Germany were comparative barbarism. Molière was still alive, and Racine was at the summit of his glory. Leibniz became acquainted with Arnaud, a disciple of Descartes, who initiated him into the motive and spirit of his master. Cartesianism as a system, with its scientific basis and its speculative consequences, thus first became to him an intellectual reality. And, perhaps most important of all, he met Huygens, who became his teacher and inspirer both in the higher forms of mathematics and in their application to the interpretation and expression of physical phenomena. His diplomatic mission took him also to London, where the growing world of mathematical science was opened yet wider to him. The name of Sir Isaac Newton need only be given to show what this meant. From this time one of the greatest glories of Leibniz’s life dates—a glory, however, which during his lifetime was embittered by envy and unappreciation, and obscured by detraction and malice—the invention of the infinitesimal calculus. It would be interesting, were this the place, to trace the history of its discovery—the gradual steps which led to it, the physical facts as well as mathematical theories which made it a necessity; but it must suffice to mention that these were such that the discovery of some general mode of expressing and interpreting the newly discovered facts of Nature was absolutely required for the further advance of science, and that steps towards the introduction of the fundamental ideas of the calculus had already been taken—notably by Keppler, by Cavalieri, and by Wallis. It would be interesting to follow also the course of the controversy with Newton—a controversy which in its method of conduct reflects no credit upon the names of either. But this can be summed up by saying that it is now generally admitted that absolute priority belongs to Newton, but that entire independence and originality characterize none the less the work of Leibniz, and that the method of approach and statement of the latter are the more philosophical and general, and, to use the words of the judicious summary of Merz, “Newton cared more for the results than the principle, while Leibniz was in search of fundamental principles, and anxious to arrive at simplifications and generalizations.”
The death of Boineburg removed the especial reasons for the return of Leibniz to Frankfurt, and in 1676 he accepted the position of librarian and private councillor at the court of Hanover. It arouses our interest and our questionings to know that on his journey back he stopped at the Hague, and there met face to face the other future great philosopher of the time, Spinoza. But our questionings meet no answer. At Hanover, the industries of Leibniz were varied. An extract from one of his own letters, though written at a somewhat later date, will give the best outline of his activities.
“It is incredible how scattered and divided are my occupations. I burrow through archives, investigate old writings, and collect unprinted manuscripts, with a view to throwing light on the history of Brunswick. I also receive and write a countless number of letters. I have so much that is new in mathematics, so many thoughts in philosophy, so many literary observations which I cannot get into shape, that in the midst of my tasks I do not know where to begin, and with Ovid am inclined to cry out: ‘My riches make me poor.’ I should like to give a description of my calculating-machine; but time fails. Above all else I desire to complete my Dynamics, as I think that I have finally discovered the true laws of material Nature, by whose means problems about bodies which are out of reach of rules now known may be solved. Friends are urging me to publish my Science of the Infinite, containing the basis of my new analysis. I have also on hand a new Characteristic, and many general considerations about the art of discovery. But all these works, the historical excepted, have to be done at odd moments. Then at the court all sorts of things are expected. I have to answer questions on points in international law; on points concerning the rights of the various princes in the Empire: so far I have managed to keep out of questions of private law. With all this I have had to carry on negotiations with the bishops of Neustadt and of Meaux [Bossuet], and with Pelisson and others upon religious matters.”
It is interesting to note how the philosophic spirit, the instinct for unity and generality, showed itself even in the least of Leibniz’s tasks. The Duke of Brunswick imposed upon Leibniz the task of drawing up a genealogical table of his House. Under Leibniz’s hands this expanded into a history of the House, and this in turn was the centre of an important study of the German Empire. It was impossible that the philosopher, according to whom every real being reflected the whole of the universe from its point of view, should have been able to treat even a slight phase of local history without regarding it in its relations to the history of the world. Similarly some mining operations in the Harz Mountains called the attention of Leibniz to geological matters. The result was a treatise called “Protogäa,” in which Leibniz gave a history of the development of the earth. Not content with seeing in a Brunswick mountain an epitome of the world’s physical formation, it was his intention to make this an introduction to his political history as a sort of geographical background and foundation. It is interesting to note that the historical studies of Leibniz took him on a three years’ journey, from 1687 to 1690, through the various courts of Europe—a fact which not only had considerable influence upon Leibniz himself, but which enabled him to give stimulus to scientific development in more ways and places than one.
His philosophical career as an author begins for the most part with his return to Hanover in 1690. This lies outside of the scope of the present chapter, but here is a convenient place to call attention to the fact that for Leibniz the multitude of his other duties was so great that his philosophical work was the work “of odd moments.” There is no systematic exposition; there are a vast number of letters, of essays, of abstracts and memoranda published in various scientific journals. His philosophy bears not only in form, but in substance, traces of its haphazard and desultory origin. Another point of interest in this connection is the degree to which, in form, at least, his philosophical writings bear the impress of his cosmopolitan life. Leibniz had seen too much of the world, too much of courts, for his thoughts to take the rigid and unbending form of geometrical exposition suited to the lonely student of the Hague. Nor was the regular progression and elucidation of ideas adapted to the later Germans, almost without exception university professors, suited to the man of affairs. There is everywhere in Leibniz the attempt to adapt his modes of statement, not only to the terminology, but even to the ideas, of the one to whom they are addressed. There is the desire to magnify points of agreement, to minimize disagreements, characteristic of the courtier and the diplomat. His comprehensiveness is not only a comprehensiveness of thought, but of ways of exposition, due very largely, we must think, to his cosmopolitan education. The result has been to the great detriment of Leibniz’s influence as a systematic thinker, although it may be argued that it has aided his indirect and suggestive influence, the absorption of his ideas by men of literature, by Goethe, above all by Lessing, and his stimulating effect upon science and philosophy. It is certain that the attempt to systematize his thoughts, as was done by Wolff, had for its result the disappearance of all that was profound and thought-exciting.
If his philosophy thus reflects the manner of his daily life, the occupations of the latter were informed by the spirit of his philosophy. Two of the dearest interests of Leibniz remain to be mentioned—one, the founding of academies; the other, the reconciling of religious organizations. The former testifies to his desire for comprehensiveness, unity, and organization of knowledge; the latter to his desire for practical unity, his dislike of all that is opposed and isolated. His efforts in the religions direction were twofold. The first was to end the theological and political controversies of the time by the reunion of the Protestant and Roman Catholic Churches. It was a plan which did the greatest honor to the pacific spirit of Leibniz, but it was predestined to failure. Both sides made concessions—more concessions than we of to-day should believe possible. But the one thing the Roman Catholic Church would not concede was the one thing which the Protestant Church demanded—the notion of authority and hierarchy. Indeed, it may be questioned whether the terms on which Leibniz conceived of their reunion do not point to the greatest weakness in his philosophy—the tendency to overlook oppositions and to resolve all contradiction into differences of degree. Hardly had this plan fallen through when Leibniz turned to the project of a union of the Lutheran and Reformed branches of the Protestant Church. This scheme was more hopeful, and while unrealized during the life of our philosopher, was afterwards accomplished.
It is noteworthy that even before Leibniz went to Paris and to London he had conceived the idea of a society of learned men for the investigation, the systematization, and the publication of scientific truth