The Analysis of Matter

another must produce a tactual percept. On this matter, we must, I think, appeal to evidence which is partly psychological. We do know, as a matter of fact, that we can, in normal circumstances, more or less infer the percept from the stimulus. If this were not the case, speaking and writing would be useless. When the lessons are read, the congregation can follow the words in their own Bibles. The differences in their "thoughts" meanwhile can be connected causally, at least in part, with differences[Pg 391] in their past experience, and these are supposed to make themselves effective by causing differences in the structure of brains. All this seems sufficiently probable to be worth taking seriously; but it lies outside physics, and does not follow from the causal autonomy of physics, supposing this to be established even for human bodies. It will be observed that what we are now considering is the converse of what is required for the inference from perception to physics. What is wanted there is that, given the percept, we should be able to infer, at least partially, the structure of the stimulus—or at any rate that this should be possible when a sufficient number of percepts are given. What we want now is that, given the structure of the stimulus (which is all that physics can give), we should be able to infer the quality of the percept—with the same limitations as before. Whether this is the case or not, is a question lying outside physics; but there is reason to think that it is the case. The aim of physics, consciously or unconsciously, has always been to discover what we may call the causal skeleton of the world. It is perhaps surprising that there should be such a skeleton, but physics seems to prove that there is, particularly when taken in conjunction with the evidence that percepts are determined by the physical character of their stimuli. There is reason—though not quite conclusive reason—for regarding physics as causally dominant, in the sense that, given the physical structure of the world, the qualities of its events, in so far as we are acquainted with them, can be inferred by means of correlations. We have thus in effect a psycho-cerebral parallelism, although the interpretation to be put upon it is not the usual one. We suppose that, given sufficient knowledge, we could infer the qualities of the events in our heads from their physical properties. This is what is really meant when it is said, loosely, that the state of the mind can be inferred from the state of the brain. Although[Pg 392] I think that this is probably true, I am less anxious to assert it than to assert, what seems to me much more certain, that its truth does not follow from the causal autonomy of physics or from physical determinism as applied to all matter, including that of living bodies. This latter result flows from the abstractness of physics, and belongs to the philosophy of physics. The other proposition, if true, cannot be established by considering physics alone, but only by a study of percepts for their own sakes, which belongs to psychology. Physics studies percepts only in their cognitive aspect; their other aspects lie outside its purview. Even if we reject the view that the quality of events in our heads can be inferred from their structure, the view that physical determinism applies to human bodies brings us very near to what is most disliked in materialism. Physics may be unable to tell us what we shall hear or see or "think," but it can, on the view advocated in these pages, tell us what we shall say or write, where we shall go, whether we shall commit murder or theft, and so on. For all these are bodily movements, and thus come within the scope of physical laws. We are often asked to concede that the beauties of poetry or music cannot result from physical laws. I should concede that the beauty does not result from physics, since beauty depends in part upon intrinsic quality; if it were, as some writers on æsthetics contend, solely a matter of form, it would come within the scope of physics, but I think these writers do not realize what an abstract affair form really is. I should concede also that the thoughts of Shakespeare or Bach do not come within the scope of physics. But their thoughts are of no importance to us: their whole social efficacy depended upon certain black marks which they made on white paper. Now there seems no reason to suppose that physics does not apply to the making of these marks, which was a movement of matter just as truly as the revolution of the earth in its orbit. In[Pg 393] any case, it is undeniable that the socially important part of their thought had a one-one relation to certain purely physical events, namely the occurrence of the black marks on the white paper. And no one can doubt that the causes of our emotions when we read Shakespeare or hear Bach are purely physical. Thus we cannot escape from the universality of physical causation. This, however, is perhaps not quite the last word on the subject. We have seen that, on the basis of physics itself, there may be limits to physical determinism. We know of no laws as to when a quantum transaction will take place or a radio-active atom will break down. We know fairly well what will happen if anything happens, and we know statistical averages, which suffice to determine macroscopic phenomena. But if mind and brain are causally interconnected, very small cerebral differences must be correlated with noticeable mental differences. Thus we are perhaps forced to descend into the region of quantum transactions, and to desert the macroscopic level where statistical averages obtain. Perhaps the electron jumps when it likes; perhaps the minute phenomena in the brain which make all the difference to mental phenomena belong to the region where physical laws no longer determine definitely what must happen. This, of course, is merely a speculative possibility; but it interposes a veto upon materialistic dogmatism. It may be that the progress of physics will decide the matter one way or other; for the present, as in so many other matters, the philosopher must be content to await the progress of science. FOOTNOTES: [75] It is thought highly probable that they do. See Dr Jeans, "Recent Developments of Cosmical Physics," Nature, December 4, 1926. [Pg 394] CHAPTER XXXVIII SUMMARY AND CONCLUSION IN the present state of physics, many questions of considerable philosophical importance cannot be answered, although they are such as science may hope to answer, and largely such as were formerly supposed to have been already answered. This makes the task of the philosopher more difficult; it is necessary to develop various hypotheses, so as to be prepared for whatever decision science may arrive at. Certain things, it is true, may be taken as definitely ascertained; these things, so far as they are relevant to philosophy, were considered in Part I. It is clear that, in some sense, there are electrons and protons, and we cannot well doubt the substantial accuracy of their estimated masses and electric charge. That is to say, these constants evidently represent something of importance in the physical world, though it would be rash to say that they represent exactly what is at present supposed. In like manner there seems to be no reasonable doubt that there is a constant , whose dimensions are those of action or angular momentum, and whose magnitude is substantially what it has been estimated to be. It would seem clear also that is a constant which is characteristic of periodic processes. Moreover, the change from one such process to another, which is what we have called a transaction, is governed by principles connected with h in addition to the conservation of energy. But it would be very rash to maintain that the current mathematical formulation of the quantum principle is the best possible; indeed, there are reasons for dissatisfaction with it. Perhaps the most important of these is that in expressing the kinetic energy we have to employ the method of separation of[Pg 395] variables, and that we do not know whether separation of variables is always possible, or whether all ways of separating the variables give equivalent results. Apart from these rather technical difficulties, there are others that are less definite but perhaps not less important. No one has succeeded in making the existence of quanta seem at all "reasonable"; that is to say, it remains isolated and separate from other physical ideas. And whereas it involves discontinuity, the whole effect of relativity has been to emphasize continuity. Moreover, no one has yet succeeded in explaining interference and diffraction by means of light-quanta, or in explaining the photo-electric effect without them. For these reasons, the time has not yet come when the philosopher can deal confidently with quantum theory; he can only suggest what would be his philosophy if this or that view had prevailed in physics. In relativity, we are on surer ground. The advance on the physics of the past, where relativity is concerned, is mainly logical and philosophical. It is true that facts led to the theory, and that the theory in turn led to the discovery of new facts. But the facts were small and only just within the limits of observation; and they had not, as facts, the revolutionary importance of the facts about quanta. And now that the theory is fairly complete, one can see that, theoretically, it ought to have been discovered by Galileo, or at any rate as soon as the velocity of light became known. It represents in its technique a better philosophy than that of Newton; indeed, one of its most remarkable features is the adaptation of the technique to the philosophy. The theory of relativity, to my mind, is most remarkable when considered as a logical deductive system. That is the reason, or one of the reasons, why I have found occasion to allude so constantly to Eddington. He, more than Einstein or Weyl, has expounded the theory in the form most apt for the purposes of the philosopher. Minkowski had the same[Pg 396] quality, but he did not live to see the general theory. For philosophical purposes, therefore, I have allowed myself to be guided almost entirely by Eddington. In the general theory of relativity, we start with a four-dimensional continuum of points, whose properties, to begin with, are purely ordinal. We then assign four co-ordinates to each point on any principle such that the ordinal properties of the co-ordinates are the same as those of the points. We then assume that, if two points are very close together, there is a quadratic function of the co-ordinates which has the same value however the co-ordinates may be assigned, subject to the above ordinal condition. If this function is positive, its square root is called the (time-like) interval; if negative, the square root of the function with its sign changed is called the (space-like) interval. Omitting niceties, we may say that the remainder of the theory turns mainly on geodesics. A geodesic is a route between two space-time points such that the integral of the interval along this route is stationary. In the important routes, it is a maximum. It appears that energy can be divided into parcels which move in geodesics; when these parcels move with a velocity less than that of light, they are regarded as pieces of matter. Weyl, by imposing certain limitations on measurement, succeeds in including electromagnetic phenomena in this scheme. Thus we have a comprehensive theory which may be taken to embrace everything except quantum phenomena. But although there is so much to give pleasure to the logician in this scheme—more especially the method of tensors and Hamiltonian derivatives—yet the philosopher cannot but feel dissatisfaction