in occult essences, in native faculties. Now, the first contention of the founders of the modern scientific movement was that such general considerations are not verifiable, and that if they are, they are entirely aside from the point—they fail to explain any given fact. Explanation must always consist in discovering an immediate connection between some fact and some co-existing or preceding fact. Explanation does not consist in referring a fact to a general power, it consists in referring it to an antecedent whose existence is its necessary condition. It was not left till the times of Mr. Huxley to poke fun at those who would explain some concrete phenomenon by reference to an abstract principle ending in—ity. Leibniz has his word to say about those who would account for the movements of a watch by reference to a principle of horologity, and of mill-stones by a fractive principle.
Mechanical explanation consists, accordingly, in making out an actual connection between two existing facts. But this does not say very much. A connection of what kind? In the first place, a connection of the same order as the facts observed. If we are explaining corporeal phenomena, we must find a corporeal link; if we are explaining phenomena of motion, we must find a connection of motion. In one of his first philosophical works Leibniz, in taking the mechanical position, states what he means by it. In the “Confession of Nature against the Atheists” he says that it must be confessed to those who have revived the corpuscular theory of Democritus and Epicurus, to Galileo, Bacon, Gassendi, Hobbes, and Descartes, that in explaining material phenomena recourse is to be had neither to God nor to any other incorporeal thing, form, or quality, but that all things are to be explained from the nature of matter and its qualities, especially from their magnitude, figure, and motion. The physics of Descartes, to which was especially due the spread of mechanical notions, virtually postulated the problem: given a homogeneous quantity of matter, endowed only with extension and mobility, to account for all material phenomena. Leibniz accepts this mechanical view without reserve.
What has been said suggests the bearing of mathematics in this connection. Extension and mobility may be treated by mathematics. It is indeed the business of the geometer to give us an analysis of figured space, to set before us all possible combinations which can arise, assuming extension only. The higher analysis sets before us the results which inevitably follow if we suppose a moving point or any system of movements. Mathematics is thus the essential tool for treating physical phenomena as just defined. But it is more. The mechanical explanation of Nature not only requires such a development of mathematics as will make it applicable to the interpretation of physical facts, but the employment of mathematics is necessary for the very discovery of these facts. Exact observation was the necessity of the growing physical science; and exact observation means such as will answer the question, How much? Knowledge of nature depends upon our ability to measure her processes—that is, to reduce distinctions of quality to those of quantity. The only assurance that we can finally have that two facts are connected in such a way as to fulfil the requirements of scientific research, is that there is a complete quantitative connection between them, so that one can be regarded as the other transformed. The advance of physical science from the days of Copernicus to the present has consisted, therefore, on one hand, in a development of mathematics which has made it possible to apply it in greater and greater measure to the discussion and formulation of the results of experiment, and to deduce laws which, when interpreted physically, will give new knowledge of fact; and, on the other, to multiply, sharpen, and make precise all sorts of devices by which the processes of nature may be measured. The explanation of nature by natural processes; the complete application of mathematics to nature—these are the two thoughts which, so far, we have seen to be fundamental to the development of the philosophy of Leibniz.
The third factor, and that which brings Leibniz nearer, perhaps, our own day than either of the others, is the growth of physiological science. Swammerdam, Malpighi, Leewenhoek—these are names which occur and recur in the pages of Leibniz. Indeed, he appears to be the first of that now long line of modern philosophers to be profoundly influenced by the conception of life and the categories of organic growth. Descartes concerned himself indeed with physiological problems, but it was only with a view to applying mechanical principles. The idea of the vital unity of all organs of the body might seem to be attractive to one filled with the notion of the unity of all in God, and yet Spinoza shows no traces of the influence of the organic conception. Not until Kant’s famous definition of organism do we see another philosopher moved by an attempt to comprehend the categories of living structure.
But it is the idea of organism, of life, which is radical to the thought of Leibniz. I do not think, however, that it can truly be said that he was led to the idea simply from the state of physiological investigation at that time. Rather, he had already learned to think of the world as organic through and through, and found in the results of biology confirmations, apt illustrations of a truth of which he was already thoroughly convinced. His writings show that there were two aspects of biological science which especially interested him. One was the simple fact of organism itself—the fact of the various activities of different organs occurring in complete harmony for one end. This presented three notions very dear to the mind of Leibniz, or rather three moments of the same idea—the factors of activity, of unity brought about by co-ordinated action, and of an end which reveals the meaning of the activity and is the ideal expression of the unity. The physiologists of that day were also occupied with the problem of growth. The generalization that all is developed ab ovo was just receiving universal attention. The question which thrust itself upon science for solution was the mode by which ova, apparently homogeneous in structure, developed into the various forms of the organic kingdom. The answer given was “evolution.” But evolution had not the meaning which the term has to-day. By evolution was meant that the whole complex structure of man, for example, was virtually contained in the germ, and that the apparent phenomenon of growth was not the addition of anything from without, but simply the unfolding and magnifying of that already existing. It was the doctrine which afterwards gave way to the epigenesis theory of Wolff, according to which growth is not mere unfolding or unwrapping, but progressive differentiation. The “evolution” theory was the scientific theory of the times, however, and was warmly espoused by Leibniz. To him, as we shall see hereafter, it seemed to give a key which would unlock one of the problems of the universe.
Such, then, were the three chief generalizations which Leibniz found current, and which most deeply affected him. But what use did he make of them? He did not become a philosopher by letting them lie dormant in his mind, nor by surrendering himself passively to them till he could mechanically apply them everywhere. He was a philosopher only in virtue of the active attitude which his mind took towards them. He could not simply accept them at their face-value; he must ask after the source of their value, the royal stamp of meaning which made them a circulatory medium. That is to say, he had to interpret these ideas, to see what they mean, and what is the basis of their validity.
Not many men have been so conscious of just the bearings of their own ideas and of their source as was he. He often allows us a direct glimpse into the method of his thinking, and nowhere more than when he says: “Those who give themselves up to the details of science usually despise abstract and general researches. Those who go into universal principles rarely care for particular facts. But I equally esteem both.” Leibniz, in other words, was equally interested in the application of scientific principles to the explanation of the details of natural phenomena, and in the bearing and meaning of the principles themselves—a rare combination, indeed, but one, which existing, stamps the genuine philosopher. Leibniz substantially repeats this idea when he says: “Particular effects must be explained mechanically; but the general principles of physics and mathematics depend upon metaphysics.” And again: “All occurs mechanically; but the mechanical principle is not to be explained from material and mathematical considerations, but it flows from a higher and a metaphysical source.”
As a man of science, Leibniz might have stopped short with the ideas of mechanical law, of the application of mathematics, and of the continuity of development. As a philosopher he could not. There are some scientific men to whom it always seems a perversion of their principles to attempt to carry them any beyond their application to the details of the subject. They look on in a bewildered and protesting attitude when there is suggested the necessity of any further inquiry. Or perhaps they dogmatically deny the possibility of any such investigation, and as dogmatically assume the sufficiency of their