1 The Birth of Science - MSRI

324 11. The Age-Long Recovery
First note that the deductive method, which was part of European culture
mainly thanks to Euclid’s Elements, is an effective antidote against
the use of peripatetic and theological approaches in science, and this in
spite of the practitioner’s own inclinations. Treated with massive doses of
the method, even an amorphous “theory” is eventually forced to take on
a deductive and logically coherent form. But this does not explain it all.
Newtonian dynamics did not just evolve toward an internally coherent
theory: it was applicable from the start as a model of real motion — and
planetary motion, no less. There must have been other factors at work.
Let’s read again the definitions that inaugurate the Principia. The first is
meaningless, since density would not be definable except by indulging in
a silly tautology. The second is unusable because it depends on the first.
But the third and fourth are very interesting, because (despite the use of
nonscientific language 121 ) they graft into the Aristotelian framework an
idea that is foreign to it: that of considering “according to nature” not
just rest but also uniform straight motion (this being the effect of giving
the name of “impressed force” to the efficient cause of a departure from
such motion). This idea, as we know, heralded great developments. But
we must note that it is being superimposed on, not superseding, the more
purely Aristotelian idea attested in our earlier excerpt, where force was
the efficient cause of “true motion”. The third and fourth definitions are
thus anomalous in comparison with the rest of the discussion.
The next definition is strange. Why should centripetal force be introduced
immediately after the extremely general notion of impressed force?
If this is just a descriptive expression, to be used later about forces di- page 398
rected toward a center, it makes no sense to place it among the very first
definitions. If, on the other hand, Newton is introducing here a “law of
nature”, it is not clear what law that is. One might think gravitation, but
then why aren’t bodies mutually attracted, rather than impelled toward a
point? What are these points that attract things? And what are they centers
of? It’s all very mysterious.
Plutarch, in the De facie quae in orbe lunae apparet, had written:
[T]o help the moon, that it may not fall [on the earth], there is its
motion itself and the whizzing nature of its rotation, just as objects
placed in a sling are prevented from falling by the circular motion.
121 These two definitions clearly belong to the essentialist (Platonist–Aristotelian) type discussed
on page 154, and cannot identify any measurable physical quantity. Newton is perhaps conscious of
this, since, in contrast with the first two definitions, he does not say that innate force and impressed
force are measures of anything.
Revision: 1.11 Date: 2003/01/06 07:48:20