But the Vasco de Gama of his day was Leibnitz. His triumphant optimism rounded the Cape of theological Good Hope. He gave the chief impulse to modern intellectual commerce. Full freighted, as he was, with Western thought, he revived the forgotten interest in the Old and Eastern World, and brought the ends of the earth together. Circumnavigator of the realms of mind, wherever he touched, he appeared as discoverer, as conqueror, as lawgiver. In mathematics, he discovered or invented the Differential Calculus,—the logic of transcendental analysis, the infallible method of astronomy, without which it could never have compassed the large conclusions of the "Mecanique Celeste." In his "Protogaea," published in 1693, he laid the foundation of the science of Geology. From his observations, as Superintendent of the Hartz Mines, and those which he made in his subsequent travels through Austria and Italy,—from an examination of the layers, in different localities, of the earth's crust, he deduced the first theory, in the geological sense, which has ever been propounded, of the earth's formation. Orthodox Lutheran as he was, he braved the theological prejudices which then, even more than now, affronted scientific inquiry in that direction. "First among men," says Flourens, "he demonstrated the two agencies which successively have formed and reformed the globe,—fire and water." In the region of metaphysical inquiry, he propounded a new and original theory of Substance, and gave to philosophy the Monad, the Law of Continuity, the Preëstablished Harmony, and the Best Possible World.
Born at Leipzig, in 1646,—left fatherless at the age of six years,— by the care of a pious mother and competent guardians, young Leibnitz enjoyed such means of education as Germany afforded at that time, but declares himself, for the most part, self-taught [6].
[Footnote 6: "Duo, ihi profuere mirifice, (quae tamen alioqui ambigna, et pluribus noxia esse solent,) primum quod fere essem [Greek: autodidaktos], alterum quod quaererem nova in unaquaque scientia." —LEIBNIT. Opera Philosoph. Erdmann. p. 162.]
So genius must always be, for want of any external stimulus equal to its own impulse. No normal training could keep pace with his abnormal growth. No school discipline could supply the fuel necessary to feed the consuming fire of that ravenous intellect. Grammars, manuals, compends,—all the apparatus of the classes,— were only oil to its flame. The Master of the Nicolai-Schule in Leipzig, his first instructor, was a steady practitioner of the Martinet order. The pupils were ranged in classes corresponding to their civil ages,—their studies graduated according to the baptismal register. It was not a question of faculty or proficiency, how a lad should be classed and what he should read, but of calendar years. As if a shoemaker should fit his last to the age instead of the foot. Such an age, such a study. Gottfried is a genius, and Hans is a dunce; but Gottfried and Hans were both born in 1646; consequently, now, in 1654, they are both equally fit for the Smaller Catechism. Leibnitz was ready for Latin long before the time allotted to that study in the Nicolai-Schule, but the system was inexorable. All access to books cut off by rigorous proscription. But the thirst for knowledge is not easily stifled, and genius, like love, "will find out his way."
He chanced, in a corner of the house, to light on an odd volume of Livy, left there by some student boarder. What could Livy do for a child of eight years, with no previous knowledge of Latin, and no lexicon to interpret between them? For most children, nothing. Not one in a thousand would have dreamed of seriously grappling with such a mystery. But the brave Patavinian took pity on our little one and yielded something to childish importunity. The quaint old copy was garnished, according to a fashion of the time, with rude wood-cuts, having explanatory legends underneath. The young philologer tugged at these until he had mastered one or two words. Then the book was thrown by in despair as impracticable to further investigation. Then, after one or two weeks had elapsed, for want of other employment, it was taken up again, and a little more progress made. And so by degrees, in the course of a year, a considerable knowledge of Latin had been achieved. But when, in the Nicolai order, the time for this study arrived, so far from being pleased to find his instructions anticipated, or welcoming such promise of future greatness,—so far from rejoicing in his pupil's proficiency, the pedagogue chafed at the insult offered to his system by this empiric antepast. He was like one who suddenly discovers that he is telling an old story where he thought to surprise with a novelty; or like one who undertakes to fill a lamp, which, being (unknown to him) already full, runs over, and his oil is spilled. It was "oleum perdidit" in another sense than the scholastic one. Complaint was made to the guardians of the orphan Gottfried of these illicit visits to the tree of knowledge. Severe prohibitory measures were recommended, which, however, judicious counsel from another quarter happily averted.
At the age of eleven, Leibnitz records, that he made, on one occasion, three hundred Latin verses without elision between breakfast and dinner. A hundred hexameters, or fifty distichs, in a day, is generally considered a fair pensum for a boy of sixteen at a German gymnasium.
At the age of seventeen, he produced, as an academic exercise, on taking the degree of Bachelor of Philosophy, his celebrated treatise on the Principle of Individuality, "De Principle Individui," the most extraordinary performance ever achieved by a youth of that age,— remarkable for its erudition, especially its intimate knowledge of the writings of the Schoolmen, and equally remarkable for its vigorous grasp of thought and its subtile analysis. In this essay Leibnitz discovered the bent of his mind and prefigured his future philosophy, in the choice of his theme, and in his vivid appreciation and strenuous positing of the individual as the fundamental principle of ontology. He takes Nominalistic ground in relation to the old controversy of Nominalist and Realist, siding with Abelard and Roscellin and Occam, and against St. Thomas and Duns Scotus. The principle of individuation, he maintains, is the entire entity of the individual, and not mere limitation of the universal, whether by "Existence" or by "Haecceity." [7] John and Thomas are individuals by virtue of their integral humanity, and not by fractional limitation of humanity. Dobbin is an actual positive horse (Entitas tota). Not a negation, by limitation, of universal equiety (Negatio). Not an individuation, by actual existence, of a non-existent but essential and universal horse (Existentia). Nor yet a horse only by limitation of kind,—a horse minus Dick and Bessie and the brown mare, etc. (Haecceitas). But an individual horse, simply by virtue of his equine nature. Only so far as he is an actual complete horse, is he an individual at all. (Per quod quid est, per id unum numero est.) His individuality is nothing superadded to his equiety. (Unum supra ens nihil addit reale.) Neither is it anything subtracted therefrom. (Negatio non potest producere accidentia individualia.) In fine, there is and can be no horse but actual individual horses. (Essentia et existentia non possunt separari.)
[Footnote 7: "Aut enim principium individuationis ponitur entitas tota, (1) aut non tota. Non totam aut negatio exprimit, (2) aut aliquid positivum. Positivum aut pars physica est, essentiam terminaus, existentia, (3) aut metaphysica, speciem terminans, haec ceitas. (4)… Pono igitur: omne individuum sua tota entitate individuatur." —De Princ. Indiv. 3 et 4.]
This was the doctrine of the Nominalists, as it was of Aristotle before them. It was the doctrine of the Reformers, except, if we remember rightly, of Huss. The University of Leipzig was founded upon it. It is the current doctrine of the present day, and harmonizes well with the current Materialism. Not that Nominalism in itself, and as Leibnitz held it, is necessarily materialistic, but Realism is essentially antimaterialistic. The Realists held with Plato,—but not in his name, for they, too, claimed to be Aristotelian, and preëminently so,—that the ideal must precede the actual. So far they were right. This was their strong point. Their error lay in claiming for the ideal an objective reality, an independent being. Conceptualism was only another statement of Nominalism, or, at most, a question of the relation of language to thought. It cannot be regarded as a third issue in this controversy,— a controversy in which more time was consumed, says John of Salisbury, "than the Caesars required to make themselves masters of the world," and in which the combatants, having spent at last their whole stock of dialectic ammunition, resorted to carnal weapons, passing suddenly, by a very illogical metabasis, from "universals" to particulars. Both parties appealed to Aristotle. By a singular fortune, a pagan philosopher, introduced into Western Europe by Mohammedans, became the supreme authority of the Christian world. Aristotle was the Scripture of the Middle Age. Luther found this authority in his way and disposed of it in short order, devoting Aristotle without ceremony to the Devil, as "a damned mischief-making heathen." But Leibnitz, whose large discourse looked before as well as after, reinstated not only Aristotle, but Plato, and others of the Greek philosophers, in their former repute;—"Car ces anciens," he said, "étaient plus solides qu'on ne croit." He was the first to turn the tide of popular opinion in their favor.
Not without a struggle was he brought to side with the Nominalists. Musing, when a boy, in the Rosenthal, near Leipzig, he debated long with himself,—"Whether he would give up the Substantial Forms of the Schoolmen." Strange matter for boyish deliberation! Yes, good youth, by all means, give them up! They have had their day. They served to amuse the imprisoned intellect of Christendom in times of ecclesiastical thraldom, when learning knew no other vocation. But the age into which you are born has its own problems, of nearer interest and more commanding import. The measuring-reed of science is to be laid to the heavens, the solar system is to be weighed in a balance; the age of logical quiddities has passed, the age of mathematical quantities has come. Give them up! You will soon have enough to do to take care of your own. What with Dynamics and Infinitesimals, Pasigraphy and Dyadik, Monads and Majesties, Concilium Ægyptiacum and Spanish Succession and Hanoverian cabals, there will be scant room in that busy brain for Substantial Forms. Let them sleep, dust to dust, with the tomes of Duns Scotus and the bones of Aquinas!