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better. Weigel, a mathematician of some fame, an astronomer, a jurist, and a philosopher, taught there, and introduced Leibniz into the lower forms of analysis. But the Thirty Years’ War had not left Germany in a state of high culture, and in after years Leibniz lamented the limitations of his early mathematical training, remarking that if he had spent his youth in Paris, he would have enriched science earlier. By 1666 Leibniz had finished his university career, having in previous years attained the degrees of bachelor of philosophy and master of philosophy. It is significant that for the first he wrote a thesis upon the principle of individuation,—the principle which in later years became the basis of his philosophy. This early essay, however, is rather an exhibition of learning and of dexterity in handling logical methods than a real anticipation of his afterthought.
For his second degree, he wrote a thesis upon the application of philosophic ideas to juridic procedure,—considerations which never ceased to occupy him. At about the same time appeared his earliest independent work, “De Arte Combinatoria.” From his study of mathematics, and especially of algebraic methods, Leibniz had become convinced that the source of all science is,—first, analysis; second, symbolic representation of the fundamental concepts, the symbolism avoiding the ambiguities and vagueness of language; and thirdly, the synthesis and interpretation of the symbols. It seemed to Leibniz that it ought to be possible to find the simplest notions in all the sciences, to discover general rules for calculating all their varieties of combination, and thus to attain the same certainty and generality of result that characterize mathematics. Leibniz never gave up this thought. Indeed, in spirit his philosophy is but its application, with the omission of symbols, on the side of the general notions fundamental to all science. It was also the idea of his age,—the idea that inspired Spinoza and the Aufklärung, the idea that inspired philosophical thinking until Kant gave it its death-blow by demonstrating the distinction between the methods of philosophy and of mathematical and physical science.
In 1666 Leibniz should have received his double doctorate of philosophy and of law; but petty jealousies and personal fears prevented his presenting himself for the examination. Disgusted with his treatment, feeling that the ties that bound him to Leipzig were severed by the recent death of his mother, anxious to study mathematics further, and, as he confesses, desiring, with the natural eagerness of youth, to see more of the world, he left Leipzig forever, and entered upon his Wanderjahre. He was prepared to be no mean citizen of the world. In his education he had gone from the historians to the poets, from the poets to the philosophers and the Scholastics, from them to the theologians and Church Fathers; then to the jurists, to the mathematicians, and then again to philosophy and to law.
He first directed his steps to the University of Altdorf; here he obtained his doctorate in law, and was offered a professorship, which he declined,—apparently because he felt that his time was not yet come, and that when it should come, it would not be in the narrow limits of a country village. From Altdorf he went to Nürnberg; here all that need concern us is the fact that he joined a society of alchemists (fraternitas roseæcrucis), and was made their secretary. Hereby he gained three things,—a knowledge of chemistry; an acquaintance with a number of scientific men of different countries, with whom, as secretary, he carried on correspondence; and the friendship of Boineburg, a diplomat of the court of the Elector and Archbishop of Mainz. This friendship was the means of his removing to Frankfurt. Here, under the direction of the Elector, he engaged in remodelling Roman law so as to adapt it for German use, in writing diplomatic tracts, letters, and essays upon theological matters, and in editing an edition of Nizolius,—a now forgotten philosophical writer. One of the most noteworthy facts in connection with this edition is that Leibniz pointed out the fitness of the German language for philosophical uses, and urged its employment,—a memorable fact in connection with the later development of German thought. Another important tract which he wrote was one urging the alliance of all German States for the purpose of advancing their internal and common interests. Here, as so often, Leibniz was almost two centuries in advance of his times. But the chief thing in connection with the stay of Leibniz at Mainz was the cause for which he left it. Louis XIV. had broken up the Triple Alliance, and showed signs of attacking Holland and the German Empire. It was then proposed to him that it would be of greater glory to himself and of greater advantage to France that he should move against Turkey and Egypt. The mission of presenting these ideas to the great king was intrusted to Leibniz, and in 1672 he went to Paris.
The plan failed completely,—so completely that we need say no more about it. But the journey to Paris was none the less the turning-point in the career of Leibniz. It brought him to the centre of intellectual civilization,—to a centre compared with which the highest attainments of disrupted and disheartened 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