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LEIBNIZ, GOTTFRIED WILHELM (b. Leipzig,
Germany, 1 July 1646; d. Hannover, Germany,
14 November 1716), mathematics, philosophy, metaphysics.
LEIBNIZ: Physics, Logic, Metaphysics
resides that is truly in motion.54 Now it is evidently
the vis primitiva that Leibniz has in mind, since
consideration of the vis derivativa (conatus or vis viva)
does not serve to identify an absolute motion, so that
we may interpret Leibniz as saying that true absolute
motion appertains to the metaphysical plane, where it
can be perceived only by God. Indeed all bodies have
an absolute motion in this sense, for since all monads
have activity, all aggregates have vis viva. The world
of phenomena is therefore conceived by Leibniz as a
world of bodies in absolute motion (rest being a mere
abstraction) but a world in which only relative changes
of position can be observed.
The theory of monads may be seen as a sustained
effort to present, in “cosmological” completeness,
a systematic unified structure of knowledge on the
basis of a logical reconstruction of the concept of
substance. Insofar as the central assertion, namely, that
because there are composite “substances,” there must
be simple substances, is not only a cosmological and
metaphysical statement, but in addition, an assertion
of the priority of synthetic over analytic procedures,
his efforts retain their original methodological meaning.
As revealed in his plan for a characteristica universalis,
analysis, for Leibniz, implies synthesis, but a synthesis
that must begin with irreducible elements. Where
there are no such elements, neither analysis nor
synthesis is possible within the framework of
Leibniz' constructive methodology. This means that
Leibniz, in the course of his protracted efforts to define
an individual substance, moved from physical
atomism to logical atomism in the modern sense, as
represented by Russell. Leibniz believed that he had
proved the thesis of an unambiguously defined world,
in which the physico-theological theme running
through the mechanistic philosophy of his age might
once again be seen as a metaphysics in the classical
sense.
Influence.
The thought of Leibniz influenced the
history of philosophy and science in two ways; first,
through the mediocre systematization of Christian
Wolff known as the “Leibnizo-Wolffian” philosophy,
and secondly, through the significance of particular
theories in the history of various sciences. While the
tradition of the Leibnizo-Wolffian philosophy ended
with Kant, the influence of particular theories of
Leibniz lasted through the nineteenth and into the
twentieth century.
The controversy with Newton and Clarke was not
conducive to the reception of Leibniz' work in
physics and hindered the objective evaluation of
important contributions such as his law of radial
acceleration. The vis viva controversy arose as a
direct result of Leibniz' criticism of Descartes and
concerned not only the measure of force but also the
nature of force itself. While ‘sGravesande and
d'Alembert (in his Traité de mécanique) judged the
dispute to be merely a semantic argument, Kant in
1747 (Gedanken von der wahren Schätzung der
lebendigen Kräfte) made an ineffective attempt at
reconciliation. Leibnizian dynamics was developed
further by Bošković, who transformed the concept of
dynamic force in the direction of a concept of relational
force.
Within the framework of rational physics, Kant
contributed some essential improvements, such as the
completion of the distinction between necessary and
contingent propositions by means of the concept of
the synthetic a priori and clarification of the principle
of causality. Leibniz' protophysical plan, however,
remained intact. It was continued later by Whewell,
Clifford, Mach, and Dingler, to mention only a few.
Insofar as the fundamental concepts of space and
time were concerned, the Newtonian ideas of absolute
space and time at first prevailed over the Leibnizian
ideas of relational space and time. Kant also tried here
to mediate between the ideas of Leibniz and Newton,
but his own suggestion (space as the origin of the
distinction between a nonreflexible figure and its
mirror image, such as a pair of gloves) strongly
resembled the Newtonian concept of absolute space.
Modern relativistic physics has turned the scales in
favor of the ideas of Leibniz.
Among the methodological principles of Leibniz,
only the principle of sufficient reason has played a
prominent role in the history of philosophy. Wolff,
disregarding Leibniz' methodological intentions, tried
to prove it by ontological means (Philosophia sive
ontologia); Kant reduced it essentially to the law of
causality and in 1813 Schopenhauer drew on it for
the elucidation of his four conditions of verification
(Über die vierfache Wurzel des Satzes vom zureichenden
Grunde). On the other hand, the methodological
project of a characteristica universalis together with
the ensuing development of logical calculi has played
a most significant role in the history of modern logic.
In 1896 Frege, recalling Leibniz, described his
Begriffsschrift of 1879 as a lingua characterica (not just
a calculus ratiocinator), thus distinguishing it from
the parallel efforts of Boole and Peano. De Morgan
and Boole tried to carry out what Scholz has described
as the “Leibniz program” of the development of a
logical algebra of classes. This connection between
logic and mathematics, evident also in Peirce and
Schröder, was once again weakened by Frege, Peano,
and Russell, whose work (especially that of Frege)
nevertheless bears the inescapable influence of
Leibniz; for even where the differences are greatest,