Conatus - in Leibniz

In Leibniz

is to motion as a point is to space, or as one to infinity, for it is the beginning and end of motion.

Gottfried Leibniz (1646–1716) was a student of Erhard Weigel (1625–1699) and learned of the conatus principle from him and from Hobbes, though Weigel used the word tendentia (Latin: tendency). Specifically, Leibniz uses the word conatus in his Exposition and Defence of the New System (1695) to describe a notion similar that of Hobbes, but he differentiates between the conatus of the body and soul, the first of which may only travel in a straight line by its own power, and the latter of which may "remember" more complicated motions.

For Leibniz, the problem of motion comes to a resolution of the paradox of Zeno. Since motion is continuous, space must be infinitely divisible. In order for anything to begin moving at all, there must be some mind-like, voluntaristic property or force inherent in the basic constituents of the universe that propels them. This conatus is a sort of instantaneous or "virtual" motion that all things possess, even when they are static. Motion, meanwhile, is just the summation of all the conatuses that a thing has, along with the interactions of things. The conatus is to motion as a point is to space. The problem with this view is that an object that collides with another would not be able to bounce back, if the only force in play were the conatus. Hence, Leibniz was forced to postulate the existence of an aether that kept objects moving and allowed for elastic collisions. Leibniz' concept of a mind-like memory-less property of conatus, coupled with his rejection of atoms, eventually led to his theory of monads.

Leibniz also uses his concept of a conatus in developing the principles of the integral calculus, adapting the meaning of the term, in this case, to signify a mathematical analog of Newton's accelerative "force". By summing an infinity of such conatuses (i.e., what is now called integration), Leibniz could measure the effect of a continuous force. He defines impetus as the result of a continuous summation of the conatus of a body, just as the vis viva (or "living force") is the sum of the inactive vis mortua.

Based on the work of Kepler and probably Descartes, Leibniz develops a model of planetary motion based on the conatus principle, the idea of aether and a fluid vortex. This theory is expounded in the work Tentamen de motuum coelestium causis (1689). According to Leibniz, Kepler's analysis of elliptical orbits into a circular and a radial component can be explained by a "harmonic vortex" for the circular motion combined with a centrifugal force and gravity, both of which are examples of conatus, to account for the radial motion. Leibniz later defines the term monadic conatus, as the "state of change" through which his monads perpetually advance.