Chapter VII: Introduction: To Part III (2)

“But is this the full truth of the matter? Are not the laws of chance a source of knowledge? And, stranger still, is it not sometimes easier to generalise (say) about random movements than about movements which obey even a simple law—witness the kinetic theory of gases? And, if this be so, how can chance be the equivalent of ignorance? Ask a physicist to explain what goes on in a gas. He might, perhaps, express his views in some such terms as these: ‘You wish me to tell you about these complex phenomena. If by ill luck I happened to know the laws which govern them, I should be helpless. I should be lost in endless calculations, and could never hope to supply you with an answer to your questions. Fortunately for both of us, I am completely ignorant about the matter; I can, therefore, supply you with an answer at once. This may seem odd. But there is something odder still, namely, that my answer will be right.’”

Now, what are the conditions which make it possible thus to extract a correct answer from material apparently so unpromising? They would seem to be a special combination of ignorance and knowledge, the joint effect of which is to justify us in supposing that the particular collection of facts or events with which we are concerned are happening “at random.” If we could calculate the complex causes which determine the fall of a penny, or the collisions of a molecule, we might conceivably deal with pennies or molecules individually; and the calculus of probability might be dispensed with. But we cannot; ignorance, therefore, real or assumed, is thus one of the conditions required to provide us with the kind of chaos to which the doctrine of chances may most fittingly be applied. But there is another condition not less needful, namely, knowledge—the knowledge that no extraneous cause or internal tendency is infecting our chaotic group with some bias or drift whereby its required randomness would be destroyed. Our penny must be symmetrical, and Maxwell’s demons[10] must not meddle with the molecules.

The slow disintegration of radium admirably illustrates the behaviour of a group or collection possessing all the qualities which we require. The myriad atoms of which the minutest visible fragment is composed are numerous enough to neutralise eccentricities such as those which, in the case of a game of chance, we call “runs of luck.” Of these atoms we have no individual knowledge. What we know of one we know of all; and we treat them not only as a collection, but as a collection made at random. Now, physicists tell us that out of any such random collection a certain proportion will disintegrate in a given time; and always the same proportion. But whence comes their confidence in the permanence of this ratio? Why are they so assured of its fixity that these random explosions are thought to provide us with a better time-keeper than the astronomical changes which have served mankind in that capacity through immemorial ages? The reason is that we have here the necessary ignorance and the necessary knowledge in a very complete form. Nothing can well exceed our ignorance of the differences between one individual radium atom and another, though relevant differences there must be. Nothing, again, seems better assured than our knowledge that no special bias or drift will make one collection of these atoms behave differently from another. For the atomic disintegration is due to no external shock or mutual reaction which might affect not one atom only, but the whole group. A milligram of radium is not like a magazine of shells, where if one spontaneously explodes all the rest follow suit. The disruption of the atom is due to some internal principle of decay whose effects no known external agent can either hasten or retard. Although, therefore, the proportion of atoms which will disintegrate in a given time can only be discovered, like the annual death-rate among men, by observation, yet once discovered it is discovered for ever. Our human death-rate not only may change, but does change. The death-rate of radium atoms changes not. In the one case, causes are in operation which modify both the organism and the surroundings on which its life depends. In the other case, it would seem that the average of successive generations of atoms does not vary, and that, once brought into existence, they severally run their appointed course unaffected by each other or by the world outside.

So far we have been concerned with groups or collections or series; and about these the doctrine of chances and the theory of error may apparently supply most valuable information. But in practical affairs—nay, even in many questions of scientific speculation—we are yet more concerned about individual happenings. We have, therefore, next to ask how we can infer the probability of a particular event from our knowledge of some group or series to which it belongs.

There seems at first sight no difficulty in this, provided we have sufficient knowledge of the group or series of which the particular event is a member. If we know that a tossed penny will in the long run give heads and tails equally often, we do not hesitate to declare that the chances of a particular throw giving “heads” are even. To expect in any given case heads rather than tails, or tails rather than heads, is inconsistent with the objective knowledge of the series which by hypothesis we actually possess.

But what if our information about the group or series is much less than this? Suppose that, instead of knowing that the two possible alternatives do in fact occur equally often, we are in the less advantageous position of knowing no reason why they should _not_ occur equally often. We ought, I suppose, still to regard the chances of a particular toss as even; although this estimate, expressed by the same fraction (½) and held with the same confidence, is apparently a conclusion based on ignorance, whereas the first conclusion was apparently based on knowledge.

If, for example, we know that a die is fairly made and fairly thrown, we can tell how often a particular number will turn up in a long series of throws, and we can tell what the chances are that it will turn up on the occasion of a single throw. Moreover, the two conclusions seem to be logically connected.

But if we know that the die is loaded we can no longer say how the numbers will be distributed in a series of throws, however long, though we are sure that the distribution will be very different from what it would have been had the die been a fair one. Nevertheless, we can still say (before the event) what the chances are of a particular number turning up on a single throw; and these chances are exactly the same whether the die be loaded or whether it be fair—namely, one-sixth. Our objective knowledge of the group or series has vanished, but, with the theory of probability to help us, our subjective conviction on this point apparently remains unchanged.

There is here, surely, a rather awkward transition from the “objective” to the “subjective” point of view. We were dealing, in the first case, with groups or series of events about which the doctrine of chances enabled us to say something positive, something which experience would always confirm if the groups or series were large enough. A perfect calculator, endowed with complete knowledge of all the separate group members, would have no correction to make in our conclusions. His information would be more complete than our own, but not more accurate. It is true that for him “averages” would have no interest and “chance” no meaning. Nevertheless, he would agree that in a long series of fair throws of a fair die any selected face would turn up one-sixth times as often as all the others taken together. But in the second case this is no longer so. Foresight based on complete knowledge would apparently differ from foresight based on the calculation of chances. Our calculator would be aware of the exact manner in which the die was loaded, and of the exact advantage which this gave to certain numbers. He would, therefore, know that in asserting the chance of any particular number turning up on the first throw to be one-sixth, we were wrong. In what sense, then, do we deem ourselves to have been right?

The answer, I suppose, is that we were right _not_ about a group of throws made with _this_ loaded die, but about a group of such groups made with dice loaded at random—a group in which “randomness” was so happily preserved among its constituent groups that its absence within each of these groups was immaterial, and no one of the six alternative numbers was favoured above another.

A similar reply might be given if we suppose our ignorance carried yet a step further. Instead of knowing that our die was loaded, and being ignorant only of the manner of its loading, we might be entirely ignorant whether it was loaded or not. The chances of a particular number turning up on the first throw would still be one-sixth. But the series to which this estimate would refer would neither be one composed of fair throws with a fair die, nor one composed of a series of throws with dice loaded at random, but one composed of a series of throws with dice chosen at random from a random collection of dice, loaded and not loaded!

It seems plain that we have no experimental knowledge of series piled on series after this fashion. Our conclusions about them are not based on observation, nor collected from statistics. They are arrived at _a priori_; and when the character of a series is arrived at _a priori_, the probability of a particular event belonging to it can be arrived at independently by the same method. No reference to the series is required. The reason we estimate the chances against any one of the six possible throws of a die as five to one under each and all of the suppositions we have been discussing is that under none of them have we any ground for thinking any one of the six more probable than another;—even though we may have ground for thinking that in a series of throws made with that particular die, some number, to us unknown, will in fact turn up with exceptional frequency.

The most characteristic examples, therefore, of problems in probability depend for their solution on a bold use of the “principle of sufficient reason.” We treat alternatives as equally likely when we cannot see any ground for supposing that one is more likely than another. This seems sensible enough; but how far may we carry this process of extracting knowledge from ignorance? An agnostic declines to offer any opinion on the being of God because it is a matter about which he professes to know nothing. But the universe either has a spiritual cause, or it has not. If the agnostic is as ignorant as he supposes, he cannot have any reason for preferring the first alternative to the second, or the second to the first. Must he, therefore, conclude that the chances of Theism are even? The man who knows this knows much. He knows, or may know, that God’s existence is slightly more probable than his own chance of winning a coup at Monte Carlo. He knows, or may know, the exact fraction by which the two probabilities differ. How, then, can he call himself an agnostic?

Every one must, I think, feel that such reasoning involves a misuse of the theory of probability. But is that misuse without some justification? The theory, unless I misread it, permits, or rather requires, us to express by the same fraction probabilities based on what is little less than complete knowledge, and probabilities based on what is little more than complete ignorance. To arrive at a clear conclusion, it seems only necessary to apply the “law of sufficient reason” to defined alternatives; and it is apparently a matter of perfect indifference whether we apply this law in its affirmative or its negative shape; whether we say “there is every reason for believing that such and such alternatives happen equally often,” or whether we say “there is no reason for thinking that one alternative happens more often than the other.” I do not criticise this method; still less do I quarrel with it. On the contrary, I am lost in admiration of this instrument of investigation, the quality of whose output seems to depend so little on the sort of raw material with which it is supplied.

III

My object, indeed, is neither to discuss the basis on which rests the calculus of probabilities—a task for which I own myself totally unfit—nor yet to show that a certain obscurity hangs over the limits within which it may properly be employed. I desire rather to suggest that, wherever those limits are placed, there lies beyond them a kind of probability yet more fundamental, about which the mathematical methods can tell us nothing, though it possesses supreme value as a “guide of life.”

Wherein lies the distinction between the two? In this: the doctrine of calculable probability (if I may so call it) has its only application, or its only assured application, within groups whose character is either postulated, or is independently arrived at by inference and observation. These groups, be they natural or conventional, provide a framework, marking out a region wherein prevails the kind of ignorance which is the subjective reflection of objective “randomness.” This is the kind of ignorance which the calculus of probabilities can most successfully transmute into knowledge: and herein lies the reason why the discoverers of the calculus found their original inspiration in the hazards of the gambling-table, and why their successors still find in games of chance its happiest illustrations. For in games of chance the group framework is provided by convention; perfect “randomness” is secured by fitting devices; and he who attempts to modify it is expelled from society as a cheat.

None of these observations apply to the kind of probability on whose importance I am now insisting. If calculable probability be indeed “common sense reduced to calculation,” intuitive probability lies deeper. It supports common sense, and it supplies the ultimate ground—be it secure or insecure—of all work-a-day practice and all scientific theory. It has nothing to do with “randomness”; it knows nothing of averages; it obeys no formal laws; no light is thrown on it by cards or dice; it cannot be reduced to calculation. How, then, is it to be treated? What place is it to occupy in our general scheme?

These are all important questions. But no answer to them can be given till we have pressed somewhat further the line of thought which the discussion in this present lecture has for a moment interrupted. Before I began this long parenthesis on the theory of chance, I was occupied with a most important example of a belief which possesses the highest degree of intuitive probability, but no calculable probability at all. I mean the belief in an independent physical universe. In the next lecture I shall resume the general thread of my argument, and consider another belief of the same kind which is not less—some would say even more—essential to natural science than the one with which I have already dealt. I mean a belief in the regularity of nature.

FOOTNOTES:

[9] Although, as a matter of fact, I do speak of it in the next lecture.

[10] Maxwell, as all who interest themselves in physics are aware, arrived at very interesting conclusions by considering what would happen if little demons interfered with the random motions of the molecules constituting a gas.

LECTURE VIII

UNIFORMITY AND CAUSATION

I

In my last lecture but one I dwelt upon the interplay of causes and reasons in one special case—the case of our immediate experiences of the external world, the world in which we move, the world investigated by the physical sciences. No case can indeed be more important; for these immediate experiences are deemed by every man to be his guide through all the hours of his waking life, and by every man of science to supply the evidence on which depends all our knowledge of natural laws.

Yet this very statement suggests the existence of another series of problems not less important and not less closely connected with my general argument. For, how do we get from particular experiences to general laws—from beliefs about individual occurrences to beliefs about the ordering of the universe? These beliefs, looked at from the scientific point of view, are, as I have so often observed, a natural product. They have a history like other natural products. They are the effects of a long train of causes; and among those causes are some which claim, rightly or wrongly, to be reasons, an uncounted multitude which make no such claim, and others, again, which occupy a doubtful position between the two.

Imagine an external intelligence studying the methods by which earth-born creatures of various types adjust themselves to future circumstances. The most primitive method is, I suppose, no more than simple nervous reaction. The most developed method involves reasoned expectation. And between these two extremes our supposed observer would see a long series of intermediate forms melting into one another by insensible gradation.

From the point of view of the argument I am endeavouring to present to you, this development is of the greatest interest. The creation of a capacity for expectation, and of an inclination to expect a future similar to the past, must be deemed one of the most remarkable triumphs of selection—if to selection it indeed be due. Here we have this irrational mimic of reason, starting from the simplest forms of response to external stimulus, improving them into such excellent imitations of inductive reasoning as those which lead a chick, no more than a few hours old, to reject food which it has once found nasty[11]; and finally evolving out of these humble beginnings a mode of inference which, according to empirical philosophy, is the true and only source of all our general knowledge, whether of nature or of man.

It must be owned, indeed, that the attempt to treat instinctive expectation as a form of rational inference has been a lamentable failure. By no exercise of ingenuity can beliefs about what is not experienced be logically extracted from particular experiences, multiply them as you will. It is in vain that empirical philosophers attempt to give an air of rationality to this leap from the known to the unknown by the use of high-sounding logical titles. “Induction by simple enumeration” is doubtless an imposing name. But those who practise the thing are in no wise improving on their predecessor, the chick. Indeed they lag behind it. For the chick expects—but gives no reason; the empirical philosopher expects—and gives a bad one.

II

Expectation, then, if it is to be rational, can only be rationally extracted from experiences by the aid of one or more general principles. What principles are they?

One of them, at all events, must be the regularity of nature. In some form or other, and to some degree or other, this is assumed in every scientific speculation and in every purposeful action reflectively performed. It is, as you may recollect, one of the “inevitable beliefs of common sense” to which I referred in my first lecture.

But you may also recollect that in the same lecture I pointed out that inevitable beliefs, though we cannot avoid holding them in some shape, are, and have been, held in many shapes; shapes which vary with the changes in our general outlook on men and things. In what shape, then, should our belief in regularity now be held?

The shape in which it is very commonly formulated is something of this kind: “everything is caused; and the same causes are always followed by the same effects.” This is the so-called “law of universal causation.” It has been treated as an assured truth by philosophers of many different schools, though not always for the same reasons; and, so far as the physical universe is concerned, the modern world accepts it without demur. It is, nevertheless, open to criticism from two points of view. It asserts somewhat more about the course of nature than experience suggests, and somewhat less than science requires. Let me take the two points separately.

When I was dealing with ethics I had occasion to point out that if the primitive manifestations of loyalty and love are products of selection, they have developed by a kind of internal momentum, to a point far beyond that to which selection can possibly have carried them. Something of the same kind has happened in the case of the causal postulate. Selection, we must suppose, has produced the capacity for acquiring habitual expectations; and habitual expectation is induction without reasoning. Like induction, it would not only be useless, but harmful, if no regularity existed; if at any moment the future ceased to bear some resemblance to the past. But the regularity asserted by the law of universal causation is far in excess of this requirement. The law applies to regions which never come within the range of finite experience; and, as regards regions which do come within that range, experience hardly confirms it. We may, of course, attribute the apparent irregularities in nature to our ignorance or our errors; and this, in fact, is what we always do. We must (we think) have observed wrongly or insufficiently; or it may be that a clearer insight would show how apparent aberrations really illustrate some larger law, or depend on conditions at present beyond our ken. Such explanations are easy; and, what is more, they are true. There is no complaint to be made of a verdict in favour of absolute uniformity except that it outruns the evidence. None surely, who understand the meaning of the words they use, will dare to assert that nature _appears_ regular. What they _may_ assert is, that the more you examine it, the more regular it appears. The reign of law is always extending. New provinces are always being added to its domains. Anomalies vanish as knowledge grows; and the absolute uniformity which we now only know by faith, we may some day know by sight.

To this “credo” (with reservations) I readily subscribe. But it sounds a little strange in the mouths of some who preach it. Does it not imply that we interpret our experiences in the light of a preconceived scheme of things; that we force our observations into a mould which they do not naturally fit? If, in unravelling a cypher, I come across passages which are unintelligible, I attribute the check to my own ignorance or dullness. Why? Because I know independently that the cypher has a meaning, if only I could find it. But the empirical agnostic professes to know nothing about the world, except what he has observed himself or what other people have observed for him. Why, then, should he suppose perfect regularity to exist when no perfect regularity appears? Why is he not content to accept what he finds, namely, a regularity which is real but incomplete?

It is no reply to say that patient genius is constantly detecting order in apparent chaos. So it is. And when this happens, by all means rearrange your map of the universe accordingly. But do not argue that chaos is therefore non-existent. The belief in universal causation is not based on argument, nor yet on observation. It depends on what I have described as intuitive probability. And if we refuse to regard nature as liable to lapses from perfect uniformity, this is not because such a theory is unthinkable, not because it is contrary to experience, not because it is incompatible with knowledge, not because it is fatal to purposeful action; for it is none of these things. We reject it because it is out of harmony with the ideal we have formed of what the material universe ought to be and is: and so strong is this speculative prepossession that there is no experimental evidence which would convince a man of science that, when physical causes were the same, physical consequences could be different.

III

But this observation brings me to my second commentary on the formula of universal causation. If, as I have contended, it goes beyond what mere experience suggests, it also falls short of what scientific inference requires. The uniformity it postulates lacks a certain kind of “structure” which is absolutely necessary if the past is to be explained and the future foreseen. It is not enough for this purpose that the course of Nature should be determined. It must be determined after a particular pattern; its uniformity must conform to a particular type.

At first sight this statement may seem rather obscure. What (you will ask) is this “structure” or pattern whose absence would be so disastrous to knowledge? It is a structure (I reply) which makes it possible to break up the flow of events into intelligible repetitions. It is not enough that the condition of the world at any moment should be strictly determined by its condition at the preceding moment. Such a world would, I suppose, completely conform to the doctrine of uniformity, and obey both in spirit and in letter the law of universal causation. Yet, unless it also conformed to the additional canon I have just laid down, it would provide no basis either for scientific knowledge or for practical decision. The same consequent would always succeed the same antecedent, if and when it recurred. But, unless we accept the cyclic theories of the Stoics, it never would recur. The completest knowledge of the past would tell us nothing about the future; not because the succession of events was arbitrary or (as the word is commonly misused) miraculous; but because each cross-section of the stream of Time (that is to say, the sum of all contemporaneous facts and events) had to be considered as a single cause, completely determining the whole cross-sections immediately in front of it; and, as a single effect, completely determined by the whole cross-section immediately behind it. Such a world might have a history, but it could never have a science.

The reason is plain. Science requires uniformities even more than uniformity; and a universe such as I have just described has uniformity but no uniformities. The very phrase “laws of nature” shows that it is these subordinate uniformities for which we look. The whole efforts of the skilled investigator are directed towards so isolating the sequences he is examining that his experiments shall become (as the phrase goes) _crucial_. If no such isolation could be effected, it would never be possible to point to some “phenomenon” and say of it “Here is a cause,” and to some other “phenomenon” and say of it “Here is its effect.” The world, in short, must have a structure which connects its successive phases in such a way that definite parts of all that exists or happens are knit with peculiar closeness to definite parts of what existed or happened before. It is on these connecting strands that we mainly fix our gaze; they are often difficult to trace, they are sometimes hopelessly entangled; but when we can bring them into clear vision, then, and not till then, we triumphantly say that we have discovered a law of nature.

We are so familiar with this “fibrous” structure of the natural world that it seems almost a matter of course. Mill, for example, assumes it, unconsciously no doubt, through all his exposition of inductive methods: and if he had not assumed it, these methods would have come tumbling about his ears in irreparable ruin. But assuredly neither he nor any other logician has a right to make such an assumption in silence. In spite of many speculative difficulties, there is no principle more vital to knowledge, practical and theoretical, than the principle of “negligibility”; the principle which asserts that sequences can be isolated and repeated, and that vast bodies of contemporaneous facts and happenings may be wholly neglected. It is much more important than the principle of causation, if by causation is meant, not a working, though possibly imperfect, regularity, but the speculative completeness implied by the phrase “universal causation” as commonly interpreted.

It may be said, and I think with truth, that these observations scarcely apply to a material world conceived in a purely mechanical fashion. In such a world negligibility is theoretically measurable. The mass of Sirius, without doubt, modifies the weight of the pen with which I am writing. But the effect is demonstrably infinitesimal, and negligibility is not assumed, but proved. Laplace’s calculator, surveying the universe, would have no difficulty either in fixing his attention on particular repetitions which exemplify the “laws of nature,” or in regarding them as integral parts of a single mechanical whole, whose successive phases (if the law of energy dissipation be universal) can never be repeated.

But this does not lighten the difficulty. The world may, or may not, be a single mechanical system; but, if it is, the fact can only be empirically known to us through induction: and induction assumes negligibility, and cannot, so far as I can see, move a step without it. Choose the most perfect experiment on record, idealise its conditions to your heart’s content; for greater security, suppose it repeated even to weariness, how will you be advanced? There are, I suppose, millions of circumstances, for the most part utterly unknown, which have co-existed with all the experiments already tried, but will have vanished before the next experiment is undertaken. Does this disturb you? Do you ask yourself whether, among the unnumbered circumstances in which the world of to-day differs from the world of yesterday, there may not be one which is necessary to the expected effect? Not at all. You brush them aside. You say they may be neglected. And doubtless you do well. But why? Not on any grounds which observation or reasoning can supply, not on any grounds formulated in the logic of induction, or the calculus of chances. You trust yourself to a feeling of antecedent probability;—the intuitive probability on whose importance I dwelt in the last lecture, which is not the flower of experience but its root;—and your trust will sometimes be betrayed.

The principle of negligibility, or (in terms of belief) the belief that observed regularities may often be treated as if they were complete and self-contained cases of cause and effect, separable from contemporary events, is thus a necessary presupposition of concrete science; and, like other presuppositions, it is incapable of scientific proof. We often hear it said, indeed, that principles of this kind should be regarded as hypotheses verified by an ever-increasing volume of experimental proof. They are found to work; what more can be desired?

But it is not accurate to say that these and other fundamental principles are, or ever have been, regarded either by common sense or science as inferences from experience or as hypotheses requiring verification. Nor is it accurate to suggest that verification differs essentially from any other kind of experimental evidence except in the date of its occurrence. If evidence follows conjecture, but not otherwise, it is called verification; and though, from the point of view of method, this chronological order is of immense importance, from the point of view of logic it is nothing. A doubtful conjecture (let us suppose) is “verified” by experiment. If the experiment had come earlier there would have been no conjecture, but there would have been equal evidence, indeed the same evidence. It is true that without the conjecture there might have been no experiment, and that without the experiment there might have been no proof. But, though the conjecture occasioned the proof, it certainly adds nothing to its force, and we therefore come back to the question already discussed—namely, whether principles without which no inference from experiences is possible, can be themselves inferred from experiences?—a question to which, as I conceive, only one answer is possible. Experiences may produce habit, and habit may produce expectation, and this process may masquerade as induction. But expectations thus engendered belong to the causal series, not the cognitive. Physiology and psychology may explain them. But they can neither be proved nor treated as axiomatic.

Axiomatic they certainly are not; nor do they possess the universality and precision of outline which we are accustomed to associate with axioms. It is curious, in this connection, to note that the philosophers who are most firmly resolved to root the principle of regularity (they ignore negligibility) in experience always insist on giving it that absolute character which our inferences from experience rarely possess. The notion that fundamental beliefs should be liable to exception, should be capable of degrees, and should apply unequally in different fields of observation, is as abhorrent to them as to any metaphysician out of the opposite camp. One would suppose, to hear them talk, that, unless causation be universal, experience is worthless.

IV

The region where these uncompromising doctrines show to least advantage is human character. I do not propose to discuss causation and free will; but I may with advantage say something on a less hackneyed theme, namely, negligibility and foreknowledge. The thesis I desire to maintain is that, in dealing with a human character, full foreknowledge is theoretically impossible, even though free will be wholly absent, and the succession of psychic states be completely determined. Practically impossible we know it to be. But most determinists would hold that this impossibility is due partly to our ignorance and partly to our incapacity. We know too little either of the general laws of mind, or of individual character, or of surrounding circumstances, to make accurate forecasts; and, even if we possessed the requisite information, we could not use it, owing to the irremediable weakness of our powers of calculation. It is this contention that I wish to traverse. I hold that, had we the supernatural powers of Laplace’s calculator, armed with a knowledge of the human heart which supernatural powers of observation could alone supply, we should still fail, because we are face to face with that which is inherently incalculable.

The contrary opinion is due, I think, to an imperfect comprehension of the doctrines I have touched on in this lecture. All human foreknowledge depends on detecting old sequences in a new context. The context, of course, is always new. There is never full or complete repetition. But, unless there be partial repetitions embedded in the universal flux, prescience is impossible. This is the doctrine of “negligibility.”

Now consider two illustrative examples.

First, imagine yourself standing on the edge of a valley down which a landslip has just let loose the waters of some great reservoir in the hills. The catastrophe is sudden in its onset, brief in its duration, wildly irregular in its character. Even the most tumultuous cataract retains a certain steadiness of outline: and few sights are more impressive than the stationary waves in a great rapid. But there is here no trace of order imposed on disorder, fixity on motion. The rushing wall of water, spouting into foam over every obstacle it encounters, the tossing flood that follows furiously behind, seem in their brief violence to present the very ideal of incalculable confusion. But we know it is not so. In the presence of such a spectacle our calculator would not feel a moment’s embarrassment. He could forecast without difficulty the whole scene down to its minutest eddy; the motions of each drop obey laws with which he was perfectly familiar; and the total effect, catastrophic though it be, is but the sum of all these component examples of natural uniformity.

Turn now and contemplate a calmer scene. Consider the commonplace life of a commonplace man as it develops in the untroubled prosperity of a steady business and a quiet home. Such a career seems as orderly and uniform as the flood I have been describing is terrible and strange. Surely no supernatural calculator is required to cast the horoscope of its hero: for he does, and leaves undone, the same actions, he thinks and leaves unthought the same ideas, as thousands of his contemporaries; and, so far as outward appearance goes, he is an indistinguishable member of an undistinguished crowd.

Yet, in spite of this, we know him to be unique. There never has been before, nor will there ever be again, another individual exactly like him. A similar statement, it may be urged, can be made about our catastrophic flood. Though this has plenty of parallels, none of them, strictly speaking, are exact. Where, then, lies the distinction on which I am trying to insist? Let me endeavour to mark the contrast.

If the material world be conceived as a mechanical system, the flood in my illustration may be regarded as a piece arbitrarily cut out of it at the whim of the spectator. It possesses no natural unity; and, like the whole of which it is a fraction, the moving particles which compose it do each obey laws which are (we assume) perfectly well known, and have been endlessly exemplified. Its behaviour is the sum of the behaviour of these several parts: and it is by estimating their movements that our imaginary calculator can prophesy its course with absolute exactness. He is never perplexed by the problem of negligibility; for negligibility in such a case can be accurately measured, and our calculator possesses all the data required for its measurement. In short, the principle of regularity may here be applied in its most uncompromising form; it requires no qualification, nor can it be pressed too boldly or too far.

But the case is otherwise when we have to abandon the strictly mechanical point of view, and investigate regions where negligibility has a small and uncertain application. Such a region is individual consciousness. This possesses a natural or intrinsic unity. Its phases are never precisely repeated; nor can it be regarded as a collection of independent elements, the sequences of which may be separately examined, verified, and repeated. Not only is the whole unique, but the parts are unique also. Or, perhaps it would be more accurate to say that there _are_ no parts possessing a fixed character of their own apart from the whole. Not only is everything qualified by everything else, but few of these qualifications are negligible. Perfect repetition is therefore impossible, and our calculator, whatever his powers, could never feel at home with his premises, or secure in his conclusions. The present would always be new, and the future would always be doubtful.

If this seems paradoxical it is, I think, mainly for two reasons. In the first place, such a doctrine seems inconsistent with the fact that, whatever Laplace’s calculator could do, humbler beings like ourselves manage somehow or other to forecast the behaviour of our neighbours with some small measure of success. This, no doubt, is true. But it is in part because the alternatives of behaviour are very few and very definite compared with the infinitely graduated variations of thought, will, and feeling. Action is “canalised.” It can flow only along channels engineered for it by circumstances, and among these the choice is commonly small. But the character which lies behind action is complex beyond all power of analysis, and variable beyond all powers of anticipation. The routine which is unwaveringly pursued from month to month and year to year is pursued each day in a different spirit: and often a critical hour strikes when some well-drilled creature of custom, to his own surprise and the scandal of his friends, deserts the ancient ways and wanders suddenly forth into the unknown.

Of course, these violent aberrations are the exception. The more familiar experience is that, in an orderly society, the alternatives of action which need be taken into account are few, and the “limits of deviation” narrow. Often, therefore, we can anticipate conduct without any real insight into the depths of character or the complexities of motive from which the conduct springs. And truly this is fortunate; for, if mutual comprehension were necessary to social intercourse, how could society exist?

But there is another reason why we take little note of the distinction I am endeavouring to draw between the calculable uniformities of a material world and the incalculable regularities of psychic life. The distinction is rather speculative than practical. It does not affect the routine of daily existence. For, although the course of the material world is calculable, we mortals have neither the time nor the knowledge nor the mental powers required to calculate it. We behave, therefore, towards nature as we behave towards man. We content ourselves with approximations, with analogies, with resemblances. Even if we had the power, we should not have the time to resolve the movement of all the bits of matter with which we have to deal from minute to minute into the exact sequences of which they are composed. We would not if we could. We apply rough methods; we are satisfied with imperfect results. Nor are these results always more imperfect in the psychic than in the material sphere of observation. The ways (for example) of British weather are even more mysterious than the ways of British men. Why, then, should we interest ourselves in a speculation which tells us, however truly, that perfect foreknowledge is theoretically possible in the first case, but theoretically impossible in the second? In practice it is impossible in both. And with this we must be content.

And yet the speculation is interesting. For the distinction between the two cases lies deep. It has nothing (let me say again) to do with free will. It has nothing to do with our ignorance of facts. It has nothing to do with our intellectual insufficiency. It is due to a fundamental difference between the uniformities of matter and the regularities of mind. Perfect foresight requires perfect repetition, and in the psychic sphere perfect repetition can never happen. Every self is unique; all its experiences are unique; and these unique wholes are not compounded of interchangeable elements obeying identical laws. They do not alter by mere addition, subtraction, or rearrangement of parts. They grow. And the sequence of one phase upon another faintly resembles that which would prevail in the imaginary universe of which I spoke just now, the universe where all contemporaneous events were treated as the single effect of the immediate past and the single cause of the immediate future. Of such a universe I observed that it would have a history, but could have no science. And though we cannot go so far when speaking of psychic unities, though we cannot rule out psychology or sociology, it must be admitted that no regularities which observation discloses can ever possess the precision which we theoretically attribute to material mechanism. Instructive likenesses we shall find in abundance, complete determination we may assume if we please; but “laws,” in the full and strict sense of the term, we shall not find, for they are not there.

NOTE

The shortcomings of mechanism have been discussed by M. Bergson in a manner which no other thinker is likely to rival. He has, however, usually dealt with the subject in connection with _freedom_; whereas in this section I have only dealt with it in connection with foreknowledge, repetition, and what I have termed the doctrine of “negligibility.” He approaches it from the side of reality. I approach it from the side of inductive inference and the law of universal causation.

FOOTNOTES:

[11] Extract from Morgan’s “Habit and Instinct,” page 40. “A young chick two days old, for example, had learnt to pick out pieces of yolk from others of white of egg. I cut little bits of orange-peel of about the same size as the pieces of yolk, and one of these was soon seized, but at once relinquished, the chick shaking his head. Seizing another, he held it for a moment in the bill, but then dropped it and scratched at the base of his beak. That was enough; he could not again be induced to seize a piece of orange-peel. The obnoxious material was now removed, and pieces of yolk of egg substituted, but they were left untouched, being probably taken for orange-peel. Subsequently, he looked at the yolk with hesitation, but presently pecked doubtfully, not seizing, but merely touching. Then he pecked again, seized, and swallowed.”

LECTURE IX

TENDENCIES OF SCIENTIFIC BELIEF

I

In the sixth and eighth lectures of this course I dealt with two inevitable beliefs which lie at the root of all science and all practice—the beliefs that an independent, or, as it is commonly called, an “external” world exists, and the belief that the world, whether external or internal, has at least a measure of regularity. In the seventh lecture I interpolated a discussion upon probability; and showed, or attempted to show, that we must take account of a kind of probability other than that which, in the hands of mathematicians, has so greatly contributed to knowledge.

If, now, we consider these subjects in their mutual relation, we perceive that an “inevitable” belief is one which possesses the highest degree of this intuitive probability. These are two descriptions of the same quality—one emphasising the objective, the other the subjective, aspects of a single fact.

But this at once suggests a further inquiry. Probability is evidently a matter of degree. A belief may be more probable or less probable. Inevitableness, on the other hand, seems at first sight to be insusceptible of gradation. It is, or it is not. Yet this extreme definiteness vanishes if we regard it as a limiting case—as the last term of a series whose earlier members represent varying degrees of plausibility. On this view we should regard our beliefs about the universe as moulded by formative forces, which vary from irresistible coercion to faint and doubtful inclination. Beliefs in the reality of the external world and in its regularity are important products of the first. I now propose to call attention to some beliefs which are due to the less obvious action of the second. Both kinds, whether capable of proof or not, are more or less independent of it. Both are to be regarded rather as the results of tendencies than as the conclusions of logic.

I am well aware that a doctrine like this will find few admirers among systematic thinkers. Inevitable beliefs which are fundamental without being axiomatic; which lack definiteness and precision; which do not seem equally applicable to every field of experience; which do not claim to be of the essence of our understanding, like the categories of the critical philosophy, or the so-called laws of thought, have little to recommend them to philosophers. And when inevitableness is treated as merely an extreme form of plausibility, when guidance is discovered in tendencies which are weak and of uncertain application, leading to error as well as to truth, their objections will scarcely be mitigated.

Many of those who look at these problems from (what they deem to be) a strictly scientific point of view are not likely to be more favourable. Their loyalty to experience takes the form of supposing that men accumulate knowledge by peering about for “sequences” among “phenomena,” as a child looks for shells upon the beach—equally ready to go north or south, east or west, as the humour of the moment moves him. They would regard any antecedent preference for this or that sort of explanation as a sin against the categorical imperatives of intellectual morals. Science, they think, should have no partialities: and as the honest investigator “entertains no belief with a conviction the least in excess of the evidence,”[12] so he will resist any leaning toward one kind of conclusion rather than another. Such is their view of scientific duty. Scientific practice, however, has been otherwise.

That the practice of ordinary humanity has been otherwise seems indeed sufficiently plain. The folk-lore, the magic, and the religions of primitive races, with all their unborrowed resemblances, are there to attest it. But these (you will say) are superstitions. The objection is not, I think, relevant; yet, for the sake of peace, let us pass to what is not regarded as a superstition, namely, morality. Here you have the singular spectacle of a close agreement among moralists as to the contents of the moral law, and a profound disagreement as to the grounds on which the moral law is to be accepted. Can the power of “tendency” be better shown? Can there be a clearer illustration of the way in which it may guide belief and anticipate proof?

II

But our business to-day is neither with magic nor morality. It is with physical science. When we survey man’s strivings to understand the world in which he lives, can we detect any secular leanings towards certain types of belief, any deep-lying inclination to guess by preference in one direction rather than another? We surely can. There are some answers, for example, which we refuse to take from experiment and observation. I have already referred to one such case in connection with causation. No man of science can be provoked, by any seeming irregularities, into supposing that the course of nature is subject to lapses from the rule of perfect uniformity. Consider, again, another case, where the tendency is far less strong, but where few can doubt that it is real. I refer to the deep-seated reluctance felt by most physicists to accept as final any scientific explanation which involves a belief in “action at a distance”—a reluctance which is the more remarkable since action at a distance seems a familiar fact of experience, while action by contact, when you attempt to work it out in detail, seems hard to comprehend.

But there are tendencies feebler and less general than these which give much food for reflection. Consider, for example, the familiar history of atomism. At least as far back as Democritus we find the confident assertion that the world consists of atoms, and that its infinite variety is due to the motions and positions of immutable and imperceptible units, which, if they are not exactly alike, at least differ less among themselves than do the visible objects into which they are compounded. Through successive centuries this theory never died. With the revival of learning and the beginning of modern science it burst into fresh life. It was believed in firmly by Bacon, the prophet of the new era. It was treated as almost self-evident by philosophers like Gassendi and Hobbes. Boyle held it in its most uncompromising form. Newton assumed it without question. After a period of varying fortunes in the eighteenth century, a modification of it in the hands of Dalton started a new era in chemistry. Taken over by the physicists, it now lies at the root of the modern theory of gases and liquids; the modern theory of matter, the modern theory of heat, and the modern theory of electricity.

This is a very strange story; and it is not really made less strange by those who emphasise the differences between the atoms of Democritus, which are the theme of its first chapter, and the electrons of Sir Joseph Thomson, which appear in its last. Different indeed they are; but, though the difference be great, the agreement is fundamental.

There are some who think that the achievement sung by Lucretius is lessened by showing that the ancients who believed in atoms had no experimental warrant for their convictions. And this is perfectly true. They had not. Nor had Bacon, nor Gassendi, nor Hobbes, nor Boyle, nor Newton. But this only brings into clearer relief the point I desire to emphasise. If experience did not establish the belief, whence came it? If it represents nothing better than an individual guess, why did it appeal so persistently to leaders of scientific thought, and by what strange hazard does it turn out to be true? It is certainly curious that Tyndal, in a once famous address to the British Association at Belfast, should have sketched the story from Democritus to Lucretius, and from Lucretius to 1874, without ever putting these questions to his audience, or, so far as I know, to himself.

But the Atomic Theory is by no means the only example of tendencies which have played an important part in the evolution of science. There are other beliefs, or kinds of beliefs, of the most far-reaching importance which have almost exactly similar characteristics. They anticipate evidence, they guide research, and in some shape or other they turn out to be true.