The Analysis of Matter

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 I wish to discuss a substance having this further attribute, I shall speak of it as a "permanent substance"; when I use the word "substance" without qualification, I shall mean only substance in the logical sense, leaving the question of duration open. It is extraordinarily difficult, in considering substance from the point of view of logic, to avoid being unduly influenced by the structure of language. All languages commonly known to civilized people consist of sentences which can be analyzed into subject and predicate, two subjects and a dyadic relation, three subjects and a triadic relation, etc., together with relations between such units, expressed by "or" or "if" or some analogous word. I do not know whether the same can be said of African, Australian, or other uncivilized languages. But certainly it can be said of all the languages that philosophers have known. Logic, as ordinarily conceived, takes over this linguistic scheme, and is inclined to attribute metaphysical importance to it. We can hardly resist the belief that the structure of the sentence reproduces the structure of the fact which it asserts, or, in the case of false sentences, of the fact which would exist if the assertion were true. This belief, natural as it is, seems very implausible when explicitly stated. Nevertheless, I believe that it has some element of truth, though it is very hard to disentangle this element. An attempt was made by Wittgenstein,[52] and I have been much influenced by his point of view. If we admit, as it seems natural to do, that some sentences, taken in their usual meaning, correspond to facts, while others do not, we must suppose that the structure of sentences is related, in some way, to the structure of facts, since otherwise such correspondence would be impossible. Moreover, a sentence is a physical fact, and may therefore be expected to be capable of correspondence with other physical facts. These[Pg 240] two arguments come from quite different intellectual regions, the one being logical, the other physical. If we were discussing anything other than physics, they would work in opposite directions, and tend to show that we cannot understand (at least verbally) anything having a structure radically different from that of events in space-time. For our purposes, however, the two arguments are concurrent. Let us, for a moment, consider a sentence as a physical occurrence. We must distinguish between spoken and written sentences, since the former are evanescent events while the latter are pieces of matter. We must also distinguish between a sentence in the sense in which it is unique on each occasion when it is uttered or written, and a sentence in the sense in which the same sentence occurs at a given place in each copy of the same book. E.g. Jeremiah xvii. 9 is a sentence in the latter sense; in the former sense, the particular series of shapes at that point in my Bible constitute a sentence, while those in yours constitute another (similar) sentence. The former sense comes first when we are considering a sentence as a physical occurrence; the latter, when we are considering it as having "meaning." A spoken sentence, considered physically, is a series of noises from the point of view of the hearer, and a series of movements in the mouth and throat from the point of view of the speaker. The "meaning" of the sentence depends upon the causes of the spoken words and the effects of the heard words.[53] But for the moment let us ignore "meaning." Then we find that the sentence consists essentially of noises in order: the order is as essential as the character