Every science, at its origin, has been qualitative, and has sometimes taken thousands of years to arrive at its quantitative period; chemistry has entered it only recently. It must not be lost sight of that science and ordinary knowledge are of the same nature, and that the one is only the extension and perfection of the other.1

Since science, by its processus of evolution, comes out of common knowledge, that which is given us by reason and our senses reduced to themselves merely; and that common knowledge itself proceeds from simple perceptions; the genesis of science ought, strictly speaking, to take the origin of knowledge as its point of departure. At the risk of beginning after an

abrupt fashion, let us take the adult savage.

In order to live, it is necessary that he should know what will nourish him, what may hurt him, what he ought to avoid; he must distinguish a great variety of substances, plants, animals, tools, persons, etc. But what does this distinction or classification of objects presuppose? A recognition of the resemblance or the dissimilarity of things. By a natural progress, classification goes from rude resemblances to more subtle ones; sub-classes, according to degrees of dissimilarity, are formed in the classes; and the mind, always eliminating the dissimilar, seeking more and more close resemblances, finally tends towards the notion of complete resemblance which supposes non-difference.

1 Here Mr. Herbert Spencer examines the classification of the sciences by Hegel, Oken, and A. Comte. He is not favourable to the bastard a priori method' of the two first. As for the third, while making much of his doctrine, he criticises him for having said that the order of decreasing generality is that in which the sciences are historically produced. In fact, algebra, which is more general than arithmetic, is posterior to it; there is an increasing generality of arithmetic in the differential calculus. The solution of A. Comte is a half-truth; the progress of science is double; it goes from the general to the special, and from the special to the general. Its serial arrangement of the sciences is a vicious conception; there is a consensus between them, which Comte has been wrong in not acknowledging. Each discovery of a science influences the others. Mr. Spencer has developed these ideas in his Classification of the Sciences, a special work; and M. Littré has discussed at length the objections of the English philosopher in his work on Auguste Comte and Positivism.

That which we have just seen in the perception and classification of objects is produced in the same way in the genesis of reasoning. To class, is to group together similar things; to reason is to group together similar relations. It is of the essence of reasoning to perceive a resemblance between cases, and the idea which is at the bottom of all our processes of reasoning, is the idea of resemblance. And in the same way as the final progress of classification consists in forming groups of completely similar objects, so the perfection of reasoning consists in forming groups of completely similar cases.

It is now possible for us to understand how the passage from qualitative to quantitative knowledge takes place. The processus of classification, by a progress proper to itself, tends towards complete resemblance, or equality; when it has attained that, science has become quantitative.

Whence comes the notion of equality? From experience. The things which we call equal (lines, angles, weights, temperatures, sounds, colours) are those 'which produce in us sensations which we cannot distinguish from one another,' the idea of equality is drawn by abstraction from artificial objects. Afterwards experience separates the idea of equality into two ideas, equality of things; equality of relations (two equal triangles and two similar triangles). The first idea is the concrete germ of the exact science; the second is the abstract germ, and both come from that resemblance of things and that resemblance of relations which we have already seen.

At the same time and in the same way distinct ideas of number are produced. Number, equality, resemblance, these are notions which are intimately related. Simple enumeration is a registration of experiences repeated in a certain way; in order that they may be susceptible of enumeration, they must be more or less. similar; and in order that absolutely true numerical results should be obtained, the units must be absolutely equal. We apply number on occasion to unequal units, like the animals on a farm, but every calculation supposes the perfect equality of the units, and reaches exact results only in virtue of that hypothesis; the first ideas of number are those derived from equal or similar magnitudes, especially in inorganic objects; and consequently geo

metry and arithmetic have a simultaneous origin. We should also remark that several nations, who do not seem to have any relation between them, have adopted ten (the ten fingers) as the basis of their enumeration, or five (the five fingers of one hand), or twenty (the fingers and toes), which shows that the fingers have been the original unit of numeration.

Thus, then, we know the idea of equality as the basis of all science, but how do we apply it? How do we pass from the vague perception of equality to the exact perception proper to science? By the juxtaposition of the things compared. Hence it arises that if we wish to judge of two shades of colour, we place them side by side; that if we wish to estimate two weights, we take one in each hand, and compare their pressure, making our thought pass rapidly from one to the other, and 'as of all greatnesses, those of linear extension are those whose equality may be most easily ascertained, it results that it is to those we should reduce all others.' It is the property of linear extension that it alone admits of absolute juxtaposition or coincidence, such as befalls two mathematical lines, equality then becoming identity. 'Thus it is that all exact science is reducible by final analysis to results measured in equal units of linear extension.'

The idea of measure by juxtaposition is suggested to us by experience. We must all have remarked that when two men, two animals, any two objects, are near one another, the inequality becomes more visible. This experience, repeated constantly, has given us our first lessons.

In short, all knowledge, whether scientific or vulgar, presupposes resemblances which may vary from the vaguest analogy to perfect equality, which alone constitutes quantitative science; equality being given and verified by an empirical juxtaposition. The terms foot, thumb, finger, pace, and others of a similar kind used in the origin of almost all languages, are they not facts which come to the support of the empirical origin of the idea of measure, if it be disputed by sceptics?

We should exceed our limits did we follow Mr. Herbert Spencer through his picture of the production of the various sciences. He brings out, by numerous facts, their close relations and their reciprocal dependence. In our time, he says, the consensus

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between the sciences has become such, that there is no considerable discovery in one order of facts which does not soon lead to important discoveries in others. And each serves the others; the observation of a star supposes the employment of highly-perfected instruments, and the assistance of optics, thermology, hygrometry, barology, electricity, for the registration of certain minute observations, and even of psychology itself, to correct the 'personal equation.' Such is the complication of sciences involved in so seemingly simple a thing as fixing the position of a star.

V.

Here we leave the law of evolution. No doubt the author will at some future time carry it into questions of morals, whither it would have been interesting to follow him; for the hypothesis of progress alone can produce an agreement between those who maintain against all evidence that morals do not vary, and those who maintain against all reason that there is nothing in morals but the mobile and the arbitrary. A short essay on Anthropomorphism (vol. i. p. 440) shows how the idea of development can also transform the study of religions, from that of the grossest fetichism to that of monotheism under its purest forms.

But what it behoves us thoroughly to understand is, that the idea of evolution, whether it explains cosmical and biological phenomena, or whether it penetrates the world of thought and of history, never explains first causes. Everything which goes beyond experience escapes it. We shall let the author state his conclusions on this point himself.

'Probably not a few will conclude that here is an attempted solution of the great questions with which philosophy in all ages has perplexed itself. Let none thus deceive themselves. Only such as know not the scope and the limits of science can fall into so grave an error. The foregoing generalizations apply not to the genesis of things in themselves, but to their genesis as manifested to the human consciousness. After all that has been said, the ultimate mystery remains just as it was. The explanation of that which is explicable does but bring out into greater clearness the inexplicableness of that which remains behind. However we

may succeed in reducing the equation to its lowest terms, we are not thereby enabled to determine the unknown quantity; on the contrary, it only becomes more manifest that the unknown quantity can never be found.

'Little as it seems to do so, fearless inquiry tends continually to give a firmer basis to all true religion. The timid sectarian, alarmed at the progress of knowledge, obliged to abandon one by one the superstitions of his ancestors, and daily finding his cherished beliefs more and more shaken, secretly fears that all things may some day be explained, and has a corresponding dread of science thus evincing the profoundest of all infidelity-the fear lest the truth be bad. On the other hand, the sincere man of science, content to follow wherever the evidence leads him, becomes by each new inquiry more profoundly convinced that the universe is an insoluble problem. Alike in the external and the internal worlds, he sees himself in the midst of perpetual changes, of which he can discover neither the beginning nor the end. If, tracing back the evolution of things, he allows himself to entertain the hypothesis that all matter once existed in a diffused form, he finds it utterly impossible to conceive how this came to be so, and equally, if he speculates on the future, he can assign no limit to the grand succession of phenomena ever unfolding themselves before him. On the other hand, if he looks inward, he perceives that both terminations of the thread of consciousness are beyond his grasp; he cannot remember when or how consciousness commenced, and he cannot examine the consciousness that at any moment exists, for only a state of consciousness that is already past can become the object of thought, and never one which is passing. When, again, he turns from the succession of phenomena, external or internal, to their essential nature, he is equally at fault. Though he may succeed in resolving all properties of objects into manifestations of force, he is not thereby enabled to realize what force is, but finds, on the contrary, that the more he thinks about it the more he is baffled. Similarly, though analysis of mental actions may finally bring him down to sensations as the original materials out of which all thought is woven, he is none the forwarder; for he cannot in the least comprehend sensation-cannot even conceive how sensation