into final causes is
rejected as an anthropomorphosis of natural events, and deduction from
efficient causes is alone accepted as scientific explanation. Size, shape,
number, motion, and law are the only and the sufficient principles of
explanation. For magnitudes alone are knowable; wherever it is impossible
to measure and count, to determine force mathematically, there rigorous,
exact science ceases. Nature a system of regularly moved particles of
mass; all that takes place mechanical movement, viz., the combination,
separation, dislocation, oscillation of bodies and corpuscles; mathematics
the organon of natural science! Into this circle of modern scientific
categories are articulated, further, Galileo's new conception of motion
and the conception of atoms, which, previously employed by physicists, as
Daniel Sennert (1619) and others, is now brought into general acceptance
by Gassendi, while the four elements are definitively discarded (Lasswitz,
_Geschichte der Atomistik_, 1890). Still another doctrine of Democritus
is now revived; an evident symptom of the quantification and mechanical
interpretation of natural phenomena being furnished by the doctrine of the
subjectivity of sense qualities, in which, although on varying grounds,
Kepler, Galileo, Descartes, Gassendi, and Hobbes agree.[1] Descartes and
Hobbes will be discussed later. Here we may give a few notes on their
fellow laborers in the service of the mechanical science of nature.

[Footnote 1: Cf. chapter vi. in Natorp's work on _Descartes'
Erkenntnisstheorie_, Marburg, 1882, and the same author's _Analekten zur
Geschichte der Philosophie_, in the _Philosophische Monatshefte_, vol.
xviii. 1882, p. 572 _seq_.]

We begin with John Kepler[1] (1571-1630; chief work, _The New Astronomy or
Celestial Physics, in Commentaries on the Motions of Mars_, 1609). Kepler's
merit as an astronomer has long obscured his philosophical importance,
although his discovery of the laws of planetary motion was the outcome of
endeavors to secure an exact foundation for his theory of the world. The
latter is aesthetic in character, centers about the idea of a universal
world-harmony, and employs mathematics as an instrument of confirmation.
For the fact that this theory satisfies the mind, and, on the whole,
corresponds to our empirical impression of the order of nature, is not
enough in Kepler's view to guarantee its truth; by exact methods, by means
of induction and experiment, a d