the former. This last remark gives the reason why choosing balls of different colours from a box, or throwing dice, are the cases taken as the types of mathematical probabilities, because the causes and conditions tending to produce or to prevent any single choice or throw are known; while all the other and unknown causes and conditions (the motions of the arm with the dice-box, or the blind choice of the hand in the box) are strictly accidental, i.e., tending equally to produce and to prevent any particular event; at one time to produce, at another to prevent, indifferently. To take then the simplest case first; what is the reason that, in a box where there are nine black balls and one white, we expect to draw a black ball nine times as much (in other words, nine times as often, frequency being the gauge of intensity in expectation) as a white? obviously because the local conditions* are nine times as favourable, because the hand may alight in nine places and get a black ball, while it can only alight in one place and find a white ball; just for the same reason that we do not expect to succeed in finding a friend in a crowd, the conditions in order that we and he should come together being many and difficult. This of course would not hold to the same extent were the white balls of smaller size than the black, neither would the probability remain the same; the larger ball would be much more likely to meet the hand. But the case more to our purpose, and which represents exactly Mr. Mill's theory (so far as it can be reached), is not that where we reason directly from known causes or conditions to the consequences, but when we pass from an effect to a similar effect (in which case, we believe that the mind always reverts to the cause, and passes from the cause to a similar effect). Bishop Butler puts the real question at issue when he remarks that a very weak presumption often repeated will amount to moral certainty. "Thus a man's having observed the ebb and flow of the tide to-day affords some sort of presumption, though the lowest possible, that it will happen again to-morrow; but the observation of

*We do not say "causes" for reasons we shall afterwards give. But if the word 'cause' be used generally, to include all the conditions, it would not be incorrect.

this event for so many days, and months, and ages together, as it has been observed by mankind, gives us a full assurance that it will." How Mr. Mill would resolve the difficulty as to the nature of this kind of inference we do not feel sure; whether causation depends upon probability, or probability on causation, or each on the other, according to his view, is not clear: we incline to the latter hypothesis, though it is not so certain that it is so here, as in the case of analogy. But certainly it would be most consistent with his theory of reasoning, from particular to particular, to suppose that he gives his judgment in favour of reasoning directly from effect to effect. Besides, analogy is identical with this kind of probability, and the only reason we have for not believing that he has identified analogical and probable inference, is, that he has given them a separate chapter. But no inference as to Mr. Mill's permanent opinion on this subject is more than a very weak presumption; and our own belief is, that in this book the principles of causation do the work, while experience gets the credit.

We believe that in the case mentioned by Butler, the rationale of the expectation is this; we refer the phenomenon of tides to a cause, and after the first happening feel some slight presumption that it will happen again, because we know that a power is in existence which can produce it, and therefore may produce it again, and will if the same conditions recur (on the principle that the same cause or force acting on the same conditions produce the same effect). If this be not so, why do we feel so much more probability added by the first instance than by any single subsequent instance? why-except that the first instance gives us its possibility (a cause adequate to it), while every other only gives us the frequency of its conditions? If no reference to a cause be supposed, possibility would have no meaning; yet it is clear, that, antecedent to its happening, we might have supposed the event impossible, i.e., have believed that there was no physical energy really existing in the world equal to producing it: the word 'impossible' does not seem to us susceptible of any meaning, if the reference to a cause be denied; it could only mean that it never actually would happen,' which certainly might be supposed, but is not equivalent to

the other, though it is the only meaning that the phenomenal school of philosophy can give to the word.* In truth, were it possible to conceive of events happening without any cause or effective antecedents, we do not believe that any expectation about their repetition could be formed at all: there might indeed be the mere associative suggestion, but nothing that could make us really look out for it, because it could tell us of no 'why' for our doubts, and yet could not overrule them, as a necessary condition of thinking at all. While we regard a phenomenon as a loose stray event happening independently in vacuo, leading our thoughts to nothing else, however often it may thus please to straggle in upon us, we can form no expectation about it; but once regard it as a proceeding from a constant cause, and we immediately feel that it has a hidden root in existence, which may again put forth signs of life. After the first time of happening, which is, then, more important to the whole probability than any other single instance (because proving the possibility), the number of times becomes important as an index to the intensity or extent of the cause, and its independence of any particular time. If we took the case of a tremendous leap for instance, and wished to form an estimate of the probability of its succeeding a certain number of times; the first instance, by showing its possibility (before doubtful), is of the most importance; but every succeeding leap shows the power to be more perfectly under control, greater and more invariable, and so increases the probability; and no one would think of reasoning in this case straight from one instance to the next, without referring to the physical energy which each leap indicated. Is it not then clear that we do not ever conclude directly from the happening of an event to the probability of its happening again; but that we refer to the cause, regarding the past cases as an index to the cause, and the cause as our guide to the future ?†

* Mr. Mill uses the word 'impossible' in the sense of opposed to a rigorous induction.' How any induction depending originally on an Inductio per enumerationem simplicem, could be rigorous enough to render a simple fact carefully attested impossible, it is difficult to see.

Besides this, Mr. Mill's method (see Vol. II. c. xviii. p. 78), of obtaining the chance, by comparing the cases in which the event occurs, and those in which it does not occur, and regarding the numbers so found as the ratio of the chances of success and failure, would generally be wholly erroneous.

It

We believe then that we have established that the theory of probabilities really depends on the two principles of causation, and with it all the inference of common life, which is merely probable inference without any help from actual calculation. When Newton concluded that because the diamond had a high refracting power, it was combustible, he guessed that those qualities would not be so often seen together, were they not connected by causation; in fact, that the refracting power was caused by something which also produced the property of combustion. If it be said, that while we refuse to admit the phenomena of yesterday as evidence for the phenomena of to-day, we yet admit the causes of yesterday as evidence for the causes of to-day; we reply that the difference is this, the phenomenon is passed, and directly it is passed it is evidence for nothing, it is a thing no more; but the cause or force is by its very conception something that does not pass away without a counteracting force, or the withdrawal of the energy hitherto exercised, and such events we have no ground to expect; the same principle that prevents us from expecting a cause or an event without a reason, prevents us from expecting a change in an existing cause without a reason for it the existing energies that produce phenomena, we expect to exist till some proof is given to the contrary; the phenomena themselves give us their own reason for not expecting them; they leave us.-When the planet changes its place in the ellipse, we do not expect it, on account of is not the true theory of probability. This would regard an event as certain which had hitherto never failed, which is exceedingly far from the truth, even for a very large number of constant successes. The true mode of obtaining the probability from past experience, is to assume that the antecedent probability (before the happening) might have been anything between 0 and 1, say 0, then to calculate the chance that it has happened as it actually has, in consequence of this particular chance 0, from that to calculate the probability that it will happen for the given number of times in future, in consequence of this particular chance, (here is assumed that the same causes produce the same effects,) and then to sum all the chances so obtained between the values 0, and 0 1, since the whole chance of getting this result will be the sum of all the chances of getting it from any one of the possible antecedent chances. Now in this process, what does the antecedent probability of an event's happening, which has never happened before, denote ?-unless it be the degree of expectation that a mind ought to have felt that could have contemplated the causes in favour of and against the event, without those which tend equally to produce either. It had a probability, before it had ever happened, and this could only depend on the cause. The assumption of an antecedent probability involves therefore the conception of a cause.

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its having had that position, ever to return to it again; that position is gone, apparently for ever, and we require positive evidence to expect it to return, which we get when we know the law of the cause or force, which never passes away, and which therefore only positive evidence could induce us to suppose gone.

In this discussion we have often assumed that cause means the whole assemblage of cause and conditions, but we have said that we believed cause and condition to be distinct. This is entirely denied by Mr. Mill, but, we think, on no sufficient grounds. The cause seems to us to be the active, the conditions the limiting or restraining element in producing phenomena. Mr. Mill argues, that what is called cause in one case is called condition in another, and adduces as instances cases in physical nature, when the confusion arises from not being able to say what is the active, and what the passive antecedents of the phenomenon, from the external position in which our mind stands to all the events of the phenomenal world. The true type of cause and condition is will and reasons (or purposes) in the mind; that which actually produces the effect, and that without which it would not so produce it (ἄλλο μέν τι ἐστι τὸ αἴτιον τῷ ὄντι, ἄλλο δ' ἐκεῖνο, ἄνευ οὗ τὸ αἴτιον οὐκ ἂν ποτ ̓ εἴη αἰτιόν*). But to take Mr. Mill on his own ground: even in external nature, we always apply the word 'cause' rather to that element in the antecedents which exercises force, and which would tend at all times to produce the same or a similar effect to that which, under certain conditions, it would actually produce. In Mr. Mill's case of a stone falling into a well, the force of gravity is thought of as the real cause, while the presence of the stone within the region where the earth's attraction is the strongest force, is the local condition of the event. Mr. Mill complicates the question by asking at the same time for the cause of more changes than One phenomenon requires a cause and conditions; but when we take a great number at once, there naturally is no possibility of picking out the cause, unless we choose, like Mr. Mill, to keep the word 'cause' for the whole assemblage of invariable antecedents (which is certainly a convenient use of it in Logic, as it is that only which we can

one.

* Plato, Phædo, 99 B.