deal with the foundations of inference rather than with this mental act itself. But the two are only different aspects of one and the same state of things. That is, wherever Uniformity exists, there we can, actually or potentially,—in other words with our present resources of observation and calculation, or with such improvements in these as we can conceive without interfering with their essential character,—draw inferences. And where it does not exist, there no conceivable employment of, or improvement in, these faculties would enable us to draw any inferences'. What might be done by beings of a higher order than ourselves, we cannot say their world is not ours-but a system of Logic intended for man must stop short at the ideal limit which we can conceive to be reached by the exercise of faculties such as we possess. Such a general indication of the Nature of Uniformity as is thus furnished is too vague to be very useful or even readily intelligible: the significance of the conception will best be brought into light by a brief discussion of the principal heads into which it may be divided.

The first two of these are, it need hardly be said, the two familiar classes which have been so recently investigated. We only recall attention briefly to them here in order to assign them their proper place.

I. First then we have the uniformities of sequence. These may for convenience be divided into two subdivisions, according to the degree of accuracy with which we are supposed to be speaking.

(1) If we interpret the formula with the reasonable stringency demanded for logical and popular scientific purposes, we have what are commonly called Laws of Nature. Understanding these in the general sense in which Brown and Mill may be considered to have popularized them, we may adopt some such statement as this, "If in any two instances the same set of antecedents occur, so will any one of the immediate consequents, and, for that matter, the sum-total of immediate consequents."

1 Some of Leibnitz's statements of the Law of Sufficient Reason seem to me to approach very nearly to this, regard being had to the fact that they are stated from the subjective side: "Rien n'arrive sans qu'il y ait une raison pourquoi cela est ainsi et non autrement" (Erdmann, p. 748).

(2) The above Laws of Nature represent the materials of what may be called first-class popular thought. For ordinary working purposes we require something looser and more convenient. The sequences to which we thus appeal on common occasions are of the kind generally described as Empirical Laws, or sometimes in more dignified terms, borrowed from Bacon, Axiomata media. That green fruit is unwholesome : that hot water will crack a tumbler: that manure will improve our crops: these, and such as these, form the staple of our reliance for ordinary purposes.

I sufficiently explained the nature of these laws, as here understood, and will therefore merely add that their characteristic depends upon the lax sense in which the 'cause' is interpreted. Instead of taking some pains to enumerate all the relevant antecedents, we just pick out one or two of the most usual or important. We thus obtain a sequence of far more prevalence, but one upon which proportionally less reliance can be placed.

II. In the next place there are the Laws of Coexistence. These have received far less notice than those of the former class, and have been generally disparaged in comparison. I endeavoured to show that the two classes were strictly analogous in all essential respects, and that they would admit therefore of the same division and arrangement, viz.:

(1) Moderately strict coexistences, in which reasonable care had been taken to include all the elements. In such cases,

-due regard being had to all the difficulties involved in the attempt to distinguish between the attributes, there seemed no reason to deny to coexistences any of the rights of inference to which the sequences are considered to be entitled.

(2) Loose coexistences, in which but few elements were introduced, possibly only two; one of these being taken as a sign of the presence of the other. The dependence to be placed upon these is, of course, not very strong; but such as they are, they form the foundation of our conclusions on a vast number of occasions in our ordinary life. The question to what extent, if any, these coexistences admit of resolution into sequences, is reserved for discussion in a future chapter. Before proceeding to the next classes of Uniformities some extremely important considerations must be attended to in

reference to the above two. It is not so much that the assumption we are now about to make is one which would in common language be regarded as a uniformity, but it certainly seems demanded in order to render the others available.

The best way in which we can introduce this is by the following query. Conceive that some ingenious and malicious agent were endowed with complete power over all the properties and forces of nature, to make and to mar at his will, and that the general problem were set before him to effect such disturbances as should entirely put a stop to all inference, and therefore to all safe and rational action, on the part of man :what had he best do? We will suppose that he is recommended to do his work efficiently but economically; that is, he is to make the minimum of change which will answer the proposed purpose. What then would be the sort and amount of mischief he would find to do in order to destroy at a stroke all the fabric of Inductive inference whether of daily or of scientific life?

Were such a question proposed to logicians of the school of Brown and Stewart, I imagine that what they would reply would in effect be this:-Just let all the causal chains' be snapped or corroded, so as to be no longer trustworthy. (We may remark here, in passing, that it would come to the same thing whether the objective regularity itself were tampered with, or merely our belief in it, or whether both were involved in one common ruin. What is necessary for successful action is the concurrence of both: the absence of either would be fatal. This however will be discussed in the next chapter; what here concerns us is the objective regularity, with which alone our agent is supposed to be allowed to meddle.) They would say that if the universal prevalence of the Law of Cause and Effect were interfered with, the whole fabric of our successful thought and action would be pulverized at once. And so it would, no doubt. If the same antecedents could no longer be insured to give the same consequents, this loss of confidence would be followed by a shock which would paralyze all thought and action. There would however be a quite needless violence in setting to work in this style: much less extreme measures would quickly bring down upon our heads a state of things not a whit less mischievous for any practical purposes. If I had

the work entrusted to me I would, like any prudent revolutionist, express the most unbounded respect for the present constitution of things. I would not touch the Law of Causation ; in fact I would interpret it with the utmost stringency and rigour. Let it remain true hereafter, as before, that the same antecedents shall be followed by the same consequents :-only neutralize the efficiency of the formula by securing that the same antecedents do not recur. A great deal more than is commonly supposed might be quietly effected in this way; indeed without even doing anything which would fall under common definitions of a miracle. For instance, let each animal and plant and fruit, and so forth, be unique of its kind, like the fabled phoenix, we might add to the number of species in proportion as we diminished the number of their representatives, so as to keep up the quantity of individuals and add to the consequent perplexity, and nearly all the generalizations and inductive extensions upon which we depend for guidance in daily life would be gone at once. Again, when we came to deal with material objects, a sudden and sufficient increase in the motion of the earth,-always leaving the law of gravitation absolutely intact,-would destroy an enormous number of the regularities on which our conduct proverbially depends: the seed-time and harvest, the day and night, and so on. For if the earth were sent out into a hyperbolic path we should never again have any one summer or winter or day or night which would be an exact repetition of the preceding one: nor would an average of any number afford safe guidance as to the repetition of such an average again: and this of course would carry its consequences throughout the whole of animate nature.

The above are but one or two instances out of multitudes which might be suggested. It is obvious what an amount of mischief our agent, if he properly understood his business, might effect without tampering with laws of causation, or at most without doing so at more than one point and once for all.

What this hypothesis is intended to enforce is the insufficiency of the Causation formula, when rigidly interpreted in concrete sequences, to serve by itself as a means of inference. It can be thus rigidly stated, as I have shown, without difficulty or inconsistency, but it has then to be couched in a hypothetical form. To render any definition of this kind of the slightest

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use we must append a rider to it, by the assumption that such repetition of similar cases as we require does actually occur. Otherwise we could never apply our formula, for the most infallible rule will fail us if we can never come across the circumstances in which alone it is available.

Repetition therefore of similar cases is essential, if we are to utilize the uniformities, but the way in which these repetitions are brought about deserves careful notice. Complete repetition of all the constituent elements, down to the most minute, is, as we have already seen, out of the question. Such repetitions as we actually find set before us are the result of two factors, one contributed by nature the other partly contributed by ourselves. There is, that is to say, an actual recurrence over and over again of a large proportion of the elements which compose the antecedent, but with this must be combined the knowledge on our part that the elements which we decide to omit, in order to secure the recurrence, are really insignificant. This involves a considerable amount of acquired information as to what is trivial and what is important, in each class of cases. There was a time when any one who wished to decide what would be the result of a battle or an expedition would have thought that amongst the essential antecedents was to be included the position of the stars at the time, or the fact of a bird being seen to the right or left of the observer. We have decided that such incidents are unimportant, and accordingly we can recognize recurrences of similar instances in cases where our ancestors would have thought the circumstances widely different.

Nature, as we have seen, and as Leibnitz was fond of insisting, never exactly repeats herself. But she does the next best thing to this for us. She gives us repetitions,―sometimes very frequent, sometimes very scarce, according to the nature of the phenomena, of all the important elements, only leaving it to us to decide what these important elements are.

One way indeed of giving these repetitions is in the form of what we call coexistences, which brings us round to the point already discussed. In fact a coexistence loosely understood is an occasion of a repetition of a sequence similarly understood; that is, it is an occasion of recognizing and applying it. This may need a moment's consideration. Recur to the lobster which we found to turn from black to red on being put into