Our Knowledge of the External World as a Field for Scientific Method in Philosophy

to be stated? The particular uniformities which we mentioned before, such as lightning being followed by thunder, are not found to be free from exceptions. We sometimes see lightning without hearing thunder; and although, in such a case, we suppose that thunder might have been heard if we had been nearer to the lightning, that is a supposition based on theory, and therefore incapable of being invoked to support the theory. What does seem, however, to be shown by scientific experience is this: that where an observed uniformity fails, some wider uniformity can be found, embracing more circumstances, and subsuming both the successes and the failures of the previous uniformity. Unsupported bodies in air fall, unless they are balloons or aeroplanes; but the principles of mechanics give uniformities which apply to balloons and aeroplanes just as accurately as to bodies that fall. There is much that is hypothetical and more or less artificial in the uniformities affirmed by mechanics, because, when they cannot otherwise be made applicable, unobserved bodies are inferred in order to account for observed peculiarities. Still, it is an empirical fact that it is possible to preserve the laws by assuming such bodies, and that they never have to be assumed in circumstances in which they ought to be observable. Thus the empirical verification of mechanical laws may be admitted, although we must also admit that it is less complete and triumphant than is sometimes supposed. Assuming now, what must be admitted to be doubtful, that the whole of the past has proceeded according to invariable laws, what can we say as to the nature of these laws? They will not be of the simple type which asserts that the same cause always produces the same effect. We may take the law of gravitation as a sample of the kind of law that appears to be verified without exception. In order to state this law in a form which observation can confirm, we will confine it to the solar system. It then states that the motions of planets and their satellites have at every instant an acceleration compounded of accelerations towards all the other bodies in the solar system, proportional to the masses of those bodies and inversely proportional to the squares of their distances. In virtue of this law, given the state of the solar system throughout any finite time, however short, its state at all earlier and later times is determinate except in so far as other forces than gravitation or other bodies than those in the solar system have to be taken into consideration. But other forces, so far as science can discover, appear to be equally regular, and equally capable of being summed up in single causal laws. If the mechanical account of matter were complete, the whole physical history of the universe, past and future, could be inferred from a sufficient number of data concerning an assigned finite time, however short. In the mental world, the evidence for the universality of causal laws is less complete than in the physical world. Psychology cannot boast of any triumph comparable to gravitational astronomy. Nevertheless, the evidence is not very greatly less than in the physical world. The crude and approximate causal laws from which science starts are just as easy to discover in the mental sphere as in the physical. In the world of sense, there are to begin with the correlations of sight and touch and so on, and the facts which lead us to connect various kinds of sensations with eyes, ears, nose, tongue, etc. Then there are such facts as that our body moves in answer to our volitions. Exceptions exist, but are capable of being explained as easily as the exceptions to the rule that unsupported bodies in air fall. There is, in fact, just such a degree of evidence for causal laws in psychology as will warrant the psychologist in assuming them as a matter of course, though not such a degree as will suffice to remove all doubt from the mind of a sceptical inquirer. It should be observed that causal laws in which the given term is mental and the inferred term physical, or vice versa, are at least as easy to discover as causal laws in which both terms are mental. It will be noticed that, although we have spoken of causal laws, we have not hitherto introduced the word “cause.” At this stage, it will be well to say a few words on legitimate and illegitimate uses of this word. The word “cause,” in the scientific account of the world, belongs only to the early stages, in which small preliminary, approximate generalisations are being ascertained with a view to subsequent larger and more invariable laws. We may say, “Arsenic causes death,” so long as we are ignorant of the precise process by which the result is brought about. But in a sufficiently advanced science, the word “cause” will not occur in any statement of invariable laws. There is, however, a somewhat rough and loose use of the word “cause” which may be preserved. The approximate uniformities which lead to its pre-scientific employment may turn out to be true in all but very rare and exceptional circumstances, perhaps in all circumstances that actually occur. In such cases, it is convenient to be able to speak of the antecedent event as the “cause” and the subsequent event as the “effect.” In this sense, provided it is realised that the sequence is not necessary and may have exceptions, it is still possible to employ the words “cause” and “effect.” It is in this sense, and in this sense only, that we shall intend the words when we speak of one particular event “causing” another particular event, as we must sometimes do if we are to avoid intolerable circumlocution. III. We come now to our third question, namely: What reason can be given for believing that causal laws will hold in future, or that they have held in unobserved portions of the past? What we have said so far is that there have been hitherto certain observed causal laws, and that all the empirical evidence we possess is compatible with the view that everything, both mental and physical, so far as our observation has extended, has happened in accordance with causal laws. The law of universal causation, suggested by these facts, may be enunciated as follows: “There are such invariable relations between different events at the same or different times that, given the state of the whole universe throughout any finite time, however short, every previous and subsequent event can theoretically be determined as a function of the given events during that time.” Have we any reason to believe this universal law? Or, to ask a more modest question, have we any reason to believe that a particular causal law, such as the law of gravitation, will continue to hold in the future? Among observed causal laws is this, that observation of uniformities is followed by expectation of their recurrence. A horse who has been driven always along a certain road expects to be driven along that road again; a dog who is always fed at a certain hour expects food at that hour and not at any other. Such expectations, as Hume pointed out, explain only too well the common-sense belief in uniformities of sequence, but they afford absolutely no logical ground for beliefs as to the future, not even for the belief that we shall continue to expect the continuation of experienced uniformities, for that is precisely one of those causal laws for which a ground has to be sought. If Hume's account of causation is the last word, we have not only no reason to suppose that the sun will rise to-morrow, but no reason to suppose that five minutes hence we shall still expect it to rise to-morrow. It may, of course, be said that all inferences as to the future are in fact invalid, and I do not see how such a view could be disproved. But, while admitting the legitimacy of such a view, we may nevertheless inquire: If inferences as to the future are valid, what principle must be involved in making them? The principle involved is the principle of induction, which, if it is true, must be an a priori logical law, not capable of being proved or disproved by experience. It is a difficult question how this principle ought to be formulated; but if it is to warrant the inferences which we wish to make by its means, it must lead to the following proposition: “If, in a great number of instances, a thing of a certain kind is associated in a certain way with a thing of a certain other kind, it is probable that a thing of the one kind is always similarly associated with a thing of the other kind; and as the number of instances increases, the probability approaches indefinitely near to certainty.” It may well be questioned whether this proposition is true; but if we admit it, we can infer that any characteristic of the whole of the observed past is likely to apply to the future and to the unobserved past. This proposition, therefore, if it is true, will warrant the inference that causal laws probably hold at all times, future as well as past; but without this principle, the observed cases of the truth of causal laws afford no presumption as to the unobserved cases, and therefore the existence of a thing not directly observed can never be validly inferred. It is thus the principle of induction, rather than the law of causality, which is at the bottom of all inferences as to the existence of things not immediately given. With the principle of induction, all that is wanted for such inferences can be proved; without it, all such inferences are invalid. This principle has not received the attention which its great importance deserves. Those who were interested in deductive logic naturally enough ignored it, while those who emphasised the scope of induction wished to maintain that all logic is empirical, and therefore could not be expected to realise that induction itself, their own darling, required a logical principle which obviously could not be proved inductively, and must therefore be a priori if it could be known at all. The view that the law of causality itself is a priori cannot, I think, be maintained by anyone who realises what a complicated principle it is. In the form which states that “every event has a cause” it looks simple; but on examination, “cause” is merged in “causal law,” and the definition of a “causal law” is found to be far from simple. There must necessarily be some a priori principle involved in inference from the existence of one thing to that of another, if such inference is ever valid; but it would appear from the above analysis that the principle in question is induction, not causality. Whether inferences from past to future are valid depends wholly, if our discussion has been sound, upon the inductive principle: if it is true, such inferences are valid, and if it is false, they are invalid. IV. I come now to the question how the conception of causal laws which we have arrived at is related to the traditional conception of cause as it occurs in philosophy and common sense. Historically, the notion of cause has been bound up with that of human volition. The typical cause would be the fiat of a king. The cause is supposed to be “active,” the effect “passive.” From this it is easy to pass on to the suggestion that a “true” cause must contain some prevision of the effect; hence the effect becomes the “end” at which the cause aims, and teleology replaces causation in the explanation of nature. But all such ideas, as applied to physics, are mere anthropomorphic superstitions. It is as a reaction against these errors that