posed to contribute towards the result it was considered that they might be actually rejected.

As this is the first occasion on which we have introduced the use of letter-symbols to represent the various elements of antecedence and consequence, a word of caution as to their employment will be advisable; for experience shows that students may possess great facility in their manipulation in formulæ, but have very faint realization of what sort of phenomena they are intended to mark. Remember then that the sharp distinctions amongst our letter-symbols have nothing at all really corresponding to them in nature. It is very seldom that the actual phenomena will possess so definite an individuality even as the open window and open door in our example above. For the most part they will be found to be modifications of one and the same substance or agency, which we can think of and speak of as distinct elements, but which cannot exist as such.

I am referring here to the symbolic usage to be presently noticed where a group of letters are introduced, rather than to the simple pair employed above:—that is, where we talk of ABCD being followed by xyzw. It is a usage which will be abundantly familiar to readers of Mill or Jevons. Consider for example what is involved when we say that in such and such a case death was caused by poison. Here the 'death' is a highly complex group of elements reduced to a unity by thought acting through language. We symbolize it by x. Similarly with the A, or the taking of the poison. This being a definite and voluntary act has a slight degree more of natural distinctiveness about it, though, like the death, its unity is largely the creation of a mental synthesis. This A and this a represent the two elements which alone are commonly taken into account in the popular estimate. But each of these, as we shall presently see more particularly,—was really one of a group of elements, and the pair of groups would commonly be symbolized by the relation of ABCD...to xyzw.... Now what I want here to enforce upon the reader is the comparative artificiality of this letter arrangement, as compared with what nature itself is disposed to show. This ABCD and xyzw do not stand side by side, so to say, like bottles in a row, or like the actual letters themselves. They do not admit, like these, of separate removal or transfer. For what are they? They are, (to begin with

the second term of the pair,) the elements of the consequent; such circumstances as the rapidity of the death, its time, place, symptoms, &c., most of these being inextricably involved in what we call the death itself, and only held apart from it by a mental abstraction, which, like the corresponding combination, acts through language. Similarly with the elements of the antecedent. The B, C, D, here are such circumstances as the time and place where the poison was swallowed, the state of health of the person, the other food which he took at the time, the remedies he took immediately afterwards, and so forth. These are not so much given in a group with A as in a concrete whole; and we can no more pick out some of them as we do letters in a row, than we can pick out the sweetness of the taste and leave that taste behind.

of an orange

When, therefore, we speak of the popular view selecting one element only of the antecedent and consequent, we necessarily imply a certain act of abstraction in such a process. But it is one of those abstractions which the primitive man can well be supposed to undertake, for it acts through, and is well within the limits of, popular speech.

II. It is this popular view which the logician takes in hand for the purpose of trimming it into better shape, in order that it may be rendered sufficiently explicit and accurate to serve his purpose. And what does he proceed to do? In the first place he rejects altogether the coexistences, and confines himself to sequences; a limitation, the grounds and justification of which will occupy our attention in the ensuing chapter. And as regards the sequences he insists upon various improvements, of which the two following seem to be the most important: (1) the enumeration of all the group of elements which comprise the antecedent or cause, or at least all which can possibly be considered relevant; (2) the closeness of sequence, that is, the comparative immediateness of the cause and effect. These improvements represent such an important advance upon the rude popular view, and are so intimately connected with the received methods of Inductive enquiry that we must examine them in some detail.

(1) I need hardly remind readers of Mill of the importance which he attaches to the enumeration of all the elements of the antecedent. It forms the staple of his exposition of the

causal relation. He criticizes at considerable length the capricious way in which the popular estimate picks out some one circumstance, and regards this as the cause, or at least calls it so. For logical purposes the criticism is quite sound, but there is nevertheless some method in the seeming caprice. The great object of speech is to convey our meaning with the least trouble, and where anything can be reasonably taken for granted, we are naturally apt to omit the direct statement of it. If some of the antecedents can be thus taken for granted, we naturally incline to omit any reference to them. Moreover it must be remembered that the popular interest centres, not in speculation, but in practice. The reason why we look out for a cause is not to gratify any feeling of curiosity, at least not primarily, but because we want to produce some particular effect. Hence every element which can commonly be trusted to supply itself gives us no anxiety, and comes to slip out of our description of the producing circumstances.

Useful as it once was to insist upon the insufficiency of this popular makeshift for a true cause, it seems needless to dwell longer here upon the mere fact that accurate reasoning stands in need of something more than this. If we are to make sure of producing or inferring any particular effect, we must clearly make a point of requiring that all the elements of the antecedent are present, whatever may be the various names,—such as condition, occasion, part-cause, &c.-which they may assume in the popular vocabulary.

(2) The second modification of the popular view will need closer attention. It consists, if one may be allowed the expression, in screwing up the cause and the effect into close juxtaposition; that is, in insisting that the sequence shall be as nearly as possible an immediate one. This is a decided departure from the plain man's way of thinking. Not only does he not feel any impulse thus to crowd up his cause and his effect; he would, on the contrary, find such a juxtaposition highly inconvenient for his purposes. What he desires is some power of prevision, in order that he may take means to avoid the evil and secure the good. With such an end in view it is clear that too close an approximation of the links of his chain would destroy most of its utility, for it would not give him any view ahead.

The object,—so far as speculative purposes are concerned,— of securing this close approximation between the elements of the sequence, is obvious. It is done simply in order to secure regularity. A remote sequence can never be a certain one. This is one of the many points in which our common metaphors are apt to mislead. For instance, the stock illustration in Causation is that of a chain where link succeeds link in endless succession. Amongst several other misleading associations connected with this metaphor there seems to be that of certainty irrespective of remoteness. Get a grip at any point of the chain, and, when you give a pull, all the rest will follow. But no security of hold at any point of what is commonly called 'a chain of causation' will give us certainty of grasp of more than a very short length beyond what we have in our hands.

The fact is that, in respect of these two logical amendments of the doctrine, the second is intimately connected with the first. The real reason why we are obliged to shorten the sequence consists in the fact that we cannot practically attempt to secure all the elements which constitute the antecedent. This is a point which must be emphatically insisted upon, since it brings into clear light the still essentially practical aspect of this stage of causal discrimination in spite of the decided advance which it presents beyond the first or merely popular one. We may talk,—as Mill and others do,—about introducing all the antecedents, but this must be understood in a conventional sense. What we really do is to confine ourselves not merely to the elements which we know to be relevant,-itself a rather considerable limitation,-but amongst these we confine ourselves to those which we regard as of some sufficient importance. But for this limitation, as will come out more plainly presently, when we proceed to discuss the third or final development of the doctrine of Causation, we should not be able to secure that repetition of occurrence which we require in order to apply the sequence we have noticed in the past to some new instance in the future. No two objects or events in nature are alike in all their details, and therefore if we want to secure repetition we must submit to let go some of the characteristics. In other words, we consent to omit what may be called the trifling or individualizing circumstances in

our antecedent in order to let it get a fair opportunity of repeated occurrence. For practical purposes there is no harm in our doing this, because we really mean nothing else by a trifling circumstance here but such a one as will not soon develop into proportions which would force us to take account of it.

Hence then the necessity of making our causal sequence a tolerably close one. This, or some equivalent resource, is the only means we have of making the sequence at once practically convenient and reasonably trustworthy. Under this safeguard we may safely proceed to omit from consideration, as mere accidents of no account, many circumstances which, if let alone, would develop before long into rather formidable dimensions'.

The wide prevalence of this particular view of the Causal relation—not merely in our systems of Inductive Logic, but also in the field of popular Science, and in the more careful procedure of common life-makes it extremely important to understand what exactly it asserts, upon what conventions it rests, and what stage of analysis it represents. So far as the recent succession of English thinkers is concerned we might give it the clumsy designation of the Brown-Herschel-Mill view, on the ground that its effective popularization is mainly due to these authors. Brown first formulated it almost in the words adopted by Mill; Herschel showed its significance and value by the rules for scientific discovery which he laid down in his Discourse; whilst Mill reduced these rules into more precise logical form, and provided them with the technical designations which have made the Four Methods universally familiar to all students of Logic. We will proceed to analyse this view somewhat more minutely.

Recur for a minute to the example of poison followed by

1 I find some help here, myself, by drawing an analogy between the physical step of advancing from one group of phenomena (the cause) to the next proximate group of phenomena (the effect), and the purely mathematical step of advancing from the expression f(x) to f(x+h). When we introduce only one term into the expansion of the latter, we must make the step a very slight one; i.e. we must make h very small. As more terms are introduced, the step can be made a little longer, with equal accuray of result. But for absolute accuracy, every term must be introduced (including the remainder), and this is equivalent in its results to practical inutility.