Article abstract: Though never employed as an academic philosopher, Leibniz was one of the greatest intellectuals of his day: He was a metaphysician, theologian, philologist, historian, genealogist, poet, inventor, scientist, mathematician, logician, lawyer, and diplomat. He contributed to the development of rationalist philosophy, and he also corresponded with or personally knew virtually every major European thinker in every field of inquiry.
Gottfried Wilhelm Leibniz was born into an academic family; his mother’s father was a professor, as was his own father (who died when Leibniz was six). Leibniz was intellectually gifted; he taught himself Latin and read profusely in the classics at an early age. When he was an adolescent, Leibniz began to entertain the notion of constructing an alphabet of human thought from which he could generate a universal, logically precise language. He regarded this language as consisting of primitive simple words expressing primitive simple concepts which are then combined into larger language complexes expressing complex thoughts. His obsession with this project played an important role throughout his life.
Leibniz was formally educated at the University of Leipzig, where he received his bachelor’s and master’s degrees for theses on jurisprudence, and at the University of Altdorf, where he received the doctorate in law in 1666. He declined a professorship at Altdorf and entered employment as secretary of the Rosicrucian Society. Eventually he was employed as a legal counsel by Johann Philipp von Schönborn, a governing official of Mainz.
Leibniz’s philosophy was rationalist. According to this theory, human knowledge has its origins in the fundamental laws of thought instead of in human experience of the world as in the doctrine of empiricism. In fact, Leibniz argued that the laws of science could be deduced from fundamental metaphysical principles and that observation and empirical work were not necessary for arriving at knowledge of the world. What was needed instead was a proper method of calculating or demonstrating everything contained in certain fundamental tenets. For example, he believed that he could deduce the fundamental laws of motion from more basic metaphysical principles. In this general conception, he followed in the intellectual footsteps of René Descartes. The great problem with interpreting Leibniz’s contribution to this tradition of thought is that he published only one major book during his lifetime, and it does not contain a systematic account of his full philosophy. Accordingly, it is necessary to reconstruct his system from the short articles and the more than fifteen thousand letters which he wrote.
Leibniz’s youthful dreams of constructing a perfect language quickly evolved into a theory of necessary and contingent propositions. He claimed that in every true affirmation the predicate is contained in the subject. This idea evolved from his conception of a perfect language which (in all of its true, complex statements) would perfectly reflect the universe. The true propositions of this language are necessarily true, and all necessary propositions are, according to Leibniz, ultimately reducible to identity statements. Such a conception was more plausible in the case of purely mathematical statements since, for example, “4 = 2 + 2” can be equated with “4 = 4.” Yet this conception seemed impossible in the case of contingent statements; for example, in “the house is blue.” Leibniz avoided this problem by arguing that the necessity in what appears as contingent truths can be revealed (or resolved) only through an infinite analysis and therefore can be carried out in full only by God. It follows that, for humans, all contingent truths are only more or less probably true. Such truths are guaranteed by the principle of sufficient reason, which states that there must be some reason for whatever is the case. Necessary truths, or truths of reason, on the other hand, are guaranteed by the principle of contradiction, which states that the denial of such a truth is a contradiction (though this can be known only by God). A logical principle closely related to the principle of sufficient reason is the notion of the “identity of indiscernibles,” now known as Leibniz’s law. This principle states that it is impossible for two things to differ only numerically, that is, to be distinct yet have no properties that differ; if two things are distinct, there must be some reason for their distinctness.
Leibniz had elaborated the rudiments of his metaphysical system while at Mainz, but it was during his sojourn in Paris that his philosophy matured. In 1672, he was sent to Paris on a diplomatic mission for the German princes to persuade Louis XIV to cease military activities in Europe and send forces to the Middle East. Leibniz remained in Paris for four years, and, though he failed to even gain an audience with the monarch, he met frequently with the greatest minds of the day, such as Christiaan Huygens, Nicolas de Malebranche, Antoine Arnauld, and Simon Foucher. He also carried out studies of the mathematics of Blaise Pascal and René Descartes and actually built one of the first computers—a calculating machine able to multiply very large numbers. While residing in Paris, he also made a brief trip to England, where he met with Robert Boyle and visited the Royal Society, to which he was elected.
When he returned to Hanover, he accepted a post as director of the library to John Frederick, the Duke of Brunswick, where he remained for the next ten years. It was only after working with Huygens in Paris on the nature of motion that Leibniz finally came to grips with the problem of the continuum. On his return trip from Paris, during which he visited Baruch Spinoza in Holland, he composed “Pacidius Philalethi” (1676), an extended analysis of this subject. This issue is traced back to the ancient Greeks and concerns the problem of resolving the motion of an object into its motions over discrete parts of space. If the body must pass through each successive parcel of space between two points, then it can never get from one point to another, since there are an infinity of such discrete parcels between any two points. It was in the context of this problem of motion and the continuum that Leibniz developed, in 1676, the differential calculus, publishing his results in 1684. Sir Isaac Newton had already discovered the calculus but did not publish his results until 1693, several years after Leibniz published his discoveries. Priority of discovery is accorded to Newton though the consensus now is that they arrived at the calculus independently.
Leibniz argued that Cartesian physics renders motion ultimately inexplicable on the basis of fundamental concepts, since it is grounded in the notion...
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