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 principles for the decision of all possible problems. But bewildered fear and dogmatic assertion are equally impotent to fix arbitrary limits to human thought. Wherever there is a subject that has meaning, there is a field which appeals to mind, and the mind will not cease its endeavors till it has made out what that meaning is, and has made it out in its entirety. So the three principles already spoken of were but the starting-points, the stepping-stones of Leibniz’s philosophic thought. While to physical science they are solutions, to philosophy they are problems; and as such Leibniz recognized them. What solution did he give?
So far as the principle of mechanical explanation is concerned, the clew is given by considering the factor upon which he laid most emphasis, namely, motion. Descartes had said that the essence of the physical world is extension. “Not so,” replied Leibniz; “It is motion.” These answers mark two typical ways of regarding nature. According to one, nature is something essentially rigid and static; whatever change in it occurs, is a change of form, of arrangement, an external modification. According to the other, nature is something essentially dynamic and active. Change according to law is its very essence. Form, arrangement are only the results of this internal principle. And so to Leibniz, extension and the spatial aspects of physical existence were only secondary, they were phenomenal. The primary, the real fact was motion.
The considerations which led him to this conclusion are simple enough. It is the fact already mentioned, that explanation always consists in reducing phenomena to a law of motion which connects them. Descartes himself had not succeeded in writing his physics without everywhere using the conception of motion. But motion cannot be got out of the idea of extension. Geometry will not give us activity. What is this, except virtually to admit the insufficiency of purely statical conceptions? Leibniz found himself confirmed in this position by the fact that the more logical of the followers of Descartes had recognized that motion is a superfluous intruder, if extension be indeed the essence of matter, and therefore had been obliged to have recourse to the immediate activity of God as the cause of all changes. But this, as Leibniz said, was simply to give up the very idea of mechanical explanation, and to fall back into the purely general explanations of scholasticism.
This is not the place for a detailed exposition of the ideas of Leibniz regarding matter, motion, and extension. We need here only recognize that he saw in motion the final reality of the physical universe. But what about motion? To many, perhaps the majority, of minds to-day it seems useless or absurd, or both, to ask any question about motion. It is simply an ultimate fact, to which all other facts are to be reduced. We are so familiar with it as a solution of all physical problems that we are confused, and fail to recognize it when it appears in the guise of a problem. But, I repeat, philosophy cannot stop with facts, however ultimate. It must also know something about the meaning, the significance, in short the ideal bearing, of facts. From the point of view of philosophy, motion has a certain function in the economy of the universe; it is, as Aristotle saw, something ideal.
The name of Aristotle suggests the principles which guided Leibniz in his interpretation of the fact of motion. The thought of Aristotle moves about the two poles of potentiality and actuality. Potentiality is not mere capacity; it is being in an undeveloped, imperfect stage. Actuality is, as the word suggests, activity. Anything is potential in so far as it does not manifest itself in action; it is actual so far as it does thus show forth its being. Now, movement, or change in its most general sense, is that by which the potential comes to the realization of its nature, and functions as an activity. Motion, then, is not an ultimate fact, but is subordinate. It exists for an end. It is that by which existence realizes its idea; that is, its proper type of action.
Now Leibniz does not formally build upon these distinctions; and yet he is not very far removed from Aristotle. Motion, he is never weary of repeating, means force, means energy, means activity. To say that the essence of nature is motion, is to say that the natural world finally introduces us to the supremacy of action. Reality is activity. Substance c’est l’action. That is the key-note and the battle-cry of the Leibnizian philosophy. Motion is that by which being expresses its nature, fulfils its purpose, reveals its idea. In short, the specific scientific conception of motion is by Leibniz transformed into the philosophic conception of force, of activity. In motion he sees evidence of the fact that the universe is radically dynamic.
In the applicability of mathematics to the interpretation of nature Leibniz finds witness to the continuity and order of the world. We have become so accustomed to the fact that mathematics may be directly employed for the discussion and formulation of physical investigations that we forget what is implied in it. It involves the huge assumption that the world answers to reason; so that whatever the mind finds to be ideally true may be taken for granted to be physically true also. But in those days, when the correlation of the laws of the world and the laws of mathematical reasoning was a fresh discovery, this aspect of the case could not be easily lost sight of.
In fact it was this correlation which filled the Zeitgeist of the sixteenth century with the idea that it had a new organ for the penetration of nature, a new sense for learning its meaning. Descartes gives the following as the origin of his philosophy: “The long chains of simple and easy reasons which geometers employ, even in their most complex demonstrations, made me fancy that all things which are the objects of human knowledge are similarly interdependent.” To Leibniz also mathematics seemed to give a clew to the order, the interdependence, the harmonious relations, of the world.
In this respect the feeling of Plato that God geometrizes found an echoing response in Leibniz. But the latter would hardly have expressed it in the same way. He would have preferred to say that God everywhere uses the infinitesimal calculus. In the applicability of the calculus to the discussion of physical facts, Leibniz saw two truths reflected,—that everything that occurs has its reason, its dependent connection upon something else, and that all is continuous and without breaks. While the formal principles of his logic are those of identity and contradiction, his real principles are those of sufficient reason and of continuity. Nature never makes leaps; everything in nature has a sufficient reason why it is as it is: these are the philosophic generalizations which Leibniz finds hidden in the applicability of mathematics to physical science. Reason finds itself everywhere expressed in nature; and the law of reason is unity in diversity, continuity.
Let us say, in a word, that the correlation between the laws of mathematics and of