LEIBNIZ, GOTTFRIED WILHELM (b. Leipzig, Germany, 1 July 1646; d. Hannover, Germany, 14 November 1716), mathematics, philosophy, metaphysics.

    scientific work. On the other hand, this broad interest, insofar as it remained oriented in architectonic principles, led to a concentration on methodological questions. In relation to the structure of a science, these are more important than concrete results. The position of Leibniz at the beginning of modern science is analogous to that of Aristotle at the beginning of ancient science. Leibniz' universality is comparable with that of Aristotle, different only in that it did not, as Aristotle's, remain grounded in essentially unchanged metaphysical distinctions but evolved by degrees from an encyclopedic multiplicity of interests. Consequently, in the strict sense in which there is an Aristotelian system, there is no Leibnizian system but rather a marked metaphysical and methodological concern that systematically expresses variations on the same theme in the various special fields (such as physics and logic) and underlies Leibniz' quest to establish a unified system of knowledge.

Leibniz' autobiographical statement in a letter to Rémond de Montmort in 1714 explains how, at the age of fifteen, though accepting the mechanical philosophy, his search for the ultimate grounds of mechanism led him to metaphysics and the doctrine of entelechies. This indicates the early orientation of Leibniz' thought towards the ideas of the Monadologie. Instead of setting out his philosophy systematically in a magnum opus, Leibniz presented piecemeal clarifications of his views in works that, in various ways, were inspired by the publications of others. After reading the papers of Huygens and Wren on collision and the Elementorum philosophiae of Hobbes, Leibniz composed his Hypothesis physica nova, consisting of two parts, Theoria motus abstracti and Theoria motus concreti, which in 1671 he presented respectively to the Paris Academy of Sciences and the London Royal Society. At this time, Leibniz owed more to Descartes, whose work he knew only at second hand, than he was later willing to admit. Closer study of the philosophy of Descartes led Leibniz to a more decisive rejection.

In 1686 he published in the Acta eruditorum a criticism of Descartes's measure of force, Brevis demonstratio erroris memorabilis Cartesii et aliorum circa legem naturae, which started a controversy with Catalan, Malebranche, and Papin lasting until 1691. Also in 1686 Leibniz sent to Arnauld, for his comments, an essay entitled Discours de métaphysique, in which he developed the ideas of the later Théodicée. The tracts entitled De lineis opticis, Schediasma de resistentia medii, and Tentamen de motuum coelestium causis, published in the Acta eruditorum in 1689, were hurriedly composed by Leibniz after he had read the review of Newton's Principia in the same journal, in an attempt to obtain some credit for results which he had derived independently of Newton. In 1692, at the instigation of Pelisson, Leibniz wrote an Essay de dynamique, which was read to the Paris Academy by Philippe de la Hire, and in 1695 there appeared in the Acta eruditorum an article entitled Specimen dynamicum, which contained the clearest exposition of Leibniz' dynamics.

Leibniz' Nouveaux essais sur l'entendement humain, completed in 1705 but not published during his lifetime, presented a detailed criticism of Locke's position. By adding nisi ipse intellectus to the famous maxim, Nihil est in intellectu quod non prius fuerit in sensu (wrongly attributed to Aristotle by Duns Scotus1), Leibniz neatly reversed the application of the principle by Locke. According to Leibniz, the mind originally contains the principles of the various ideas which the senses on occasion call forth.

In 1710 Leibniz published his Essais de Théodicée sur la bonté de Dieu, la liberté de l'homme et l'origine du mal, a work composed at the instigation of Sophia Charlotte, with whom Leibniz had conversed concerning the views of Bayle. In response to a request from Prince Eugene for an abstract of the Théodicée, Leibniz in 1714 wrote the Principes de la nature et de la grâce fondées en raison and the Monadologie. When in 1715 Leibniz wrote to Princess Caroline of Wales, criticizing the philosophical and theological implications of the work of Newton, she commissioned Samuel Clarke to reply. The ensuing correspondence, containing Leibniz' most penetrating criticism of Newtonian philosophy, was published in 1717.

Rational Physics (Protophysics).

In his efforts to clarify fundamental physical principles, Leibniz followed a plan which he called a transition from geometry to physics through a “science of motion that unites matter with forms and theory with practice.”2 He sought the metaphysical foundations of mechanics in an axiomatic structure. The Theoria motus abstracti3 offers a rational theory of motion whose axiomatic foundation (fundamenta praede-monstrabilia) was inspired by the indivisibles of Cavalieri and the notion of conatus proposed by Hobbes. Both the word conatus and the mechanical idea were taken from Hobbes,4 while the mathematical reasoning was derived from Cavalieri. After his invention of the calculus, Leibniz was able to replace Cavalieri's indivisibles by differentials and this enabled him to apply his theory of conatus to the solution of dynamical problems.

The concept of conatus provided for Leibniz a path of escape from the paradox of Zeno. Motion is continuous and therefore infinitely divisible, but if motion is real, its beginning cannot be a mere nothing.5 Conatus is a tendency to motion, a mind-like quality