DPG Frühjahrstagung 2014

Newton and Leibniz on the absolute space

The idea of the absolute space had been introduced by Newton in
the 1680s to combat Cartesian relativism and to establish the laws
of mechanics. The complete theory was eventually published in the
Principia by 1687. Already in the 1670s, Leibniz discussed, however,
independently just the same model of the absolute space and absolute
motion, but used it as a counterexample in order to confirm and im-
prove Cartesian relativism and to demonstrate that "space and motion
are really relations". Newton started from the position that "the nature
of the body is to fill the place which is considered as a part of
the space", i.e. the absolute space. In Leibniz's anticipated reply from
1677 it is demonstrated that "space is not such a thing and motion is
not something absolute", an assertion which he renewed and underlined
later in his correspondence with Clarke in 1716. Leibniz's earlier
interpretation had been only published in the 20th century. It follows
that the elaboration of the model of the absolute space is a decisive
intermediate step towards a relational theory of space and motion.
Thus, it can be concluded that Einstein's summary from 1953 is
in conformity with the historical development: "It required a severe
struggle to arrive at the concept of independent and absolute space,
indispensable for the development of theory. It has required no less
strenuous exertions subsequently to overcome this concept { a process
which is probably by no means as yet completed.


Granada, 3-5 Abril 2014

Leibniz’s Theory of Abstract Motion as a prerequisite of the Monadology

The Theoria Motus Abstracti of 1671 and the Monadology of 1714 are among the few of Leibniz's writings published soon after they were written. The early writing on physics provides the basis for later metaphysical writings like Definitiones cogitationesque metaphysicae of 1678-1680, in which the concept body from 1671 (corpus est extensum resistens) is expanded to the notion of the body as a substance (corpus est substantia extensa). Likewise, the Theoria is also mentioned by Leibniz in the Specimen Dynamicum of 1695 in order to explain why he has changed his mind concerning the previous idea of inert mass. The former notion of body as an extensum resistens is now exemplified by the notion of derivative forces. Moreover, Leibniz already concluded in 1678 that the “phenomena of nature are explained by the efficient causes, as if there were no final causes”, which he later related in the Monadology to the pre-established harmony between souls and bodies. In the Monadology, the monad is considered eventually as an extensionless substance, there is “neither extension nor figure”, and is basically contrasted and simultaneously correlated with the extended substance.

In this paper it is argued that Leibniz takes obviously advantage from the formerly developed concept of the body as a substance (in Definitiones 1678-1680) and repeats concerning the monads the same figure of thought that he had already successfully tested in the transition from the concept of the body as extensum resistens to the body as substantia extensa. This procedure demonstrates that the early writing Theoria Motus Abstracti had not been discarded by Leibniz, but rather used as an essential methodological prerequisite for the latercompletion of theory in the Monadology where souls and bodies are maintained as the constitutive parts of the world. But finally, Leibniz claimed that the monads are the only real things or the only substances and the bodies are mere phenomena, “there is no need of extended substance” (letter to Dangicourt) or, after having removed the intermediate step (corpus est substantia extensa), Leibniz abandoned definitively and irrevocably the previous principles of the Theoria Motus Abstracti.