The Analysis of Matter

in favour of such-and-such a law without having evidence for laws in general. But here we must make some distinctions. Evidence in favour of a particular law is evidence that a certain class of phenomena are subject to a rule which we have succeeded in discovering. If so, they are sure to be also subject to other rules sensibly indistinguishable from the one for which we have evidence; but these will in general be more complicated than the rule which we adopt. Complication may be of two kinds: it may be in the formula, or in the amount of hypothetical matter needed to make the rule work. The great merit of Newtonian gravitation was that it was simple in both respects. But clearly any set of observations on planetary motions could have been fitted into the Newtonian formula by postulating a sufficient number of invisible bodies or a sufficient complication in the law of attraction. For any given set of observations, there would have been many such possible methods of bringing harmony between observation and theory; most of these would not have been compatible with a fresh set of observations, but some of them would have been, given sufficient mathematical ingenuity. What is remarkable, therefore, is not the reign of law, but the reign of simple laws. If the transfer of energy were subject to laws as complicated as those governing the transfer of English land, we should never succeed in discovering them: there would always remain a number of possible codes, all of which would fit all known relevant facts.[Pg 233] The principle of induction, as practically employed, is the principle that the simplest law which fits the known facts will also fit the facts to be discovered hereafter. This principle, in all its naked simplicity, has come to the fore in Einstein's theory of gravitation, which consists in taking the simplest available tensor equation in preference to the others that are mathematically possible. It may be said that the principle of simple laws is purely heuristic, and of course this is true to a considerable extent. No sensible mathematician would test a complicated formula before testing a simple one. But the remarkable thing is that the simple formula so often turns out right. From the trend of physics, it seems as though complication were geographical rather than legal. Organic compounds have an immensely complicated structure, but there is no reason to suppose that their fundamental laws are other than those which govern the hydrogen atom. Professor J. B. Haldane, it is true, thinks otherwise, and so do all varieties of vitalists. But, to a layman, their arguments seem inconclusive, and they are rejected by many competent authorities. It is therefore at least a tenable hypothesis that all matter is governed by very simple laws. This is so remarkable that it almost suggests some relation to Mr Keynes's "principle of limitation of variety," and seems to confirm his hint that Nature may be really like the urn containing white and black balls which plays such a prominent part in the theory of probability. Some Mendelians would make us think of human beings in this way. Suppose there were a hundred pairs of characters, , , , , , , etc., such that every human being possessed by inheritance one but not both of the characters in each pair. This would make the number of differing human embryos —i.e. about . If this is thought too few, we can take more pairs of characters. Views of this sort cannot be rejected out of hand, and they are strongly suggested by the success of[Pg 234] induction and the prevalence of simple laws. Let us, therefore, ask once more: What evidence is there that simple laws prevail, and how much reason have we to be surprised by the degree of their prevalence? As I have pointed out on a former occasion, it would be fallacious to argue inductively from the simplicity of the laws we have discovered to the probable simplicity of undiscovered laws. For, if some laws are simple and some complicated, we are likely to discover the simple laws first. We have toi proceed more cautiously. First, is it surprising that there are any simple laws? Secondly, have we any ground for believing, as was suggested just now, that all phenomena are governed by simple laws? Simplicity is best established at the two opposite extremes of size: astronomy and the atom. The latter, however, is much more significant for our inquiry, since the simplicity of astronomy may result from averaging. As we saw in Part I., the theory of the atom amounts, broadly, to this: An atom is composed of electrons and protons, the latter being all in the nucleus, the former partly in the nucleus (except in hydrogen), partly planetary. The number of protons in the nucleus gives the atomic weight; the excess of the number of protons over that of electrons in the nucleus gives the atomic number. When the atom is unelectrified, the number of planetary electrons is equal to the atomic number. If the quantum theory is correct, an atom has a certain number of characters, each measured by integers called quantum numbers, which are always small. It has also a property called energy, which is a function of the quantum numbers; and in connection with each of the quantum numbers there is a periodic process which is subject to quantum rules. Each quantum number is capable of changing suddenly from one integer to another. When the atom is left to itself, these changes will only be such as to diminish the energy, but when it is receiving energy from[Pg 235] elsewhere the changes may increase the energy. All this, however, is more or less hypothetical. What we really know about is the interchange of energy between the atom and the surrounding space; here there are simple laws as to the form the radiant energy will take. But there are at present no laws determining when quantum changes will take place in the atom, though the changes that are possible are a definite known set. As we are only considering how far simple laws can account for the phenomena, we may accept the view of the atom as a miniature solar system, governed, except as to quantum changes, by attractions and repulsions among its electrons. Nevertheless it remains a fact that the atom only indicates its presence when it suffers a quantum change, and that we know of no laws determining why, at a given moment, such a change takes place in some atoms rather than in others. The laws governing the intensity of the light emitted by a gas are statistical laws. This suggests a world in which the number of possibilities is finite, but the choice among possibilities is left purely to chance. We might suppose, as Poincaré once suggested, and as Pythagoras apparently believed, that space and time are granular, not continuous—i.e. the distance between two electrons may be always an integral multiple of some unit, and so may the time between two events in the history of one electron. This, together with the fact that the number of electrons is finite, would give a finite number of possible situations for each electron. And it may be that the choice among possible situations is wholly a matter of chance. In that case, the apparent regularity of the world will be due to the absence of laws. I think it improbable that such a view could be developed satisfactorily, but at least we must take account of it before we attach undue importance to the appearance of law in the world. The real objection to a philosophy founded upon such a[Pg 236] theory of the universe as we have been considering is that, after all, we still need statistical laws, which will involve a "random distribution," or something of the kind. Such laws are still laws, though they differ from others by seeming a priori probable instead of improbable. To this extent, it is a gain if we can base science upon them; but it would not be correct to say that, in that case, science would have succeeded in doing without laws. We could no longer say, however, that the laws of science were surprising; on the contrary, we should be surprised by their failure. There is another question to be considered, and that is as to the scope of simple laws. It cannot be pretended that we know the laws governing the hydrogen atom to be sufficient to account for all that happens to matter, especially to organic matter. This is at present merely a hypothesis. All science uses laws based upon observation, which may or may not be deducible by a celestial mathematician from the laws governing electrons, but are not likely ever to be deducible by mathematicians on this planet. And when we come to such matters as physiology, the laws are no longer such as to enable us to say, with any confidence, just what is going to happen; they give tendencies rather than precise mathematical rules. It would be rash to maintain that such rules must exist; we may do well to look for them, but not well to feel quite certain that they are to be found. On the whole, the tendency of the foregoing discussion has been to suggest that it is easy to exaggerate the evidence for simple laws in the physical world. Where we know most— i.e. in regard to the structure of the atom—there is, so far as we know, a complete absence of law in certain very important respects. Where we know less, the laws may be purely statistical. The amount of law known to exist in the physical world is, therefore, less surprising than it seems at first sight, and there is no conclusive reason for believing that all natural[Pg 237] occurrences happen in accordance with laws which suffice to determine them given a sufficient knowledge of their antecedents. Science must continue to postulate laws, since it is coextensive with the domain of natural law. But it need not assume that there are laws everywhere; it need only assume, what is evident since it is a tautology, that there are laws wherever there is science. FOOTNOTES: [50] Chap, I., especially p. 5 ff. [51] Cf. "On the Notion of Cause," in Mysticism and Logic. [Pg 238] CHAPTER XXIII SUBSTANCE THE question of substance in the philosophy of physics has three branches: logical, physical, and epistemological. The first is a problem in pure philosophy: is the notion of "substance" in any sense a "category," i.e. forced upon us by the general nature either of facts or of knowledge? The second is a question of the interpretation of mathematical physics: is it (a) necessary or (b) convenient to interpret our formulæ in terms of permanent entities with changing states and relations? The third concerns the special topics with which we are concerned in Part II.—namely, the relation of perception to the physical world. The first and second problems really belong to other portions of the philosophy of matter, but I shall discuss them here in order to obtain a unified discussion of the problem of substance. Logically, "substance" has played a very important part in the past, and is still perhaps less obsolete than might be supposed. A substance may be defined in purely logical terms as "that which can only enter into a proposition as subject, never as predicate or relation." This definition is practically that of Leibniz, except that he does not mention relations, since he held them to be unreal. We shall do well, however, to include them, because the logical position of substance is not much affected thereby, and it may, I hope, be now taken for granted that relations areas "real" as predicates. Metaphysically, substances have generally been held to be indestructible. But this opinion is not justified by the logical definition, though many philosophers have supposed that it[Pg 239] was. When