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

by Bertrand Russell

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.

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.