The analysis of matter

WHEN a man of science speaks of his "data," he knows very well in practice what he means. Certain experiments have been conducted, and have yielded certain observed results, which have been recorded. But when we try to define a "datum" theoretically, the task is not altogether easy. A datum, obviously, must be a fact known by perception. But it is very difficult to arrive at a fact in which there is no element of inference, and yet it would seem improper to call something a "datum" if it involved inference as well as observation. This constitutes a problem which must be briefly considered.

What is recorded as the result of an experiment or observation is never the bare fact perceived, but this fact as interpreted by the help of a certain amount of theory. Take, say, the eclipse observations by which Einstein's theory of gravitation was confirmed. What in fact was given in perception was—apart from the previous arrangements—a visual pattern of dots, interpreted as a photograph of stars near the sun; a tactual-visual experience called "measuring," and finally coincidences of certain visual appearances with certain others called "numbers on a scale." At least, whether this is actually a correct account or not, it represents the sort of thing that occurred. A considerable amount of theory was involved in merely measuring the photographs. And of course a vast structure was involved in interpreting the photographs as photographs of stars, and in inferring thence the course which the light from the stars had pursued. It is the theoretical element in measuring the photographs that most needs to be stressed, since it is easily overlooked.

It is sometimes maintained that there is something of the nature of inference at an even earlier stage. The effects of a given sensory stimulus upon two men with indistinguishable sense-organs but different experiences may be very different. The most obvious illustration is the effect of print upon a man who can read and upon a man who cannot. A child learning to read is aware of each letter in turn as a certain shape, and finally arrives, with pain and labour, at the word. A man who learned to read as a child is quite unconscious of the letters, unless he is interested in typography or looking out for misprints; normally, he passes straight to the words, and to the words as having meaning, not as black marks on white paper. Nevertheless, he is very likely to notice an oddity at once—say if someone omitted the in "Nietzsche." In writing to a philosopher to ask for a testimonial, it would be very unsafe to assume that he would not detect an error of this sort. But the detection of the error is due to the element of surprise: the philosopher is expecting a and has a shock when it is not there, like that of a man who has reached the bottom of a staircase but thinks there is another step. The philosopher's body was expecting a , though his mind was otherwise occupied.

A more orthodox illustration is the difference between the effect of a visual stimulus upon an ordinary man and upon a man born blind but enabled to see as the result of an operation. The latter has not the tactual associations of the ordinary man, and cannot "interpret" what he sees. Are we to include in perception this element of unconscious interpretation, or are we to include only what we imagine that the same stimulus would have produced if there had been no such previous experience as would make interpretation possible? This is not an altogether easy question. On the one hand, the interpretation depends upon correlations which are frequent but probably not invariable, so that, if it is included, it might seem as though perception would sometimes contain an element of error. On the other hand, the element of interpretation can only be eliminated by an elaborate theory, so that what remains—the hypothetical bare "sensation"—is hardly to be called a "datum," since it is an inference from what actually occurs. This last argument is, to my mind, conclusive. Perception must include those elements which are irreducibly physiological, but it need not on that account include those elements which come, or can be made to come, within the sphere of conscious inference. When we hear (say) a donkey braying, we are quite conscious of inference from the noise of the donkey, or at any rate we can easily become conscious of it. I should not, therefore, in this case, include anything else of the donkey with the perception, but only the noise. And if you see a donkey, though you may have reactions connected with the sense of touch, these are never confounded with what you feel when you actually touch him. I should therefore say that a great deal of the interpretation that usually accompanies a perception can be made conscious by mere attention, and that this part ought not to be included in the perception. But the part which can only be discovered by careful theory, and can never be made introspectively obvious, ought to be included in the perception. Perhaps the line between the two is not so sharp as could be wished; but I do not see how else to meet the conflicting considerations which present themselves.

We have still to ask ourselves whether perception, so defined, will sometimes contain an element of error. Here we must distinguish. It may be, and often is, accompanied by expectations which are disappointed; and we agreed to take this as the mark of error. But the expectations can be distinguished from the perception, although in practice this may not always be easy. The tactual accompaniments of visual perceptions are of the nature of expectations. There are no such accompaniments of perceptions of the heavenly bodies. I think that in all cases in which error occurs it is easy to distinguish the erroneous expectation from the perception. Whatever "interpretation" does not involve expectations need not be regarded as erroneous. It is supposed that indistinguishable stimuli may fall upon indistinguishable sense-organs, and yet result in distinguishable perceptions because of differences in the brains of the two percipients—these differences in their brains being the result of different experiences. But there is not on that account anything erroneous in the perception of either. A different event occurs in the one from that which occurs in the other; but each event really occurs. This topic,, however, cannot be adequately discussed until we come to the causal theory of perception and the relation between perception and physical stimulus.

I come now to the question of inferences, which has already been touched on. As we have seen, there is a purely physiological form of inference which belongs to an earlier stage than explicit inference, though it persists in the habits of even the most sophisticated philosopher, such as Hume. The next stage is where there is an actual passage from one belief to another, but the passage is a mere occurrence, not a transition motived by an argument. In this case, the transition is usually caused by a physiological inference. Then there is inference based upon some belief; but even then the belief may be wholly irrational, or it may not logically warrant the inference, which is the case of fallacious reasoning. Lastly, there is valid inference by means of a true principle—but of this I cannot give an indubitable instance.

In historical fact, these types of inference emerge successively, but a later type does not cause an earlier one to disappear. Moreover, the later type tends to be adapted to the earlier. First we have physiological inference: this is exemplified when a bird flies so as not to bump into solid 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 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. 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 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] 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.