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 detailed proof from empirical facts must be
found for the existence not only of a general harmony, but of definitely
fixed proportions. Herewith the philosophical application of mathematics
loses that obscure mystical character which had clung to it since the time
of Pythagoras, and had strongly manifested itself as late as in Nicolas of
Cusa. Mathematical relations constitute the deepest essence of the real and
the object of science. Where matter is, there is geometry; the latter is
older than the world and as eternal as the divine Spirit; magnitudes are
the source of things. True knowledge exists only where quanta are known;
the presupposition of the capacity for knowledge is the capacity to count;
the spirit cognizes sensuous relations by means of the pure, archetypal,
intellectual relations born in it, which, before the advent of
sense-impressions, have lain concealed behind the veil of possibility;
inclination and aversion between men, their delight in beauty, the pleasant
impression of a view, depend upon an unconscious and instinctive perception
of proportions. This quantitative view of the world, which, with a