Electronic edition published by Cultural Heritage Langauge Technologies (with permission from Charles Scribners and Sons) and funded by the National Science Foundation International Digital Libraries Program. This text has been proofread to a low degree of accuracy. It was converted to electronic form using data entry.
LEIBNIZ, GOTTFRIED WILHELM (b. Leipzig,
Germany, 1 July 1646; d. Hannover, Germany,
14 November 1716), mathematics, philosophy, metaphysics.
LEIBNIZ: Physics, Logic, Metaphysics
having the same relation to motion as a point to
space (in Cavalieri's terms) or a differential to a
finite quantity (in terms of the infinitesimal calculus).
Conatus represents virtual motion; it is an intensive
quality that can be measured by the distance traversed
in an infinitesimal element of time. A body can possess
several conatuses simultaneously and these can be
combined into a single conatus if they are compatible.
In the absence of motion, conatus lasts only an
instant,6 but however weak, its effect is transmitted
to infinity in a plenum. Leibniz' doctrine of conatus, in
which a body is conceived as a momentary mind, that
is, a mind without memory, may be regarded as a
first sketch of the philosophy of monads.
Mathematically, conatus represents for Leibniz
accelerative force in the Newtonian sense, so that, by
summing an infinity of conatuses (that is, by integration),
the effect of a continuous force can be measured.
Examples of conatus given by Leibniz are centrifugal
force and what he called the solicitation of gravity.
Further clarifications of the concept of conatus are
given in the Essay de dynamique and Specimen
dynamicum, where conatus is compared with static
force or vis mortua in contrast to vis viva, which is
produced by an infinity of impressions of vis mortua.
Physics (Mechanical Hypothesis).
Leibniz soon
recognized that the idea of conatus could not by
itself explain the results of the experiments of Huygens
and Wren on collision. Since in the absence of
motion conatus lasts only an instant, a body once
brought to rest in a collision, Leibniz explains, could
not then rebound.7 A new property of matter was
needed and this was provided for Leibniz by the
action of an ether. As conceived by Leibniz in his
Theoria motus concreti,8 the ether was a universal
agent of motion, explaining mechanically all the
phenomena of the visible world. This essentially
Cartesian notion was adopted by Leibniz following
a brief attachment to the doctrine of physical atomism
defended in the works of Bacon and Gassendi.
Leibniz did not, however, become a Cartesian, nor did
he aim to construct an entirely new hypothesis but
rather to improve and reconcile those of others.9
A good example of the way in which Leibniz
pursued this goal is provided by the planetary theory
expounded in his Tentamen de motuum coelestium
causis. In this work, Leibniz combined the mechanics
of conatus and inertial motion with the concept of a
fluid vortex to give a physical explanation of planetary
motion on the basis of Kepler's analysis of the
elliptical orbit into a circulation and a radial motion.
Leibniz' harmonic vortex accounted for the circulation
while the variation in distance was explained by the
combined action of the centrifugal force arising from
the circulation and the solicitation of gravity. This
solicitation he held to be the effect of a second independent
vortex of the kind imagined by Huygens, to
whom he described Newton's attraction as “an
immaterial and inexplicable virtue,” a criticism he
made public in the Théodicée and repeated in the
correspondence with Clarke.
Although Leibniz' planetary theory could be
described as a modification of that of Descartes, he
did not acknowledge any inspiration from this source.
Attributing the idea of a fluid vortex to Kepler and
also, but incorrectly, the idea of centrifugal force,
Leibniz claimed that Descartes had made ample use
of these ideas without acknowledgment. Leibniz had
already, in a letter to Arnauld,10 rejected the Cartesian
doctrine that the essence of corporeal substance is
extension. One reason that led him to this rejection
was the theological problem of transubstantiation
which he studied at the instigation of Baron Boyneburg,11
but the most important dynamical reason was
connected with the relativity of motion. As explained
by Leibniz in the Discours de métaphysique,12 since
motion is relative, the real difference between a
moving body and a body at rest cannot consist of
change of position. Consequently, as the principle
of inertial motion precludes an external impulse for a
body moving with constant speed, the cause of
motion must be an inherent force. Another argument
against the Cartesian position involves the principle
of the identity of indiscernibles. From this principle it
follows that, besides extension, which is a property
carried by a body from place to place, the body must
have some intrinsic property which distinguishes it
from others. According to Leibniz, bodies possess
three properties which cannot be derived from
extension: namely, impenetrability, inertia, and
activity. Impenetrability and inertia are associated
with materia prima, which is an abstraction, while
materia secunda (the matter of dynamics) is matter
endowed with force.
Since, for Leibniz, force alone confers reality to
motion, the correct measure of force becomes the
central problem of dynamics. Now Descartes had
measured what Leibniz regarded as the active force
of bodies, that is, the cause of their activity, by their
quantity of motion. But, as Leibniz remarked in a
letter of 1680,13 Descartes's erroneous laws of collision
implied that his basic principle of the conservation
of motion was false. In 1686 Leibniz published his
criticism of the Cartesian principle of the conservation
of motion in his Brevis demonstratio erroris mirabilis
Cartesii, thereby precipitating the vis viva controversy.
According to Leibniz, Descartes had incorrectly
generalized from statics to dynamics. In statics or