Newton & the absolute, true, mathematical quantities themselves (materialism)

[ish mailian]

A “Scholium” at the beginning of the Principia, inserted between the
“Definitions” and the “Laws of Motion”, lays out Newton's views on
time, space, place, and motion. He begins by saying that, since in
common life these quantities are conceived of in terms of their
relations to sensible bodies, it is incumbent to distinguish between,
on the one hand, the relative, apparent, common conception of them,
and, on the other, the absolute, true, mathematical quantities
themselves. To paraphrase:

Absolute, true, and mathematical time, from its own nature, passes
equably without relation to anything external, and thus without
reference to any change or way of measuring of time (e.g., the hour,
day, month, or year).
Absolute, true, and mathematical space remains similar and immovable
without relation to anything external. (The specific meaning of this
will become clearer below from the way it contrasts with Descartes'
concept of space.) Relative spaces are measures of absolute space
defined with reference to some system of bodies or another, and thus a
relative space may, and likely will, be in motion.
The place of a body is the space which it occupies, and may be
absolute or relative according to whether the space is absolute or
relative.
Absolute motion is the translation of a body from one absolute place
to another; relative motion the translation from one relative place to
another.

Newton devotes the bulk of the Scholium to arguing that the
distinction between the true quantities and their relative measures is
necessary and justified.

It is evident from these characterizations that, according to Newton:

space is something distinct from body and exists independently of the
existence of bodies,
there is a fact of the matter whether a given body moves and what its
true quantity of motion is, and
the true motion of a body does not consist of, or cannot be defined in
terms of, its motion relative to other bodies.

The first of these theses was a point of major contention in
17th-century natural philosophy and one assailed by Newton's critics
such as Leibniz, Huygens, and Berkeley. The second was not in general
dispute. Descartes, Leibniz, and Berkeley all believed that, to put it
in somewhat scholastic terms, the predicate ‘x is in true motion’ is a
complete predicate in the sense that it holds or fails to hold for any
given body. (Huygens, at least in his post-Principia views,
constitutes a special case.) Thus, for those who denied the first
thesis, it was necessary to secure a definition, or an analysis, of
what it means for a body be in true motion (and what determines the
quantity of that motion), so as to be as adequate to the facts as
Newton's characterization of true motion. The figures mentioned above
all deemed that motion relative to other bodies is a necessary
condition for true motion, although not, by itself, a sufficient
condition.

Over the course of years, the consensus in the 17th and early 18th Centuries....

http://plato.stanford.edu/entries/newton-stm/
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