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- Georges-Louis Leclerc, count de Buffon
George Berkeley , in a tract called The Analyst and elsewhere, ridiculed this and other aspects of the early calculus, pointing out that natural science grounded in the calculus required just as big of a leap of faith as theology grounded in Christian revelation. Modern calculus emerged in the nineteenth century, and banished infinitesimals into the wilderness of obsolete mathematics although engineers, physicists, and economists continued to use them. But beginning in , Abraham Robinson showed how to make sense of Leibniz's infinitesimals, and how to give them algebraic properties free of paradox.
The resulting nonstandard analysis can be seen as a great belated triumph of Leibniz's mathematical and ontological intuition. From until his death, Leibniz's life was envenomed by a long dispute with John Keill, Newton, and others, over whether Leibniz had invented the calculus independently of Newton, or whether he had merely invented another notation for ideas that were fundamentally Newton's. Today, the predominant view is that Newton developed his calculus first, then mentioned to Leibniz several things that his new method could accomplish without specifying anything about the method itself.
Leibniz took this cue to develop his own calculus, which he published quickly, perhaps with less-than-admirable motives. Leibniz wrote in three languages: scholastic Latin, French, and least often German. During his lifetime, he published many pamphlets and scholarly articles, but relatively little philosophy.
Only one substantial book appeared posthumously, his Nouveaux essais sur l'entendement humain a response to John Locke's Essay Concerning Human Understanding. Only in , when Bodemann completed his catalogs of Leibniz's manuscripts and correspondence, did the enormous extent of Leibniz's Nachlass become clear: about 15, letters to more than one thousand recipients plus more than 40, other items. Moreover, quite a few of these letters are of essay length.
Much of his vast correspondence, especially the letters dated after , remains unpublished, and much of what is published has been so only in recent decades. The amount, variety, and disorder of Leibniz's writings are a predictable result of a situation he described as follows:. I cannot tell you how extraordinarily distracted and spread out I am.
I am trying to find various things in the archives; I look at old papers and hunt up unpublished documents. From these I hope to shed some light on the history of the [House of] Brunswick. I receive and answer a huge number of letters. At the same time, I have so many mathematical results, philosophical thoughts, and other literary innovations that should not be allowed to vanish that I often do not know where to begin.
Revision of translation in Mates The extant parts of the critical edition of Leibniz's writings are organized as follows:. Some of these volumes, along with work in progress, are available online, for free. Even though work on this edition began in , only 22 volumes had appeared by , in part because the only additions between and were four volumes in Series 1. When Leibniz died, his reputation was in decline.
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Leibniz had an ardent disciple, Christian Wolff , who briefly generated much enthusiasm for 'Leibnizian-Wolffian' philosophy, only to become a principal target of Kant. Much of Europe came to doubt that Leibniz had invented the calculus independently of Newton, and much of his whole work in mathematics and physics was neglected.
His work on law, diplomacy, and history was seen as of ephemeral interest. The vastness and richness of his correspondence went unsuspected. Leibniz's long march to his present glory began with the publication of the Nouveaux Essais , which Kant read closely. In Dutens edited the first multi-volume edition of Leibniz's writings, followed in the nineteenth century by a number of editions, including those edited by Erdmann, Foucher de Careil, Gerhardt, Gerland, Klopp, and Mollat.
Publication of Leibniz's correspondence with notables such as Antoine Arnauld , Sophia of Hanover, and her daughter Sophia Charlotte of Hanover, began. In , Bertrand Russell published a study of Leibniz's metaphysics. Shortly thereafter, Louis Couturat published an important study of Leibniz, and edited a volume of Leibniz's heretofore-unpublished writings, mainly on logic.
While their conclusions have been debated, they made Leibniz respectable among twentieth-century analytical and linguistic philosophers. With analytic philosophy's renewed interest in metaphysics in the s and s, Leibniz's work has received more and more attention. There are at least three challenges in developing a plausible summary of Leibniz's philosophy. First, unlike nearly every other figure in early modern philosophy, Leibniz left no single philosophical work that can be taken as the definite expression of his main thought.
Second, Leibniz's views appear differently in different places, not only because of the development of his thought, but also because he often tailored his writings to his audience. Finally, there is the fact of the vastness of the Leibnizian corpus, which is, for all intents and purposes, simply too large for any one person to adequately survey. Despite these challenges, certain themes are particularly noteworthy, both because they recur in what seem to be Leibniz's main philosophical works, and because of their distinctive influence on later philosophers.
Unlike Descartes and Spinoza , Leibniz had a thorough university education in ancient and scholastic philosophy , one which he took seriously.
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His writings show his desire to find some element of truth in each of the various positions. Whereas the Cartesians were eager to abandon the Aristotelian notion of forms, Leibniz attempted to integrate talk of forms into a metaphysics derived from that of Descartes. Leibniz is probably the most important logician between Aristotle and , when George Boole and Augustus De Morgan each published books that began modern formal logic.
Leibniz enunciated the principal properties of what we now call conjunction, disjunction, negation, identity, set, inclusion, and the empty set. He also provided some groundwork for what would become epistemic and modal logic. Yet Leibniz's vision of logic was far grander than that of any modern logician; perhaps grander than that of any other figure in the history of philosophy.
Leibniz had a remarkable faith that a great deal of human reasoning could be reduced to calculations of a sort, and that such calculations could resolve many differences of opinion:. The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate [ calculemus ], without further ado, to see who is right. The Art of Discovery , W He proposed the creation of a characteristic universalis or "universal characteristic," built on an alphabet of human thought in which each fundamental concept would be represented by a unique "real" character.
It is obvious that if we could find characters or signs suited for expressing all our thoughts as clearly and as exactly as arithmetic expresses numbers or geometry expresses lines, we could do in all matters insofar as they are subject to reasoning all that we can do in arithmetic and geometry.
For all investigations which depend on reasoning would be carried out by transposing these characters and by a species of calculus. Preface to the General Science , Revision of Rutherford's translation in Jolley , Also W I. More complex thoughts would be represented by combining in some way the characters for simpler thoughts. Leibniz saw that the uniqueness of prime factorization suggests a central role for prime numbers in the universal characteristic. An example of what Leibniz envisioned is as follows: say that the concept 'man' is composed of the more simple concepts 'rational' and 'animal.
By multiplying these together, we get a number for 'man': If one later wanted to know whether men were animals, all one would have to do is to find whether the number for the later was a factor of the former. Leibniz envisioned such a means of evaluating the truth of propositions as extending to much more contentious propositions, and thus as a promising means for resolving disputes. Of course, matters would become much more complex with more complex concepts, and one can see Leibniz's interests in establishing academies and developing calculating machines as aimed in this direction.
Much of Leibniz's philosophy makes use of two logical-metaphysical principles whose names he coined. Though these principles are present in earlier philosophers, Leibniz makes the most explicit use of them of anyone up to his time.
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Leibniz's best known contribution to metaphysics is his theory of monads, as exposited in his Monadology. Roughly speaking, monads are to the mental realm what atoms were seen as being to the physical. While making use of the analogy with atoms, however, Leibniz argued that matter was infinitely divisible, and so denied that physical atoms exist Leibniz in fact sometimes argued first that there must be monads, and then established that such monads could not be extended.
Monads, along with God, are the ultimate elements of the universe. The monads are "substantial forms of being" with the following properties: they are eternal, indecomposable, individual, active, subject to their own laws, causally independent of one another, and each reflecting the entire universe in a pre-established harmony. The ontological essence of a monad is its irreducible simplicity.
Unlike extended substances as conceived by Descartes, monads possess no material or spatial character. They also differ from Cartesian extended substance by their complete mutual independence, so that interactions among monads are only apparent. Instead, by virtue of the principle of pre-established harmony see below , every modification of any monad in the universe was matched by some corresponding modification in every other monad in the universe. Each monad can then be said to 'mirror' the entire universe. Leibniz believed that each monad was metaphysically independent of everything else in the universe, save God.
This independence is both ontological and causal. As long as God continues to preserve it, any particular monad could continue to exist while all others are destroyed. Further, no monad is capable of causally affecting another monad, or being affected. Such a view raises an obvious question: if as Leibniz held my mind and body are both monads, why is it that they appear to affect each other.
For instance, when I choose to raise my arm, my arm lifts, and when I jam my toe, I experience a certain sensation. Descartes had explained such correlations in terms of genuine causal interaction via the pineal gland. Many of Descartes' successors found such interaction unintelligible, though, and by Leibniz's time the main alternative was the occasionalist view most prominently advanced by Malebranche. Occasionalism held that, in all such cases, the causal force came directly from God. Leibniz, however, claimed that occasionalism made causation unacceptably mysterious, with the universe filled with 'miracles.
On this basis, he formulated an alternative he dubbed 'pre-established harmony.
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Throughout its existence, then, its changes were merely the result of the unfolding of its nature. Original: Le Clerc, Jean. Modern reprint: Le Clerc, Jean. Geneve: Slatkine Reprints. The two works are available in the Eighteenth Century Collections Online database. Please note that access to the database is proprietary. Ballard, G. Evans, in the Strand, Near York-Buildings.
Boyer, Abel. Year the Third. London: printed for A. Roper, at the Black Boy against St. Hathi Trust Duke University original. Hathi Trust Princeton University original. Ballard, George, and Ruth Perry, editors.
Georges-Louis Leclerc, count de Buffon
Detroit: Wayne State University Press. The following is an attempt to identify a complete list of references pertaining to Masham to date. London: Batsford. Atherton, Margaret.