centre of perspective, the ideas of the Sceptics in attributing to sensible things only a slight degree of reality; of the Pythagoreans and Platonists, who reduce all to harmonies, numbers, and ideas; of Parmenides and Plotinus, with their One and All; of the Stoics, with their notion of necessity, compatible with the spontaneity of other schools; of the vital philosophy of the Cabalists, who find feeling everywhere; of the forms and entelechies of Aristotle and the Schoolmen, united with the mechanical explanation of phenomena according to Democritus and the moderns”?
But we must hurry along over the succeeding years of his life. In the university the study of law was his principal occupation, as he had decided to follow in the footsteps of his father. It cannot be said that the character of the instruction or of the instructors at Leipzig was such as to give much nutriment or stimulus to a mind like that of Leibniz. He became acquainted there, however, with the Italian philosophy of the sixteenth century,—a philosophy which, as formulated by Cardanus and Campanella, formed the transition from Scholastic philosophy to the “mechanical” mode of viewing the universe. He had here also his first introduction to Descartes. The consequences of the new vision opened to Leibniz must be told in his own words: “I was but a child when I came to know Aristotle; even the Scholastics did not frighten me; and I in no way regret this now. Plato and Plotinus gave me much delight, not to speak of other philosophers of antiquity. Then I fell in with the writings of modern philosophy, and I recall the time when, a boy of fifteen years, I went walking in a little wood near Leipzig, the Rosenthal, in order to consider whether I should hold to the doctrine of substantial forms. Finally the mechanical theory conquered, and thus I was led to the study of the mathematical sciences.”
To the study of the mathematical sciences! Surely words of no mean import for either the future of Leibniz or of mathematics. But his Leipzig studies did not take him very far in this new direction. Only the elements of Euclid were taught there, and these by a lecturer of such confused style that Leibniz seems alone to have understood them. In Jena, however, where he went for a semester, things were somewhat 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
