1661 the boy Leibniz, fifteen years old, entered the University of Leipzig. If we glance back upon his attainments, we find him thoroughly at home in Latin, having made good progress in Greek, acquainted with the historians and poets of antiquity, acquainted with the contemporary range of science, except in mathematics and physics, deeply read and interested in ancient and scholastic philosophy and in the current theological discussions. Of himself he says:—
“Two things were of extraordinary aid to me: in the first place, I was self-taught; and in the second, as soon as I entered upon any science I sought for something new, even though I did not as yet thoroughly understand the old. I thus gained two things: I did not fill my mind with things empty and to be unlearned afterwards—things resting upon the assertion of the teacher, and not upon reason; and secondly, I never rested till I got down to the very roots of the science and reached its principles.”
While there is always a temptation to force the facts which we know of a man’s early life, so as to make them seem to account for what appears in mature years, and to find symbolisms and analogies which do not exist, we are not going astray, I think, if we see foreshadowed in this early education of Leibniz the two leading traits of his later thought—universality and individuality. The range of Leibniz’s investigations already marks him as one who will be content with no fundamental principle which does not mirror the universe. The freedom with which he carried them on is testimony to the fact that even at this age the idea of self-development, of individual growth from within, was working upon him. In the fact, also, that he was self-taught we find doubtless the reason that he alone of the thinkers of this period did not have to retrace his steps, to take a hostile attitude towards the ideas into which he was educated, and to start anew upon a foundation then first built. The development of the thought of Leibniz is so gradual, continuous, and constant that it may serve as a model of the law by which the “monad” acts. Is not his early acquaintance with ancient literature and mediæval philosophy the reason that he could afterwards write that his philosophical system “connects Plato with Democritus, Aristotle with Descartes, the Scholastics with the moderns, theology and morals with reason”? And who can fail to see in the impartiality, the comprehensiveness, of his self-education the prophecy of the time when he can write of his ideas that “there are united in them, as in a 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
