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.
Chapter III.
The Problem, and its Solution.
Leibniz, like every great man, absorbed into himself the various thoughts of his time, and in absorbing transformed them. He brought into a focus of brilliancy the diffused lights of truth shining here and there. He summed up in a pregnant and comprehensive category the scattered principles of his age. Yet we are not to suppose that Leibniz considered these various ideas one by one, and then patched them into an artificial unity of thought. Philosophies are not manufactured piecemeal out of isolated and fragmentary thoughts; they grow from a single root, absorbing from their environment whatever of sustenance offers itself, and maturing in one splendid fruit of spiritual truth. It is convenient, indeed, to isolate various phases of truth, and consider them as distinct forces working to shape one final product, and as a convenient artifice it is legitimate. But it answers to no process actually occurring. Leibniz never surrendered his personal unity, and out of some one root-conception grew all his ideas. The principles of his times were not separate forces acting upon him, they were the foods of which he selected and assimilated such as were fitted to nourish his one great conception.
But it is more than a personal unity which holds together the thinking of a philosopher. There is the unity of the problem, which the philosopher has always before him, and in which all particular ideas find their unity. All else issues from this and merges into it. The various influences which we have seen affecting Leibniz, therefore, got their effectiveness from the relation which he saw them bear to the final problem of all thought. This is the inquiry after the unity of experience, if we look at it from the side of the subject; the unity of reality, if we put it from the objective side. Yet each age states this problem in its own way, because it sees it in the light of some difficulty which has recently arisen in consciousness. At one time, the question is as to the relation of the one to the many; at another, of the relation of the sensible to the intelligible world; at another, of the relation of the individual to the universal. And this last seems to have been the way in which it specifically presented itself to Leibniz. This way of stating it was developed, though apparently without adequate realization of its meaning, by the philosophy of scholasticism. It stated the problem as primarily a logical question,—the relation of genera, of species, of individuals to each other. And the school-boy, made after the stamp of literary tradition, knows that there were two parties among the Schoolmen,—the Realists, and the Nominalists; one asserting, the other denying, the objective reality of universals. To regard this discussion as useless, is to utter the condemnation of philosophy, and to relegate the foundation of science to the realm of things not to be inquired into. To say that it is an easy matter to decide, is to assume the decision with equal ease of all the problems that have vexed the thought of humanity. To us it seems easy because we have bodily incorporated into our thinking the results of both the realistic and the nominalistic doctrines, without attempting to reconcile them, or even being conscious of the necessity of reconciliation. We assert in one breath that the individual is alone real, and in the next assert that only those forms of consciousness which represent something in the universe are to be termed knowledge. At one moment we say that universals are creations of the individual mind, and at the next pass on to talk of laws of nature, or even of a reign of law. In other words, we have learned to regard both the individual and the universal as real, and thus ignoring the problem, think we have solved it.
But to Leibniz the problem presented itself neither as a logical question, nor yet as one whose solution might be taken for granted. On the contrary, it was just this question: How shall we conceive the individual to be related to the universe? which seemed to him to be the nerve of the philosophic problem, the question whose right answer would solve the problems of religion, of morals, of the basis of science, as well as of the nature of reality. The importance of just this way of putting the question had been rendered evident by the predecessors and contemporaries of Leibniz, especially by Descartes, Spinoza, and Locke. His more specific relations to the last-named will occupy us hereafter; at present we must notice how the question stood at the hands of Descartes and Spinoza.
Descartes had separated the individual from the universal. His philosophy began and ended with a dualism. I have just said that the problem of philosophy is the unity of experience. Yet we find that there have been thinkers, and those of the first rank, who have left the matter without discovering any ultimate unity, or rather who have made it the burden of their contention that we cannot explain the world without at least two disparate principles. But if we continue to look at the matter in this historical way, we shall see that this dualism has always been treated by the successors of such a philosopher, not as a solution, but as a deeper statement of the problem. It is the function of dualistic philosophies to re-state the question in a new and more significant way. There are times when the accepted unity of thought is seen to be inadequate and superficial. Men are thrashing old straw, and paying themselves with ideas which have lost their freshness and their timeliness. There then arises a philosopher who goes deep, beyond the superficial unity, and who discovers the untouched problem. His it is to assert the true meaning of the question, which has been unseen or evaded. The attitude of dualism is thus always necessary, but never final. Its value is not in any solution, but in the generality and depth of the problem which it proposes,