are the requirements made by Galileo and brilliantly fulfilled in his discoveries; this, the "inductive speculation," as Dühring terms it, which derives laws of far-reaching importance from inconspicuous facts; this, as Galileo himself recognizes, the distinctive gift of the investigator. Galileo anticipates Descartes in regard to the subjective character of sense qualities and their reduction to quantitative distinctions,[2] while he shares with him the belief in the typical character of mathematics and the mechanical theory of the world. The truth of geometrical propositions and demonstrations is as unconditionally certain for man as for God, only that man learns them by a discursive process, whereas God's intuitive understanding comprehends them with a glance and knows more of them than man. The book of the universe is written in mathematical characters; motion is the fundamental phenomenon in the world of matter; our knowledge reaches as far as phenomena are measurable; the qualitative nature of force, back of its quantitative determinations, remains unknown to us. When Galileo maintains that the Copernican theory is philosophically true and not merely astronomically useful, thus interpreting it as more than a hypothesis, he is guided by the conviction that the simplest explanation is the most probable one, that truth and beauty are one, as in general he concedes a guiding though not a controlling influence in scientific work to the aesthetic demand of the mind for order, harmony, and unity in nature, to correspond to the wisdom of the Creator. [Footnote 1: Cf. Natorp's essay on Galileo, in vol. xviii. of the _Philosophische Monatshefte_, 1882.] [Footnote 1: This doctrine is developed by Galileo in the controversial treatise against Padre Grassi, _The Scales (Il Saggiatore_, 1623, in the Florence edition of his collected works, 1842 _seq_., vol. iv. pp. 149-369; cf. Natorp, _Descartes' Erkenntnisstheorie_, 1882, chap. vi.). In substance, moreover, this doctrine is found, as Heussler remarks, _Baco_, p. 94, in Bacon himself, in _Valerius Terminus (Works_, Spedding, vol. iii. pp. 217-252.)]