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What is true of all men is true of philosophers, and of Leibniz among them. Speaking generally, what they are unconsciously and fundamentally, they are through absorption of their antecedents and surroundings. What they are consciously and reflectively, they are through their reaction upon the influence of heredity and environment. But there is a spiritual line of descent and a spiritual atmosphere; and in speaking of a philosopher, it is with this intellectual heredity and environment, rather than with the physical, that we are concerned. Leibniz was born into a period of intellectual activity the most teeming with ideas, the most fruitful in results, of any, perhaps, since the age of Pericles. We pride ourselves justly upon the activity of our own century, and in diffusion of intellectual action and wide-spread application of ideas the age of Leibniz could not compare with it. But ours is the age of diffusion and application, while his was one of fermentation and birth.

Such a period in its earlier days is apt to be turbid and unsettled. There is more heat of friction than calm light. And such had been the case in the hundred years before Leibniz. But when he arrived at intellectual maturity much of the crudity had disappeared. The troubling of the waters of thought had ceased; they were becoming clarified. Bacon, Hobbes, Descartes, each had crystallized something out of that seething and chaotic mass of new ideas which had forced itself into European consciousness. Men had been introduced into a new world, and the natural result had been feelings of strangeness, and the vagaries of intellectual wanderings. But by the day of Leibniz the intellectual bearings had been made out anew, the new mental orientation had been secured.

The marks of this “new spiritual picture of the universe” are everywhere to be seen in Leibniz. His philosophy is the dawning consciousness of the modern world. In it we see the very conception and birth of the modern interpretation of the world. The history of thought is one continuous testimony to the ease with which we become hardened to ideas through custom. Ideas are constantly precipitating themselves out of the realm of ideas into that of ways of thinking and of viewing the universe. The problem of one century is the axiom of another. What one generation stakes its activity upon investigating is quietly taken for granted by the next. And so the highest reach of intellectual inspiration in the sixteenth century is to-day the ordinary food of thought, accepted without an inquiry as to its source, and almost without a suspicion that it has a recent historic origin. We have to go to Bacon or to Leibniz to see the genesis and growth of those ideas which to-day have become materialized into axiomatic points of view and into hard-and-fast categories of thought. In reading Leibniz the idea comes over us in all its freshness that there was a time when it was a discovery that the world is a universe, made after one plan and of one stuff. The ideas of inter-relation, of the harmony of law, of mutual dependence and correspondence, were not always the assumed starting-points of thought; they were once the crowning discoveries of a philosophy aglow and almost intoxicated with the splendor of its far-reaching generalizations. I take these examples of the unity of the world, the continuity and interdependence of all within it, because these are the ideas which come to their conscious and delighted birth in the philosophy of Leibniz. We do not put ourselves into the right attitude for understanding his thought until we remember that these ideas—the commonest tools of our thinking—were once new and fresh, and in their novelty and transforming strangeness were the products of a philosophic interpretation of experience. Except in that later contemporary of Leibniz, the young and enthusiastic Irish idealist, Berkeley, I know of no historic thinker in whom the birth-throes (joyous, however) of a new conception of the world are so evident as in Leibniz. But while in Berkeley what we see is the young man carried away and astounded by the grandeur and simplicity of a “new way of ideas” which he has discovered, what we see in Leibniz is the mature man penetrated throughout his being with an idea which in its unity answers to the unity of the world, and which in its complexity answers, tone to tone, to the complex harmony of the world.

The familiarity of the ideas which we use hides their grandeur from us. The unity of the world is a matter of course with us; the dependent order of all within it a mere starting-point upon which to base our investigations. But if we will put ourselves in the position of Leibniz, and behold, not the new planet, but the new universe, so one, so linked together, swimming into our ken, we shall feel something of the same exultant thrill that Leibniz felt,—an exultation not indeed personal in its nature, but which arises from the expansion of the human mind face to face with an expanding world. The spirit which is at the heart of the philosophy of Leibniz is the spirit which speaks in the following words: “Quin imo qui unam partem materiæ comprehenderet, idem comprehenderet totum universum ob eandem περιχώρησιν quam dixi. Mea principia talia sunt, ut vix a se invicem develli possint. Qui unum bene novit, omnia novit.” It is a spirit which feels that the secret of the universe has been rendered up to it, and which breathes a buoyant optimism. And if we of the nineteenth century have chosen to bewail the complexity of the problem of life, and to run hither and thither multiplying “insights” and points of view till this enthusiastic confidence in reason seems to us the rashness of an ignorance which does not comprehend the problem, and the unity in which Leibniz rested appears cold and abstract beside the manifold richness of the world, we should not forget that after all we have incorporated into our very mental structure the fundamental thoughts of Leibniz,—the thoughts of the rationality of the universe and of the “reign of law.”

What was the origin of these ideas in the mind of Leibniz? What influences in the philosophic succession of thinkers led him in this direction? What agencies acting in the intellectual world about him shaped his ideal reproduction of reality? Two causes above all others stand out with prominence,—one, the discoveries and principles of modern physical science; the other, that interpretation of experience which centuries before had been formulated by Aristotle. Leibniz has a double interest for those of to-day who reverence science and who hold to the historical method. His philosophy was an attempt to set in order the methods and principles of that growing science of nature which even then was transforming the emotional and mental life of Europe; and the attempt was guided everywhere by a profound and wide-reaching knowledge of the history of philosophy. On the first point Leibniz was certainly not alone. Bacon, Hobbes, Descartes, Spinoza, each felt in his own way the fructifying touch of the new-springing science, and had attempted under its guidance to interpret the facts of nature and of man. But Leibniz stood alone in his interest in the history of thought. He stands alone indeed till he is greeted by his compeers of the nineteenth century. To Bacon previous philosophy—the Greek, the scholastic—was an “eidol of the theatre.” The human mind must be freed from its benumbing influence. To Descartes it was useless rubbish to be cleared away, that we might get a tabula rasa upon which to make a fresh start. And shall Locke and the empirical English school, or Reid and the Scotch school, or even Kant, be the first to throw a stone at Bacon and Descartes? It was reserved to Leibniz, with a genius almost two centuries in advance of his times, to penetrate the meaning of the previous development of reflective thought. It would be going beyond our brief to claim that Leibniz was interested in this as a historical movement, or that he specially concerned himself with the genetic lines which connected the various schools of thought. But we should come short of our duty to Leibniz if we did not recognize his conscious and largely successful attempt to apprehend the core of truth in all systems, however alien to his own, and to incorporate it into his own thinking.

Nothing could be more characteristic of Leibniz than his saying, “I find that most systems are right in a good share of that which they advance, but not so much in what they deny;” or than this other statement of his, “We must not hastily believe that which the mass of men, or even of authorities, advance, but each must demand for himself the proofs of the thesis sustained. Yet long research generally convinces that the old and received opinions are good, provided they be interpreted justly.” It is in the profound union in Leibniz of the principles which these quotations image that his abiding worth lies. Leibniz was interested in affirmations, not in denials. He was interested in securing the union of the modern method, the spirit of original research and independent judgment, with the conserved results of previous thought. Leibniz was a man of his times; that is to say, he was a scientific man,—the contemporary, for example, of men as different as Bernouilli, Swammerdam, Huygens, and Newton, and was himself actively engaged in the prosecution of mathematics, mechanics, geology, comparative philology, and jurisprudence. But he was also a man of Aristotle’s times,—that is to say, a philosopher, not satisfied until the facts, principles, and methods of science had received an interpretation which should explain and unify them.

Leibniz’s acquaintance with the higher forms of mathematics was due, as we have seen, to his acquaintance with Huygens. As he made the acquaintance of the latter at the same time that he made the acquaintance of the followers of Descartes, it is likely that he received his introduction to the higher developments of the scientific interpretation of nature and of the philosophic interpretation of science at about the same time. For a while, then, Leibniz was a Cartesian; and he never ceased to call the doctrine of Descartes the antechamber of truth. What were the ideas which he received from Descartes? Fundamentally they were two,—one about the method of truth, the other about the substance of truth. He received the idea that the method of philosophy consists in the analysis of any complex group of ideas down to simple ideas which shall be perfectly clear and distinct; that all such clear and distinct ideas are true, and may then be used for the synthetic reconstruction of any body of truth. Concerning the substance of philosophic truth, he learned that nature is to be interpreted mechanically, and that the instrument of this mechanical interpretation is mathematics. I have used the term “received” in speaking of the relation of Leibniz to these ideas. Yet long before this time we might see him giving himself up to dreams about a vast art of combination which should reduce all the ideas concerned in any science to their simplest elements, and then combine them to any degree of complexity. We have already seen him giving us a picture of a boy of fifteen gravely disputing with himself whether he shall accept the doctrine of forms and final causes, or of physical causes, and as gravely deciding that he shall side with the “moderns;” and that boy was himself. In these facts we have renewed confirmation of the truth that one mind never receives from another anything excepting the stimulus, the reflex, the development of ideas which have already possessed it. But when Leibniz, with his isolated and somewhat ill-digested thoughts, came in contact with that systematized and connected body of doctrines which the Cartesians presented to him in Paris, his ideas were quickened, and he felt the necessity—that final mark of the philosophic mind—of putting them in order.

About the method of Descartes, which Leibniz adopted from him, or rather formulated for himself under the influence of Descartes, not much need be said. It was the method of Continental thought till the time of Kant. It was the mother of the philosophic systems of Descartes, Leibniz, and Spinoza. It was equally the mother of the German Aufklärung and the French éclaircissement. Its fundamental idea is the thought upon which Rationalism everywhere bases itself. It says: Reduce everything to simple notions. Get clearness; get distinctness. Analyze the complex. Shun the obscure. Discover axioms; employ these axioms in connection with the simple notions, and build up from them. Whatever can be treated in this way is capable of proof, and only this. Leibniz, I repeat, possessed this method in common with Descartes and Spinoza. The certainty and demonstrativeness of mathematics stood out in the clearest contrast to the uncertainty, the obscurity, of all other knowledge. And to them, as to all before the days of Kant, it seemed beyond doubt that the method of mathematics consists in the analysis of notions, and in their synthesis through the medium of axioms, which are true because identical statements; while the notions are true because clear and distinct.

And yet the method led Leibniz in a very different direction. One of the fundamental doctrines, for example, of Leibniz is the existence everywhere of minute and obscure perceptions,—which are of the greatest importance, but of which we, at least, can never have distinct consciousness. How is this factor of his thought, which almost approaches mysticism, to be reconciled with the statements just made? It is found in the different application which is made of the method. The object of Descartes is the erection of a new structure of truth upon a tabula rasa of all former doctrines. The object of Leibniz is the interpretation of an old body of truth by a method which shall reveal it in its clearest light. Descartes and Spinoza are “rationalists” both in their method and results. Leibniz is a “rationalist” in his method; but his application of the method is everywhere controlled by historic considerations. It is, I think, impossible to over-emphasize this fact. Descartes was profoundly convinced that past thought had gone wrong, and that its results were worthless. Leibniz was as profoundly convinced that its instincts had been right, and that the general idea of the world which it gave was correct. Leibniz would have given the heartiest assent to Goethe’s saying, “Das Wahre war schon längst gefunden.” It was out of the question, then, that he should use the new method in any other than an interpreting way to bring out in a connected system and unity the true meaning of the subject-matter.

So much of generality for the method of Leibniz. The positive substance of doctrine which he developed under scientific influence affords matter for more discussion. Of the three influences which meet us here, two are still Cartesian; the third is from the new science of biology, although not yet answering to that name. These three influences are, in order: the idea that nature is to be explained mechanically; that this is to be brought about through the application of mathematics; and, from biology, the idea that all change is of the nature of continuous growth or unfolding. Let us consider each in this order.

What is meant by the mechanical explanation of nature? To answer a question thus baldly put, we must recall the kind of explanations which had satisfied the scholastic men of science. They had been explanations which, however true, Leibniz says, as general principles, do not touch the details of the matter. The explanations of natural facts had been found in general principles, in substantial forces, 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 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 physics is the evidence of the rational character of nature. Nature may be reduced to motions; and motions can be understood only as force, activity. But the laws which connect motions are fundamentally mathematical laws,—laws of reason. Hence force, activity, can be understood only as rational, as spiritual. Nature is thus seen to mean Activity, and Activity is seen to mean Intelligence. Furthermore, as the fundamental law of intelligence is the production of difference in unity, the primary law of physical change must be the manifestation of this unity in difference,—or, as Leibniz interpreted it, continuity. In nature there are no breaks, neither of quantity nor of quality nor of relationship. The full force of this law we shall see later.

Such an idea can hardly be distinguished from the idea of growth or development; one passes naturally into the other. Thus it is equally proper to say that the third scientific influence, the conception of organism and growth, is dominant in the Leibnizian thought, or that this is swallowed up and absorbed in the grand idea of continuity. The law of animal and vegetable life and the law of the universe are identified. The substance of the universe is activity; the law of the universe is interdependence. What is this but to say that the universe is an organic whole? Its activity is the manifestation of life,—nay, it is life. The laws of its activity reveal that continuity of development, that harmony of inter-relation, which are everywhere the marks of life. The final and fundamental notion, therefore, by which Leibniz interprets the laws of physics and mathematics is that of Life. This is his regnant category. It is “that higher and metaphysical source” from which the very existence and principles of mechanism flow. The perpetual and ubiquitous presence of motion reveals the pulsations of Life; the correlation, the rationality, of these motions indicate the guiding presence of Life. This idea is the alpha and omega of his philosophy.