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

    virtual motion, Leibniz explains, the force is as the velocity but when the body has acquired a finite velocity and the force has become live, it is as the square of the velocity. As Leibniz remarked on several occasions, there is always a perfect equation between cause and effect, so that the force of a body in motion is measured by the product of the mass and the height to which the body could rise (the effect of the force). Using the laws of Galileo, this height was shown by Leibniz to be proportional to the square of the velocity, so that the force (vis viva) could be expressed as mv2.

Since vis viva was regarded by Leibniz as the ultimate physical reality,14 it had to be conserved throughout all transformations. Huygens had shown that, in elastic collision, vis viva is not diminished. The vis viva apparently lost in inelastic collision Leibniz held to be in fact simply distributed among the small parts of the bodies.15

Leibniz discovered the principle of the conservation of momentum, which he described as the “quantité d'avancement.”16 Had Descartes known that the quantity of motion is preserved in every direction (so that motion is completely determined, leaving no opportunity for the directing influence of mind), Leibniz remarks, he would probably have discovered the preestablished harmony. But in Leibniz' view, the principle of the conservation of momentum did not correspond to something absolute, since two bodies moving together with equal quantities of motion would have no total momentum. Leibniz' discovery of yet another absolute quantity in the concept of action enabled him to answer the Cartesian criticism that he had failed to take time into account in his consideration of vis viva. In his Dynamica de potentia et legibus naturae corporeae, Leibniz made an attempt to fit this new concept into his axiomatic scheme.

Although succeeding generations described the vis viva controversy as a battle of words, there can be no doubt that Leibniz himself saw it as a debate about the nature of reality. Referring to his search for a true dynamics, Leibniz remarked in 1689 that, to escape from the labyrinth, he could find “no other thread of Ariadne than the evaluation of forces, under the supposition of the metaphysical principle that the total effect is always equal to the complete cause.”17

Scientia Generalis.

According to the usual distinctions, the position that Leibniz took in physics, as well as in other fundamental questions, was rationalistic, and to that extent, despite all differences in detail, was related to Descartes's position. Evident confirmation of this may be seen in Leibniz' controversy with Locke; although he does not explicitly defend the Cartesian view, he uses arguments compatible with this position. It is often overlooked, however, that Leibniz was always concerned to discuss epistemological issues as questions of theoretical science. For example, while Locke speaks of the origins of knowledge, Leibniz speaks of the structure of a science which encompasses that particular field. Thus Leibniz sees the distinction between necessary and contingent truths, so important in the debate with Locke, as a problem of theoretical science which transcends any consideration of the historical alternatives, rationalism and empiricism. Neither an empiricist in the sense of Locke nor yet a rationalist in the sense of Descartes, Leibniz saw the refutation of the empiricist's thesis (experience as the nonconceptual basis of knowledge) not as the problem of a rational psychology as it was then understood (in Cartesian idiom, the assumption of inborn truths and ideas) but as a problem that can be resolved only within the framework of a general logic of scientific research. Nevertheless, he shares with Descartes one fundamental rationalistic idea, namely the notion (which may be discerned in the Cartesian mathesis universalis) of a scientia generalis. In connection with his theoretical linguistic efforts towards a characteristica universalis, this thought appears in Leibniz as a plan for a mathématique universelle.18

Inspired by the ideas of Lull, Kircher, Descartes, Hobbes, Wilkins, and Dalgarno, Leibniz pursued the invention of an alphabet of thought (alphabetum cogitationum humanarum)19 that would not only be a form of shorthand but a formalism for the creation of knowledge itself. He sought a method that would permit “truths of reason in any field whatever to be attained, to some degree at least, through a calculus, as in arithmetic or algebra.”20 The program of such a lingua philosophica or characteristica universalis was to proceed through lists of definitions to an elementary terminology encompassing a complete encyclopedia of all that was known. Leibniz connected this plan with others that he had, such as the construction of a general language for intellectual discourse and a rational grammar, conceived as a continuation of the older grammatica speculativa.

While Leibniz' programmatic statements leave open the question of just how the basic language he was searching for and the encyclopedia were to be connected (the characteristica universalis, according to other explanations, was itself to facilitate a compendium of knowledge), a certain ars combinatoria, conceived as part of an ars inveniendi, was to serve in the creation of the lists of definitions. As early as 1666, in Leibniz' Dissertatio de arte combinatoria, the ars inveniendi was sketched out under the name logica inventiva (or logica inventionis) as a calculus of concepts in which, in marked contrast to the traditional