CHAPTER VII

SOME PROBLEMS OF PHILOSOPHY

We have now concluded our summary of the findings of modern physics, and may turn to consider how these findings affect the practical problems of philosophy and of everyday life. But let us first recapitulate the conclusions we have reached in our scientific discussion.

 

Recapitulation

Because we are human beings and not mere animals, we try to discover as much as we can about the world in which our lives are cast. We have seen that there is only one method of gaining such knowledge—the method of science, which consists in a direct questioning of nature by observation and experiment.

The first thing we learn from such questioning is that the world is rational; its happenings are not determined by caprice but by law. There exists what we have called a ‘pattern of events’, and the primary aim of physical science is the discovery of this pattern. This, as we have seen, will be capable of description only in mathematical terms.

The new quantum theory explained in the preceding chapter has provided a mathematical description of the pattern of events which is believed to be complete and perfect. For it enables us—in principle at least—to predict every possible phenomenon of physics, and not one of its predictions has so far proved to be wrong. In a sense, then, we might say that theoretical physics has achieved the main purpose of its being, and that nothing remains but to work out the details.

But we not only wish to predict phenomena, but also to understand them. Thus it is not surprising that philosophy and science have alike found this mathematical description unsatisfying, and have tried to attach concrete meanings to the mathematical symbols involved—to replace unintelligible universals by intelligible particulars. We may argue that if there is a pattern, there must be some sort of loom for ever weaving it; we want to know what this loom is, how it works, and why it works thus rather than otherwise.

The physicists of the last century thought that one of the primary concerns of science should be to devise models or draw pictures to illustrate the workings of this loom. It was supposed that a model which reproduced all the phenomena of a science, and so made it possible to predict them all, must in some way correspond to the reality underlying the phenomena. But obviously this cannot be so. After one perfect model had been found, a second of equal perfection might appear, and as both models could not correspond to reality, we should have at least one perfect model which did not correspond to reality. Thus we could never be sure that any model corresponded to reality. In brief, we can never have certain knowledge as to the nature of reality.

We know now that there is no danger of even one perfect model appearing—at least of a kind which is intelligible to our minds. For a model or picture will only be intelligible to us if it is made up of ideas which are already in our minds. Of such ideas some, as for instance the ideas of abstract mathematics, have no special relation to our particular world; all those which have must, as we have seen, have entered our minds through the gateways of the senses. These are restricted by our having only five senses of which only two are at all important for our present purpose.

A detailed investigation of the sources of our ideas has shown that there is only one type of model or picture which could be intelligible to our restricted minds, namely one in mechanical terms. Yet a review of recent physics has shown that all attempts at mechanical models or pictures have failed and must fail. For a mechanical model or picture must represent things as happening in space and time, while it has recently become clear that the ultimate processes of nature neither occur in, nor admit of representation in, space and time. Thus an understanding of the ultimate processes of nature is for ever beyond our reach; we shall never be able—even in imagination—to open the case of our watch and see how the wheels go round. The true object of scientific study can never be the realities of nature, but only our own observations on nature.

The Particle-picture and the Wave-picture

 

Although there can be no complete picture of the workings of nature which will be intelligible to our minds, yet we can still draw pictures to represent partial aspects of the truth in an intelligible way. The new physics places two such partial pictures before us—one in terms of particles, and one in terms of waves. Neither of these can of course tell the whole truth.

In the same way, an atlas may contain two maps of North America drawn on different projections: neither of them will represent the whole truth, but each will faithfully represent some aspect of it. An equal-area projection, for instance, represents the relative areas of any two regions accurately, but their shapes wrongly, while a Mercator projection represents the shapes rightly, but the areas wrongly. So long as we can only draw our maps on flat pieces of paper, such imperfections are inevitable; they are the price we pay for limiting our maps to the kind that can be bound up in an atlas.

The pictures we draw of nature show similar limitations; these are the price we pay for limiting our pictures of nature to the kinds that can be understood by our minds. As we cannot draw one perfect picture, we make two imperfect pictures and turn to one or the other according as we want one property or another to be accurately delineated. Our observations tell us which is the right picture to use for each particular purpose—for instance, we know we must use the particle-picture for the photo-electric effect, the wave-picture for illumination effects, and so on.

Yet some properties of nature are so far-reaching and general that neither picture can depict them properly of itself. In such cases we must appeal to both pictures, and these sometimes give us different and inconsistent information. Where, then, shall we find the truth?

For instance, is nature governed by causal laws or not? The particle-picture answers: No, the motions of my particles can only be compared to the random jumps of kangaroos, with no causal laws controlling the jumps. But the wave-picture says: Yes, at every instant my waves follow uniquely, and so inevitably, from those of the preceding instant.

Or again, is reality ultimately atomic or is it not? The particle-picture tells us of a material world in which matter, electricity and radiation occur only in indivisible units; the wave-picture merely tells us that it knows of none of these things.

The two pictures seem to tell different stories, but we must remember that they are not equally trustworthy. The particle-picture embodies the findings of the old quantum theory which we discussed in Chapter v. This proved to be both inaccurate and incomplete, so that the new quantum theory was brought into being to remedy its deficiencies—which it has successfully done. The wave-picture is not only a pictorial representation of the new quantum theory, but also, as regards the mathematical facts involved, is its exact equivalent. Thus the predictions of the wave-picture cannot be other than true, whereas those of the particle-picture may or may not be true. When there is a conflict, the evidence of the wave-picture must be accepted, while we may be sure that the conflict results from some imperfection of the particle-picture. In the instances just given, it is not difficult to trace out a possible origin for the conflict.

The mathematical laws of the quantum theory show that radiant energy is transferred by complete quanta. But in depicting a beam of light as a hail of bullet-like photons, the particle-picture is clearly going further than the facts warrant. A man’s balance at the bank always changes by an integral number of pence, but this does not justify him in picturing its changes as caused by a flight of bronze pennies. If he does, his child may ask him what decides which particular pennies shall be sent to pay the rent. The father may reply: Mere chance—a foolish answer but no more foolish than the question. In the same way, if we make the initial mistake of depicting radiation as identifiable photons, we shall have to call on mere chance to get us out of our difficulties—and here is the origin of the indeterminacy of the particle-picture.

For instance, when a beam of light falls on a half-silvered mirror (p. 137), the particle-picture shows half the photons being turned back by the silvering of the mirror, while the other half pass on their way undisturbed. We ask at once: What singles out the lucky photons? It is a question which had confronted Newton’s corpuscular theory of light, and he had answered it by a vague wave of the hand towards Fortune’s wheel—his corpuscles, he had said, were ‘subject to alternate fits of easy transmission and easy reflection’. In the same way, if we depict radiation as identifiable photons, we can find nothing but the finger of Fate to separate the sheep from the goats. But the finger of Fate, like the sheep and the goats, is mere pictorial detail. As soon as we turn to the more trustworthy wave-picture, all this pictorial drapery drops out of the picture, and we find a complete determinism. Yet this determinism, as we have seen, does not control events, but our knowledge of events. The wave-picture does not show the future following inexorably from the present, but the imperfections of our future knowledge following inexorably from the imperfections of our present knowledge.

What is true of radiation is true also of electricity. We know that electricity is always transferred from place to place by complete electron-units, but this does not justify us in replacing a current of electricity by a shower of identifiable particles. Indeed, the quantum theory definitely tells us that we must not do so. When two balls A, B collide on a billiard-table, A may go to the right and B to the left. When two electrons A, B collide, we might also expect to be able to say that A would go to the right and B to the left; actually we cannot, because we have no right to identify the two electrons which went into the collision with the two which come out; we must rather think of the two electrons A and B which entered into collision as combining into a drop of electric fluid, which then breaks up again to form two new electrons C and D. If we ask which way A will go after collision, the true answer is that A no longer exists. The superficial answer is that it is an even chance whether A goes to the right or to the left, for it is a toss-up whether we identify A with C or D. But the toss-up is not in nature; it is in our minds.

We see, then, that the particle-picture goes wrong in attributing indeterminism to nature; it is not a property of nature, but of our way of looking at nature. The particle-picture further goes wrong in attributing atomicity to the ingredients of the material world, whether matter or radiation; the atomicity does not reside in these ingredients but in the events which affect them. To return to our former analogy, all payments into and out of a bank account are by complete mathematical pence, but they do not consist of bronze pennies flying hither and thither. But we can now carry this train of ideas a little further; we know matter only through the energy or particles it emits, but this provides no warrant for assuming that matter itself consists of atoms either of substance or of energy—this would be like assuming that our balance at the bank must consist of a pile of bronze pennies.

NEW PHILOSOPHICAL PRINCIPLES

We have seen that efforts to discover the true nature of reality are necessarily doomed to failure, so that if we are to progress further it must be by taking some other objective and utilizing some new philosophical principles of which we have not so far made use. Two such suggest themselves. The first is the principle of what Leibniz described as probable reasoning; we give up the quest for certain knowledge, and concentrate on that one of the various alternatives before us which seems to be most probably true. But how are we to decide which of the alternatives is most likely to be true? This question has been much discussed of late, particularly by H. Jeffreys. For our purpose it is sufficient to rely on what may be described as the simplicity postulate; this asserts that of two alternatives, the simpler is likely to be the nearer to the truth.

Let us try to illustrate these new principles by considering a simple, although very artificial, analogy.

Let us imagine that in the centre of Europe there lives a peasant who has never seen or heard of the sea, and cannot even read about it, but is in possession of a super-perfect radio-set which can pick up messages from every ship in the world. Suppose further that every ship is continually sending out its position in a standard form, such as

‘Queen Mary’, + 41° 10’, −72° 26’,

this meaning that, at the moment of speaking, the ship ‘Queen Mary’ is in latitude 41° 10’ north and longitude 72° 26’ west.

At first he may merely amuse himself by listening to the various messages, but after a time he may take to recording them and, if he is of an inquiring turn of mind, he may try to discover some method or order in them. He will soon notice that all latitudes lie between +90° and −90°, and all longitudes between +180° and −180°. If he then tries plotting out these numbers on squared paper, he will find that successive positions of any one ship form a continuous chain, and may begin to construct a mental picture for himself by thinking of the senders of the messages as moving objects. He will then find that each supposed object moves at an approximately uniform rate on his chart, although this law is not exact or universal. A ship may move from longitude +170° to + 1740 in one day, and on to +178° the next, but the third day may take it to −178°, an apparent journey of 356°. Further, a ship may move at a regular 4° a day when its latitude is near to o°, but this daily motion will increase as the latitude increases, and may shoot up almost beyond limits if ever the latitude approaches to 90°.

If, notwithstanding their peculiar nature, our listener succeeds in formulating exact laws, he will then be able to predict the motions of the ships. Or, to be more precise, he will be able, without assuming that he is dealing with either motions or ships, to predict what he will hear when he turns on his radio. He can predict the result of every experiment he can perform, since the only experiment within his power is to turn a knob and listen.

Those who are content with a positivist conception of the aims of science will feel that he is in an entirely satisfactory position; he has discovered the pattern of events, and so can predict accurately; what more can he want? A mental picture would be an added luxury, but also a useless luxury. For if the picture did not bear any resemblance at all to the reality it would be valueless, and if it did it would be unintelligible, since we are supposing that our listener cannot imagine either sea or ships.

Probable Reasoning

At this point, let us notice that the supposition that the signals came from moving objects was hypothetical in the sense that nothing in the observations compelled it—from the nature of the case the observer is debarred from knowing whether the signals come from moving objects or not. It expresses a possibility and not certain knowledge, and can never be proved true. In real science also a hypothesis can never be proved true. If it is negatived by future observations we shall know it is wrong, but if future observations confirm it we shall never be able to say it is right, since it will always be at the mercy of still further observations. A science which confines itself to correlating the phenomena can never learn anything about the reality underlying the phenomena, while a science which goes further than this, and introduces hypotheses about reality, can never acquire certain knowledge of a positive kind about reality; in whatever way we proceed, this is for ever denied us.

Certain knowledge is, however, equally beyond our reach in most departments of life. Oftener than not, we cannot wait for certain knowledge, but order our affairs in the light of probabilities. There is no reason why we should not do the same in our efforts to understand the universe, provided we always bear in mind that we are discussing probabilities and not certainties.

The philosopher does it as much as the rest of us. I am conscious only of my own thoughts and sensations, so that, for aught I know to the contrary, I may be the only conscious being in the universe. If I choose on these grounds to become a solipsist—i.e. one who supposes that he is the only conscious being in the whole universe—nothing can definitely prove me wrong. But my sensations inform me of other objects that look like my body, and seem to experience sensations and thoughts like my own. I assume, although only on grounds of probable reasoning, that these other objects are beings essentially similar to myself. If we refused to admit probability considerations, we ought all to be solipsists; with things as they are, any genuine solipsists there may be are kept safely shut up.

The physicist also relies on probability considerations every day of his life. He measures the wave-lengths of spectral lines in the light emitted by Sirius, and finds they are identical with those in the light emitted by hydrogen at a temperature of 10,000° C. He concludes without more ado that there are atoms of hydrogen at 10,000° in Sirius. There is no proof of this and never can be, for we shall never be able to go to Sirius to find out. But the probabilities against the agreement being a mere coincidence are so overwhelming that the physicist feels justified in disregarding this possibility, and announces that this part of the light of Sirius comes from hydrogen at a temperature of 10,000°.

In these two instances, the philosopher and physicist are both guided by probable reasoning rather than by certain deductions. If our radio listener allows himself to be guided by similar considerations, he may decide provisionally that his signals come from moving objects. This idea may lead him to think of pasting together his +180° and −180° lines, thus transforming his plane diagram into a cylinder. This simplifies the situation enormously, for it now seems the most natural thing in the world that a sequence of readings equidistant in time should read 170°, 174°, 178°, −178°, etc. But he is still faced with the peculiarity that his moving objects traverse more degrees of longitude per day in high latitudes than in low. With a little ingenuity, he may further think of crumpling in the two ends of his cylinder, and so making the degrees of longitude smaller in higher latitudes. If he finally tries the experiment of replacing his cylinder by a sphere, he will find that his laws assume an exceedingly simple form from which all oddity has disappeared. Each ship takes the shortest course from point to point, and performs its journey at a uniform speed.

Even the original laws were true laws, since they enabled the listener to predict accurately. But they were not simple, because their discoverer had expressed them against a bad background. As soon as he changed from one background to another—from a rectangular projection to a spherical surface—the laws changed from being strange but true to being simple and true. Precisely for this reason, most men will consider that the second set of laws was preferable. Without assigning any special attributes to the Designer of the universe, we probably feel that the simpler laws are likely to be in some way closer to that reality which we can never understand, than complicated and odd laws—in brief, that artificiality comes from man, and not from nature. In the example just considered, it is certainly more true to say that the earth’s surface is spherical than to picture it as plane.

And in the real problems of science also, it is true, as Einstein has remarked, that ‘In every important advance the physicist finds that the fundamental laws are simplified more and more as experimental research advances. He is astonished to notice how sublime order emerges from what appeared to be chaos. And this cannot be traced back to the workings of his own mind but is due to a quality that is inherent in the world of perception.’

This not only shows that our minds are in some way in harmony with the workings of nature—a harmony which Einstein compares with the pre-established harmony of Leibniz (p. 27)—but also that our investigations of nature are proceeding on the right lines; it further shows that the simplicity which is inherent in nature is of the kind which our minds adjudge to be simple. Indeed any other kind of simplicity would probably escape our notice.

The Simplicity Postulate

This suggests the introduction of a further principle, if not into the technique of scientific investigation at least into the practice of philosophical discussion—the principle of simplicity. When two hypotheses are possible, we provisionally choose that which our minds adjudge to be the simpler, on the supposition that this is the more likely to lead in the direction of the truth. It includes as a special case the principle of Occam’s razor—entia non multi-plicanda praeter necessitatem.

There can of course be no absolute criterion as to which of two hypotheses is the simpler; in the last resort this must be a matter of private judgment. In the fictitious example we have just been discussing there could be no room for doubt, but in actual scientific practice there have been cases in which two investigators have differed as to which of two hypotheses was the simpler, as for example with the one-fluid and two-fluid theories of electricity.

The history of science provides many instances of situations such as we have been discussing. To begin with the most obvious, Ptolemy and his Arabian successors built up the famous system of cycles and epicycles which enabled them to predict the future positions of the planets with almost perfect precision. At first, the sun, moon and stars were supposed to revolve round the fixed central earth, while the planets revolved about other centres which themselves revolved about the earth. It was soon found that this did not quite fit the facts, and the orbits had to be changed to slightly eccentric circles—neither the earth nor the moving centres were any longer at the exact centres of the circles which were described around them. Finally, as the planetary motions came to be known to a still higher degree of accuracy, epicycle was piled on epicycle until the system became exceedingly complex.

Many, indeed, felt that it was too complex to correspond to the ultimate facts. In the thirteenth century, Alphonso X of Castile is reported to have said that if the heavens were really like that, ‘I could have given the Deity good advice, had He consulted me at their creation.’ At a later date Copernicus also thought the Ptolemaic system too complex to be true and, after years of thought and labour, showed that the planetary motions could be described much more simply if the background of the motions were changed: Ptolemy had assumed a fixed earth; Copernicus substituted a fixed sun. We know now that neither the earth nor the sun is in any true sense at rest, but we also know why it introduces fewer complications to suppose the sun to be at rest rather than the earth—why it is, in a sense, nearer to the truth to say that the earth moves round the sun than to say that the sun moves round the earth.

We may notice in passing that Copernicus did not claim any absolute truth for his hypotheses, saying that they need not be true or even plausible; it was enough for them to reconcile the observations with the calculations—‘neque enim necesse est, eas hypotheses esse veras, imo ne verisimiles quidem, sed sufficit hoc unum, si calculum observationibus congruentem exhibeant’. This reads like a foreshadowing of positivist doctrines, but it may have been only an attempt to propitiate ecclesiastical and religious readers who might have taken fright at the implications of the new hypotheses.

Copernicus had still to retain a few minor epicycles to make his system agree with the facts of observation. This, as we now know, was the inevitable consequence of his assumption that the planetary orbits were circular: neither he nor anyone else had so far dared to challenge Aristotle’s dictum that the planets must necessarily move in circular orbits, because the circle was the only perfect curve. As soon as Kepler substituted ellipses for the Copernican circles, epicycles were seen to be unnecessary, and the theory of planetary motions assumed an exceedingly simple form—the form it was to retain for more than three centuries, until an even greater simplicity was imparted to it by the relativity theory of Einstein, to which we shall come in a moment.

The restricted (or physical) theory of relativity provides a second illustration of the same thing. The Newtonian mechanics, with its background of absolute space and time, had explained the motion of objects well enough so long as their speeds of motion were not comparable with that of light. But, as experiment ultimately showed, it could only explain the motion of rapidly moving objects at the price of introducing extreme complications. Objects in rapid motion had to contract and assume new shapes, while no one could ever quite say what happened to objects in rapid rotation. The theory of relativity introduced a tremendous simplification into the whole subject when it discarded Newton’s absolute space and time as a background, and substituted the new space-time unity, as explained on p. 63.

The generalized (or gravitational) theory of relativity provides an even more striking instance of the same thing. The Newtonian theory of gravitation, which required the planets to move round the sun in elliptical orbits, gave an excellent account of the movements of the outer planets, but failed with the inner. Attempts were made to remedy this by slightly altering the Newtonian law of gravitation, by supposing the sun to be surrounded by clouds of gas or dust which impeded the free motion of the inner planets, and in a variety of other ways. The relativity theory of gravitation then cleared up the whole situation at one stroke by rejecting Newton’s force of gravitation altogether, and impressing a curvature on the space-time unity in which the motions of the planets were depicted. Once again the change was from an unsuitable to a suitable background. The whole motion of planets and other bodies, as well as of rays of light, could now be described by the simple statement that they all described geodesics—i.e. took the shortest possible course from point to point—in the new curved space-time unity.

The simplification which this change introduced was not only tremendous in itself, but was in line with a number of earlier simplifications, all based on the idea of a length of path or some similar quantity assuming the smallest value which was possible for it.

Fig. 2

The principle made its first appearance in optics. If a candle is burning at C, and my eye at E looks at a mirror MM’, I shall seem to see the candle at some point A in the mirror. This shows that rays of light are travelling along the path CAE from the candle to my eye, and along no others; for if they travelled along any other path CBE as well, I should seem to see candles at both A and B, which I do not. Hero of Alexandria set himself the problem of finding what it was that specially distinguished the path CAE which the light actually took from every other possible path such as CBE which it might have taken, but did not. He found that CAE was the shortest path from C to E which touched the mirror on its way. Even though the light is reflected from hundreds of mirrors, the path is still determined by the same principle; it is the shortest path that can be found, subject to the condition of its touching all the mirrors in turn. Alternatively the path may be described as the quickest from C to E; the light chooses its path on the principle of wasting as little time as possible on the way.

Fermat (1601–1665) showed that this latter principle still determines the path when the light travels through water, glass, or other refracting substances of any kind whatever. Thus it is true under all circumstances that light always travels by the quickest route; this provides another instance of the tremendous simplifications to which Einstein refers (p. 183).

Maupertuis (1698–1759) subsequently conjectured that the motions of tangible objects must conform to some similar principle, arguing that Divine perfection would be opposed to any expenditure of energy by moving bodies, beyond the absolute minimum necessary to get from one place to another. In time such a principle was found to govern the motion of all bodies of tangible size—the principle of ‘Least Action’. This principle includes the Newtonian mechanics and the classical mechanics as special cases, so that it covers not only mechanical activities but those of electricity and magnetism as well. It can best be understood through a simple analogy.

When I hire a taxicab, the taximeter piles up the charges against me at a rate which depends both on where I am, and on how fast I am travelling. I have to pay one sum per five minutes when I am at rest in a city, some other sum per five minutes when I travel at 15 miles an hour in the city, twice as much when I travel at 30 miles an hour in the city, and so on, and on an entirely different tariff when I am outside the city limits. Now let us imagine a taximeter attached to every moving object in the universe, piling up charges at a rate which depends on both the speed of motion and the position of the object. Let all the objects move for some specified time, such as an hour, and at the end of the motion let all the charges shown on the various taximeters be added up. The principle of Least Action tells us that the actual objects in nature will have chosen their paths so as to make the total charge shown by all the taximeters a minimum—Nature, setting her face against unnecessary expenditure on taxicabs, always chooses the cheapest route.

Suppose, for instance, that a single particle has to be transferred, within a specified time, from one point A to another point B, through a region in which conditions are absolutely uniform, so that the taxicab tariff is of course uniform also. The cheapest way of making the journey will be to travel in a perfectly straight line at a perfectly uniform speed, which is what Newton’s law of motion tells the particle to do. Or again, suppose that a planet has to be transported from its present position to the corresponding position at the other side of the sun. The shortest route would be straight through the centre of the sun, but, as the tariff in intense gravitational fields is exorbitant, the charges by this route would be prohibitive. We find we can avoid these excessive charges by taking a curved path round the sun, even though this lengthens the journey somewhat. If part of the route still goes near to the sun, it is cheapest to perform this part of the journey at high speed, so as to spend as little time as possible in the region of exorbitant tariffs. Exact mathematical analysis is needed to find exactly what combination of path and speed reduces the total charge to an absolute minimum; it tells us that the path must be an ellipse having the sun in one of its foci. This is precisely the path demanded by the Newtonian mechanics, but we notice that it is no longer mapped out by the action of ‘forces’ of the Newtonian kind.

Logically, and to some extent chronologically also, the principle of Least Action forms a direct successor to the principle of Least Time of Hero and Fermat. The principle of Least Distance, or geodesics, in the curved space-time of relativity is clearly in the same line of succession. It introduces a great simplicity by changing to the new background of a curved space—like the change of background of our radio listener when he changed from a rectangular projection to a curved spherical surface. Like the principles of Least Time and of Least Action, this principle of Least Distance shows an extreme simplicity which suggests that we are keeping in close touch with the true significance of natural processes.

The old quantum theory did not show any such simplicity. We need not concern ourselves with it any further since it has now become clear that it was only an unsatisfactory hybrid between the classical mechanics and the new quantum theory, being, in fact, a last desperate effort to represent nature against a background of time and space.

In the new quantum theory the same simplicity reappears in full strength and almost in the same form. So far as its formal mathematical description goes, the theory is a genuine extension of the old Newtonian mechanics, so much so that the same mathematical equations will serve for the description of both, namely the canonical equations of which we spoke on p. 113, these in turn being an expression of the principle of Least Action.

But the pictorial representations that must be given to these equations differ widely in the two cases. The classical mechanics came into existence as an effort to describe the continuous motions of objects under pushes and pulls; it is in this way that it is usually interpreted. But the new quantum mechanics must be interpreted rather as a description of steady states in which either there is no motion or else the state of motion does not change. Now and then, as we have seen, a jump occurs from one of these steady states to another, and it is with jumps of this kind rather than with gradual changes that the new mechanics is concerned. Are these jumps final, or will they ultimately be resolved into some kind of rapid continuous motions of which we have so far no knowledge, either observational or theoretical? We simply cannot form a judgment.

The main difference between the old mechanics and the new is, however, once again a difference of background. The classical mechanics and the old quantum theory had both assumed that the whole world existed in time and space; the new mechanics is most simply expressed in terms of symbols which are best interpreted by passing beyond space and time. In transcending space and time, the new quantum mechanics finds a new background which makes for far greater simplicity and so probably comes nearer to ultimate truth. In passing from the old mechanics to the new, the mathematical description of the pattern of events stands almost unaltered, while the interpretation we put upon the symbols is utterly changed.

The history of theoretical physics is a record of the clothing of mathematical formulae which were right, or very nearly right, with physical interpretations which were often very badly wrong. When Newton had found laws of motion of a mechanical system which were true (apart from the minor refinements of the theory of relativity), he put science on a wrong track for two centuries by interpreting them in terms of forces and absolute space and time. It was much the same with his supposed force of gravitation. Again, when the true laws of the propagation of light had been discovered, they were interpreted as applying to the propagation of waves in an ether which was supposed to fill all space, and again science was started along a wrong road which it was to follow for nearly two centuries.

Now when philosophy has availed itself of the results of science, it has not been by borrowing the abstract mathematical description of the pattern of events, but by borrowing the then current pictorial description of this pattern; thus it has not appropriated certain knowledge but conjectures. These conjectures were often good enough for the man-sized world, but not, as we now know, for those ultimate processes of nature which control the happenings of the man-sized world, and bring us nearest to the true nature of reality.

One consequence of this is that the standard philosophical discussions of many problems, such as those of causality and free-will or of materialism or mentalism, are based on an interpretation of the pattern of events which is no longer tenable. The scientific basis of these older discussions has been washed away, and with their disappearance have gone all the arguments, such as they were, that seemed to require the acceptance of materialism and determinism and the renunciation of human free-will. This does not mean that the conclusions previously reached were necessarily wrong, for a bad argument may lead to a good conclusion. But it does mean that the situation must be reviewed afresh. Everything is back in the melting-pot, and we must start anew and try to discover truth on the basis of the new physics. Apart from our knowledge of the pattern of events, our tools can only be probable reasoning and the principle of simplicity.

THE NEW PICTURE OF MODERN PHYSICS

We may appropriately start from those things of which we have the most certain knowledge, namely ourselves and our sensations. These sensations come to us through our senses, the most important of which is the sense of seeing. We see through the impact of radiation on the retina, this arriving in the form of the individual units we call photons. Other sense-organs act in a similar way, the smallest unit of sensation being produced by the arrival of a single quantum of energy from the world outside.

We have seen that photons may be represented as travelling in a space of three dimensions. This we may at once identify with the space of ordinary everyday life, because by space the ordinary man means the space through which photons travel to his eyes, the space in which he seems to see things shining or reflecting light, moving or standing still, the space in which he meets his friends.

These photons end their journeys by falling into our eyes, and so affecting our consciousness. But they are far from being projectiles falling at random. If we stand in the open on a clear night, we shall find that there are some directions of space from which photons arrive in a continuous stream and others from which no photons arrive. From such observations as this we deduce the existence of certain permanent sources of photons, or, more generally, of permanent sources of sensations; these we designate as matter.

This leads us to postulate the existence of a world of photons and matter, existing in ordinary space; it is what the plain man describes as the material world.

So far this material world has been nothing more than a mental construct private to ourselves; the space is our perceptual space, and may have no existence outside our own consciousness. If we now go asleep, or if our consciousness ceases for any other reason to function for a time, we shall find on awakening new sources of sensations which it is reasonable to identify with the old; the bedroom I find when I waken in the morning is so exactly similar to the room I left when I fell asleep that a tremendous simplicity is introduced by assuming that it is the same, and that it has been in existence all the time.

On the same principle, the moon, planets and stars outside the room may be identified with those I left behind me when I fell asleep. These, however, are no longer in the same positions. If I study these changes of position, I shall find that they are precisely those that would have occurred if the bodies had described geodesics in a curved space-time unity of the kind described on p. 63. A tremendous gain in simplicity is now secured by supposing that a curved space-time has been in existence during my sleep, and that the astronomical bodies have moved in this. Thus we conclude, with a high degree of probability, that the space-time unity and the objects which figure in it cannot be mere constructs of our individual minds, but must have existences of their own, although we know that space and time separately are abstractions of our individual minds from the space-time unity. This does not of course touch the question, to which we shall return later, of whether space, time and the material world are or are not of a mental nature, being perhaps the constructs of a consciousness superior to our own. So long as we are concerned only with our sensations, it is all the same whether we regard the world as a mental construct or as having an existence of its own independent of mind—the essential point at the moment is that it cannot be a private mental construct of our own.

APPEARANCE AND REALITY

The doctrine of materialism asserted that this space, time and material world comprised the whole of reality; it regarded consciousness as only a minor incident in the history of the material world, a somewhat exceptional episode in the haphazard muddle resulting from the chaotic movements of photons, electrons and matter in general. It interpreted thought as a mechanical motion in the brain, and emotion as a mechanical motion in the body. It seemed at one time to receive substantial support from science. For consciousness was never experienced except in conjunction with matter; a man’s mental state was obviously influenced by the food, drink and drugs given to his body; and many thought it possible that all mental activities might be interpreted in terms of various physico-mental processes occurring in the associated body. At the same time astronomy was finding that only an inconceivably minute fraction of space provided any possibility for the existence of the kind of life we know, and it seemed impossible that the rest of the universe should contain anything but inanimate matter. It was hard to imagine that consciousness should be of fundamental importance in such a world.

The new physics suggests that, besides the matter and radiation which can be represented in ordinary space and time, there must be other ingredients which cannot be so represented. These are just as real as the material ingredients, but do not happen to make any direct appeal to our senses. Thus the material world as defined above constitutes the whole world of appearance, but not the whole world of reality; we may think of it as forming only a cross-section of the world of reality.

We may picture the world of reality as a deep-flowing stream; the world of appearance is its surface, below which we cannot see. Events deep down in the stream throw up bubbles and eddies on to the surface of the stream. These are the transfers of energy and radiation of our common life, which affect our senses and so activate our minds; below these lie deep waters which we can only know by inference. These bubbles and eddies show atomicity, but we know of no corresponding atomicity in the currents below.

This dualism of appearance and reality pervades the history of philosophy, again dating back to Plato. In a famous parable, Plato depicts mankind as chained in a cave in such a way that they can look only on the wall which forms the back of the cave; they cannot see the busy life outside, but only the shadows—the appearances—which objects moving in the sunshine cast on the walls of the cave. For the captives in the cave, the shadows constitute the whole world of appearance—the phenomenal world—while the world of reality lies for ever beyond their ken.

Our phenomenal world consists of the activities of matter and photons; the theatre of this activity is space and time. Thus the walls of the cave in which we are imprisoned are space and time; the shadows of reality which we see projected on the walls by the sunshine outside are the material particles which we see moving against a background of space and time, while the reality outside the cave which produces these shadows is outside space and time.

Many philosophers have regarded the world of appearance as a kind of illusion, some sort of creation or selection of our minds which had in some way less existence in its own right than the underlying world of reality. Modern physics does not confirm this view; the phenomena are seen to be just as much a part of the real world as the causes which produce them, being simply those parts of the real world which affect our senses, while the space and time in which they occur have the same sort of reality as the substratum which orders their motions. The walls of the cave and the shadows are just as real as the objects outside in the sunshine.

As the new physics has shown, all earlier systems of physics, from the Newtonian mechanics down to the old quantum theory, fell into the error of identifying appearance with reality; they confined their attention to the walls of the cave, without even being conscious of a deeper reality beyond. The new quantum theory has shown that we must probe the deeper substratum of reality before we can understand the world of appearance, even to the extent of predicting the results of experiment.

For, whatever may happen in reality, there is no reason why the shadows on the wall should change in accordance with a causal law. There will be many different arrangements of the figures out in the sunshine which all produce the same arrangement of shadows on the wall; these many arrangements will be followed by new arrangements which will not only be different in themselves but are likely to produce different shadows on the wall. It is the same with the happenings in the world of appearance; experiments that are precisely identical so far as the phenomena go may produce entirely different results. In this way causality disappears from the world of phenomena.

It comes back when we explore the substratum of reality, although in a strange new guise. Because we have only complete photons at our disposal, and these form blunt probes, the world of phenomena can never be seen clearly and distinctly, either by us or by our instruments. Instead of seeing clearly defined particles clearly located in space and executing clear-cut motions, we see only a collection of blurs—like a badly focused lantern slide. As we have seen (p. 144), this is enough of itself to prevent our ever observing strict causality in the world of phenomena.

Each blur represents the unknown entity which the particle-picture depicts as a particle, or perhaps a group of such entities. The blurs may be pictured as wave-disturbances, the intensity of the waves at any point representing the probability that, with infinitely refined probes at our disposal, we should find a particle at that point. Or again we may interpret the waves as representations of knowledge—they do not give us a picture of a particle, but of what we know as to the position and speed of motion of the particle. Now these waves of knowledge exhibit complete determinism; as they roll on, they show us knowledge growing out of knowledge and uncertainty following uncertainty according to a strict causal law. But this tells us nothing we do not already know. If we had found new knowledge appearing, not out of previous knowledge but spontaneously and of its own accord, we should have come upon something very startling and of profound philosophical significance; actually what we find is merely what was to be expected, and the problem of causality is left much where it was.

MENTALISM OR MATERIALISM?

In addition to the dualism of appearance and reality, many pictures of the world have exhibited a second dualism, that of mind and matter or of body and soul.

This also, so far as our knowledge carries us, started with Plato. We have seen how his picture of the world consisted of forms, which exist only in our minds, and of sensible objects which, on Plato’s view, display the imprint of the forms and so exemplify the qualities embodied in the forms. Plato maintained that the forms possessed a higher degree of reality than the material objects which exemplify them, so that the world was primarily a world of ideas and only secondarily a world of material objects.

We have further seen how Descartes, two thousand years later, drew a picture of the world in which mind and matter again figured, but they were now so distinct in their natures that neither could act on the other.

Then came the Idealist (or Mentalist) philosophers, who still divided the world into mind and matter, but argued that matter had no existence in its own right; it was of the same nature as mind, and existed only so far as it was a creation of mind. Under the leadership of Bishop Berkeley, they reached their conclusions by a twofold argument.

The First Argument for Mentalism

The first was an argument we have already noticed. Galileo, Descartes, Locke and others divided the qualities of objects and substances into the two classes which Locke designated as primary and secondary. Secondary qualities are those which are perceived by the senses, and so may be differently estimated by different percipients; primary qualities are those which are essential to the object or substance and so are inherent in it whether they are perceived or not.

We have seen that physics gives no support to this division of qualities into primary and secondary. The idealists were at one with the physicists in this, but whereas the physicists consider that all physical qualities are primary, in Locke’s sense of being ‘utterly inseparable from the body in what state soever it be’, the idealists argued that all qualities were secondary since they could be differently estimated by different percipients, a flower looking scarlet to one man but purple to another, the leg of a cheese-mite looking minute to a man but of quite a decent size to the cheese-mite, and so on. This being so, they argued, colour and size cannot be objective properties of objects; they cannot reside in the objects themselves, but in the minds perceiving the objects. And if an object is nothing but the sum of its qualities, then when all qualities reside only in percipient minds, the object itself must do the same. In brief, the object is of the nature of an idea; existence consists in being perceived by a mind.

If so, of course, an object would be non-existent when it was not being perceived by a mind. Yet the planet Pluto was certainly in existence, and impressing its image on photographic plates, many years before anyone suspected its existence. And to all appearances things go on happening inside an empty room—the fire continues to burn and the clock to keep time; when we return we find no reason for suspecting that the clock and fire have been out of existence in our absence. Berkeley got over difficulties of this kind by supposing that an object, even though it might at times not be perceived by any human mind, was yet kept permanently in existence through being continually perceived by the mind of God. Thus the whole world became an idea in the mind of God.

We have already found reasons why science can give no countenance to any arguments which suppose objects to be the sum of their secondary qualities (p. 90); they are, in brief, as follows.

Whatever capacity a red flower may have for producing a sensation of redness in a man’s mind, it also has a capacity for reflecting red light whether there is anyone to see it or not, as may be very simply proved by photography. This capacity is obviously a primary quality, being ‘utterly inseparable from the body in what state soever it be’, and Berkeley’s argument cannot touch it. Berkeley’s argument fails through his not seeing that each quality such as redness must have primary ingredients as well as its alleged secondary ingredients; there is an objective scientific redness as well as the subjective philosophic redness.

The Second Argument for Mentalism

The second line of argument ran somewhat as follows. When I hear a bell, a hammer has given a mechanical blow to a piece of metal and set it into vibration. The vibrations have been communicated in turn to the surrounding air, to my eardrums, and to a succession of elaborate pieces of mechanism and fluids inside my ears, with the result that a sequence of minute electric currents finally reaches my brain and produces certain physical changes there. These changes result in something crossing the mysterious mind-body bridge and producing certain happenings in the mind on the far side. These happenings we describe as the hearing of a bell, a purely mental idea because we might equally well experience it in a dream when there was no bell to produce it. Berkeley argued that effects must always be of the same general nature as their causes, a mechanical effect being traceable to a mechanical cause, and so on. Or, to put it rather more precisely, whatever crosses the mind-body bridge must be of the same general nature as its cause on the one side of the bridge and as its effect on the other. Thus Berkeley maintained that as the effects A on the mind side of the mind-body bridge are purely mental, their causes B on the body side must also be purely mental. In brief, as A is an idea, and ‘an idea can be like nothing but an idea’, therefore B also must be an idea, or of course a set of ideas.

The argument is obviously double-edged, and just as effective when reversed. For if B must be of the same nature as A, it is equally valid to argue that A must be of the same nature as B. Since A is purely material, the argument would now prove that our mental processes must be material in their nature, as the materialists claim.

Berkeley was only able to see one side of the argument; he wished to serve theology by proving the existence of God. Before him, Descartes had been unable to see either side, claiming that mind and matter were so dissimilar, as a matter of experience, that they could have nothing in common; he too desired to serve theology—by establishing the freedom of the will. Disregarding all its theological implications, Berkeley’s argument seems to provide a valid proof that mind and matter must have something in common; we can see how much real substance there is in it if we reflect on the straits to which Descartes and Leibniz were reduced when they tried to show how the opposite might be true (p. 28).

In more recent times, Bertrand Russell has expressed what is essentially the same argument in the words: ‘So long as we adhere to the conventional notions of mind and matter, we are condemned to a view of perception which is miraculous. We suppose that a physical process starts from a visible object, travels to the eye, there changes into another physical process, causes yet another physical process in the optic nerve, and finally produces some effect in the brain, simultaneously with which we see the object from which the process started, the seeing being something “mental”, totally different in character from the physical processes which precede and accompany it. This view is so queer that metaphysicians have invented all sorts of theories designed to substitute something less incredible ....’

‘Everything that we can directly observe of the physical world happens inside our heads, and consists of mental events in at least one sense of the word mental. It also consists of events which form part of the physical world. The development of this point of view will lead us to the conclusion that the distinction between mind and matter is illusory. The stuff of the world may be called physical or mental or both or neither as we please; in fact the words serve no purpose.’

If we accept this argument, the dualism of Descartes drops out of the picture altogether, and the only question left is whether we ought to say with the materialists that mind is material, or with the mentalists that matter is mental.

Whole libraries have, as Jeffreys pungently remarks, been filled with bad arguments on both sides. The materialists felt very sure, partly because of the success of science, that there was an external world of small hard atoms existing and moving in space and time, and concluded that mind must be material, and consciousness an activity of small hard atoms in space and time. The small hard atoms have now departed from science, and we picture matter as consisting mostly of empty space. Some writers have seemed to consider that this involves far-reaching philosophical consequences, and in particular, that it carries us in the direction of mentalism. It is hard to see why. Being hit by a golf-ball hurts just as much now that we know that it is little more than empty space; we realize that its material properties of solidity and hardness have not been demolished, but are merely explained in a new way.

The materialists also felt sure, partly on account of the success of science, that the absolute space and time of Newton had real existences in their own right. The physical theory of relativity now indicates—to a high degree of probability, although without absolute certainty—that space and time do not exist separately in their own right, but are subjective selections from a wider space-time unity. Some writers have argued as though this too implied a drift towards mentalism, but again it is hard to see why. Whatever degree of reality was possessed by the space and time of the older physics has not been banished from the world, but merely transferred to the space-time unity; this joint structure is every bit as objective, and may be every bit as real, as its components space and time were once thought to be separately. The two components have simply entered into a partnership, so that they now form a single entity in the eyes of the law of science, but this makes them neither less real nor more mental than before.

The physical theory of relativity has, however, other considerations to bring forward. For the materialists, space was filled with real particles, exercising on one another forces which were electric or magnetic or gravitational in their nature; these directed the motions of the particles and so were responsible for all the activity of the world. These forces were of course as real as the particles they moved.

But the physical theory of relativity has now shown (pp. 134, 171) that electric and magnetic forces are not real at all; they are mere mental constructs of our own, resulting from our rather misguided efforts to understand the motions of the particles. It is the same with the Newtonian force of gravitation, and with energy, momentum and other concepts which were introduced to help us understand the activities of the world—all prove to be mere mental constructs, and do not even pass the test of objectivity. If the materialists are pressed to say how much of the world they now claim as material, their only possible answer would seem to be: Matter itself. Thus their whole philosophy is reduced to a tautology, for obviously matter must be material. But the fact that so much of what used to be thought to possess an objective physical existence now proves to consist only of subjective mental constructs must surely be counted a pronounced step in the direction of mentalism.

The gravitational theory of relativity again brings considerations of a new kind into play. It provides an outstanding example of the truth of Einstein’s general remark (p. 183) that, as experimental research advances, the fundamental laws of nature become simplified more and more, and, as in many other departments of physics, we find this simplicity residing neither in the physical facts nor in their pictorial representations, but solely in the mathematical formulae which describe the pattern of events. These seem simple to our minds because they are expressible in the kind of mathematics to which we take naturally, and studied for the pure intellectual interest we found in it before we saw it would help us to understand nature—in brief, in pure and not in applied mathematics. Thus the pure mathematician finds it much easier to interpret gravitation in terms of his science than does the mechanic or engineer. But the pure mathematician deals with the mental sphere, the mechanic and the engineer with the material. Thus the relativity theory of gravitation, because of its close association with pure mathematics, seems to carry us yet further along the road from materialism to mentalism, and the same may be said of most of the recent developments of physical science.

The new quantum theory brings still further factors into the situation. We have seen how it puts before us the two pictures which we have described as the particle-picture and the wave-picture.

The particle-picture depicts the phenomena; its ingredients are those of the ordinary picture of the material world, namely matter and radiation existing and moving in time and space.

The ingredients of the wave-picture are wave-like disturbances. Whatever a particle may be in itself, we can never experience it as a point, but if we insist on picturing it as such, then the relative intensities of the waves indicate the relative proprieties of supposing it to exist at the various points of space.

Proprieties relative to what? The answer is: Relative to our knowledge. If we know nothing about a particle except that it exists, all places are equally likely for it, so that its waves are uniformly spread throughout the whole of space. By experiment after experiment we can restrict the extent of the waves, but we can never reduce it to a point, or indeed below a certain minimum; the coarse-grainedness of our probes precludes this, so that there must always be a finite region of wave-disturbance left. The waves in this region depict our knowledge and its imperfections exactly and precisely.

Thus the ingredients of the particle-picture are particles existing and moving in physical space, while the ingredients of the wave-picture are mental constructs existing and moving in conceptual spaces; the ingredients of the particle-picture are material, those of the wave-picture mental.

The first complete particle-picture was provided by Newton’s mechanics in conjunction with his corpuscular theory of light. The mechanics supposed that those permanent sources of sensation which we call matter consisted of particles moving in physical space, while the corpuscular theory of light further supposed that the radiation by which our sense-organs are affected also consist of particles. This scheme was found not to give an adequate account of the facts of observation, and in due course the corpuscular picture of light was replaced by the present wave-picture. This resulted in complete agreement with the facts of observation so far as optical phenomena were concerned. But, until the theory of relativity appeared, it was not suspected that the ingredients of this picture were purely mental constructs.

Thus physics continued to believe that it was studying an objective nature which existed in its own right independently of the mind which perceived it, and had existed from all eternity whether it was perceived or not; this belief was the soil in which materialism had its roots. Physics would have gone on holding this belief to this day, had the electron which the physicist observed behaved as, on this supposition, it ought to have done.

But it did not so behave, and the new quantum theory was brought into existence to make good the defects. It discovered what we believe to be the true pattern of events, with the wave-picture of matter as its pictorial representation. The particle-picture of radiation had already given place to a wave-picture; it now appeared that the particle-picture of matter must also be replaced by a wave-picture. The result was a complete agreement with experiment. In this progress towards the truth, let us notice that each step was from particles to waves, or from the material to the mental; the final picture consists wholly of waves, and its ingredients are wholly mental constructs.

We must remember that this picture is not a picture of reality, it is a picture we draw to help us imagine the course of events in reality. Thus we are not entitled to argue that reality is like the ingredients of the picture, although there is a certain presumption that the two are not altogether dissimilar in their natures; the pictorial representation does not take us into the mansion of reality, but does take us to its doorstep. Thus, when it was believed that the course of events could be most easily understood in terms of forces and mechanical models, most people thought that the picture or model must be like the reality, and jumped to the conclusion that reality was mechanical in its nature. Before this, when the course of events had seemed to be governed by the caprices and passions of gods and demons, it had been assumed that reality was of a similar nature; we have seen how Thales maintained that all things must be full of gods. And now that we find that we can best understand the course of events in terms of waves of knowledge, there is a certain presumption—although certainly no proof—that reality and knowledge are similar in their natures, or, in other words, that reality is wholly mental.

Apart from arguments of this type, we can have no means of knowing the true nature of reality. The most we can say is that the cumulative evidence of various pieces of probable reasoning makes it seem more and more likely that reality is better described as mental than as material.

Even if the two entities which we have hitherto described as mind and matter are of the same general nature, there remains the question as to which is the more fundamental of the two. Is mind only a by-product of matter, as the materialists claimed? Or is it, as Berkeley claimed, the creator and controller of matter?

Before the latter alternative can be seriously considered, some answer must be found to the problem of how objects can continue to exist when they are not being perceived in any human mind. There must, as Berkeley says, be ‘some other mind in which they exist’. Some will wish to describe this, with Berkeley, as the mind of God; others with Hegel as a universal or Absolute mind in which all our individual minds are comprised. The new quantum mechanics may perhaps give a hint, although nothing more than a hint, as to how this can be.

In the particle-picture, which depicts the phenomenal world, each particle and each photon is a distinct individual going its own way. When we pass one stage further towards reality we come to the wave-picture. Photons are no longer independent individuals, but members of a single organization or whole—a beam of light—in which their separate individualities are merged, not merely in the superficial sense in which an individual is lost in a crowd, but rather as a raindrop is lost in the sea. The same is true of electrons; in the wave-picture these lose their separate individualities and become simply fractions of a continuous current of electricity. In each case, space and time are inhabited by distinct individuals, but when we pass beyond space and time, from the world of phenomena towards reality, individuality is replaced by community.

It seems at least conceivable that what is true of perceived objects may also be true of perceiving minds; just as there are wave-pictures for light and electricity, so there may be a corresponding picture for consciousness. When we view ourselves in space and time, our consciousnesses are obviously the separate individuals of a particle-picture, but when we pass beyond space and time, they may perhaps form ingredients of a single continuous stream of life. As it is with light and electricity, so it may be with life; the phenomena may be individuals carrying on separate existences in space and time, while in the deeper reality beyond space and time we may all be members of one body. In brief, modern physics is not altogether antagonistic to an objective idealism like that of Hegel.

The new dualism of the particle- and wave-pictures is in many ways reminiscent of the old dualism of Descartes. There is no longer a dualism of mind and matter, but of waves and particles; these seem to be the direct, although almost unrecognizable, descendants of the older mind and matter, the waves replacing mind and the particles matter. The two members of this dualism are no longer antagonistic or mutually exclusive; rather they are complementary. We need no longer devise elaborate mechanisms, as Descartes and Leibniz did, to keep the two in step, for one controls the other—the waves control the particles, or in the old terminology the mental controls the material.

THE PROBLEM OF FREE-WILL

We have seen how the materialists interpreted thought and emotion as mechanical activities of the brain and body respectively, and imagined that if all the physical and chemical changes in a brain and body could be traced out, it would be possible, at least in principle, to deduce all the mental and emotional experiences of the associated mind. Thus, if material changes were bound by a causal chain, mental and emotional experiences would also be so bound, and there could be no room left for free-will.

There were nevertheless two schools of thought—the determinists who maintained that all events, including human acts, were causally determined and so compelled by past events and acts, including such events as those of heredity, environment, acquired habits and so forth; and the indeterminists who maintained that human acts are not entirely determined by the past, but that at every moment we can exercise a certain amount of guidance through a fiat which is our own.

On the determinist view, a man’s actions would of course be completely predictable in principle by one who had a sufficiently intimate knowledge of his nature, of his past and of the character he has acquired in the past. On the indeterminist view, this is not so; a man can falsify all predictions by a capricious, and so unpredictable, choice.

The Determinists

Practically all modern philosophers of the first rank—Descartes, Spinoza, Leibniz, Locke, Hume, Kant, Hegel, Mill, Alexander, as well as many others—have been determinists in the sense of admitting the cogency of the arguments for determinism, but many have at the same time been indeterminists in the sense of hoping to find a loophole of escape from these arguments. Often they conceded that our apparent freedom is an illusion, so that the only loophole they could hope to find would be an explanation as to how the illusion could originate.

Descartes and Kant, as we have seen, may fairly be described as determinists trying to shed their determinism, while Leibniz, Locke and Hume are perhaps better described as determinists trying to explain their determinism. Spinoza, Mill and Alexander were out-and-out determinists, although like many other determinists they were not always consistent in their determinism.

Leibniz thought that there are always sufficient reasons in the nature and character of each one of us to determine for us any decision we may be called upon to make. We are, then, never free, because our acts at every moment are completely determined by our nature which came to us in the past, and by our character which was formed in the past. Hume also thought that our decisions are always determined by our characters, so that to make a different decision we should need to be a different person. Locke thought our decisions are based on our desires to enjoy pleasure and avoid pain, and so are determined by our estimates of future pleasure and pain—although of course our judgments may be wrong. Spinoza thought that our actions and experiences are in actual fact determined by a sort of mathematical necessity, like that of a wheel in a machine, but that we feel ourselves free if we enjoy doing what actually we are doing under compulsion; a stone in the air, he said, would think itself free if it could forget the hand that had thrown it. Or, to take a more homely illustration which is not Spinoza’s, I know that I choose jam-roll because I like it, and I feel myself free in so choosing because I do not stop to think that my liking is the inevitable result of my inheritance and upbringing, of the present state of my health and of my sugar metabolism, and of all sorts of things which it is quite beyond my power to change at the moment. Hegel and, at a later period, Alexander held very similar opinions. Kant thought that we feel ourselves free just in so far as our actions appear rational to us ; if I rationally run downstairs to welcome a friend, my action seems free to me, but if I run downstairs irrationally because I am afraid of a ghost, it will seem to me that I acted under compulsion. Mill believed that all human actions are so completely determinate that sociology could be made into a perfectly exact science, in which the future of a society would be seen to follow from its past with a mechanical certainty and after unvarying laws. He then, with the characteristic irrationality of the thoroughgoing determinist, wanted these laws to be studied with a view to improving the future of the race!

The average plain man who is no philosopher will probably consider that the springs of human action are too varied, too intricate and too complex to be summed up in any single formula. His own philosophy is not very clear-cut, but may perhaps be described as one of determinism for others and freedom for himself. Yet this supposed freedom applies only to his present acts, and not to the past; we see our past selves as other men. For, as Henry Sidgwick says: ‘We always explain the voluntary action of all men except ourselves on the principle of causation by character and circumstances. We infer generally the future actions of those whom we know from their past actions; and if our forecast turns out in any case to be erroneous, we do not attribute the discrepancy to the disturbing influence of free-will, but to our incomplete acquaintance with their character and motives....Nay even as regards our own actions, however free we feel ourselves at any moment, however unconstrained by present motives and circumstances and unfettered by the result of what we have previously been and felt our volitional choice may appear, still when it is once well past, and we survey it in the series of our actions, its relations of causation and resemblance to other parts of our life appear, and we naturally explain it as an effect of our nature, education and circumstances.’

Not only so, but the freedom we claim for our present selves is almost indistinguishable from the determinism we attribute to others. We usually claim no freedom for ourselves beyond that of being able to do what we want to do, which simply means yielding to the strongest impulse, the freedom of the beam of the weighing scale to incline to the heavier side, the kind of freedom which philosopher and scientist agree in describing as determinism—since, under it, the future is fully determined; it follows from the past with the inevitability of a machine.

We can see this by examining special instances. Mr Average Man thinks over his past, and proclaims that if he were young again, he would choose a different profession. He may insist that he would be free to make his own choice, but all he means is that if, at the age of eighteen, he had had the knowledge and experience of life which he now has at fifty, he would have acted differently. Of course he would, and so would we all, but this is no evidence of freedom. If Mr Man now had to make his choice again, with precisely the same knowledge and experience as he had at eighteen, he would review the situation in the same way as he did before, the same considerations would be thrown into the scales, and the balance would again swing in the same direction as before. He will not claim a freedom to act from pure caprice, but only a freedom to yield to the strongest motive—the freedom of Newton’s apple to fall towards the earth rather than towards the moon, because the earth attracted it more forcibly than the moon. And this is not freedom of any kind; it is pure determinism. As Hume said, to have made a different decision, he would have had to be a different man.

Or perhaps he may claim he is free to choose in trivial matters, as for instance whether he will ask for black or white coffee. Perhaps he usually asks for black, and if on some rare occasion he asks for white, he may imagine that in so trivial a matter his choice was wholly undetermined. But a psychologist will tell him that, even here, he can only yield to the strongest motive, no matter how weak these motives may be. When he made his unusual choice, his mind may have been far away from food and drink, absorbed in the pages of a book he was looking at, so that, when politeness compelled him to make a choice, he merely mentioned the colour suggested by the pages of his book. Or he may have felt a temporary but unconscious aversion to black and blackness through some association, such as mourning or a funeral. There are endless possibilities and only one impossibility, which is that he said ‘white’ out of pure caprice, without having any guiding motive in his mind. The presence of milk in his coffee in two minutes’ time will be a direct consequence of the state of his mind now, just as surely as the state of the material universe in two minutes’ time will, on the deterministic view, be a direct consequence of its state now.

Although Mr Average Man may occasionally protest that he is incapable of acting meanly or dishonourably, yet in general he would hate to think that he is not free to choose his own course of action at every moment of his life. Thus he likes to think that his own actions are wholly unpredictable, and yet, when other men behave in a wholly unpredictable way, he describes them as weak fools. In brief, freedom in ourselves is a virtue, but in others a vice; freedom is something we possess, but that others do not.

Not only plain men, but philosophical writers also, seem to confuse free-will with determinism of this unconscious kind. Thus Henry Sidgwick (Methods of Ethics) says that the question at issue in the free-will controversy, as he understands it, is whether his action at any moment is completely determined by his character and the external influences, including his bodily condition, which act on him at the moment, our is there always a possibility of my choosing to act in the manner that I now judge to be reasonable and right, whatever my previous actions and experiences may have been?’

But a judgment as to what is reasonable and right cannot be based on nothing at all—if it is, it is no judgment but pure caprice. And it cannot be based on anything other than a man’s character, which is founded in his previous actions and experiences, and the external influences acting on him at the moment—in brief, on the past and the present, or on what is inside him and on what is outside him. Thus Sidgwick’s second alternative, which is clearly intended to represent free-will, is that our actions are determined by our judgments, and our judgments by our inner character and external influences—which brings us round to precisely his description of determinism. Thus his two alternatives are not determinism and freedom at all, but merely conscious and unconscious determinism, and he never reaches the real issue of free-will.

The same is true of theological attempts to solve the problem by adding Divine intervention to the external influences acting on a man—‘We have no power to do good works ... without the grace of God by Christ preventing us, that we may have a good will, and working with us when we have that good will.’ Such Divine intervention does not add to a man’s freedom, but to the restrictions on it.

Attempts have been made to find an alternative to determinism in what is described as ‘teleological causation’, according to which the future determines the present, or at least influences it, like the legendary carrot held in front of the donkey’s nose. If a student is working hard in the hope of passing an examination, it is argued that the present spell of hard work is the effect of a future cause, namely an examination which is to be held at some future date. But it is surely more true to say that the cause is not the examination—which after all may never take place, and so can hardly be the cause of something which has already taken place—but the hope of passing the examination. This hope is not in the future; a man will not be working for an examination at this moment unless the hope of passing it has been in his mind at some previous moment, so that the proximate cause of his hard work is in the past, and not in the future. To some extent, the whole matter is one of juggling with words, but in whatever sense words are used, ideas such as teleological causation can throw no new light on the ultimate problem.

The Indeterminists

On the other side, Lotze (1817–1881) and William James (1842–1910) were consistent and logical indeterminists. Lotze agreed with the determinists that both natural events and human acts lie on strings of causal chains, and that such causal chains when once started have no end in future time, but he thought that such chains may have capricious beginnings. William James advocated the doctrine he described as tychism—chance playing its part in ordering the course of events. According to him, the pattern of events is not unalterably fixed; we introduce novelties when we make choices (but it is not explained why one novelty rather than another is introduced).

We have already seen that modern physics is not entirely hostile to such ideas in their application to inanimate nature, although we also saw (p. 178) that they should not be applied to the underlying realities, but only to the phenomena as seen and understood by us—in other words, the indeterminacy does not reside in objective nature, but only in our subjective interpretation of nature.

Let us, however, ignore the distinction, and state the case in the form most favourable to indeterminism and freedom by imagining that an assigned state A of the inanimate world may be followed by any one of a number of different states B, C, D, . . . all of which lead to different future states of the world. In the inanimate world we find no apparent reason why A should be followed by B rather than by C or D. But suppose that in situations in which the human mind is concerned, the mind has some power of directing minute bits of the world to any one of the states, B, C, D, . . . as it chooses. Since all the transitions A → B, A → C, A → D, etc. conform to the conservation of energy and momentum, we have mind acting on matter without the exercise of any material force or any transfer of energy, and moulding the universe within limits to its choice. This brings us to something very like Descartes’s original explanation of the action of mind on matter (p. 25), but it is no longer open to the objections raised by Leibniz.

Essentially the same solution was propounded by Clerk Maxwell. The course of a railway train is uniquely prescribed for it at most points of its journey by the rails on which it runs. Here and there, however, it comes to a junction at which alternative courses are open to it, and it may be turned on to one or the other by the quite negligible expenditure of energy involved in moving the points. Maxwell thought that the human body might come to similar junctions, at which it could be turned into one course or another by the action of the mind, without any expenditure of mechanical energy—the body is the train, the mind is the pointsman. The indeterminacy of atomic motions has seemed to many to provide just the kind of junction, and possibly also of points, that Maxwell needed.

This may suggest a possible way in which mind can act on matter, but it leaves the deeper problem of freedom of choice untouched. Even if the pointsman can move the points and divert the motion of the train in so doing, the question of why he moves the points in one direction rather than in another remains. If he moves them according to a pre-arranged plan, the train is simply following a schedule, which makes its motion as determinate as if the points and junction were non-existent. If, as most people would say, he moves them in a particular direction ‘because he chooses to’, the question is why he chooses this direction rather than the other. If something determines his choice, we are back to determinism; if nothing, he acts from pure caprice, and this leads to a free-will which is neither of the kind we want to find nor of the kind we feel we do find. We like to imagine that we hold determinism at bay by our wisdom or virtue or foresight, and not through a mere random caprice over which we have no control and so for which we are in no way responsible. A man who has done a foolish deed may find comfort in thinking that he was the plaything of capricious forces, but not so the man who has been prudent or generous or has put his money on a winner.

Neither does a capricious indeterminism give us a free-will at all resembling that of our experience or imagined experience. If every event were not determined by a sufficient reason, the whole world would, as Leibniz remarked, be a chaos. A mind endowed with free-will of the capricious variety would be a prey to spontaneous and wholly irrational impulses; we should describe it as the mind of a madman, although in actual fact no madman’s mind is ever quite so crazy. The further psychology and common sense probe into the question, the more necessary they find it to accept orthodox determinism—our acts are determined by our volitions, our volitions by our motives, and our motives by our past. The psychologist will think of this past in terms of heredity and environment, the moralist in terms of ethical and spiritual influences, and the physiologist in terms of physico-chemical activities. But all will agree that the relative strength of the various motives is determined by past events, so that a man never chooses for himself; his past always chooses for him.

Present-day Opinion

Notwithstanding the apparent want of determinism disclosed in inanimate nature by the quantum theory, this is still the opinion of the vast majority of present-day physicists. Thus in his book, Where is science going? Planck, the founder of the quantum theory, writes: ‘No biographer will attempt to solve the question of the motives that govern the acts of his hero by attributing these to mere chance. He will rather attribute his inability to the lack of source materials, or he will admit that his own powers of spiritual penetration are not capable of reaching down into the depths of these motives. And in practical everyday life our attitude to our fellow-beings is based on the assumption that their words and actions are determined by distinct causes, which lie in the individual nature itself or in the environment, even though we admit that the source of these causes cannot be discovered by ourselves.... The principle of causality must be held to extend even to the highest achievements of the human soul. We must admit that the mind of each one of our great geniuses—Aristotle, Kant or Leonardo, Goethe or Beethoven, Dante or Shakespeare—even at the moments of its highest flights of thought or in the most profound inner workings of his soul—was subject to the causal fiat and was an instrument in the hands of an almighty law which governs the world.’

In the same book, Einstein is reported as saying: ‘Honestly I cannot understand what people mean when they talk about the freedom of the will. I feel that I will to light my pipe and I do it, but how can I connect this up with the idea of freedom? What is behind the act of willing to light the pipe? Another act of willing? Schopenhauer once said: Der Mensch kann was er will; er kann aber nicht wollen was er will.’

Modern philosophy also seems to have come to the conclusion that there is no real alternative to determinism, with the result that the question now discussed is no longer whether we are free but why we think we are free. We have seen how Alexander divides the world into levels which are at different stages of evolution—space-time, matter, life, mind, Deity. While conceding that all events are in actual fact deterministic, he considers that the inhabitants of each level may feel themselves free, while noting the absence of freedom prevailing in the levels lower than their own. Thus atoms, in the lowest level but one, feel themselves free when they contemplate space-time in which no freedom is possible; we have already quoted Spinoza’s remark that a stone in the air would think itself free if it could forget the hand that had thrown it. In the same way, we think ourselves free, but think that machines and even plants—the levels just beneath us—are determinate. And again God, contemplating our activities from His higher level, feels Himself free but sees that we are not.

Without accepting any such scheme in detail, many philosophers would agree that we are able to do what we wish within limits, and so feel ourselves free, but this is only because we do not pause to reflect that our wishes themselves—the springs of our actions—are thrust on us by our pasts. On the other hand, as we have no immediate experience of this feeling of freedom in others, we see that their acts are thrust on them by their pasts, and so regard these acts as determinate.

In brief, neither the philosophical study nor the physical research of the last 300 years has shown any cause for changing Descartes’s dicta that ‘nothing cannot be the efficient cause of anything’ and that ‘the power of the will consists only in this, that...we so act that we are not conscious of being determined to a particular action by any external force’. Thus free-will is only our name for unconscious determinism. But Kant would presumably have argued that all this does not prove that we are devoid of freedom, so much as that a deterministic way of looking at things is ingrained in our minds; it is our way of interpreting the temporal sequence of events.

And of course it may be. After a few individual experiences of the type ‘I have bumped my head, and I feel a pain’, the growing child generalizes to such propositions as ‘I have bumped my head, and therefore I feel a pain’ and If I bump my head, I shall feel a pain’. Such associations of ideas prove helpful in avoiding further misadventures, and so are extended, and the habit of finding cause-effect relations grows. But there is a continuous transition from cases such as those just mentioned to ‘It is night, so it will soon be day’ or ‘I am hungry, so shall soon get something to eat’, which are not cause-effect relations at all. In these and similar ways the post hoc ergo propter hoc habit of mind may become ingrained, and it may be possible to find a perfectly simple psychological explanation of the cause-effect habit of the human mind without even calling upon any inborn mental ‘category’.

In any case there can be no question that all our conscious experiences of inanimate nature, which are limited to the man-sized world, show that determinism does prevail here. It may be that, because of this, we are unable to imagine how anything but determinism can govern the inanimate world—although modern physics shows that it does so far as the phenomena are concerned—and that we then transfer this inhibition from the material to the mental world. If so, it is neither abstract physics nor concrete experience that thrusts determinism upon us, but rather the inability of our minds to imagine anything other than determinism.

Before the era of modern physics, it was a simple matter to define what we meant by causality and free-will. We supposed the world to consist of atoms and radiation; we imagined that precise positions could be assigned, in principle, to every atom and to every element of radiation, and the question of causality was simply whether, knowing these positions, it was possible in principle to predict the future course of events with certainty. The question of free-will was whether it was still possible to predict this course when consciousness and human volitions intervened in the picture.

But modern physics shows that these formulations of the questions have become meaningless. It is no longer possible to know the exact positions of particles or of elements of radiation, and, even if we could, it would still be impossible to predict what was going to happen next. So far as the inanimate world is concerned, we may picture a substratum below space and time in which the springs of events are concealed, and it may be that the future already lies hidden, but uniquely and inevitably determined, in this substratum. Such a hypothesis at least fits all the known facts of physics. But as we pass from the phenomenal world of space and time to this substratum, we seem, in some way we do not understand, to be passing from materialism to mentalism, and so possibly also from matter to mind. It may be then that the springs of events in this substratum include our own mental activities, so that the future course of events may depend in part on these mental activities.

At least the new physics has shown that the problems of causality and free-will are in need of a new formulation. If those who believe in freedom of the will could explain what they mean by freedom, and could show precisely where it differs from what we have called unconscious determinism, it is at least conceivable that what they want would be found in modern physics. The classical physics seemed to bolt and bar the door leading to any sort of freedom of the will; the new physics hardly does this; it almost seems to suggest that the door may be unlocked—if only we could find the handle. The old physics showed us a universe which looked more like a prison than a dwelling-place. The new physics shows us a universe which looks as though it might conceivably form a suitable dwelling-place for free men, and not a mere shelter for brutes—a home in which it may at least be possible for us to mould events to our desires and live lives of endeavour and achievement.

CONCLUSION

There is a temptation to try to round off our discussion by summarizing the conclusions we have reached. But the plain fact is that there are no conclusions. If we must state a conclusion, it would be that many of the former conclusions of nineteenth-century science on philosophical questions are once again in the melting-pot.

Just because of this, we cannot state any positive conclusions of any kind, as for instance that materialism is dead, or that a deterministic interpretation of the world is obsolete, but we can say that determinism and freedom, matter and materialism need to be redefined in the light of our new scientific knowledge. When this has been done, the materialist must decide for himself whether the only kind of materialism which science now permits can be suitably labelled materialism, and whether the ghostly remains of matter should be labelled as matter or as something else; it is mainly a question of terminology.

What remains is in any case very different from the full-blooded matter and the forbidding materialism of the Victorian scientist. His objective and material universe is proved to consist of little more than constructs of our own minds. In this and in other ways, modern physics has moved in the direction of mentalism.

Again we can hardly say that the new physics justifies any new conclusions on determinism, causality or free-will, but we can say that the argument for determinism is in some respects less compelling than it seemed to be fifty years ago. There appears to be a case for reopening the whole question as soon as anyone can discover how to do so.

This may seem a disappointing harvest to have garnered from so extensive a field of new scientific activity, and from one, moreover, which comes so close to the territory of philosophy. Yet we may reflect that physics and philosophy are at most a few thousand years old, but probably have lives of thousands of millions of years stretching away in front of them. They are only just beginning to get under way, and we are still, in Newton’s words, like children playing with pebbles on the sea-shore, while the great ocean of truth rolls, unexplored, beyond our reach. It can hardly be a matter for surprise that our race has not succeeded in solving any large part of its most difficult problems in the first millionth part of its existence. Perhaps life would be a duller affair if it had, for to many it is not knowledge but the quest for knowledge that gives the greater interest to thought—to travel hopefully is better than to arrive.