etailed 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
consciousness of its novelty as well as of its scope, is opposed to the
qualitative view of Aristotle;[2] the opinion that the essence of the human
spirit, as well as of the divine, nay, the essence of all things, consists
in activity; that, consequently, the soul is always active, being conscious
of its own harmony at least in a confused way, even when not conscious of
external proportions; further, the doctrine that nature loves simplicity,
avoids the superfluous, and is accustomed to accomplish large results with
a few principles--these remind one of Leibnitz. At the same time, the law
of parsimony and the methodological conclusions concerning true hypotheses
and real causes (an hypothesis must not be an artificially constructed set
of fictions, forcibly adjusted to reality, but is to trace back phenomena
to their real grounds), obedience to which enabled him to deduce _a priori_
from causes the conclusions which Copernicus by fortunate conjecture had
gathered inductively from effects--these made our thinker a forerunner of
Newton. The physical method of explanation must not be corrupted either
by theological conceptions (comets are entirely natural phenomena!) or by
anthropomorphic views, which endow nature with spiritual powers.

[Footnote 1: See Sigwart, _Kleine Schriften_, vol. i. p. 182 _seq_.; R.
Euc