1 The Birth of Science - MSRI

322 11. The Age-Long Recovery
had of course triumphed irreversibly after Kepler’s work), so that it no
longer corresponds to any empirical datum. It follows that the motions
that are the object of Newton’s axioms or laws of motion are beyond our
perception. The Nature that concerns his natural philosophy transcends
experience, unlike Aristotle’s, and the first step toward it is to “abstract
from our senses”. This is not, mind you, an abstraction arising from the
substitution of a theoretical model for real objects, but one imposed by
the need to completely give up “sensible measures”. In this scheme there
can be no correspondence rule between relative movements and absolute
ones, because the latter refer to a fixed space beyond perception, and bear
no relation to phenomena. Thus Newton is forced, as he himself admits,
not to deal with “common affairs”. If this is the “experimental method”
characteristic of modern science, it is likely that it was indeed unknown to
scientists like Archimedes, Ctesibius and Herophilus.
(It is true that the Principia later does characterize absolute space, in the
following way. Newton establishes that the barycenter of the solar system
is at rest or in uniform motion, using an implicit, and arguably reasonable,
assumption of isolation. At the same time — and here is the crux — he opts
for rest over uniform motion, a gratuitous choice for which there is no
logical justification in his scientific mechanics, but which is very important
from the viewpoint of his metaphysical notion of space. 117 )
Building, with full methodological coherence, on his notion of space,
Newton next talks of motion and force:
[E]ntire and absolute motions can be no otherwise determined than
by immovable places. . . . Now no other places are immovable but
those that, from infinity to infinity, do all retain the same given position
one to another; and upon this account must ever remain unmoved;
and do thereby constitute immovable space.
The causes by which true and relative motions are distinguished, one
from the other, are the forces impressed upon bodies to generate motion.
True motion is neither generated nor altered, but by some force
impressed upon the body moved; but relative motion may be generated
or altered without any force impressed upon the body. 118
117 See Principia, Book III, proposition XI / theorem XI and its proof. The selection is effected
through the immediately preceding hypothesis, “That the centre of the system of the world is immovable”,
which is justified by a single argument: “This is acknowledged by all.” In this metaphysical
statement, based on an appeal to common sense, Newton prefers to talk of “the system of the
world” and abandons previously defined terms. The proof of proposition XI / theorem XI shows
that he conceives “the centre of the the system of the world” as coinciding with the barycenter of
the solar system.
118 Newton, Principia mathematica, Definitions, scholium, at 55%, Motte/Cajori translation.
Revision: 1.11 Date: 2003/01/06 07:48:20