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 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 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