smallest number of independent properties which could serve as a basis for deducing the others.

(3) The two former subdivisions may be called 'natural', in the sense that these coexistences are presented to us by nature, human powers having comparatively little effect in introducing modifications. In the case of simple substances we may be said to have no such power at all. Even if we can alter some one property, which we cannot always do, we cannot help altering all the others at the same time. In the case of natural species, though we have long known that much can be done by persistent efforts aiming always in the same direction, and though we are beginning to recognize that much more than this can be done when the influences are continued through enormous intervals of time, yet so far as short intervals are concerned we are practically powerless.

In marked contrast with this stands a third class of more or less conventional actions, which present the same kind of regularity, though in a much less degree. In the proceedings of a law court, in the series of actions which constitute a coronation, in the positions and attitudes of the players in any game, we may find a group of coexistences presenting great regularity. When we consider how large a portion of our daily life and thought is devoted to considerations in which such conventions play a principal part; and how confidently we infer that where such things are found, or such actions are being performed, there will simultaneously other things and actions present themselves, it will be absurd to neglect this class of uniformity on the ground of its assumed unscientific character.

It need hardly be pointed out that there is no great difficulty here in attempting to analyze the ground of unity which underlies such uniformities. We do not require a soul or vital principle or substance of any kind to effect this. We need only start with a few coexistences of a common sort, viz. the tastes and powers of men; combine with this the wish to secure the same general end on different occasions, and we already have the basis of a class of regular coexistences. Then add on the natural inertia or imitative disposition, and the distinct advantages secured in many ways by exact repetition, and we easily get that stereotyped group of properties which really presents many points of resemblance to a Natural Kind.

Groups of this sort correspond for the most part to those which Locke distinguished under the name of Mixed Modes, and between which and Substances he made so sharp a distinction on the ground that the Mixed Modes are our own arbitrary institution, being put together by men for their own purposes.' This seems to overrate the openings which lie before us for caprice in the selection of groups and the consequent imposition of names upon them. Take the extremest limit of artificiality, offered by popular games. That men can decide for themselves according to what rules cricket shall be played, is obvious; but inasmuch as it is played according to the same rules year after year all the world over, the result is to place it, to other persons, viz. to the bulk of mankind, in much the same position as that occupied by any natural object. The game is presented to me as an 'object', just as substances and natural kinds are. I can study its characteristics, and I should find a necessity for giving it a name, if it did not already possess one, in much the same way as I find myself situated when dealing with things which are not within human control at all.

Still more is this the case when we are dealing with the actions of men in primitive times, or with those comparatively simple and widespread social phenomena which give but little opening to mere arbitrary choice. Much of our power of interpreting the past depends upon the assumption that the common practices of men, if one may use the language of the farmer and gardener, 'breed true'; that is, that the same groups of attributes will continue to recur again and again over large tracts of time and space. The agents could, of course, if they chose, introduce a capricious irregularity in many of these cases; but so long as from sluggishness, or imitativeness, or from proved convenience, they do not do so, so long will the uniformities persist and demand recognition.

The above are, I think, the only groups of coexistences sufficiently important and widespread to deserve notice in such a brief sketch as this. That is, they are the principal ones of a concrete character. They necessarily demand a certain amount of analysis, of course, for the recognition and distinction of any attribute demands this; but they do not demand more than is implied in any use of the common language of life. They stand, as has been repeatedly pointed out, on the stage, not of

advanced science but, of merely practical requirement. The A, B, C which we regard as a group of coexistent attributes present themselves, so to say, with a good quantity of flesh and blood upon them, rather than as merely anatomical outlines.

(4) As soon, however, as we determine to regard the A, B, C, viz. the coexistent attributes, as more distinctly abstract in their character, we find an opening to a very extensive and rigidly accurate set of coexistences of a new description. These are, I need not say, the data of Geometry, with all its attendant axioms and theorems. The raindrops that we examine present concurrent attributes of coldness, softness, and moisture, &c., and these when put together constitute the drop almost in its entirety. But if we take the raindrop, and by effort of abstraction isolate everything but its geometrical form, we find that this mere form will by itself give rise to an immensely extensive set of coexistences. The spherical form presents the attributes of perfect uniformity of shape all over, and maximum capacity within a given surface area. These may be considered 'coexistent attributes' in the sense of the term which we have used above; and to these we may add, if we care to do so, all the other characteristic qualities of a sphere which geometers have yet discovered.

Here, as above, the reader will understand that we are merely making a preliminary enumeration. We are not concerned, at this point, with enquiries into the nature and origin of mathematical truths; all that we have to do at this descriptive stage is to direct attention to their existence as a very important class of coexistences, which furnish frequent and confident grounds of inference. If, having paced the sides of a triangular field, I find that one side is the longest I may feel sure that the opposite angle is the largest; just as when I have smelt an orange I know what sort of taste will accompany that smell. In both cases alike we are trusting to the simultaneous existence of certain attributes, and in neither case do we make any appeal to causation in its ordinary logical sense of regular sequence.

So much for the directions in which available coexistences are mostly to be found. The next thing which deserves enquiry is the extent of the area over which they can be found to prevail.

The question has sometimes been put in this way, Are there any universal coexistences? - the comparison being intended to be made between them and sequences, in respect of which latter it is considered that universality may really be detected. This comparison in the way in which it is sometimes made does not seem quite fairly expressed. If it be intended to ask, Is there any universal law or formula of coexistence? we have already seen that this may be answered in the affirmative in the case of both orders of uniformity. If it be intended to ask, Is there any example which can be advanced of a concrete kind of coexistence which is really universal? then I should say that there is not, nor, for that matter, could we find one in the case of sequences.

It could not, in fact, be otherwise. A concrete instance, however wide the class to which it belongs, is necessarily from the very meaning of the term a limited one. It has been suggested, for example, that the coexistence of gravity and inertia is universal throughout all the material world, every particle of matter seeming to be simultaneously and always endowed with both these attributes'. This is probably as extensive a regularity of this kind as can be found; for all heavy bodies offering resistance to motion, and heavy bodies existing everywhere, the coexistence is perpetually coming under our notice. So with the coexistence, for which there is much evidence, though we cannot call it positively established, that all psychical activity is accompanied by nervous stimulation or action of some kind. The vast majority of the coexistences to which we appeal for purposes of inference are, of course, of much narrower range than this, and may be found of diminishing range and frequency until we come down to such special and determined coexistences as those of the smell and taste of some scarce fruit, or any of the properties of the very rare minerals.

sense.

In speaking here of the 'generality' of such laws of coexistence the word is not used quite in its customary logical A general proposition is properly contrasted with a particular one, and simply implies that the statement is made without exception. All bodies are heavy' is not considered more general than 'All English-grown pineapples are pale in colour', simply because generality is not an attribute that admits

1 Bain's Inductive Logic, p. 13.

of degree. But what we are referring to above is not liability to exception, but actual prevalence in nature. In fact what we are asked to determine is not so much a matter of formal logic as a point which is convenient in carrying out the details of an Inductive system.

Another small point also deserves notice here. When we speak of 'coexistences', are we to be supposed to mean that of the two or more attributes said to coexist, say A and B, neither is ever found apart from the other: that is, that both all A is B', and 'all B is A';-or is it sufficient that a certain one of them is always accompanied by the other, so that only one of the above pair of propositions will hold good? The statement is really ambiguous, and would scarcely be worth pausing over if it did not serve to remind us that we have exactly the same point involved here as that which gave rise to the so-called Plurality of Causes in the last chapter. A regularity of sequence, in its common acceptation, is never understood to imply more than that A shall always be followed by B: we expressly guard ourselves against any supposed implication that B must always be preceded by A. I explained that this distinction arose, not out of any difference between these elements in themselves, but out of a difference in our practical attitude towards them. Howsoever arisen, the distinction is easily retained; partly owing to the fact that, the cause preceding the effect, we gain the extra differentiation of time between them, partly also to the still-lingering associations of efficiency' in the causal connection. It does not seem unnatural therefore to put the cause and the effect upon a slightly different footing. When however we come to coexistences, the very fact that the two elements concur in time, and the absence of such traditional association about them, tend to prompt us to be perfectly impartial in our attitude towards the two elements. There is therefore a slight disposition, I think, to interpret a regularity of coexistence as intimating that either of the two elements is a certain indication of the other. This does, of course, hold good in the case of the attributes gravity and inertia, neither of which is ever found unaccompanied by the other.

There seems however no real occasion to interpret so rigidly as this, and it will be best to consider that we have a regularity of sequence whenever any attribute A is accompanied