Our Knowledge of the External World as a Field for Scientific Method in Philosophy · Bertrand Russell
LECTURE VIII
ON THE NOTION OF CAUSE, WITH APPLICATIONS TO THE FREE-WILL PROBLEM The nature of philosophic analysis, as illustrated in our previous lectures, can now be stated in general terms. We start from a body of common knowledge, which constitutes our data. On examination, the data are found to be complex, rather vague, and largely interdependent logically. By analysis we reduce them to propositions which are as nearly as possible simple and precise, and we arrange them in deductive chains, in which a certain number of initial propositions form a logical guarantee for all the rest. These initial propositions are _premisses_ for the body of knowledge in question. Premisses are thus quite different from data--they are simpler, more precise, and less infected with logical redundancy. If the work of analysis has been performed completely, they will be wholly free from logical redundancy, wholly precise, and as simple as is logically compatible with their leading to the given body of knowledge. The discovery of these premisses belongs to philosophy; but the work of deducing the body of common knowledge from them belongs to mathematics, if "mathematics" is interpreted in a somewhat liberal sense.
But besides the logical analysis of the common knowledge which forms our data, there is the consideration of its degree of certainty. When we have arrived at its premisses, we may find that some of them seem open to doubt, and we may find further that this doubt extends to those of our original data which depend upon these doubtful premisses. In our third lecture, for example, we saw that the part of physics which depends upon testimony, and thus upon the existence of other minds than our own, does not seem so certain as the part which depends exclusively upon our own sense-data and the laws of logic. Similarly, it used to be felt that the parts of geometry which depend upon the axiom of parallels have less certainty than the parts which are independent of this premiss. We may say, generally, that what commonly passes as knowledge is not all equally certain, and that, when analysis into premisses has been effected, the degree of certainty of any consequence of the premisses will depend upon that of the most doubtful premiss employed in proving this consequence. Thus analysis into premisses serves not only a logical purpose, but also the purpose of facilitating an estimate as to the degree of certainty to be attached to this or that derivative belief. In view of the fallibility of all human beliefs, this service seems at least as important as the purely logical services rendered by philosophical analysis.
In the present lecture, I wish to apply the analytic method to the notion of "cause," and to illustrate the discussion by applying it to the problem of free will. For this purpose I shall inquire: I., what is meant by a causal law; II., what is the evidence that causal laws have held hitherto; III., what is the evidence that they will continue to hold in the future; IV., how the causality which is used in science differs from that of common sense and traditional philosophy; V., what new light is thrown on the question of free will by our analysis of the notion of "cause." I. By a "causal law" I mean any general proposition in virtue of which it is possible to infer the existence of one thing or event from the existence of another or of a number of others. If you hear thunder without having seen lightning, you infer that there nevertheless was a flash, because of the general proposition, "All thunder is preceded by lightning." When Robinson Crusoe sees a footprint, he infers a human being, and he might justify his inference by the general proposition, "All marks in the ground shaped like a human foot are subsequent to a human being's standing where the marks are." When we see the sun set, we expect that it will rise again the next day. When we hear a man speaking, we infer that he has certain thoughts. All these inferences are due to causal laws.
A causal law, we said, allows us to infer the existence of one _thing_ (or _event_) from the existence of one or more others. The word "thing" here is to be understood as only applying to particulars, _i.e._ as excluding such logical objects as numbers or classes or abstract properties and relations, and including sense-data, with whatever is logically of the same type as sense-data.[56] In so far as a causal law is directly verifiable, the thing inferred and the thing from which it is inferred must both be data, though they need not both be data at the same time. In fact, a causal law which is being used to extend our knowledge of existence must be applied to what, at the moment, is not a datum; it is in the possibility of such application that the practical utility of a causal law consists. The important point, for our present purpose, however, is that what is inferred is a "thing," a "particular," an object having the kind of reality that belongs to objects of sense, not an abstract object such as virtue or the square root of two. [56] Thus we are not using "thing" here in the sense of a class of correlated "aspects," as we did in Lecture III. Each "aspect" will count separately in stating causal laws.
But we cannot become acquainted with a particular except by its being actually given. Hence the particular inferred by a causal law must be only _described_ with more or less exactness; it cannot be _named_ until the inference is verified. Moreover, since the causal law is _general_, and capable of applying to many cases, the given particular from which we infer must allow the inference in virtue of some general characteristic, not in virtue of its being just the particular that it is. This is obvious in all our previous instances: we infer the unperceived lightning from the thunder, not in virtue of any peculiarity of the thunder, but in virtue of its resemblance to other claps of thunder. Thus a causal law must state that the existence of a thing of a certain sort (or of a number of things of a number of assigned sorts) implies the existence of another thing having a relation to the first which remains invariable so long as the first is of the kind in question. It is to be observed that what is constant in a causal law is not the object or objects given, nor yet the object inferred, both of which may vary within wide limits, but the _relation_ between what is given and what is inferred. The principle, "same cause, same effect," which is sometimes said to be the principle of causality, is much narrower in its scope than the principle which really occurs in science; indeed, if strictly interpreted, it has no scope at all, since the "same" cause never recurs exactly. We shall return to this point at a later stage of the discussion.
The particular which is inferred may be uniquely determined by the causal law, or may be only described in such general terms that many different particulars might satisfy the description. This depends upon whether the constant relation affirmed by the causal law is one which only one term can have to the data, or one which many terms may have. If many terms may have the relation in question, science will not be satisfied until it has found some more stringent law, which will enable us to determine the inferred things uniquely. Since all known things are in time, a causal law must take account of temporal relations. It will be part of the causal law to state a relation of succession or coexistence between the thing given and the thing inferred. When we hear thunder and infer that there was lightning, the law states that the thing inferred is earlier than the thing given. Conversely, when we see lightning and wait expectantly for the thunder, the law states that the thing given is earlier than the thing inferred. When we infer a man's thoughts from his words, the law states that the two are (at least approximately) simultaneous.
If a causal law is to achieve the precision at which science aims, it must not be content with a vague _earlier_ or _later_, but must state how much earlier or how much later. That is to say, the time-relation between the thing given and the thing inferred ought to be capable of exact statement; and usually the inference to be drawn is different according to the length and direction of the interval. "A quarter of an hour ago this man was alive; an hour hence he will be cold." Such a statement involves two causal laws, one inferring from a datum something which existed a quarter of an hour ago, the other inferring from the same datum something which will exist an hour hence. Often a causal law involves not one datum, but many, which need not be all simultaneous with each other, though their time-relations must be given. The general scheme of a causal law will be as follows: "Whenever things occur in certain relations to each other (among which their time-relations must be included), then a thing having a fixed relation to these things will occur at a date fixed relatively to their dates." The things given will not, in practice, be things that only exist for an instant, for such things, if there are any, can never be data. The things given will each occupy some finite time. They may be not static things, but processes, especially motions. We have considered in an earlier lecture the sense in which a motion may be a datum, and need not now recur to this topic.
It is not essential to a causal law that the object inferred should be later than some or all of the data. It may equally well be earlier or at the same time. The only thing essential is that the law should be such as to enable us to infer the existence of an object which we can more or less accurately describe in terms of the data. II. I come now to our second question, namely: What is the nature of the evidence that causal laws have held hitherto, at least in the observed portions of the past? This question must not be confused with the further question: Does this evidence warrant us in assuming the truth of causal laws in the future and in unobserved portions of the past? For the present, I am only asking what are the grounds which lead to a belief in causal laws, not whether these grounds are adequate to support the belief in universal causation.
The first step is the discovery of approximate unanalysed uniformities of sequence or coexistence. After lightning comes thunder, after a blow received comes pain, after approaching a fire comes warmth; again, there are uniformities of coexistence, for example between touch and sight, between certain sensations in the throat and the sound of one's own voice, and so on. Every such uniformity of sequence or coexistence, after it has been experienced a certain number of times, is followed by an expectation that it will be repeated on future occasions, _i.e._ that where one of the correlated events is found, the other will be found also. The connection of experienced past uniformity with expectation as to the future is just one of those uniformities of sequence which we have observed to be true hitherto. This affords a psychological account of what may be called the animal belief in causation, because it is something which can be observed in horses and dogs, and is rather a habit of acting than a real belief. So far, we have merely repeated Hume, who carried the discussion of cause up to this point, but did not, apparently, perceive how much remained to be said. Is there, in fact, any characteristic, such as might be called causality or uniformity, which is found to hold throughout the observed past? And if so, how is it 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 Mach and others have urged a purely "descriptive" view of physics: physics, they say, does not aim at telling us "why" things happen, but only "how" they happen. And if the question "why?" means anything more than the search for a general law according to which a phenomenon occurs, then it is certainly the case that this question cannot be answered in physics and ought not to be asked. In this sense, the descriptive view is indubitably in the right. But in using causal laws to support inferences from the observed to the unobserved, physics ceases to be _purely_ descriptive, and it is these laws which give the scientifically useful part of the traditional notion of "cause." There is therefore _something_ to preserve in this notion, though it is a very tiny part of what is commonly assumed in orthodox metaphysics.
Ideas discussed in this chapter
Text from Project Gutenberg, public domain in the United States.