is not according to law: it is an event produced, without, or in spite of law.

That's true for one class of miracles, but not for coincidence miracles, which piggyback on continuous antecedent conditions, but are more discriminating than physical causes alone would select for. 

It will perhaps be said that a miracle does not necessarily exclude the intervention of second causes. If it were the will of God to raise a thunderstorm by miracle, he might do it by means of winds and clouds. Undoubtedly; but the winds and clouds were either sufficient when produced to excite the thunderstorm without other divine assistance, or they were not. If they were not, the storm is not a fulfilment of law, but a violation of it. If they were sufficient, there is a miracle, but it is not the storm; it is the production of the winds and clouds, or whatever link in the chain of causation it was at which the influence of physical antecedents was dispensed with. If that influence was never dispensed with, but the event called miraculous was produced by natural means, and those again by others, and so on from the beginning of things; if the event is no otherwise the act of God than in having been foreseen and ordained by him as the consequence of the forces put in action at the Creation; then there is no miracle at all, nor anything different from the ordinary working of God’s providence.

To take an counterexample, God's judgment on Sodom and Gomorrah was a natural disaster. That was consistent with natural laws. Indeed, that employed natural mechanisms. It was, however, targeted in time and space in a way that was more specific than merely natural forces, which are aimless. Of course, Mill denies the historicity of that account, but I use it to illustrate the idea of a miracle.

For another example: a person professing to be divinely commissioned, cures a sick person, by some apparently insignificant external application. Would this application, administered by a person not specially commissioned from above, have effected the cure? If so, there is no miracle; if not, there is a miracle, but there is a violation of law.

I'm curious about Mill's fixation with natural law. Natural laws are the most general classifications. Many physical forces, much less organic processes, operate at lower levels of generality and contingency. Is it a law of nature that a human heart has an average number of beats per minute? 

It will be said, however, that if these be violations of law, then law is violated every time that any outward effect is produced by a voluntary act of a human being. Human volition is constantly modifying natural phenomena, not by violating their laws, but by using their laws. Why may not divine volition do the same? The power of volitions over phenomena is itself a law, and one of the earliest known and acknowledged laws of nature. It is true, the human will exercises power over objects in general indirectly, through the direct power which it possesses only over the human muscles. God, however, has direct power not merely over one thing, but over all the objects which he has made. There is, therefore, no more a supposition of violation of law in supposing that events are produced, prevented, or modified by God’s action, than in the supposition of their being produced, prevented, or modified by man’s action. Both are equally in the course of nature, both equally consistent with what we know of the government of all things by law.

i) It's true that if God subsists outside of time and space, then divine agency differs from human agency. 

ii) However, Mill equivocates over "nature" and "law". If he's using "natural" as a synonym for "physical," then it begs the question to say that human volition is natural in the sense of physical. 

iii) Moreover, human volitions aren't law-like in the way that gravity is law-like, or even natural processes. Natural processes are mechanical. They don't think, deliberate, or make choices. They do whatever they were programmed to do. That's what makes them predicable in a way that human agents are not. For that matter, even animal behavior is unpredictable and "unlawful" compared to, say, crystal formation. 

Mill seems to be imprisoned in a 19C mechanical paradigm, where he overextends the operations of some invariant natural forces, as if everything in the natural world has the law-like character of some natural forces or natural processes. 

Those who thus argue are mostly believers in Free Will, and maintain that every human volition originates a new chain of causation, of which it is itself the commencing link, not connected by invariable sequence with any anterior fact. Even, therefore, if a divine interposition did constitute a breaking-in upon the connected chain of events, by the introduction of a new originating cause without root in the past, this would be no reason for discrediting it, since every human act of volition does precisely the same. If the one is a breach of law, so are the others. In fact, the reign of law does not extend to the origination of volition.

Those who dispute the Free Will theory, and regard volition as no exception to the Universal law of Cause and Effect, may answer, that volitions do not interrupt the chain of causation, but carry it on, the connection of cause and effect being of just the same nature between motive and act as between a combination of physical antecedents and a physical consequent. But this, whether true or not, does not really affect the argument: for the interference of human will with the course of nature is only not an exception to law when we include among laws the relation of motive to volition; and by the same rule interference by the Divine will would not be an exception either; since we cannot but suppose the Deity, in every one of his acts, to be determined by motives.

But even if human volitions are produced by chains of cause and effect, if that's mental rather than physical, then when human agents manipulate nature, that's still a "breach" or "breaking-in" in relation to the physical continuum of cause and effect. 

The alleged analogy therefore holds good: but what it proves is only what I have from the first maintained—that divine interference with nature could be proved if we had the same sort of evidence for it which we have for human interferences. The question of antecedent improbability only arises because divine interposition is not certified by the direct evidence of perception, but is always matter of inference, and more or less of speculative inference. And a little consideration will show that in these circumstances the antecedent presumption against the truth of the inference is extremely strong.

Our evidence for human "interference" is hardly confined to direct perception in contrast to inference. We constantly infer human agency in reference to past events which fall outside direct perception. 

When the human will interferes to produce any physical phenomenon, except the movements of the human body, it does so by the employment of means: and is obliged to employ such means as are by their own physical properties sufficient to bring about the effect. Divine interference, by hypothesis, proceeds in a different manner from this: it produces its effect without means, or with such as are in themselves insufficient. In the first case, all the physical phenomena except the first bodily movement are produced in strict conformity to physical causation; while that first movement is traced by positive observation, to the cause (the volition) which produced it. In the other case, the event is supposed not to have been produced at all through physical causation, while there is no direct evidence to connect it with any volition. The ground on which it is ascribed to a volition is only negative, because there is no other apparent way of accounting for its existence.

Actually, there are well-documented cases of psychokinesis. Moreover, Mill is obfuscating the issue. Lifting a glass with my hand employs means, and bodily movements are physical. But is willing to lift my hand a physical act or a mental act? Is mental causation prior to physical causation in that respect?  

But in this merely speculative explanation there is always another hypothesis possible, viz., that the event may have been produced by physical causes, in a manner not apparent. It may either be due to a law of physical nature not yet known, or to the unknown presence of the conditions necessary for producing it according to some known law. 

A basic problem with appealing to unknown laws is that natural laws are entirely general and unintelligent. Natural laws lack the rational discretion to single out particular outcomes in the way that miracles reflect.

Supposing even that the event, supposed to be miraculous, does not reach us through the uncertain medium of human testimony but rests on the direct evidence of our own senses; even then so long as there is no direct evidence of its production by a divine volition, like that we have for the production of bodily movements by human volitions—so long, therefore, as the miraculous character of the event is but an inference from the supposed inadequacy of the laws of physical nature to account for it,—so long will the hypothesis of a natural origin for the phenomenon be entitled to preference over that of a supernatural one. The commonest principles of sound judgment forbid us to suppose for any effect a cause of which we have absolutely no experience, unless all those of which we have experience are ascertained to be absent. Now there are few things of which we have more frequent experience than of physical facts which our knowledge does not enable us to account for, because they depend either on laws which observation, aided by science, has not yet brought to light, or on facts the presence of which in the particular case is unsuspected by us. Accordingly when we hear of a prodigy we always, in these modern times, believe that if it really occurred it was neither the work of God nor of a demon, but the consequence of some unknown natural law or of some hidden fact. 

Although experience can show us what happens, or at least what has happened, and therefore what can happen, it fails to show us what can't happen or won't happen. Experience refers to the past, not the future, and to what is the case, not what must be the case. Although experience contributes to our belief that some kinds of events are naturally inexplicable if they happened, it's not raw experience which yields that conclusion, but interpreted experience. When we understand how things physically work together, we understand when and why they don't work. The causal pathway is blocked. It's not possible for certain things to happen by that means if the connection is broken. Which doesn't rule out the event, but it can't happen through that medium if a link is missing. If it happens, it must be by some other cause, which doesn't require that intervening element.

Nor is either of these suppositions precluded when, as in the case of a miracle properly so called, the wonderful event seemed to depend upon the will of a human being. It is always possible that there may be at work some undetected law of nature which the wonder-worker may have acquired, consciously or unconsciously, the power of calling into action; 

What kind of "law" is Mill talking about? Is he alluding to something like psychokinesis? If so, that precludes naturalism (i.e. physicalism-cum-causal closure). For that involves action at a distance, which is impossible if human volitions are generated by the brain. In that case, all mental activity is confined to the brain, and can have no direct effect on anything outside the body. Once he allows for minds that can operate apart from corporeal constraints, how can he exclude God, angels, and demons? 

or that the wonder may have been wrought (as in the truly extraordinary feats of jugglers) by the employment, unperceived by us, of ordinary laws: which also need not necessarily be a case of voluntary deception; 

Mill is contriving an unfalsifiable position, where no kind of evidence could ever countenance a miracle, even if it occurred. He's sealed himself off from reality by a web of intellectual evasions. How is that different, in principle, from a brilliant psychotic who deems the sensible world to be a cunning illusion, who deems the mental ward, the patients and psychiatrists, to be a cunning illusion? He has ingenious explanations that defect any possible disconfirmatory evidence. 

or, lastly, the event may have had no connection with the volition at all, but the coincidence between them may be the effect of craft or accident, the miracle-worker having seemed or affected to produce by his will that which was already about to take place, as if one were to command an eclipse of the sun at the moment when one knew by astronomy that an eclipse was on the point of taking place. 

That only works in like cases. It fails in cases that are not analogous to that. Mill's tactic is to operate at a level of high abstraction, so that he doesn't have to engage specific evidence for specific miracles. He avoids the details. 

In a case of this description, the miracle might be tested by a challenge to repeat it; but it is worthy of remark, that recorded miracles were seldom or never put to this test. No miracle-worker seems ever to have made a practice of raising the dead: that and the other most signal of the miraculous operations are reported to have been performed only in one or a few isolated cases, which may have been either cunningly selected cases, or accidental coincidences. There is, in short, nothing to exclude the supposition that every alleged miracle was due to natural causes: and as long as that supposition remains possible, no scientific observer, and no man of ordinary practical judgment, would assume by conjecture a cause which no reason existed for supposing to be real, save the necessity of accounting for something which is sufficiently accounted for without it.

i) Even if miracles were confined to a few isolated cases, that's sufficient to overturn a universal negative. If you say all crows are black, it only takes one albino crow to prove otherwise. 

ii) Moreover, magical tricks involve elaborate preparations. Special equipment. Controlled conditions. That doesn't account for the unstructured setting of many reported miracles. 

Were we to stop here, the case against miracles might seem to be complete. But on further inspection it will be seen that we cannot, from the above considerations, conclude absolutely that the miraculous theory of the production of a phenomenon ought to be at once rejected. We can conclude only that no extraordinary powers which have ever been alleged to be exercised by any human being over nature, can be evidence of miraculous gifts to any one to whom the existence of a supernatural Being, and his interference in human affairs, is not already a vera causa. The existence of God cannot possibly be proved by miracles, for unless a God is already recognized, the apparent miracle can always be accounted for on a more probable hypothesis than that of the interference of a Being of whose very existence it is supposed to be the sole evidence. Thus far Hume’s argument is conclusive.

i) What makes divine agency less probable than a naturalistic explanation? In relation to what frame of reference is that less probable? Not in a world where an interventionist God exists. So Mill's strictures are prejudicial. 

ii) Take the discovery of a new pathogen. Must the existence of the pathogen already be recognized before we can point to evidence? The fact that the existence of a hitherto unsuspected pathogen is required to explain the medical condition doesn't mean an investigation must begin with prior belief in the pathogen. 

But it is far from being equally so when the existence of a Being who created the present order of Nature, and, therefore, may well be thought to have power to modify it, is accepted as a fact, or even as a probability resting on independent evidence. Once admit a God, and the production by his direct volition of an effect which in any case owed its origin to his creative will, is no longer a purely arbitrary hypothesis to account for the fact, but must be reckoned with as a serious possibility. The question then changes its character, and the decision of it must now rest upon what is known or reasonably surmised as to the manner of God’s government of the universe: whether this knowledge or surmise makes it the more probable supposition that the event was brought about by the agencies by which his government is ordinarily carried on, or that it is the result of a special and extraordinary interposition of his will in supersession of those ordinary agencies.

That's true. However, it's unnecessary to first prove God's existence before you can appreciate how miracles provide evidence for God's existence, for reasons stated (see above).

In the first place, then, assuming as a fact the existence and providence of God, the whole of our observation of Nature proves to us by incontrovertible evidence that the rule of his government is by means of second causes; that all facts, or at least all physical facts, follow uniformly upon given physical conditions, and never occur but when the appropriate collection of physical conditions is realized. I limit the assertion to physical facts, in order to leave the case of human volition an open question: though indeed I need not do so, for if the human will is free, it has been left free by the Creator, and is not controlled by him either through second causes or directly, so that, not being governed, it is not a specimen of his mode of government. Whatever he does govern, he governs by second causes. This was not obvious in the infancy of science; it was more and more recognized as the processes of nature were more carefully and accurately examined, until there now remains no class of phenomena of which it is not positively known, save some cases which from their obscurity and complication our scientific processes have not yet been able completely to clear up and disentangle, and in which, therefore, the proof that they also are governed by natural laws could not, in the present state of science, be more complete. The evidence, though merely negative, which these circumstances afford that government by second causes is universal, is admitted for all except directly religious purposes to be conclusive. When either a man of science for scientific or a man of the world for practical purposes inquires into an event, he asks himself what is its cause? and not, has it any natural cause? A man would be laughed at who set down as one of the alternative suppositions that there is no other cause for it than the will of God.

i) The "whole of our observation of nature" includes many reported miracles, so Mill's appeal is self-refuting. 

ii) If, moreover, miracles occur, but science disallows miraculous explanations, then science is out of touch with what actually happens in the world. If men of science can't bring themselves to admit reality into their explanatory repertoire, then science becomes a self-enclosed fiction. It's no longer about the world, but what scientists wish to believe, even when their beliefs don't match reality. 

Against this weight of negative evidence we have to set such positive evidence as is produced in attestation of exceptions; in other words, the positive evidences of miracles. And I have already admitted that this evidence might conceivably have been such as to make the exception equally certain with the rule. If we had the direct testimony of our senses to a supernatural fact, it might be as completely authenticated and made certain as any natural one. But we never have. The supernatural character of the fact is always, as I have said, matter of inference and speculation: and the mystery always admits the possibility of a solution not supernatural. 

i) That's a good example of self-reinforcing ignorance. Mill isn't merely confessing that he himself never saw a miracle; rather, he presumes to speak on behalf of everyone else! But, of course, many observers say they do have the direct testimony of their senses to a supernatural fact. That's not firsthand evidence for Mill, but he's in no position to say they can't have the experience they report. He can't speak on their behalf, because he wasn't there. 

ii) Moreover, there's nothing wrong with inference. Take a medical diagnosis, in which a physician infers a particular disease based on distinctive symptoms. 

To those who already believe in supernatural power, the supernatural hypothesis may appear more probable than the natural one; but only if it accords with what we know or reasonably surmise respecting the ways of the supernatural agent. Now all that we know, from the evidence of nature, concerning his ways, is in harmony with the natural theory and repugnant to the supernatural. There is, therefore, a vast preponderance of probability against a miracle, to counterbalance which would require a very extraordinary and indisputable congruity in the supposed miracle and its circumstances with something which we conceive ourselves to know, or to have grounds for believing, with regard to the divine attributes.

Mill keeps repeating the same tendentious claims. Moreover, is he simply speaking in quantitative terms? Is he saying natural explanations are more probable than supernatural explanations because natural events are more frequent than supernatural events? Even if that were so, the inference is fallacious. We explain natural events naturally, not because they are more frequent, but because they have the character of natural events. We ought to explain supernatural events supernaturally because they have the character of supernatural events. Relative frequency is irrelevant. 

Suppose we discovered an ancient alien space craft that crashed on Mars. The frequency or rarity of such phenomenon in our experience has no bearing on the proper interpretation. 

This extraordinary congruity is supposed to exist when the purpose of the miracle is extremely beneficial to mankind, as when it serves to accredit some highly important belief. The goodness of God, it is supposed, affords a high degree of antecedent probability that he would make an exception to his general rule of government, for so excellent a purpose. For reasons, however, which have already been entered into, any inference drawn by us from the goodness of God to what he has or has not actually done, is to the last degree precarious. If we reason directly from God’s goodness to positive facts, no misery, nor vice nor crime ought to exist in the world. We can see no reason in God’s goodness why if he deviated once from the ordinary system of his government in order to do good to man, he should not have done so on a hundred other occasions; nor why, if the benefit aimed at by some given deviation, such as the revelation of Christianity, was transcendent and unique, that precious gift should only have been vouchsafed after the lapse of many ages; or why, when it was at last given, the evidence of it should have been left open to so much doubt and difficulty. 

i) It's unclear how Mill's conclusion follows from his assumption. Let's grant that there's no intrinsic cutoff between one exception and a hundred exceptions. If, then, any exception will be arbitrary in the sense that there could always be one more exception more or one less exception, then there's no antecedent objection to the rarity of miracles (assuming miracles are rare). For Mill's objection is reversible. If miracles were more frequent, the logic of Mill's objection would then be the opposite: they could be less frequent!

ii) In addition, his principle is fallacious. Something that's beneficial in fewer cases may not be equally beneficial in more cases. Some things have special value to us because they are unusual, unexpected, or even unique. If you had a happy childhood, you're nostalgic about your childhood because it's unrepeatable. Something that's routine may be taken for granted. It's enjoyable to listen to my favorite musical numbers every so often. It would be unbearable to listen to them every day and every hour. 

Suppose I'm at the end of my tether. Then an old friend shows up out of the blue. I haven't seen in for years. It's so opportune that he turned up at a low point of my life. Like a providential windfall. If, however, I saw him every week, it wouldn't have the same effect. That would still be good, but a different kind of good. What makes a pleasant surprise pleasant is the element of surprise. Because Mill suffers from an irrational animus towards Christianity, he overlooks many objections to his position. 

Let it be remembered also that the goodness of God affords no presumption in favour of a deviation from his general system of government unless the good purpose could not have been attained without deviation. If God intended that mankind should receive Christianity or any other gift, it would have agreed better with all that we know of his government to have made provision in the scheme of creation for its arising at the appointed time by natural development; which, let it be added, all the knowledge we now possess concerning the history of the human mind, tends to the conclusion that it actually did.

i) What is Mill even talking about? How could mankind receive Christianity through a process of natural development if Christianity is defined by such events as Adam's fall, the call of Abraham, the Exodus, the Incarnation, Resurrection, and return of Christ (to name a few)? These involve personal agency and supernatural intervention. It's not analogous to organic growth. 

ii) What makes miracles a deviation rather than ordinary providence? What makes ordinary providence the standard of comparison? Each has independent value. Each serves a distinctive purpose. 

To all these considerations ought to be added the extremely imperfect nature of the testimony itself which we possess for the miracles, real or supposed, which accompanied the foundation of Christianity and of every other revealed religion. 

i) Miracles aren't confined to the founding of Christianity. Reported miracles occur throughout church history right up until the present. Although not all reports are credible, some are well-attested. 

ii) How many candidates for revealed religions are there?

This is one of Mill's persistent weaknesses. He takes refuge in fact-free generalities. 

Take it at the best, it is the uncross-examined testimony…

What do we know about ancient history and medieval history that's not based on uncross-examined testimony? Most of what we believe about anything is based on secondhand information. We haven't cross-examined our sources of information. 

Mill's objection is self-refuting. He himself relies on the uncross-examined testimony of ancient historians and medieval historians to tell us what conditions were like back then. He unwittingly depends on testimonial evidence to impugn testimonial evidence. 

…of extremely ignorant people, credulous as such usually are, honourably credulous when the excellence of the doctrine or just reverence for the teacher makes them eager to believe; unaccustomed to draw the line between the perceptions of sense, and what is superinduced upon them by the suggestions of a lively imagination; unversed in the difficult art of deciding between appearance and reality, and between the natural and the supernatural; 

That's silly on the face of it. For Bible writers and their audience, miracles stand out precisely because they run counter to the ordinary course of nature. That's what makes them signs and wonders. 

Is it a difficult art to distinguish between appearance and reality? What is Mill's referring to? Walking on water? Turning water into wine? Healing the blind? Replicating food?

…in times, moreover, when no one thought it worth while to contradict any alleged miracle, because it was the belief of the age that miracles in themselves proved nothing, since they could be worked by a lying spirit as well as by the spirit of God. 

They prove the existence of God and evil spirits. That establishes a worldview which is entirely at odds with Mill's naturalism. 

Such were the witnesses; and even of them we do not possess the direct testimony; the documents, of date long subsequent, even on the orthodox theory

Within living memory.

which contain the only history of these events, very often do not even name the supposed eyewitnesses. 

What difference would that make? These are ordinary people. What's the relevance of having someone's name from the past? How does that add to the credibility of the report? What's the difference between a named witness and an anonymous witness at our distance from events? 

If one historical account says a medieval farmer discovered a meteorite on his property while a parallel account says farmer John discovered a meteorite on his property, what does that detail contribute to the credibility of the report? In one case we know the name of the medieval peasant. A name he shared in common with many other medieval peasants.   

They put down (it is but just to admit), the best and least absurd of the wonderful stories such multitudes of which were current among the early Christians.

Is he saying there were many more stories in circulation regarding the miracles of Christ when the Gospels were written? 

but when they do, exceptionally, name any of the persons who were the subjects or spectators of the miracle, they doubtless draw from tradition, and mention those names with which the story was in the popular mind, (perhaps accidentally) connected: for whoever has observed the way in which even now a story grows up from some small foundation, taking on additional details at every step, knows well how from being at first anonymous it gets names attached to it; the name of some one by whom perhaps the story has been told, being brought into the story itself first as a witness, and still later as a party concerned.

i) So his initial appeal to the evidential value of named witnesses was duplicitous. He doesn't care if they were anonymous or not. 

ii) My parents and grandmother used to tell me stories about their lives. There was no growth in their stories. To the contrary, their anecdotes were fixed in memory with a stereotypical form. The wording would vary, but not the content. 

It is also noticeable and is a very important consideration, that stories of miracles only grow up among the ignorant and are adopted, if ever, by the educated when they have already become the belief of multitudes. Those which are believed by Protestants all originate in ages and nations in which there was hardly any canon of probability, and miracles were thought to be among the commonest of all phenomena. 

That statement was demonstrably false even when Mill wrote it, and it hasn't aged well. There are many reported miracles by modern educated witnesses, some of which enjoy independent corroboration. There are collections of vetted miracles by scholars like Robert Larmer and Craig Keener. And that's just what's in the public domain. Most Christians aren't famous. The miracles they experience or witness go unreported. But they know what they saw.

The Catholic Church, indeed, holds as an article of faith that miracles have never ceased, and new ones continue to be now and then brought forth and believed, even in the present incredulous age—yet if in an incredulous generation certainly not among the incredulous portion of it, but always among people who, in addition to the most childish ignorance, have grown up (as all do who are educated by the Catholic clergy) trained in the persuasion that it is a duty to believe and a sin to doubt; that it is dangerous to be sceptical about anything which is tendered for belief in the name of the true religion; and that nothing is so contrary to piety as incredulity. But these miracles which no one but a Roman Catholic, and by no means every Roman Catholic believes, rest frequently upon an amount of testimony greatly surpassing that which we possess for any of the early miracles; and superior especially in one of the most essential points, that in many cases the alleged eyewitnesses are known, and we have their story at firsthand.

There's a lot of truth to that, and I'm no friend of Catholicism. That said, I've read a couple of articles by Stanley Jaki on two miracles attributed to Lourdes. I find his analysis credible.  

Thus, then, stands the balance of evidence in respect to the reality of miracles, assuming the existence and government of God to be proved by other evidence. On the one side, the great negative presumption arising from the whole of what the course of nature discloses to us of the divine government, as carried on through second causes and by invariable sequences of physical effects upon constant antecedents. 

I've responded to that fallacious claim. In addition, Mill erects a false dichotomy between miracles and second causes. But coincidence miracles employ second causes. There are three explanatory categories: natural, preternatural, supernatural. Many amazing answers to prayer are preternatural. 

On the other side, a few exceptional instances, attested by evidence not of a character to warrant belief in any facts in the smallest degree unusual or improbable

There are many well-documented miracles. Not just a "few exceptional instances". Notice, too, that Mill doesn't examine any specific examples. 

the eyewitnesses in most cases unknown, in none competent by character or education to scrutinize the real nature of the appearances which they may have seen

That's demonstrably false. 

and moved moreover by a union of the strongest motives which can inspire human beings to persuade, first themselves, and then others, that what they had seen was a miracle. 

Miracles can be deeply unwelcome when they induce an observer to convert on pain of persecution or martyrdom. There's a powerful disincentive to credit miracles in that case. Take Muslims who attribute their Christian conversion to dreams and visions of Jesus. That's a huge personal risk. 

The facts, too, even if faithfully reported, are never incompatible with the supposition that they were either mere coincidences, or were produced by natural means; even when no specific conjecture can be made as to those means, which in general it can. The conclusion I draw is that miracles have no claim whatever to the character of historical facts and are wholly invalid as evidences of any revelation.

What is Mill's criterion to distinguish coincidence from design? 

What can be said with truth on the side of miracles amounts only to this: Considering that the order of nature affords some evidence of the reality of a Creator, and of his bearing good will to his creatures though not of its being the sole prompter of his conduct towards them: considering, again, that all the evidence of his existence is evidence also that he is not all-powerful, and considering that in our ignorance of the limits of his power we cannot positively decide that he was able to provide for us by the original plan of Creation all the good which it entered into his intentions to bestow upon us, or even to bestow any part of it at any earlier period than that at which we actually received it—considering these things, when we consider further that a gift, extremely precious, came to us which though facilitated was not apparently necessitated by what had gone before, but was due, as far as appearances go, to the peculiar mental and moral endowments of one man, and that man openly proclaimed that it did not come from himself but from God through him, then we are entitled to say that there is nothing so inherently impossible or absolutely incredible in this supposition as to preclude any one from hoping that it may perhaps be true. I say from hoping; I go no further; for I cannot attach any evidentiary value to the testimony even of Christ on such a subject, since he is never said to have declared any evidence of his mission (unless his own interpretations of the Prophecies be so considered) except internal conviction; and everybody knows that in prescientific times men always supposed that any unusual faculties which came to them they knew not how, were an inspiration from God; the best men always being the readiest to ascribe any honourable peculiarity in themselves to that higher source, rather than to their own merits.

The case for Christianity is hardly confined to the sole testimony of Jesus.