The Analysis of Matter

not to bump into solid[Pg 191] objects, and fails when it bumps into a window-pane. Then there is the transition from the belief expressing the premiss of the physiological inference to that expressing its conclusion, without any consciousness of how the transition is effected. Then there is belief in a causal law which is the intellectualized expression of the habit embodied in the physiological inference. And last of all there is the search for criteria by which to distinguish between true and false causal laws, these criteria being intellectual, not mere habits of the body. This last stage is only reached when we come to science. One of the main purposes of scientific inference is to justify beliefs which we entertain already; but as a rule they are justified with a difference. Our pre-scientific general beliefs are hardly ever without exceptions; in science, a law with exceptions can only be tolerated as a makeshift. Scientific laws, when we have reason to think them accurate, are different in form from the common-sense rules which have exceptions: they are always, at least in physics, either differential equations, or statistical averages. It might be thought that a statistical average is not very different from a rule with exceptions, but this would be a mistake. Statistics, ideally, are accurate laws about large groups; they differ from other laws only in being about groups, not about individuals. Statistical laws are inferred by induction from particular statistics, just as other laws are inferred from particular single occurrences. All this, however, is by the way; the point is that inference as a practice has a long history before it becomes scientific. The most important inference which science takes over from common sense is inference to unperceived entities. One form in which common sense makes this inference is that of a belief that objects which have been perceived still exist when they are not perceived. If, at a dinner-party, the electric light suddenly goes out, no one doubts that his neighbours and the[Pg 192] dinner-table and the food and drink still exist, although at the moment they are unperceived. When the light goes on again, this belief appears to be confirmed; if there are fewer spoons than before, we do not infer that they have ceased to exist, but that someone present is a thief. This belief in the permanence of perceived objects has gone through all stages from physiological inference to advanced scientific or philosophical theory; the inquiry into its justification is the central problem in the analysis of matter, philosophically considered. No one, not even Berkeley, has treated it with quite the seriousness that it deserves, because the physiological inference is so irresistible that it is difficult to achieve a purely intellectual attitude towards the problem. This inference is the source of the philosophical notion of "substance" and the physical notion of "matter." For the present, I am only noting the inferences to be considered; I am not attempting to investigate their validity. Unperceived entities are also inferred by common sense when it believes that other people have "minds." I wish to make it clear that even the most rigid behaviourist makes this inference, although in a slightly different form. Dr Watson, for example, would admit that his own toothache can lead him to say, "I have a toothache," whereas another person's toothache will not lead him to say "You have a toothache" without some intermediate link. Whatever may be our analysis of "knowledge," we certainly know things about our own bodies in ways which are not open to us where other people's bodies are concerned. There is nothing mysterious about this: it is analogous to the fact that some sounds are within earshot while others are not. The point is that we infer, from the behaviour of others, the existence of things (such as toothaches) which we cannot perceive. Whether we say that these things are "mental" or "bodily" makes no difference to the fact that we make inferences.[Pg 193] These inferences, also, are at first purely physiological. From the point of view of physics, the inference to other people's "minds" has a twofold importance. The first, which is not specially physical, is concerned with testimony. What is commonly accepted as the experimental evidence on any topic of physics includes not only what a given physicist has himself observed, but whatever has been reliably recorded. Everything that we learn from what other people say and write involves inference from something perceived (spoken or written words) to something unperceived—namely, the "mental" events of the speaker or writer. It may be that the primary inference is only to another person's percepts, but it is none the less an inference to something which we do not perceive. The second point about the inference to other people's percepts is specially physical; it concerns the fact that different people live in a common world. The percepts of two different people, if we accept testimony, are found to be often very similar, though not exactly alike; this leads to the theory of a common external cause—i.e. to the causal theory of perception, and to the division of the qualities of the perceived object into such as belong to the external cause and such as are supplied by the body or mind of the percipient. The development of science out of common sense has not been by way of a radically new start at any moment, but rather by way of successive approximations. That is to say, where some difficulty has arisen which current common sense could not solve, a modification has been made at some point, while the rest of the common-sense view of the world has been retained. Subsequently, using this modification, another modification has been introduced elsewhere; and so on. Thus science has been an historical growth, and has assumed, at each moment, a more or less vague background of theory derived[Pg 194] from common sense. This is one difference between science and philosophy: philosophy attempts, though not always successfully, to set out its inferences in a form which assumes nothing on the mere ground that it has always been assumed hitherto. It may be doubted whether science can retain its vitality if it is severed from its root in our animal habits; when set forth quite abstractly, it loses plausibility. Induction, for example, is difficult to justify, and yet indispensable in science. In such cases, I shall allow myself to accept what seems necessary on pragmatic grounds, being content, as science is, if the results obtained are often verifiably true and never verifiably false. But wherever a principle is accepted on such grounds as these, the fact should be noted, and we should realize that there remains an intellectual problem, whether soluble or not. The actual procedure of science consists of an alternation of observation, hypothesis, experiment, and theory. The only difference between a hypothesis and a theory is subjective: the investigator believes the theory, whereas he only thinks the hypothesis sufficiently plausible to be worth testing. A hypothesis should accord with all known relevant observations, and suggest experiments (or observations) which will have one result if the hypothesis is true, and another if it is false. This is an ideal: in actual fact, other hypotheses will always exist which are compatible with what is meant to be an experimentum crucis. The crucial character can only be as between two hypotheses, not as between one hypothesis and all the rest. When a hypothesis has passed a sufficient number of experimental tests, it becomes a theory. The argument in favour of a theory is always the formally invalid argument: " implies , and is true, therefore is true." Here is the theory, and is the observed relevant facts. We are most impressed when is very improbable a priori. For example,[42][Pg 195] observation gives Rydberg's constant as: while Bohr's theory gives: which is within the degree of accuracy to be expected if the theory is right. Numerical confirmations of this kind are always the most striking. Nevertheless, even they must be received with caution; Bohr's theory of circular orbits required modification by the admission of elliptic orbits, and thus turned out to be not the only theory which would give a correct value of Rydberg's constant. When a theory fits a number of facts, but goes slightly astray in regard to certain others, it happens generally, though not always, that it can be absorbed, by a slight modification, into a new theory which includes the hitherto discrepant facts. There are exceptions, of which the theory of relativity is perhaps the most notable: here an immense theoretical reconstruction was required to account for very minute discrepancies. But in general a partially successful theory is an essential step towards its successor. And a result deduced from a hitherto successful theory is more likely to be right than the theory is: the theory is only right if all its consequences are true (at least, so far as they can be tested), but a verifiable consequence of the theory is likely to be true if most of the verifiable consequences are true. That is why the practical value of scientific theories is so much greater than their philosophic value as contributions to ultimate truth. To some extent, we can distinguish, among the consequences of a theory, which are the most reliable; they will be those in the region of the facts which have given rise to the theory. No one is surprised to find that an empirical law connecting specific heat with temperature fails for temperatures much lower than those for which it has been found to be correct; but if, in the middle of these latter, there was found to be a small range of temperatures where the law failed, we should be very much surprised. Thus there is a kind of common sense to be used in applying theories: some applications can be made with confidence, while others will be felt to be questionable. FOOTNOTES: [42] Sommerfeld, op. cit., p. 217. [Pg 197] CHAPTER XX THE CAUSAL THEORY OF PERCEPTION[43] COMMON sense holds—though not very explicitly—that perception reveals external objects to us directly: when we "see the sun," it is the sun that we see. Science has adopted a different view, though without always realizing its implications. Science holds that, when we "see the sun," there is a process, starting from the sun, traversing the space between the sun and the eye, changing its character when it reaches the eye, changing its character again in the optic nerve and the brain, and finally producing the event which we call "seeing the sun." Our knowledge of the sun thus becomes inferential; our direct knowledge is of an event which is, in some sense, "in us." This theory has two parts. First, there is the rejection of the view that perception gives direct knowledge of external objects; secondly, there is the assertion that it has external causes as to which something can be inferred from it. The first of these tends towards scepticism; the second tends in the opposite direction. The first appears as certain as anything in science can hope to be; the second, on the contrary, depends upon postulates which have little more than a pragmatic justification. It has, however, all the merits of a good scientific theory—i.e. its verifiable consequences are never found to be false. Epistemologically, physics might be expected to collapse if perceptions have no external causes; therefore the matter must be examined before we can go further. We must first give somewhat more precision to the common-sense[Pg 198] view which is rejected by the causal theory. We have to ask what is meant by "external objects." One would naturally say "spatially external." But "space" is very ambiguous: in visual space, the objects which we see are mutually external, and objects other than the visual appearances of parts of our own body are spatially external to those appearances. In the space derived from the combination of touch