Part 2

THE HOPE OF SCIENCE 145

THE RETURN OF MYSTERY 151

MATHEMATICS AND MUSIC 159

HUMAN TESTIMONY 177

THE INTEREST OF SCIENCE

The conception of science as a body of thought embracing the whole of our rational convictions about reality has hardly yet been generally reached. Man is still so far from being a rational animal that the application of rational methods of inquiry to all branches of his experience is still instinctively resisted--as if reason were an alien and hostile intruder. Beliefs which are held with passion, being the expression of instinctive preferences, are felt not to belong to the “sphere” of science. On all questions where his passions are strongly engaged, man prizes certitude and fears knowledge. Dispassionate inquiry is welcomed only when the result is indifferent. Nearly every great scientific generalisation has incurred the odium theologicum--which is not the exclusive possession of theologians--from the Copernican hypothesis to the theory of herd instinct. That science, although continually wounding men, should nevertheless have progressed, is evidence that it serves impulses deeply rooted in man’s nature. The great scientific innovator, like the great altruist, is treated with ignominy by the society whose deepest instincts he lives to serve.

Science, the child of irrational impulse, has inherited something of the parental character. Its history reveals it as purblind and fumbling, with no clear vision of its aim, no premonition of its imperial state. Unlike philosophy, it did not aspire to universal dominion. It was content to investigate the particular instance, and did not reject a certain incoherence in explanation rather than accept a generalisation which did not spring from its own ground. It refused foreign assistance, but kept its independence. That scientific men did not always understand that science must, from its nature, be autonomous, is evident from the history of every particular science. Even as late as Descartes it was considered quite natural to deduce phenomena from metaphysical principles; and an admixture of mythical elements is not entirely absent from some branches of science, even at the present day. Science has not yet reached full consciousness of its proper ground and aims.

The values served by science, in terms of which its claim to consideration is to be judged, have become more numerous as science has developed. The earliest scientific researches were concerned wholly with the particular event, with, at most, the vaguest inkling of large perspectives. The savage who discovers that the branch lying partly in the stream is not really bent, is prompted by the same localised and detached curiosity which led to most of the early scientific discoveries. Interest in the oddity of an event is undoubtedly the root of scientific observations. The more closely the events concern us, the more pregnant they may be with possible pleasure or pain, the greater the degree of abstraction necessary to see them in their relations. Human beings remain miracles to us long after we have learned to predict the motion of a planet. Psychology is the latest of the sciences, not so much because of the intrinsic difficulty of its subject-matter as because our interest in the subject-matter is so vehement that it is almost impossible to be indifferent to the results. An intelligent fish would probably have found most of the painfully won results of human psychology fairly obvious.

From the accumulation of facts and the attempt to see them in relation springs the scientific theory. With the construction of theories science enters on a new phase in its development, and serves a different set of human values. Its facts, the products of local curiosities, now take on an order, and serve the desire for comprehension. The apparently dissimilar becomes related; law supervenes on chaos. The desire for knowledge becomes transformed into the desire for significant knowledge--significant primarily for contemplation, and secondarily for practice. It is the scientific theory alone that gives to science its true being and makes it worthy of a deep concern. The desire for comprehension is deeply rooted in human nature. Religious myths and philosophical systems arose in obedience to this impulse. Science also exists to satisfy this craving, and the terms on which it does so are altogether to its advantage. The fact that it is an extension of common knowledge, and infers nothing that cannot be verified, differentiates it from myth, and is the secret of the grave and serious satisfaction it affords. Those accustomed to this homely, invigorating atmosphere find the rarer air of much traditional philosophy quite insupportable. A certain indifference to other methods of describing reality becomes more evident as the years advance and the domain of science becomes more and more extended. Peaceful penetration takes the place of open warfare, and in face of rival systems men of science feel less inclined to disprove what they feel more at liberty to ignore.

Science still falls far short of affording complete comprehension or of providing so finished a picture of reality that we feel no need of other speculations. The different sciences do not yet conspire to form one single coherent body of truth. The interstices between them are still sufficiently large to admit foreign interpretations. But the impulse to comprehension, which created science, will be justified by it: we may have so much faith. Even that moiety of mankind who care for little beyond pure immediacy will find that science alone can give them much of what they desire. Scientific theories possess a value even to those who are strangers to the pleasures of contemplation, for science has powerful reactions in the world of practice. To those who have lost their birthright it can offer a mess of pottage.

Besides serving curiosity, comprehension and practice, science offers richly satisfying objects to the æsthetic impulse. The language of æsthetics is not far to seek in the writings of men of science, and were it not that the word arouses such a proprietary fury, we should agree, reviewing their motives and the kind of their satisfactions, to call them artists. The matter of the highest art, like that of true science, is reality, and the measure in which science falls short as art is the measure in which it is incomplete as science. All good philosophy, art or science partakes of the nature of the other two. When these three are regarded as one, each will have reached its apotheosis.

It is unfortunately true that as a science advances it grows more complex. Not only does its language depart more and more from ordinary speech by the accumulation of technical terms, but the terms in current use at any time are defined in terms of others which are defined in terms of others--something after the manner of the description of the house that Jack built. The most obvious case of this Chinese box kind of language is, of course, that of mathematics. A mathematical theorem occupying one line of type might very well occupy a volume if written out in ordinary prose in which no terms were used which were not common property. For this reason modern mathematical discoveries, except in very special instances, cannot be made intelligible except to mathematicians. To learn the language of a highly developed science like mathematics takes about as long as to learn Chinese, but the task of translation into English is very much harder. For this reason mathematicians cannot hope for intelligent popular recognition; they must be content to be regarded either as vaguely impressive figures or else as mild lunatics busied with incomprehensible and probably trifling abstractions. Compared with writers, musicians or painters, they are, for social purposes, mental outlaws. It is apparent, however, that mathematics was not always so remote. It was possible for Voltaire to take an interest which was, at any rate, enthusiastic, in the work of Newton. This was doubtless due, in some degree, to the obviously dramatic quality of Newton’s discoveries, but it was also due to the fact that his discoveries could be expressed in comparatively simple language. Again, physics and chemistry at that time, and for some years later, were not only intelligible to men without special training, but such men could actually make valuable discoveries in these sciences. As these sciences progressed their language became more and more forbidding and their fundamental notions more and more abstract. Men without special training, but with scientific curiosity, turned their attention to the biological sciences. They collected birds’ eggs and butterflies; they bought microscopes and wrote little papers on the sea-shells they discovered in a morning’s walk. But biology has now developed a technical language, and the days of the untrained observer are almost over. The one science which is still, to some extent, accessible to these amiable people is psychology. It is growing more technical, it is true, but the majority of the books dealing with psychology may still be read almost as easily as a treatise on the history of the Balkans. And the “psychological” novelist can still regard himself as being, from one point of view, a scientific man. Psycho-analysis is, as yet, a favourite subject of discussion in advanced drawing-rooms where discussions of the principle of relativity are comparatively rare.

The divorce between science and the general intellectual world is unfortunate, but inevitable. It is unfortunate both for the scientific man and for the general intelligentsia. The scientific man, mentally companionless except for the little circle of his immediate co-workers, becomes less complete as a human being; he fails as a humanist. He too often accepts his outlawed position and turns his special interests into his exclusive interests, as if, through some inverted generosity, he refused to take where he could not give. He may grow to ignore the other intellectual activities of his time, as Darwin, to his distress, found he had grown to ignore poetry, or he may actually become intolerant of such activities and so add contempt to the ignorance with which his preoccupations are regarded by the outside world. For the outside world, also, this divorce is unfortunate. For science, in its own way, satisfies just the same impulses as do other intellectual interests, and some of them it satisfies more completely and in a richer way. A great waste of mental energy and much inconclusive discussion would be avoided were certain scientific results more generally known, and, more particularly, were the advantages of the scientific method more widely recognised and the method itself more extensively practised. An air of superiority is often noticed in the references of scientific men to certain current discussions. It is a fault of manner, but one difficult to avoid. “Inside” information usually has this effect on the possessor, and when it is information that cannot be shared the attitude is apt to become chronic. Both sides, then, are the poorer for their lack of intercourse. But this state of affairs seems to be inevitable. The claims of the Latin and Greek literatures to attention, whether they are justified or not, have led to the study of these languages being imposed on perhaps the majority of the people in this country who are predominantly interested in intellectual affairs. It is a training which consumes several years: is a training in the sciences to be added? This is manifestly impossible. Even if our whole educational system were radically altered, only those sciences, such as biology and psychology, which may be understood with comparatively little training, could ever become objects of common knowledge. But sciences where, in addition to a severe and prolonged discipline, special aptitude is necessary, must always be the property of the few. As, every year, all the sciences grow more complex, so the difficulty of obtaining an adequate knowledge of them increases. A dead language may be learnt once for all, but the language of a science must be learnt afresh every few years. The popular article of Huxley’s day, the link between the man of science and the general public, is now the link between the more and less advanced students of the same science. A so-called “popular” account of Relativity Theory, for instance, is like an annotated edition of Pindar; a very fair knowledge of the language is assumed beforehand. It might be thought that the process of reduction, as it were, could be continued, until finally an account was prepared where no technical terms were used. But such an account would be, at best, like a translation of Greek poetry; the essential quality would be gone. Such translations have, of course, their uses, but the attraction of science for the scientific man, like the attraction of a poem for the poet, is not to be communicated in this way. In art the separation of matter and form is not really possible, and the same is true of the sciences.

III

In their apologias, which have now become so common, men of science never weary of pointing out that it is the method of science which is really worthy of adoption by philosophers and that the results of science are merely provisional. The philosopher who bases his system upon the results reached at any given time by any given science has ensured the ultimate downfall of his system. He is sometimes told that the adoption of scientific methods, on the other hand, will enable him to make sure progress. At first sight there seems to be a contradiction here, for if the scientific method is infallible why are the results reached by it provisional? To judge from the history of science, the scientific method is excellent as a means of obtaining plausible conclusions which are always wrong, but hardly as a means of reaching the truth. The contradiction is only apparent, however, for it will be found that there is a part of every discarded hypothesis which is incorporated in the new theory. The discarded hypothesis proves to have been too general; the scientific man made a mistake of the same kind as the philosopher who uses the hypothesis as the basis of a general system. It is now known, for instance, that Newton’s theory of gravitation is very probably not exactly true; in most cases, however, it remains very nearly true, and there are large regions of dynamical astronomy which are unaffected by the alteration. The Newtonian laws of motion, again, are not sufficient to describe the motion of bodies moving with very large velocities, but they are very nearly true for all ordinary velocities. That the theories which have taken the place of those abandoned are exactly true is very improbable; they are, however, nearer the truth. We may say, therefore, that while the scientific method may, quite possibly, never enable us to reach the exact truth, successive applications of it enable us to approximate nearer and nearer to the exact truth. In this lies its chief difference from the methods usually adopted in philosophy, which aim at obtaining, at one blow, theories which shall never need revision. It is for this reason that philosophy does not progress.

In what, then, does the scientific method consist? It would be difficult to give a precise definition; it has, however, two main characteristics, the choice of facts and the treatment of facts. It does not seem to be generally recognised that scientific men do choose their facts; there are many people who suppose that all facts are of equal interest to scientific men, and that information respecting the number of nightingales heard in Hertfordshire during a certain month, for instance, is a contribution to scientific knowledge. It should be obvious, however, that a mere random collection of facts is very unlikely to aid either practice or theory. The aim of science is not to form catalogues, but to form theories describing phenomena, and to this end some facts are pertinent and a very great number are not. All men, faced with a problem of any kind, choose such facts for examination as they consider relevant. Sherlock Holmes often bewildered Watson by pondering over facts that Watson considered irrelevant, but Watson’s surprise was a proof that even he had a standard of relevance. The history of any science shows that the facts first chosen were those most likely to be repeated. Such facts obviously lead to statements which have a greater or less degree of generality. That an unsupported stone falls to the ground is a fact of this kind. The facts chosen by the man of science are those that permit generalisation. For this reason they usually differ entirely from the facts of interest to historians. After selecting, in accordance with this principle, the facts which are to be examined, the next step consists in establishing relations between sets of these facts. The precise expression of these relations is called a law of nature, to use a somewhat old-fashioned terminology. If now all the relations between certain sets of facts can be expressed in one general statement, that general statement is called a scientific theory. The ultimate aim of the scientific method is to create scientific theories. The scientific theory, however, usually introduces an element which has not been or cannot be directly observed, and also, as we have seen, usually proves to have been too hasty a generalisation. Its function is to co-ordinate known phenomena and to predict hitherto unobserved phenomena. The extent to which it does this is the measure of its success as a scientific theory, and, since the primary object of the scientific theory is to express the harmonies which are found to exist in nature, we see at once that these theories must have an æsthetic value. The measure of the success of a scientific theory is, in fact, a measure of its æsthetic value, since it is a measure of the extent to which it has introduced harmony in what was before chaos.

It is in its æsthetic value that the justification of the scientific theory is to be found, and with it the justification of the scientific method. Since facts without laws would be of no interest, and laws without theories would have, at most, a practical utility, we see that the motives which guide the scientific man are, from the beginning, manifestations of the æsthetic impulse. The reason why certain facts and not others interest the scientific man, the reason why he makes a choice, is because truth without beauty is as uninteresting to him as to any other artist. In the words of Poincaré: “Le savant n’étudie pas la nature parce que cela est utile; il l’étudie parce qu’il y prend plaisir, et il y prend plaisir parce qu’elle est belle. Si la nature n’était pas belle, elle ne vaudrait pas la peine d’être connue, la vie ne vaudrait pas la peine d’être vécue.”

A PHYSICIST ON PHYSICS

The well-meant and industrious efforts of professional metaphysicians to explain to men of science in what sense science is true, in what sense it has meaning and in what its value really consists, practically all suffer from the defect that men of science do not recognise the subject of investigation as being science at all. It is almost true to say that the professional philosopher is only convincing when he is talking about the Absolute, for that is a subject with which nobody else is concerned; but when he devotes his attention to subjects with which other people are familiar, it often becomes possible to put the book down before finishing it. Thus treatises on æsthetics are usually convincing to everybody but poets, painters and musicians, and philosophical writings on science are probably in great demand amongst classical scholars. Nevertheless, since philosophising on these subjects is an agreeable mental exercise, we find that some artists are now engaged in developing an æsthetic for themselves, and some men of science are engaged in trying to find out what science is. In each case the work consists chiefly in making explicit processes which are instinctive. This fact is of the greatest importance, for, if the instinctive equipment be lacking, the results will inevitably be unsatisfactory. There are treatises on æsthetics, for instance, whose chief effect on the poet is to make him doubt whether the author could tell a good poem from a bad one; this is an absolutely fatal objection. If poets cannot recognise what they call poetry as being the subject of the discussion, then, as a discussion of poetry, that discussion is worthless. Practitioners, whether artists or men of science, seldom have the inclination to uncover and dissect what is to them an instinctive and delightful process; but it is quite easy for them to see (or, rather, to feel) that a suggested explanation is unsatisfactory, although they may find it wholly impossible to give reasons for their dissatisfaction. Nevertheless, when this dissatisfaction is due to an inability to recognise the subject-matter, the explanation must be condemned. It is perfectly possible, for instance, that psycho-analysis, by introducing a mother-complex, an inferiority-complex, and two or three more, might “explain” the Ode to a Nightingale. But if this explanation left out everything which made poets regard that composition as a poem, it would not be a satisfactory explanation.

We have treated this point at some length because Dr. Campbell, in a recent valuable book on the Elements of Physics, insists that the physics he is talking about is that of physicists. He has endeavoured to supply a criticism of the terms used in Physics, to find what is meant by a Law, by a Theory, what a physicist means when he says a proposition is “true,” or that something “exists,” or that a theory has “meaning.” Mr. Campbell is perfectly aware that all these subjects have already been treated by the professional metaphysician, but he claims, and we have no doubt that his claim is just, that he is speaking not only for himself but for the great majority of scientific men when he says that in these discussions he not only does not recognise the subject-matter, but he does not recognise any subject-matter. Such words as “reality” and “existence,” as they are employed by metaphysicians, he finds productive of nothing but great discomfort and intense mental confusion. As he unhesitatingly rejects the hypothesis that metaphysicians are imbeciles, he thinks this confusion can be due only to the fact that these words are used by metaphysicians in senses quite different from those they bear to men of science. He has not been able to explain precisely in what the difference consists, since he has not been able to discover what meanings metaphysicians attach to these words. Accordingly he has confined himself to explaining the meanings these words have in science. The result is a subtle, fairly clear, and frequently entertaining piece of analysis. He acknowledges that his two masters have been Poincaré and Bertrand Russell, and he shows complete familiarity with other writers of the kind. But part of his reason for publishing the book, he tells us, is that even the mathematical philosophers occasionally misrepresent science as the experimental physicist knows it. That they are mathematicians and not physicists is a little too evident in some of their conclusions. Thus Mach’s idea that the object of science is to economise thought is only plausible, he thinks, to a mathematician; and a fundamental proposition that Russell and Whitehead find quite necessary to thought Mr. Campbell does not find necessary at all. He thinks it quite likely, also, that scientific thinking is illogical, but not therefore invalid. The point of view, in fact, is that there are different kinds of minds with different needs and different satisfactions, and Mr. Campbell claims that physicists, for example, belong to a certain species and that the science of physics is something which exists in the minds of physicists. Therefore this book, as he insists, is not only written by a physicist, but it is written for physicists. He is confident that what he has to say will be found an explicit statement of their instinctive processes, and he thinks the highest compliment that could be paid to his book would be for physicists to say they knew it all before.

Now it is true that nobody but a physicist could have written this book and that nobody ignorant of physics could understand it. It may also be true that none but a practising physicist could understand it with the intimacy that Mr. Campbell desires. But any reader who is not, in Mr. Campbell’s sense, half-educated (the other half consists of science--preferably physics) will find the book not only valuable, but delightful. The slight touch of brusquerie that the metaphysician or the equally unfortunate “half-educated” person might attribute to Mr. Campbell from the above exposition is not in the least that of the horny-handed son of toil, but is the half-humorous impatience of a subtle and vigorous thinker who is by no means naïve. There is no reason why the audience that reads Poincaré’s popular four volumes should not also read this book, and there are many reasons why it should. Many of the questions raised there are here developed more fully; most of the questions, in fact, raised by the speculations of such men as Poincaré, Russell, Mach, etc., in so far as they affect science, are here given systematic treatment. We hope to devote a future article to the exposition of some of Mr. Campbell’s more interesting results; we are concerned here to indicate the nature and scope of the book.

The present volume is in two pretty distinct parts, the first part being concerned with the propositions of science, and the second part with measurement. These are to be followed by Part III. on Space and Time, Part IV. on Force, and Part V. on Energy, although, regarding these parts, Mr. Campbell says: “I have not the remotest idea when, if ever, they will be published.” Without anticipating a future discussion of the more technical parts of Mr. Campbell’s work, we may refer here, because of the general interest taken in the subject, to the explanation he gives of the fact that while the outside world resolutely marks off Science from Art, yet this distinction is not at all clear to scientific men. It is difficult, for example, in studying the life of a great man of science, to resist the conclusion that his incentives and satisfactions are indistinguishable from those of a great artist. Yet it seems to be undoubtedly true that a work of Art is something personal, whereas Science is obviously impersonal. Mr. Campbell asks us to distinguish between truth and meaning. The truth of science is something impersonal, but its meaning is personal. The achievement of Newton and Maxwell is as personal as that of Giotto, Shakespeare and Bach. Their dreams were not less personal, nor less delightful, and it is nothing to their discredit that their dreams also came true. And the fact that the meaning of a scientific theory is something that exists, perhaps, only for men of science, has an obvious parallel in Art. The following passage from Mr. Campbell’s book is one to which every man of science would give instant assent:

Nobody who has any portion of the scientific spirit can fail to remember times when he has thrilled to a new discovery as if it were his own. He has greeted a new theory with the passionate exclamation, “It must be true!” He has felt that its eternal value is beyond all reasoning, that it is to be defended, if need be, not by the cold-blooded methods of the laboratory or the soulless processes of formal logic, but, like the honour of a friend, by simple affirmation and eloquent appeal. The mood will and should pass; the impersonal enquiry must be made before the new ideas can be admitted to our complete confidence. But in that one moment we have known the real meaning of science, we have experienced its highest value; unless such knowledge and such experience were possible, science would be without meaning and therefore without truth.

What kind of Physics would be developed by a man alone on an island? We are assuming, of course, that this favourite figure of speculative writers enjoys the properties usually attributed to him; he is remarkably intelligent, and can create by a word any scientific apparatus he requires. The point is that he has no need to take into account the judgments of other people. Let us choose an experiment designed to make clear the consequences of his isolated state. Suppose our islander, after looking at a red patch, glances at a white ceiling. He sees a green patch. Now suppose that he heats a copper wire in the flame of a Bunsen burner. The flame turns green. Will our islander proceed to construct a physics which shall embrace both these observations? Before we can answer this question we must consider why our own physics distinguishes so sharply between them. In the first place, it may be said that all observers, except the man who contemplated a patch of red, agree that the colour of the ceiling is unchanged, whereas, in the case of the copper wire, all observers agree that the flame has turned green. In the first case, therefore, we say that there has occurred a change in the observer, and in the second case a change in the flame. We invoke the criterion of universal assent. But it can readily be shown that we have not, in fact, invoked this criterion, for in saying that the flame has turned green, we have left out the testimony of colour-blind persons. Not everybody would agree that the flame has turned green, and on what principle are we to decide between the conflicting opinions of different observers? Mr. Campbell’s examination of this question appears to take us to the root of the matter. Universal assent is involved, but also something more, and it is the something more which will probably enable our islander to form a physics like our own. Let us first consider the way in which universal assent is involved in science.

We must obviously leave out judgments of colour; similarly, science does not now measure electrical quantities in the manner of Cavendish, by comparing the intensities of electric shocks experienced by the observer. Science makes a choice of the judgments it shall consider; it does not even embrace all judgments for which universal assent may be obtained. The judgments on which science is based, and for which universal agreement may be obtained, are divided by Mr. Campbell into three groups: (1) Judgments of simultaneity, consecutiveness and “betweenness” in time; (2) Judgments of coincidence and betweenness in space; (3) Judgments of number, such as, The number of the group A is equal to, greater than or less than, the number of the group B. Now it is judgments of this kind that are involved in physical observations: the deflection of a spot of light on a scale, the reading of a stop-watch, and so on. These judgments are fundamental to science and are such that universal assent may be obtained for them. Let us now consider the case of the copper wire in the Bunsen flame. We have said that not all people will agree that the flame has turned green. But the light from the Bunsen has other properties than its colour; it has a measurable refrangibility and a measurable wave-length. The important point for physics is that all observers, both “normal” and colour-blind, would agree on these measurements, since they are connected with the fundamental judgments mentioned above. The fact that different observers associate these same measurements with different colours is a fact of no importance for physics; “colour” is not a notion essential to physics at all; when phrases containing such words as “red” or “yellow” occur in physics they may always be replaced by words depending for their meaning solely on fundamental time, space and number judgments. It is for this reason, then, that science builds on perfectly sure foundations; its foundations can only be denied by an imposter, that is, by one whose actions show that he actually believes what he says he denies. Now, how does this apply to our islander? We may assume that he can measure refrangibility and wave-length. He finds that, in these particulars, the light from the ceiling is unaltered, while the light from the Bunsen flame is altered. But these observations have no greater support than his colour judgments. On both occasions the only testimony is his own. But he would notice a great difference directly he began to establish the laws connecting these phenomena. The laws derived from the second set of observations would be much more satisfactory than those derived from the first set. He would undoubtedly prefer them and would unhesitatingly adopt them. When it is put in this way, there certainly seems something arbitrary about the process by which science selects its fundamental judgments. They are selected because they fall neatly and satisfactorily into laws. Mr. Campbell further suggests that the laws used in science are selected from amongst other possible laws because the selected laws fit into theories, “the form of which is dictated chiefly by preconceived ideas of what a theory should be.” It may be stated at once that Mr. Campbell admits the presence of an arbitrary element in science, but it is precisely his case that this arbitrary element gives to science its value.

We cannot here summarise his exposition, because it would be unintelligible except to readers with a scientific training, since Mr. Campbell has adopted the very sound method of analysing the actual laws and theories current in physics. We may indicate, however, the general lines of his investigation. He attempts to analyse the kind of relation involved in a scientific “law.” It has been generally assumed by philosophers that this relation is the “causal” relation, but, in fact, it is very doubtful whether this relation is ever used in the statement of laws. It is a very special kind of relation, and its supposed importance to science seems to rest on a confusion between the psychological process in an observer performing an experiment and the relation stated to exist between his observations. Thus, in Ohm’s Law, does the potential difference enter as cause or effect of the current? The question is sufficient to show that the causal relation is not concerned. Mr. Campbell admits that he has not succeeded in making a final analysis of the propositions called laws, but we think that he has certainly established several points of great value. It is more to our present purpose, however, that this analysis shows more clearly how an arbitrary element enters into scientific laws. A law does not simply relate concepts in a manner consistent with observation; it would be perfectly possible, for instance, to replace Ohm’s Law, expressing simple proportionality between current and potential difference, by a much more complicated expression which should agree equally well with observation. There are always several laws which will satisfy the observations; the one that is chosen is chosen for its simplicity, i.e., because of the mental satisfaction it affords. The fact that it does fit the observations gives it what Mr. Campbell calls its “truth,” and the fact that it affords intellectual satisfaction gives it what he calls its “meaning.”

When we pass from laws to theories we find that the element of “meaning” becomes much more prominent. Now the truth of a law is something that rests on universal assent; this is not the case, however, for the meaning of a law. It may be that the contemplation of Ohm’s Law gives you no satisfaction whatever; if it satisfies me, however, then to me it has meaning. It is only necessary, therefore, that scientific laws should have meaning for scientific men; their truth, however, is the same for all. When we come to consider theories we find that, concerning their meaning, there is much more difference of opinion. This difference, in fact, almost follows national lines, so that of the two great classes of theories, the “mechanical” and the “mathematical,” the former is largely a product of British physicists, while continental physicists prefer the second type. Mr. Campbell analyses very acutely the differences between the two classes as well as the elements they have in common. As he says, there may be a “taste” for certain kinds of theories, as there is a taste for oysters. The result of this analysis is to show very clearly in what respects science is impersonal and in what respects personal; it also helps to make clear what science is. It is true that the impersonal element in science is the most important, in this sense, that if any law or theory can be shown not to be true, then, however much meaning it may have, it must be at once rejected. It is also true that it is the meaning of laws and theories, particularly theories, which gives them their value to scientific men. We therefore reach once more the conclusion, sufficiently familiar, but seldom so satisfactorily prepared, that the value of science is in the æsthetic satisfactions it affords. In Mr. Campbell’s words, “Science is the noblest of the arts.”

FOOTNOTES: