LECTURE V
INTRODUCTION TO PART III
I
In the preceding lectures I have given reasons for thinking that in two great departments of human interest—Æsthetics and Ethics—the highest beliefs and emotions cannot claim to have any survival value. They must be treated as by-products of the evolutionary process; and are, therefore, on the naturalistic hypothesis, doubly accidental. They are accidental in the larger sense of being the product of the undesigned collocation and interplay of material entities—molecular atoms, sub-atoms, and ether—which preceded, and will presumably outlast, that fraction of time during which organic life will have appeared, developed, and perished. They are also accidental in the narrower sense of being only accidentally associated with that process of selective elimination, which, if Darwinism be true, has so happily imitated contrivance in the adaptation of organisms to their environment. They are the accidents of an accident.
I disagreed with this conclusion, but I did not attempt to refute it. I contented myself with pointing out that it was destructive of values; and that, the greater the values, the more destructive it became. The difficulty, indeed, on which I have so far insisted is not a logical one. We have not been concerned with premises and conclusions. Neither our Æsthetic emotions nor our moral sentiments are the product of ratiocination; nor is it by ratiocination that they are likely to suffer essential wrong. If you would damage them beyond repair, yoke them to a theory of the universe which robs them of all general significance. Then, at the very moment when they aspire to transcendent authority, their own history will rise up in judgment against them, impugning their pretensions, and testifying to their imposture.
II
The inquiry on which I now propose to enter will follow a more or less parallel course, and will reach a more or less similar conclusion. Yet some characteristic differences it must necessarily exhibit. In the higher regions of Æsthetics and ethics, emotions and beliefs are inextricably intertwined. They are what naturalists describe as “symbiotic.” Though essentially different, they are mutually dependent. If one be destroyed, the other withers away.
But Knowledge—the department of human interest to which I now turn—is differently placed. The values with which we shall be concerned are mainly rational; and intellectual curiosity is the only emotion with which they are associated. Yet here also two questions arise corresponding to those which we have already dealt with in a different connection: (1) what are the causes of our knowledge, or of that part of our knowledge which concerns the world of common sense and of science? (2) does the naturalistic account of these causes affect the rational value—in other words the validity—of their results?
We are, perhaps, more sensitive about the pedigree of our intellectual creed than we are about the pedigree of our tastes or our sentiments. We like to think that beliefs which claim to be rational are the product of a purely rational process; and though, where others are concerned, we complacently admit the intrusion of non-rational links in the causal chain, we have higher ambitions for ourselves.
Yet surely, on the naturalistic theory of the world, all such ambitions are vain. It is abundantly evident that, however important be the part which reason plays among the immediate antecedents of our beliefs, there are no beliefs which do not trace back their origin to causes which are wholly irrational. Proximately, these beliefs may take rank as logical conclusions. Ultimately, they are without exception rooted in matter and motion. The rational order is but a graft upon the causal order; and, if Naturalism be true, the causal order is blind.
III
Before I further develop this line of speculation it may help you to understand what I am driving at if I venture upon an autobiographical parenthesis. The point I have just endeavoured to make I have made before in these lectures, and I have made it elsewhere. It is one of a number of considerations which have led me to question the prevalent account of the theoretical ground-work of our accepted beliefs. Taken by itself, its tendency is sceptical; and, since it has been associated with arguments in favour of a spiritual view of the universe, I have been charged (and not always by unfriendly commentators) with the desire to force doubt into the service of orthodoxy by recommending mankind to believe what they wish, since all beliefs alike are destitute of proof. As we cannot extricate ourselves from the labyrinth of illusion, let us at least see to it that our illusions are agreeable.
This, however, is not what I have ever wanted to say, nor is it what I want to say now. If I have given just occasion for such a travesty of my opinions, it must have been an indirect consequence of my early, and no doubt emphatically expressed, contempt for the complacent dogmatism of the empirical philosophy, which in Great Britain reigned supreme through the third quarter of the nineteenth century. But was this contempt altogether unreasonable?
I went to Cambridge in the middle sixties with a very small equipment of either philosophy or science, but a very keen desire to discover what I ought to think of the world, and why. For the history of speculation I cared not a jot. Dead systems seemed to me of no more interest than abandoned fashions. My business was with the ground-work of living beliefs; in particular, with the ground-work of that scientific knowledge whose recent developments had so profoundly moved mankind. And surely there was nothing perverse in asking modern philosophers to provide us with a theory of modern science!
I was referred to Mill; and the shock of disillusionment remains with me to the present hour. Mill possessed at that time an authority in the English Universities, and, for anything I know to the contrary, in the Scotch Universities also, comparable to that wielded forty years earlier by Hegel in Germany and in the Middle Ages by Aristotle. Precisely the kind of questions which I wished to put, his Logic was deemed qualified to answer. He was supposed to have done for scientific inference what Bacon tried to do, and failed. He had provided science with a philosophy.
I could have forgiven the claims then made for him by his admirers; I could have forgiven, though young and intolerant, what seemed to me the futility of his philosophic system, if he had ever displayed any serious misgiving as to the scope and validity of his empirical methods. If he had admitted, for example, that, when all had been done that could be done to systematise our ordinary modes of experimental inference, the underlying problem of knowledge still remained unsolved. But he seemed to hold, in common with the whole empirical school of which, in English-speaking countries, he was the head, that the fundamental difficulties of knowledge do not begin till the frontier is crossed which divides physics from metaphysics, the natural from the supernatural, the world of “phenomena” from the world of “noumena,” “positive” experiences from religious dreams. It may be urged that, if these be errors, they are errors shared by ninety-nine out of every hundred persons educated in the atmosphere of Western civilisation, whatever be their theological views: and I admit that it has sunk deep into our ordinary habits of thought. Apologetics are saturated with it, not less than agnosticism or infidelity. But, for my own part, I feel now, as I felt in the early days of which I am speaking, that the problem of knowledge cannot properly be sundered in this fashion. Its difficulties begin with the convictions of common sense, not with remote, or subtle, or otherworldly speculations; and if we could solve the problem in respect of the beliefs which, roughly speaking, everybody shares, we might see our way more clearly in respect of the beliefs on which many people are profoundly divided.
That Mill’s reasoning should have satisfied himself and his immediate disciples is strange. But that the wider public of thinking men, whom he so powerfully influenced, should on the strength of this flimsy philosophy adopt an attitude of dogmatic assurance both as to what can be known and what cannot, is surely stranger still. Thus, at least, I thought nearly half a century ago, and thus I think still.
Consider, for example, a typical form of the ordinary agnostic position: that presented by Leslie Stephen. The best work of this excellent writer was biographical and literary; but he was always deeply interested in speculation; and his own creed seems early to have taken its final shape under the philosophical influences of the British empiricists. He regarded the “appeal to experience” as the fundamental dogma of agnosticism, and by the “appeal to experience” he meant what Mill meant by it. He sincerely supposed that this gave you indisputable knowledge of “phenomena,” and that if you went beyond “phenomena” you were dreaming, or you were inventing.
This is a possible creed; and it is, in fact, the creed held implicitly, or explicitly, by many thousands of quite sensible people. But why should those who hold it suppose that it must always satisfy impartial inquirers? Why should they assume that those who reject it are sacrificing their reason to their prejudices or their fancies? It may represent the best we can do, but is it, after all, so obviously reasonable? On this subject the empirical agnostic has no doubts. He holds, with unshaken confidence, that nothing deserves to be believed but that which in the last resort is proved by “experience”; that the strength of our beliefs should be exactly proportioned to the evidence which “experience” can supply, and that every one knows or can discover exactly what this evidence amounts to. Leslie Stephen refers to a well-known aphorism of Locke, who declared that “there is one unerring mark by which a man may know whether he is a lover of truth in earnest, viz. the not entertaining any proposition with greater assurance than the proofs it is built on will warrant.” Upon which Leslie Stephen observes that the sentiment is a platitude, but, in view of the weakness of human nature, a useful platitude.
Is it a platitude? Did Locke act up to it? Did Hume act up to it, or any other of Leslie Stephen’s philosophic progenitors? Does anybody act up to it? Does anybody sincerely try to act up to it?
Read through the relevant chapters in Locke’s Essay, and observe his ineffectual struggles, self-imprisoned in the circle of his own sensations and ideas, to reach the external world in which he believed with a far “greater assurance” than was warranted by any proofs which he, at all events, was able to supply. Read Hume’s criticism of our grounds for believing in a real world without, or a real self within, and compare it with his admission that scepticism on these subjects is a practical impossibility.
But we need not go beyond the first chapter of “An Agnostic’s Apology” to find an illustration of my argument. Leslie Stephen there absolves himself from giving heed to the conclusions of philosophers, because there are none on which all philosophers are agreed, none on which there is even a clear preponderance of opinion. On the other hand, he is ready to agree with astronomers, because astronomers, “from Galileo to Adams and Leverrier,” substantially agree with each other. Agreement among experts is, in his opinion, a guarantee of truth, and disagreement a proof of error.
But then he forgets that these distressing differences among philosophers do not touch merely such entities as God and the soul, or the other subjects with which agnostics conceive man’s faculties are incapable of dealing. They are concerned (among other things) with the presuppositions on which our knowledge of “phenomena”—including, of course “astronomy from Galileo to Adams and Leverrier,” is entirely constructed. What, in these circumstances, is Locke’s “sincere lover of truth” to do? How is he to avoid “entertaining propositions with greater assurance than the proofs they are built on will warrant”? Where will he find a refuge from the “pure scepticism” which is, in Leslie Stephen’s opinion, the natural result of divided opinions? How is he to get on while he is making up his mind whether any theory of the world within his reach will satisfy unbiased reason?
The fact is that the adherents of this philosophic school apply, quite unconsciously, very different canons of intellectual probity to themselves and to their opponents. “Why,” asks Mr. Stephen, “should a lad who has just run the gauntlet of examination and escaped to a country parsonage be dogmatic?” If to be dogmatic is to hold opinions with a conviction in excess of any reason that can be assigned for them, there seems to be no escape for the poor fellow. The common lot of man is not going to be reversed for him. Though he abandon his parsonage and renounce his Church, though he scrupulously purify his creed from every taint of the “metempirical,” though he rigidly confine himself to themes which his critics declare to be within the range of his intellectual vision, fate will pursue him still. He may argue much or argue little; he may believe much or believe little; but, however much he argues and however little he believes, his beliefs will always transcend his arguments, and to faith, in his own despite, he must still appeal.
Those who accept Leslie Stephen’s philosophy suppose that for this young man, as for all others, a way of escape may be found by appealing to experience. But surely none are so sanguine as to suppose that, by appealing to experience, they are going to avoid what Mr. Stephen describes as “endless and hopeless controversies.” Alas, this is not so! The field of experience is no well-defined and protected region under whose clear skies useful knowledge flourishes unchallenged, while the mist-enshrouded territories of its metaphysical neighbours are devastated by unending disputations. On the contrary, it is the very battlefield of philosophy, the cockpit of metaphysics, strewn with abandoned arguments, where every strategic position has been taken and retaken, to which every school lays formal claim, which every contending system pretends to hold in effective occupation. Indeed, by a singular irony, the thinkers who, at this particular moment, talk most about experience are those metaphysicians of the Absolute in whose speculations Mr. Stephen saw no beginning of interest, except that of being (as he supposed) at once the refuge and the ruin of traditional religion. But these philosophers have no monopoly. All men nowadays speak well of experience. They begin to differ only when they attempt to say what experience is, to define its character, explain its credentials, and expound its message. But, unhappily, when this stage is reached their differences are endless.
IV
I am, of course, not concerned with Mr. Stephen except as a brilliant representative of a mode of thought to which I most vehemently object. I do not object to it merely because it is in my judgment insufficient and erroneous, still less because I dislike its conclusion. I object to it because it talks loudly of experience, yet never faces facts; and boasts its rationality, yet rarely reasons home. These are far graver crimes against the spirit of truth than any condemned in Locke’s pretentious aphorism, and they lead to far more serious consequences.
If you ask me what I have in mind when I say that agnostic empiricism never faces facts, I reply that it never really takes account of that natural history of knowledge, of that complex of causes, rational and non-rational, which have brought our accepted stock of beliefs into being. And if you ask me what I have in mind when I say that though it reasons, it rarely reasons home, I reply that, when it is resolved not to part with a conclusion, anything will serve it for an argument; only when it is incredulous does it know how to be critical.
This is not an error into which I propose to fall. But I hope that I shall not on that account be deemed indifferent to the claims of reason, or inclined to treat lightly our beliefs either about the material world or the immaterial. On the contrary, my object, and my only object, is to bring reason and belief into the closest harmony that at present seems practicable. And if you thereupon reply that such a statement is by itself enough to prove that I am no ardent lover of reason; if you tell me that it implies, if not permanent contentment, at least temporary acquiescence in a creed imperfectly rationalised, I altogether deny the charge. So far as I am concerned, there is no acquiescence. Let him that thinks otherwise show me a better way. Let him produce a body of beliefs which shall be at once living, logical, and sufficient;—not forgetting that it cannot be sufficient unless it includes within the circuit of its doctrines some account of itself regarded as a product of natural causes, nor logical unless it provides a rational explanation of the good fortune which has made causes which are not reasons, mixed, it may be, with causes which are not good reasons, issue in what is, by hypothesis, a perfectly rational system. He who is fortunate enough to achieve all this may trample as he likes upon less successful inquirers. But I doubt whether, when this discoverer appears, he will be found to have reached his goal by the beaten road of empirical agnosticism. This, though it be fashionably frequented, is but a blind alley after all.
In the meanwhile we must, I fear, suffer under a system of beliefs which is far short of rational perfection. But we need not acquiesce, and we should not be contented. Whether this state of affairs will ever be cured by the sudden flash of some great philosophic discovery is another matter. My present aim, at all events, is far more modest. But they, at least, should make no complaint who hold that common-sense beliefs, and science which is a development of common-sense beliefs, are, if not true, at least on the way to truth. For this conviction I share. I profess it; I desire to act upon it. And surely I cannot act upon it better than by endeavouring, so far as I can, to place it in the setting which shall most effectually preserve its intellectual value. This, at all events, is the object to which the four lectures that immediately follow are designed to contribute.
LECTURE VI
PERCEPTION, COMMON SENSE, AND SCIENCE
I
Nothing would seem easier, at first sight, than to give a general description of the ordinary beliefs of ordinary people about our familiar world of things and persons. It is the world in which we live; it is for all men a real world; it is for many men the real world; it is the world of common sense, the world where the plain man feels at home, and where the practical man seeks refuge from the vain subtleties of metaphysics. Our stock of beliefs about it may perhaps be difficult to justify, but it seems strange that they should be difficult to describe; yet difficult, I think, they are.
Some statements about it may, however, be made with confidence. It is in space and time; i.e. the material things of which it is composed, including living bodies, are extended, have mutual position, and possess at least some measure of duration.
Things are not changed by a mere change of place, but a change of place relative to an observer always changes their appearance for him. Common sense is, therefore, compelled in this, as in countless other cases, to distinguish the appearance of a thing from its reality; and to hold, as an essential article of its working creed, that appearances may alter, leaving realities unchanged.
Common sense does not, however, draw the inference that our experiences of material things is other than direct and immediate. It has never held the opinion—or, if you will, the heresy—that what we perceive (at least by sight and touch) are states of our own mind, which somehow copy or represent external things. Neither has it ever held that the character or duration of external things in any way depends upon our observations of them. In perception there is no reaction by the perceiving mind on the object perceived. Things in their true reality are not affected by mere observation, still less are they constituted by it. When material objects are in question, common sense never supposes that esse and percipi are identical.
But then, what, according to common sense, are things in their true reality? What are they “in themselves,” when no one is looking at them, or when only some of their aspects are under observation?
We can, at all events, say what (according to common sense) things are not. They are more than collections of aspects. If we could simultaneously perceive a “thing” at a thousand different distances, at a thousand different angles, under a thousand varieties of illumination, with its interior ideally exposed in a thousand different sections, common sense, if pressed, would, I suppose, still hold that these were no more than specimens of the endless variety of ways in which things may appear, without either changing their nature or fully revealing what that nature is. But though common sense might give this answer, it would certainly resent the question being put. It finds no difficulty in carrying on its work without starting these disturbing inquiries. It is content to say that, though a thing is doubtless always more than the sum of those aspects of it to which we happen to be attending, yet our knowledge that it is and what it is, however imperfect, is, for practical purposes, sufficiently clear and trustworthy, requiring the support neither of metaphysics nor psychology.—This, with all its difficulties, is, I believe, an account, true as far as it goes, of the world of things as common sense conceives it. This is the sort of world which science sets out to explain. Let me give an illustration.
We perceive some object—let us say the sun. We perceive it directly and not symbolically. What we see is not a mental image of the sun, nor a complex of sensations caused by the sun; but the sun itself. Moreover, this material external object retains its identity while it varies in appearance. It is red in the morning; it is white at midday; it is red once more in the evening; it may be obscured by clouds or hidden in eclipse; it vanishes and reappears once in every twenty-four hours; yet, amid all these changes and vanishings, its identity is unquestioned. Though we perceive it differently at different times, and though there are times when we do not perceive it at all, we know it to be the same; nor do we for a moment believe (with Heraclitus) that when it is lost to view it has, on that account, either altered its character or ceased to exist.
In the main, therefore, experience is, according to common sense, a very simple affair. We see something, or we feel something, or, like Dr. Johnson, we kick something, and “there’s an end on’t.” Experience is the source of all knowledge, and therefore of all explanation; but, in itself, it seems scarcely to require to be explained. Common sense is prepared to leave it where it finds it. No doubt the occurrence of optical or other illusions may disturb this mood of intellectual tranquillity. Common sense, when it has to consider the case of appearances, some of which are held, on extraneous grounds, to be real and others to be illusory, may feel that there are, after all, problems raised by perception—by the direct experience of things—which are not without their difficulties. But the case of illusions is exceptional, and rarely disturbs the even tenor of our daily round.
II
Now science, as it gladly acknowledges, is but an extension of common sense. It accepts, among other matters, the common-sense view of perception. Like common sense, it distinguishes the thing as it is from the thing as it appears. Like common sense, it regards the things which are experienced as being themselves unaffected by experience. But, unlike common sense, it devotes great attention to the way in which experience is produced by things. Its business is with the causal series. This, to be sure, is a subject which common sense does not wholly ignore. It would acknowledge that we perceive a lamp through the light which it sheds, and recognise a trumpet through the sound which it emits; but the nature of light or sound, and the manner in which they produce our experience of bright or sonorous objects, it hands over to science for further investigation.
And the task is cheerfully undertaken. Science also deems perception to be the source of all our knowledge of external nature. But it regards it as something more, and different. For perception is itself a part of nature, a natural process, the product of antecedent causes, the cause of subsequent effects. It requires, therefore, like other natural facts, to be observed and explained; and it is the business of science to explain it.
Thus we are brought face to face with the contrast on which so much of the argument of these lectures turns: the contrast between beliefs considered as members of a cognitive series, and beliefs considered as members of a causal series. In the cognitive series, beliefs of perception are at the root of our whole knowledge of natural laws. In the causal series, they are the effects of natural laws in actual operation. This is so important an example of this dual state that you must permit me to consider it in some detail.
We may examine what goes on between the perceiving person and the thing he perceives from either end; but it is by no means a matter of indifference with which end we begin. If we examine the relation of the perceiver to the perceived it does not seem convenient or accurate to describe that relation as a process. It is an experience, immediate and intuitive; not indeed infallible, but direct and self-sufficient. If I look at the sun, it is the sun I see, and not an image of the sun, nor a sensation which suggests the sun, or symbolises the sun. Still less do I see ethereal vibrations, or a retinal image, or a nervous reaction, or a cerebral disturbance. For, in the act of perceiving, no intermediate entities are themselves perceived.
But now if we, as it were, turn round, and, beginning at the other end, consider the relation of the perceived to the perceiver, no similar statements can be made. We find ourselves concerned, not with an act of intuition, but with a physical process, which is complicated, which occupies time, which involves many stages. We have left behind cognition; we are plunged in causation. Experience is no longer the immediate apprehension of fact; it is the transmission of a message conveyed from the object to the percipient by relays of material messengers. As to how the transmission is effected explanations vary with the growth of science. They have been entirely altered more than once since the modern era began, and with each alteration they become more complicated. They depend, not on one branch of science only, but on many. Newtonian astronomy, solar physics, the theory of radiation, the optical properties of the atmosphere, the physiology of vision, the psychology of perception, and I daresay many other branches of research, have to be drawn upon: and all this to tell us what it is we see, and how it is we come to see it.
III
Now there is no one who possesses the least smattering of philosophy who does not know that the views I have just endeavoured to describe are saturated with difficulties: difficulties connected with the nature of perception; difficulties connected with the nature of the object as perceived; difficulties connected with its unperceived physical basis; difficulties connected with the relation in which these three stand to each other. For common sense the material object consists of a certain number of qualities and aspects which are perceived, an inexhaustible number which might be perceived, but are not, and (perhaps) a vaguely conceived “somewhat” lying behind both. The medieval Aristotelian, if I rightly understand him (which very likely I do not), developed this “somewhat” into the notion of substance—an entity somewhat loosely connected with the qualities which it supported, and in no way explaining them. There was “substance” in a piece of gold, and “substance” in a piece of lead; but there was nothing unreasonable in the endeavour to associate the qualities of gold with the substance of lead, and thus for all practical purposes to turn lead into gold.
Modern science teaches a very different lesson. It has, perhaps, not wholly abandoned the notion of material substance, if this be defined as the unperceivable support of perceivable qualities; but it persistently strives to connect the characteristics of matter with its structure, and, among other characteristics, that of producing, or helping to produce, in us those immediate perceptions which we describe as our experience of matter itself.
An important stage in this endeavour was marked by the famous distinction between the primary and the secondary qualities of matter: the primary qualities being the attributes of external material things which were deemed to be independent of the observer (for example, impenetrability, density, weight, configuration); the secondary qualities being those which, apart from observers endowed with senses like our own, would either exist differently, or would not exist at all (for example, colour and taste). On this view the primary qualities were among the causes of the secondary qualities, and the secondary qualities were transferred from the thing perceived to the person perceiving.
I am not the least concerned to defend this theory. It has been much derided, and is certainly open to attack. But something like it seems to be an inevitable stage in the development of modern views of nature. The whole effort of physical science is to discover the material or non-psychical facts which shall, among other things, account for our psychical experiences. It is true that there are men of science, as well as philosophers, who regard all such constructions as purely arbitrary—mere labour-saving devices which have nothing to do with reality. But though I shall have something to say about these theories in my next course of lectures, for the present I need only observe that they do not represent ordinary scientific opinion, either as it is, or as it has ever been. Science thinks, rightly or wrongly, that she is concerned with a real world, which persists independently of our experience: she has never assented to the doctrine that the object of her patient investigations is no more than a well-contrived invention for enabling us to foretell, and perhaps to modify, the course of our personal feelings.
But then, if science is right, we are committed to a division between the contents of immediate experience and its causes, which showed itself dimly and tentatively in the distinction between the secondary and the primary qualities of matter, but has become deeper and more impassable with every advance in physics and physiology. It was possible to maintain (though, I admit, not very easy) that, while the secondary qualities of matter are due to the action of the primary qualities on our organs of perception, the primary qualities themselves are, nevertheless, the objects of direct experience. The fact, for example, that colour is no more than a sensation need not preclude us from perceiving the material qualities which, like shape, or motion, or mass, are the external and independent causes to which the sensation is due. I do not say that this view was ever explicitly entertained—nor does it signify. For, if we accept the teaching of science, it can, I suppose, be entertained no more. The physical causes of perception are inferred, but not perceived. The real material world has been driven by the growth of knowledge further and further into the realm of the unseen, and now lies completely hidden from direct experience behind the impenetrable screen of its own effects.
IV
For consider what the causal process of perception really is if we trace it from the observed to the observer—if we follow the main strands in the complex lines of communication through which the object seen reveals itself to the man who sees it.
I revert to my previous example—the sun. We need not consider those of its attributes which are notoriously arrived at by indirect methods—which are not perceived but inferred—its magnitude, for example, or its mass. Confining ourselves to what is directly perceived, its angular size, its shape (projected on a plane), its warmth, its brightness, its colour, its (relative) motion, its separation from the observer in space—how are these immediate experiences produced?
The answers have varied with the progress of science; nor, for my present purpose, does it greatly matter which answers we adopt. Let us take those which are commonly accepted at the present moment. They are not only the truest, but the fullest; and for that very reason they put the difficulty with which we are concerned in the highest relief. We begin our causal series with electrons, or, if you do not accept the electric theory of matter in any of its forms, then with atoms and molecules. We start with these, because the sun is a collection of them, and because it is their movements which set going the whole train of causes and effects by which the sun produces in us the perception of itself.
We may take, as the next stage, ethereal vibrations, of various lengths and various amplitudes, sent travelling into space by the moving particles. A fraction of these waves reaches our atmosphere, and of that fraction a fraction reaches our eyes, and of that fraction a further fraction falls within the narrow limits of length to which our eyes are sensitive. It is through these that we are able to see the sun. Still another fraction, not necessarily identical in wave-lengths, affects the nerves which produce in us the sensation of warmth. It is through these that we are able to feel the sun.
But, before we either see or feel, there is much still to be accomplished. The causal series is not nearly completed. Complicated neural processes, as yet only imperfectly understood; complicated cerebral processes—as yet understood still less—both involving physiological changes far more complicated than the electrical “accelerations” or electro-magnetic disturbances with which we have hitherto been dealing, bring us to the end of the material sequence of causes and effects, and lay the message from the object perceived on the threshold of the perceiving consciousness. So does a postman slip into your letter-box a message which has been first written, then carried by hand, then by a mail-cart, then by a train, then by hand again, till it reaches its destination, and nothing further is required except that what has been written should be read and understood.
Thus far the material process of transmission. The psychical process has still to come. Psychology is a science, not less than physiology or physics; and psychology has much to say on the subject of perception. It is true that scientific explorers whose point of departure is introspective; who concern themselves primarily with ideas, conceptions, sensations, and so forth, rarely succeed in fitting their conclusions without a break to those of their colleagues who begin with the “external” causes of perception. The two tunnels, driven from opposite sides of the mountain, do not always meet under its crest. Still, we cannot on that account ignore the teaching of psychology on the genesis of perceptual experience regarded, not as the ground of knowledge, but as a natural product.
I do not mean to attempt a summary of psychology from this point of view, any more than I have attempted a summary of physics or physiology. My argument is really independent, in this case as in the other, of particular systems. All I ask for is the admission that in perception there are conditions antecedently supplied by the perceiving consciousness which profoundly modify every perceptual experience—and that these conditions (unlike Kant’s forms) are natural growths, varying, like other natural growths, from individual to individual. This admission must, I think, be made by every empirical psychologist, to whatever school he happens to belong.
If this statement seems obscure in its general and abstract form, consider a particular application of it. Let us assume, with many psychologists, that Will, in the form of selective attention, lies at the root of our perceptual activities; that we may therefore be said, in a sense, voluntarily to create the objects we perceive; that experience of the present is largely qualified by memories of the past, and that the perceptual mould into which our sensations are run is largely a social product—born of the intercourse between human beings, and, in its turn, rendering that intercourse possible. Is it not clear that, on assumptions like these, consciousness, so far from passively receiving the messages conveyed to it through physical and physiological channels, actively modifies their character?
V
But why, it may be asked, should these considerations involve any difficulty? And, if there be a difficulty, what is its exact character?
In its most general form the difficulty is this. It is claimed by science that its conclusions are based upon experience. The experience spoken of is unquestionably the familiar perception of external things and their movements as understood by common sense; and, however much our powers of perception be increased by telescopes, microscopes, balances, thermometers, electroscopes, and so forth, this common-sense view suffers no alteration. The perceptions of a man of science are, in essence, the perceptions of ordinary men in their ordinary moments, beset with the same difficulties, accepted with the same assurance. Whatever be the proper way of describing scientific results, the experimental data on which they rest are sought and obtained in the spirit of “naÏf realism.”
On this foundation science proceeds to build up a theory of nature by which the foundation itself is shattered. It saws off the branch on which it is supported. It kicks down the ladder by which it has climbed. It dissolves the thing perceived into a remote reality which is neither perceived nor perceivable. It turns the world of common sense into an illusion, and on this illusion it calmly rests its case.
But this is not the only logical embarrassment in which we are involved. When science has supplied us with a description of external things as they “really are,” and we proceed to ask how the physical reality reveals itself to us in experience, a new difficulty arises, or, if you like, the old difficulty with a new face. For science requires us to admit that experience, from this point of view, is equivalent to perception; and that perception is a remote psychological effect of a long train of causes, physical and physiological, originally set in motion by the external thing, but in no way resembling it. Look carefully at this process from the outside, and ask yourselves why there should be any such correspondence between the first of these causes and the last of these effects, as should enable us to know or infer the one from the other? Why should the long train of unperceivable intermediaries that connect the perceived with the perceiver be trusted to speak the truth?
I just now likened these intermediaries to relays of messengers. But messengers are expected to hand on their message in the form in which they have received it. The messengers change, but not the message. The metaphor, therefore, is far too complimentary to the train of physical causes which reveal the material thing to the perceiving consciousness. The neural changes which are in immediate causal contiguity with that psychical effect which we call “the experience of an external object” have no resemblance whatever either to the thing as it is perceived or to the thing as it really is. Nor have they any resemblance to the proximate cause which sets them going, namely, the ethereal vibrations; nor have these to the accelerated electrons which constitute the incandescent object which we “experience” as the sun. Nor has the sun, as experienced, the slightest resemblance to the sun as it really is.
Hume, in his “Dialogues on Natural Religion,” urges the absurdity of arguing from an effect like the universe to a cause like God, since the argument from a particular effect to a particular cause, or from a particular cause to a particular effect, is only legitimate when we have had some previous experience of that particular class of causal sequence; and nobody, it is plain, has had the opportunity of observing Creation. Whatever be the value of this argument in the case of God and the world, it seems to me conclusive in the case of matter and man. We cannot argue from purely psychical effects, like perceptions and sensations, to external causes, like physiological processes or ethereal vibrations, unless we can experience both sets of facts in causal relation. And this, if we accept the conclusions of science, we can never do—partly because the intermediate members of the causal series are unperceivable; partly because, if they were perceivable, perception has been reduced by science to a purely psychical effect—which obviously cannot include its material cause. This last must for ever remain outside the closed circle of sensible experiences.
Here, of course, we find ourselves face to face with a familiar objection to those philosophies of perception which deny that we have any access to external reality, except through ideas which are its copy. But they are in a better case than science. They need not explicitly admit a discrepancy between their premises and their conclusions. They arrive at the subjectivity of perception by methods of introspection. They interrogate consciousness, and are convinced that every experience can be analysed into sensations and ideas, some of which, no doubt, suggest externality, but none of which are external. If, then, the worst comes to the worst, they can, and often do, lighten their philosophic ship by pitching the whole material universe overboard as a bit of superfluous cargo. But physical science cannot (at least in my opinion) do anything of the kind. Its whole business is with the material universe. Its premises are experiences of external things, not of internal sensation and ideas. And if it has associated its fortunes with a theory of perception which treats experience as a natural effect of the thing experienced; if it has thereby wandered within sight of the perilous problems which haunt the frontier where mind and matter meet, it has not done so in a spirit of reckless adventure, but in the legitimate pursuit of its own affairs.
This does not necessarily make things easier. We are not here concerned with questionings about the remoter provinces of knowledge—provinces unexplored except by specialists, negligible by ordinary men engaged on ordinary business. On the contrary, the difficulties to which I have called your attention threaten the unquestioned assumption of daily life, the presupposition of every scientific experiment, and the meaning of every scientific generalisation. They cannot be ignored.
On the other hand, threaten as they may, these difficulties can never modify our attitude either towards practical action or scientific theory. Beliefs which were inevitable before remain inevitable still. The supreme act of instinctive faith involved in the perception of external objects stands quite unshaken. Whatever we may think of Berkeley, we cannot give up Dr. Johnson. “Seeing,” says the proverb, “is believing”; and it speaks better than it knows.
VI
Can we, then, adopt a middle course, and, imitating the serene acquiescence of Hume, accept the position of sceptics in the study and believers in the market-place? This seems eminently unsatisfactory; and, since believers on this subject we must perforce remain, it behoves us to consider how, and on what terms, we can best qualify our scepticism.
Observe, then, that the particular difficulty which has been occupying our attention arises in the main from the assumption that our common-sense beliefs in the reality and character of material things have no other foundation than the fact that we so perceive them. From such premises it was impossible, it seemed, to infer that they exist otherwise than as they are perceived; and still more impossible to regard the immediate intuition by which we apprehend the object, and the long-drawn sequence of causes by which the object is revealed, as being the same process looked at from different ends.
But this difficulty is greatly mitigated if we hold that our belief in an independent world of material objects, however it may be caused, is neither a conclusion drawn from this or that particular experience nor from all our experiences put together, but an irresistible assumption. Grant the existence of external things, and it becomes possible and legitimate to attempt explanations of their appearance, to regard our perceptions of them as a psychical and physiological product of material realities which do not themselves appear and cannot be perceived. Refuse, on the other hand, to grant this assumption, and no inductive legerdemain will enable us to erect our scientific theories about an enduring world of material things upon the frail foundation of successive personal perceptions.
If this does not seem clear at first sight it is, I think, because we do not consider our experiences as a whole. A limited group of experiences—say Faraday’s experiments with electro-magnets—may guide us into new knowledge about the external world, including aspects of that world which are not open to sense perception. But then these experiences assume that this external world exists, they assume it to be independent of perception, they assume it to be a cause of perception. These assumptions once granted, experiment may be, and is, the source of fresh discoveries. But experiment based on these assumptions never can establish their truth; and if our theory of knowledge requires us to hold that “no proposition should be entertained with greater assurance than the proofs it is built on will warrant,” our fate is sealed, and we need never hope to extricate ourselves from the entanglements in which a too credulous empiricism has involved us. This means that one at least of the inevitable beliefs enumerated in the first lecture—the belief in an external world—is a postulate which science is compelled to use but is unable to demonstrate. How, then, are we to class it? It is not a law of thought in the accepted meaning of that expression. We are not rationally required to accept it by the very structure of our thinking faculties. Many people, indeed, theoretically reject it; none, so far as I know, regard it as self-evident. On the other hand, it is not an inference from experience; neither is it an analytic judgment in which the predicate is involved in the subject. Described in technical language, it would seem to be a priori without being necessary, and synthetic without being empirical—qualities which, in combination, scarcely fit into any familiar philosophic classification.
According to the view which I desire to press in these lectures, this marks a philosophic omission. I regard the belief in an external world as one of a class whose importance has been ignored by philosophy, though all science depends on them. They refuse to be lost in the common herd of empirical beliefs; though they have no claim to be treated as axioms. We are inclined to accept them, but not rationally compelled. The inclination may be so strong as practically to exclude doubt; and it may diminish from this maximum to a faint feeling of probability. But, whatever be the strength of these beliefs, and whatever the nature of their claims, the importance of the part they play in the development and structure of our current creed cannot easily be exaggerated.
Before, however, I consider other specimens of this class, I must interpolate a long parenthesis upon probability. I have just described these fundamental beliefs as being “probable” in varying degrees. Gradations of probability are familiar to the mathematical theorist. Are we, then, here concerned with probability as conceived by the mathematician? It is evidently essential to settle this question before proceeding with the main argument; and I propose, therefore, to turn aside and devote the next lecture to its consideration.
LECTURE VII
PROBABILITY, CALCULABLE AND INTUITIVE
I
I wish I were a mathematician. There is in the history of the mathematical sciences, as in their substance, something that strangely stirs the imagination even of the most ignorant. Its younger sister, Logic, is as abstract, and its claims are yet wider. But it has never shaken itself free from a certain pretentious futility: it always seems to be telling us, in language quite unnecessarily technical, what we understood much better before it was explained. It never helps to discover, though it may guarantee discovery; it never persuades, though it may show that persuasion has been legitimate; it never aids the work of thought, it only acts as its auditor and accountant-general. I am not referring, of course, to what I see described in recent works as “modern scientific logic.” Of this I do not presume to speak. Still less am I referring to so-called Inductive Logic. Of this it is scarce worth while to speak.9 I refer to their more famous predecessor, the formal logic of the schools.
But in what different tones must we speak of mathematics! Mill, if I remember rightly, said it was as full of mysteries as theology. But while the value of theology for knowledge is disputed, the value of mathematics for knowledge is indisputable. Its triumphs can be appreciated by the most foolish, they appeal to the most material. If they seem sometimes lost to ordinary view in the realms of abstract infinities, they do not disdain to serve us in the humbler fields of practice. They have helped mankind to all the greatest generalisations about the physical universe: and without them we should still be fumbling over simple problems of practical mechanics, entangled in a costly and ineffectual empiricism.
But while we thank the mathematician for his aid in conquering Nature, we envy him his powers of understanding her. Though he deals, it would seem, entirely with abstractions, they are abstractions which, at his persuasion, supply the key to the profoundest secrets of the physical universe. He holds the clues to mazes where the clearest intellect, unaided, would wander hopelessly astray. He belongs to a privileged caste.
I intend no serious qualification of this high praise when I add that, as regards the immediate subject of this lecture, I mean Probability, mathematicians do not seem to have given ignorant inquirers like myself all the aid which perhaps we have a right to ask. They have treated the subject as a branch of applied mathematics. They have supplied us with much excellent theory. They have exercised admirable skill in the solution of problems. But I own that, when we inquire into the rational basis of all this imposing superstructure, their explanations, from the lay point of view, leave much to be desired.
“Probability,” says an often-quoted phrase of Butler, “is the guide of life.” But the Bishop did not define the term; and he wrote before the theory of probability had attained to all its present dignities. Neither D’Alembert nor Laplace had discussed it. Quetelet had not applied it to sociology, nor Maxwell to physics. Jevons had not described it as the “noblest creation of the intellect.” It is doubtful whether Butler meant by it exactly what the mathematicians mean by it, and certain that he did not suspect any lurking ambiguity in the expression.
Nor, indeed, would the existence of such ambiguity be commonly admitted by any school of thought. The ordinary view is that the theory of probabilities is, as Laplace described it, “common sense reduced to calculation.” That there could be two kinds of probability, only one of which fitted this description, would be generally regarded as a heresy. But it is a heresy in which I myself believe; and which, with much diffidence, I now propose to defend.
II
The well-known paradox of the theory of probabilities is that, to all seeming, it can extract knowledge from ignorance and certainty from doubt. The point cannot be better put than by PoincarÉ in discussing the physical theory of gases, where the doctrine of probability finds an important application. Let me give you his view—partly in paraphrase, partly in translation. “For omniscience,” he says in substance, “chance would not exist. It is but the measure of our ignorance. When we describe an event as accidental we mean no more than that we do not fully comprehend the conditions by which it was brought about.
“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 demons10 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.
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 nasty11; 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.
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.
Consider, for example, the group of beliefs which may be described generally as beliefs in persistence, or beliefs in conservation—the kind of belief which has been applied at different periods, and by different schools of scientific thought, to matter, mass, bulk, weight, motion, force, heat, and energy. As every one knows, these ascriptions have not always been correct. But this only emphasises the strength of the tendency. Weight was at one time supposed to be invariable. We know now that the weight of a body varies with its position relatively to other bodies. It is different, for example, at the poles from what it is at the Equator. But how was the error discovered? Not by experiment. There were experiments, no doubt. But those who undertook them already believed in the law of gravitation; and the law of gravitation made it necessary to distinguish the mass of any given fragment of matter both from its weight and from the occult quality of gravity, which is one of the factors on which its weight in any given situation depends. The desire for conservation was not, however, defeated; since physicists, till within the last few years, regarded both mass and gravity as unalterable characteristics of all material bodies.
Again, consider the case of heat. This also has been regarded by powerful schools of scientific thought as a substance that was “conserved.” It is so regarded no longer. But is the inclination to believe in conservation thereby defeated? Not at all. Though heat may vanish, energy remains, and heat is a form of energy.
This doctrine of the conservation of energy is indeed the crowning triumph of the tendency I am discussing, and provides the best illustrations of its strength. For natural philosophers, intent on finding conservation wherever they could, started too boldly on their quest. Descartes regarded the conservation of motion as a self-evident inference from the rationality of God. It is true that he neither had experimental evidence of his doctrine, nor could he, under any circumstances, have obtained it; for the energy of motion, as he incorrectly described it, is not conserved. Leibnitz described it correctly, and had as great a confidence as his predecessor in its conservation, and as little proof to support him. So confident indeed was he, and so independent of experimental evidence was his faith, that he dogmatically asserted that, when motion seemed to disappear, what was lost by the bodies which we see, was exactly taken up by their component elements which we do not see; so that nothing in the nature of what he called vis viva was either lost or created. That this transformation of energy from molar to molecular motion is constantly occurring we now have sufficient proof. But Leibnitz had no proof; and apparently thought none was required other than the Cartesian deduction from the rationality of God. He made a bold anticipation of experience, with nothing to support him but a priori inclination.
His anticipation, however, was not only bold; it was fortunate. Kinetic energy may really be transformed from molar to molecular motion, and suffer no variation. It is conserved. On the other hand, it may not. It may altogether cease, and what becomes of conservation then?
The scientific formula which satisfies both the facts of the case and our desire for conservation is well known.13 Energy, we are taught, is of two kinds: kinetic and potential energy—energy in act and energy in possibility. Each may turn into the other, and is continually so turning. Each, therefore, may vary in quantity, and does vary in quantity. It is only their sum which is indestructible.
Few scientific generalisations have been more fruitful; few have been accepted on more slender evidence; none are more certain; none more clearly illustrate our natural appetite for beliefs of conservation. For, indeed, to the over-critical this sort of conservation must needs leave something to be desired. When we assert the indestructibility of matter we mean that a real entity continues through time unchanged in quantity. But the word has a less obvious meaning when it is applied to energy. The propriety of describing motion as energy seems indeed clear enough; and if all energy were energy of motion, and if energy of motion were always conserved, the conservation of energy would be on all fours with the conservation of matter. But this is not the case. In spite of Leibnitz, the amount of vis viva is not indestructible. What, then, happens when some of it is destroyed? In that case, says science, energy changes its form but not its quantity. Energy of motion becomes energy of position. What was kinetic becomes potential; and, as the transformation is effected without loss, the principle of conservation is saved.
When, however, energy thus becomes potential, in what sense does it still exist, and why do we still call it energy? Energy suggests “doings” and “happenings.” In the case of “potential” energy there are no “doings” and no “happenings.” It is “stored”; and stored it may for ever remain, hibernating (as it were) to all eternity, neither changing nor causing change.
I do not quarrel with this; but I ask myself why “energy” should be treated more leniently than “force.” Though force is now known not to be “conserved,” ordinary thought attributes to it a certain continuity of existence even when it does not show itself in motion. Force may be exerted though nothing moves; as, for example, by a book pressing on a table. But this view is profoundly unsatisfactory to many scientific thinkers. For them force is nothing apart from “acceleration”; it does not represent a cause, it only measures an effect. And if in our ordinary moments we think otherwise, this (they think) is simply because we illegitimately attribute to matter something which corresponds to muscular effort in man.
It is not, perhaps, so easy as these critics suppose to extrude from scientific thought (I say nothing of scientific language) this notion of latent force—force which would produce movement if it could; and is actively, though imperceptibly, striving to show itself in motion. But why should they try? They welcome potential energy—why should they anathematise latent force?
I think the answer is to be found in the fact that, whether force has, or has not, any being apart from acceleration, it is certainly not conserved; while, if energy be as real when it is potential as when it is kinetic, it certainly is conserved. A lapse into anthropomorphism, therefore, is without excuse in the first case, while a lapse into metaphysics is justified in the second. Any heresy may be forgiven, and any evidence is worth respectful attention when conservation is the thing to be proved.
I have sometimes amused myself by wondering what would have happened about the year 1842 if the conservation of energy had been a theological dogma instead of a scientific guess. Descartes, as I mentioned just now, inferred the conservation of motion from the attributes of God. Colding and Joule used the same argument in favour of the conservation of energy. Now, if a belief in the conservation of energy had been an integral part of religious orthodoxy in the early forties of the last century surely some positivist philosopher would have used Joule’s first investigation on Work and Heat to upset the very dogma they were intended to establish. “Here” (he would have said) “you have a believer in these metaphysico-theological methods of discovering the laws of nature; and mark what happens. In true medieval fashion he begins with some fanciful deductions from the way in which he thinks God must have made the world. Fortunately, however, though his principles are medieval, his methods are modern. Not only is he a most brilliant experimenter, but he has the courage to put his own speculations to an experimental test. He takes the minutest precautions, he chooses the most favourable conditions, and what happens? Does he prove his case? Do his results square with his theories? Does he find a fixed relation between work and heat? Does he justify his views of God? Not at all. Between his lowest determination of the mechanical equivalent of heat, and his highest, there is an immense and lamentable gap. What does he do? He takes their mean value:—a very proper method if he knew there was a mechanical equivalent of heat; a very improper method if the reality of such an equivalent was the thing to be proved. Clearly, if he had not put his theological opinions into his scientific premises when he began his experiment, he never would have got them out again as scientific conclusions when he had reached its end.”
For my own part, I think this imaginary critic would, at that date, have had something to say for himself—supposing always we are prepared to accept his presuppositions about scientific method. If sound reason and intellectual integrity require us to follow the lead of observation and experiment with no antecedent preference for one class of conclusions rather than another, then no doubt Joule and a long line of distinguished predecessors were the spoilt children of fortune. They made their discoveries in advance of their evidence, and in spite of their methods. If they turned out to be right, or, at least, on the right road, what can we do but criticise their credulity and wonder at their luck? unless, indeed, their luck be a form of inspiration.
Before leaving beliefs of conservation, I must say one more word about the most famous of them all—the belief in the conservation of matter. This was an important article in the scientific creed of the early atomists, who had no better evidence for it than they had for the Atomic Theory itself. The material “substance” of the medieval Aristotelians was, I imagine, also conserved; though as all that could be known about it were its qualities, and as these were not necessarily conserved, the doctrine in practice did not, perhaps, amount to much. Then came the theory which, chiefly in the hands of Boyle14 at the end of the seventeenth century, initiated modern chemistry. What was conserved, according to this view, was not a metaphysical substance with detachable qualities, but elementary kinds of matter with inseparable qualities; and out of these qualified entities was compounded the whole material universe. I may incidentally observe that a company promoter who should issue a prospectus based on no better evidence than Boyle could advance for this tremendous theory would certainly be in peril of the law. Yet Boyle was right: and, notwithstanding subsequent developments, his conjecture remains the corner-stone of modern chemical research.
Now, what is it that we intend to assert when we say that matter is conserved, or is indestructible? We certainly do not mean that its qualities never suffer change: for most of those which are obvious and striking are always liable to change. If you sufficiently vary temperature or pressure; if you effect chemical composition or decomposition, the old characteristics will vanish and new characteristics will take their place. What, then, is conserved?
In the first place, the lost qualities can (in theory) always be restored, though not always without the expenditure of energy. Water never ceases to be convertible into steam, nor steam into water. The characteristics may vanish, but in appropriate conditions they will always reappear.
Now science, as we have just seen, is tolerant of this notion of latency or potentiality, and is ready enough to use it in aid of beliefs in conservation. It was so used in connection with heat when heat was regarded as a material substance. It is still so used in connection with energy, which is sometimes described as an immaterial substance. But (as I have already noted) it has never been so used in connection with matter. The reason, I suppose, is that the conservation of matter is much more a belief of common sense than the conservation of energy. Energy is a conception which has but recently been disengaged from other conceptions, like force and momentum, and has but recently been associated with heat, with chemical reactions, with changes of physical phase, and with electro-magnetic phenomena. It is, therefore, a remote and somewhat abstract product of scientific reflection; and science may do what it will with its own.
The notion of matter, on the other hand, is the common possession of mankind. Whatever difficulties it may present to reflective analysis, it presents none to our work-a-day beliefs. We are quite ready to regard it as indestructible; but we are not ready to combine this conviction with the view that it possesses no single characteristic which may not be temporarily etherealised into a “potentiality.” On such terms the eternal and unchanging identity of this or that parcel of matter would seem a difficult and elusive doctrine, inappropriate to the familiar and substantial world in which we suppose ourselves to live. A belief in the conservation of matter has therefore always, or almost always, carried with it a belief in the unchanging continuity of at least some material qualities; though as to what these qualities are there has been much dispute.
Descartes, though not consistent, found unchanging continuity in the attribute of size; so also did Hobbes. I presume that the older atomists, who explained the appearances of matter by the shape of its constituent atoms, would have regarded both atomic form and atomic magnitude as persistent. But it was the assumption that the same piece of ponderable matter always possessed the same gravitating power, and that the same gravitating power was always associated with the same mass, which, in the hands of Lavoisier, made so great a revolution in eighteenth-century chemistry. Matter might change its size, its shape, its colour, its phase, its power of acting and reacting; but its mass and the quality which caused its weight it could not change; these characteristics were always associated with each other, and were never in abeyance.
To Lavoisier this double principle seemed self-evident. It was not a hypothesis that required testing, but a touchstone by which other hypotheses might safely be tested. If, in the course of some chemical operation, weight increased, then no further proof was required to show that mass had increased also, and that matter had been added. If, on the other hand, weight diminished, then no further proof was required to show that mass had diminished also, and that matter had been subtracted. Whatever other qualities matter might gain or lose, mass and gravity were indestructible and unchanging.
Men of science seemed, on the whole, content silently to assume these principles of conservation without inconveniently raising the question of evidence. Philosophers have not always been so cautious. Kant supposed himself to have demonstrated them a priori. Schopenhauer followed suit. Spencer declared their contraries to be inconceivable. Mill said they were proved by experience. In short, all these eminent thinkers vied with each other in conferring upon this doctrine the highest honours permitted by their respective philosophies. But apparently they were hasty. Recent discoveries have changed our point of view. Mass (it seems) is no longer to be regarded as unchanging. When bodies move at speeds approaching the velocity of light their mass rapidly increases; so that this quality, which is peculiarly characteristic of matter, must be removed from the category of those which persist unchanged, and placed in the category of those which change but can always be restored. Are we so to class gravitation? Would the weight of a body moving nearly at the speed of light increase as, in like circumstances, its inertia increases? If the answer is “no,” then the link is broken which has for long been thought to connect gravity and mass. If the answer is “yes,” then what Kant regarded as certain a priori is false; what Spencer regarded as “inconceivable” is true; another carrier of “persistence” is lost, and some fresh characteristic must be found which will remain unchanged through all time, and under all conditions.
If this characteristic should turn out to be electric charge, what a curious light it will throw upon our tendency to “beliefs of conservation”15. After long seeking for some indestructible attribute of matter; after taking up and rejecting size, shape, weight, mass, and (perhaps) impenetrability, we shall at last find the object of our quest in a conception which has (I suppose) been clearly realised only within the last hundred years, about which our senses tell us nothing, and of which the general run of educated mankind are still completely ignorant!
III
It is possible, but not, I hope, probable, that some hasty reader may suppose that in this and the preceding lectures I am recommending a new method or instrument of discovery. “If you want to reach truth, follow your unreasoned inclination,” may be his summary of my doctrine: brief—but also unjust.
Of the manner in which discoveries are going to be made I say nothing, for I know nothing. I am dealing with the past: and in the historic movements of scientific thought I see, or think I see, drifts and currents such as astronomers detect among the stars of heaven. And, as the law of gravitation will hardly (I suppose) explain the last, so observation, experiment, and reasoning will hardly explain the first. They belong to the causal, not to the cognitive, series; and the beliefs in which they issue are effects rather than conclusions.
Those who feel little sympathy for such a view may be inclined to regard the relatively faint inclinations dealt with in this lecture as ordinary scientific hypotheses confirmed by ordinary scientific methods. This view, as I have already observed, is not applicable to the inevitable beliefs dealt with in earlier lectures. Whatever philosophers may say after the event the conviction that we live in an external world of things and persons, where events are more or less regularly repeated, has never been treated as a speculative conjecture about which doubt was a duty till truth was proved. Beliefs like these are not scientific hypotheses, but scientific presuppositions, and all criticism of their validity is a speculative after-thought. The same may be said, though with less emphasis and some qualification, about beliefs fostered by the intellectual tendencies considered in this chapter. These, as we have seen, are many. They are often inconsistent; they are never inevitable; and they perpetually change their form under the pressure of scientific discovery. Atomism in one shape follows atomism in another; doctrines of conservation rise, fall, and rise again; incredulity about “action at a distance” breeds explanations whose failure (in the case of gravity) leaves the hope of final success untouched.
Now, it would be an error to say that science does not, when it can, apply to these various theories its ordinary methods of verification. They are in a different position from inevitable beliefs, which can hardly be verified because the process of verification assumes them. Yet they must not be confounded with ordinary scientific hypotheses, for they are something more and something different. Like these, they are guesses, but they are guesses directed, not by the immediate suggestion of particular experiences (which indeed they sometimes contradict), but by general tendencies which are enduring though sometimes feeble. Those who make them do not attempt the interrogation of Nature wholly free from certain forms of bias. In cross-examining that most stubborn and recalcitrant of witnesses they never hesitate to ply her with leading questions; and, whether this procedure be logically defensible or not, no lover of truth need regret its results.
Readers of M. Bergson’s “Creative Evolution” may remember the picture he draws of the Élan vital—the principle of life—forcing its way along different paths of organic evolution, some without issue or promise of progress; others leading on through regions hitherto untraversed to ends remote and unforeseen. The secular movements of science, as I conceive them, somewhat resemble this process, even though it be faintly and at a distance. There is in both a striving towards some imperfectly foreshadowed end; and in both the advance is irregular, tentative, precarious, with many changes of direction, and some reversals. Yet I would not press the parallel over-far or plunge too deeply into metaphor. It is enough to say that as, according to M. Bergson, the course followed by organic evolution cannot be wholly due to Selection, so the course followed by scientific discovery, as I read its history, cannot be wholly due to reasoning and experience. In both cases we seem forced to assume something in the nature of a directing influence, and (as I should add, though perhaps M. Bergson would not) of supramundane design. And if “a Power that makes for truth” be required to justify our scientific faith, we must surely count ourselves as theists.
NOTE
Extracts from a letter from Sir Oliver Lodge on certain passages in this lecture relating to Energy and its transformations.
You say, on page 226, “Energy, we are taught, is of two kinds: kinetic and potential energy—energy in act and energy in possibility.”
So long as emphasis is laid upon the words “we are taught,” I have no objection. People have taught that, though I strongly object to such teaching, because I object to the idea “Energy in possibility” or “possible Energy” of any kind. I teach the identity of Energy in much the same terms as the identity of Matter; not merely the conservation, with the idea that one quantity can disappear and another quantity reappear. It is not another quantity, but the same; though it may have been locked up for any length of time. But then it has not been usually taught so, and I think you are dealing with what is usual.
Again, you say on page 227, “Energy suggests ‘doings’ and ‘happenings.’” No, say I, activity suggests doings and happenings, and activity is Energy in transformation. Energy alone is something stored, like Capital. The earth’s rotational energy, for instance, is stored just as really as, and for a longer time than, the vegetation of the carboniferous epoch.
Lower down you observe that “Force may be exerted though nothing moves.” Certainly it may, when resisted by an equal opposite force. But I fully admit that a lot of nonsense has been talked about the acceleration measure of force, as if it were the only measure, and that some criticism on this procedure is useful. But I should not speak of “latent” force; it is real force you have in mind, or at least real stress—i.e. two equal and opposite forces. It is latent Activity which becomes active when the other factor, viz. Motion, is supplied or allowed—e.g. by the release of a bent bow, or a wound-up spring, or a raised weight.
So it is also with the Energy of a fly-wheel. That, too, is latent Activity until the other factor, viz. Force, is supplied, i.e. when it is employed to overcome resistance, and therefore do work. Otherwise its Motion will be stored to all eternity.
In short, activity, or doing of work, has two factors, Force and Motion. When both are present, work is done; when either is present alone, Energy is stored. Static Energy is the Force factor, with the possibility of a certain range of effectiveness understood; like a head of water, for instance, a certain height above the sea. Kinetic Energy is the Motion factor, with a certain inertia or possibility of Force understood; not Motion alone, but a mass in motion, so that it may be able to overcome resistance.
There is no real reason why one form of Energy should be considered more “actual” or real than another; our eyes appreciate the one form, our muscles could appreciate the other.
In considering cases of Potential Energy, it is wise to realise that our knowledge about Gravitation is altogether too vague to make the case of a raised weight useful. And our knowledge of solid elasticity, though not so insignificant, is small enough to make the case of a bent bow or wound spring not very easy for fundamental contemplation. A case of chemical Energy, like gun-cotton, is in much the same predicament.
But a typical and satisfactory example of Potential Energy is the case of a vessel of compressed air. Here is Energy stagnant enough, and violent enough when released, and one that can be locked up apparently to all eternity, and yet released by the pulling of a trigger. It represents, however, a case of which we know something concerning the internal mechanism; and we have learnt that in this case the force statically exerted on the walls of a vessel is really a kinetic bombardment of the molecules. In other words, we recognise in this case that Potential Energy is ultimately resolvable into Kinetic. It may be so in the other cases. And on Kelvin’s Kinetic Theory of Elasticity, which he showed a tendency in later life to abandon, all strain or stress in Ether may be ultimately due to its ultramicroscopic vortex circulation.
But none of this is yet proven.
The general argument of your lecture deals with the ease with which certain general propositions are accepted as it were intuitively, without real conclusive evidence. I am entirely with you. And the way we feel secure about general laws, when adequate evidence for them is really impossible, has often struck me as remarkable. Even when facts appear to go against them, we question the facts, and find after all that in so doing we have been right.
