use to him if he could appeal to it. Equally so with the other modification. What we all want to guide us aright in life is some power of prevision. There must be some reasonable interval between the sign and the thing signified, if the sign is to be of any service to us1.

In fact we may go further, and say that the accurate statement of the Causal relation can only be couched in the hypothetical form. If the antecedents recur, so will the consequents; but we know they never will do so. We may illustrate this by an analogy. Conceive a man endowed with an infallible memory for any face he has once seen, but who in the multitudinous intercourse of life never succeeds in coming across the same person twice. We can say with certainty what would happen if he succeeded in such an encounter, but his hypothetical powers would not avail him much. This consideration will come under our notice in the course of a future chapter, when we shall have to consider in what respect, if any, such a hypothetical regularity differs from actual irregularity, and what sort of additional assumptions are demanded in order to render it of practical avail. At present we are only concerned with it in the form in which it is commonly offered, provided that form is rigidly understood.

Once more. The causal relation, thus stated, becomes absolutely necessary; we cannot conceive its being other than it is. Try, for instance, to picture an infraction of the law on either of the interpretations in question. I am quite aware that nothing is commoner, especially on the part of those who are unfamiliar with physics and mathematics, than examples intended to illustrate the readiness with which the mind can conceive infractions of what they would term merely physical sequences. For instance we are told to think of a stone dropped twice into the water, but sinking once and floating the other time; of wax held to the fire, melting on one occasion and remaining solid on another, and so on; and we are bidden to contrast the facility of conception of such capricious behaviour

1 We have, remember, no Integral Calculus in practical life. In mathematics we may succeed, given an expression which strictly involves only tendencies, i.e. instantaneously successive states, in eliciting from it information as to a result at a discrete interval. But this help fails us in physical problems of such a really concrete nature as those in question.

Y

here, with the necessary inviolability of such subjective laws as those, say, of mathematical axioms.

I cannot but think that the possibility in the former case only arises from a degree of weakness or slovenliness of thought; that it springs from the fact that we do not realize the details clearly and insist upon introducing them all; and that in fact, with similar license, we might postulate infractions of laws which the writers in question would strenuously maintain to be absolutely necessary. For instance, fallacies are notoriously possible even in Formal Logic; i.e. owing to slovenliness of thought, or to momentary breach of continuity of attention, we succeed in reaching a result which, if we had steadily thought our way through, step by step, we could not possibly have reached. So in Arithmetic: whenever we make a blunder in addition we can be shown to have gone through a verbal or symbolic process which, if consciously reproduced, would have been seen to involve our making two and three, say, equal to six. So with the stone or the wax. The possibility of picturing to ourselves diverse consequences only comes from the fact that we are omitting a quantity of the details which really go to make up the concrete instance in question. We may illustrate the distinction by such an example as the following. It is easy enough to conceive two curves drawn on paper, absolutely alike in all respects up to a certain point, but from that point diverging and assuming different forms. They might begin as equal segments of the same or equal circles, and then whilst one continues to produce a circumference the other might go off in the tangent. It is easy enough to do this in respect of the abstract lines. But even here, it seems to me, if we fill in the details by considering the concrete circumstances under which such lines could be produced, the possibility of such discontinuity disappears. The simplest way of rendering such an example concrete would be to suppose the paths to be traced out by moving bodies restrained by threads; that in one case the thread snaps so that the body flies off in a tangent, whilst in the other it continues to restrain the body in a circle. The mere statement of the example in these terms shows that we were not presupposing the same antecedents in the two cases. And the same explanation seems to apply in the case of every similar example which I can picture to myself.

The general conclusion which I deduce from all this is that any attempt to over-refine the expression of the Causal relation necessarily results in rendering it useless for any purposes of inference. Make it perfectly complete and accurate, and you make it at once hypothetical and the statement of what is to all intents and purposes a mere identity. For purposes of Inductive Logic, therefore, I regard the second,—or BrownMill,-statement of the relation to be the most serviceable. Where I differ mostly from these writers, and in fact from the majority of those who have treated of the subject, is in regarding the statement in question as being essentially a practical one, which does not aim at scientific rigour; as being, in fact, nothing more than a moderate improvement of the primitive or popular conceptions on the subject.

That something of this sort is the necessary outcome of the above attempts at refinement has been admitted, explicitly or implicitly, by several recent writers.

For instance, Clerk-Maxwell, with that clear insight which he shows into all questions of first principles in Physical Science, has had occasion (Matter and Motion, p. 20) to notice the maxim that "the same causes will always produce the same effects." After stating briefly that no event in strictness ever recurs, he says that "what is really meant is that if the causes differ only as regards the absolute time or the absolute place at which the event occurs, so likewise will the effects":-a formula, it need not be pointed out, which is perfectly useless for all purposes of inductive inference. In fact this appears to me to be an expression of that view of Time and Space which was held by Newton and Locke, and probably by most astronomers, in accordance with which these entities are regarded as of infinite duration and extent and as existing, without contents, prior to the insertion in them of the material Universe. And what it asserts is that no variation in the orderly sequences of the world would be produced by any arbitrary change in the place where, or the time when, the whole performance commenced.

Jevons, again, in some of his interpretations of his principle of the Substitution of Similars', so explains it as to imply

1 There seems to me to be a permanent ambiguity in his interpretation of this term. When using it, he generally takes in the true sense of similarity,

that only absolute repetitions in every detail ought to count. Thus (Pr. of Science, p. 238) quoting the remark of Euler that "although he had never made trial of the stones which compose the Church of Magdeburg, yet he had not the least doubt that all of them were heavy..." he goes on to say that "the belief ought not to amount to certainty until the experiment has been tried, and in the mean time a slight amount of uncertainty enters, because we cannot be sure that the stones of the Magdeburg Church resemble other stones in all their properties."

The same view I understand to have been held by G. H. Lewes, when, in a passage much too long to quote or criticize here, he came to the conclusion that "the true expression of Nature's Uniformity" is "the assertion of identity under identical conditions: whatever is, is and will be, so long as the conditions are unchanged: and this is not an assumption but an identical proposition." (Problems, II. 99.)

On the whole therefore it seems decidedly preferable, for the purposes of practical inference, the special function of Inductive Logic,--to take our stand on the intermediate interpretation of the formula of Causation; rather than to attempt to refine it into a needless and merely hypothetical condition of accuracy.

for then only can we secure repetitions. But when defining it, he often takes it in the sense of identity; and maintains that since we can never obtain this we ought never to claim certainty. His particular example above seems to me a reduction to absurdity. For so "certain" are we that every stone is heavy that, if we did try the experiment and found it fail, we should simply at the time postulate hallucination, trickery, or defect in the balance; and next day resume, if it had been shaken, our customary belief. Surely a single direct experiment would not, and ought not to, convert uncertainty into certainty on such a point.

CHAPTER III.

(II) COEXISTENCES.

IN the last chapter we discussed the results which would follow from a systematic attempt to refine upon the common statements of the Law of Causation, with a view to rendering its expression absolutely precise. It was found that this could be done; not indeed without couching the expression in a hypothetical and therefore impracticable form, but at any rate without being driven to a merely verbal or identical formula. So far we were dealing with Laws of Sequence; we have now to turn to the discussion of Laws of Coexistence, and see whether any better success will attend us in dealing with them. Here, as there, the motive of the reform would of course be to establish a rigid objective uniformity among phenomena, with a view to drawing inferences.

It is, I think, commonly assumed, and the opinion has the deliberate sanction of J. S. Mill, that the two kinds of uniformity, those, namely, of sequence and of coexistence, -stand upon a totally different footing. The latter, it is held, are essentially inferior to the former in respect of their certainty and their generality. There is "one great deficiency which precludes the application to the ultimate uniformities of coexistence, of a system of rigorous scientific induction, such as the uniformities in the succession of phenomena have been found to admit of. The basis of such a system is wanting: there is no general axiom, standing in the same relation to the uniformities of coexistence as the law of causation does to those of succession" (Mill's Logic, II. 115). And there can be no doubt that the ordinary treatment of Causation by logicians and metaphysicians, widely as it differs in many important respects from the System of Logic here quoted, recognizes the same distinction.