principles are "deriv'd from nothing but the senses and imagination," and "'tis absurd to talk of any perfection beyond what these faculties can judge of." In the Inquiry,[1] arithmetic, algebra, and geometry are regarded, generally, as exact and certain sciences; although here, again, there are some statements—especially with regard to geometry[2]—that contradict this view. No good reason can be assigned for Hume's change of treatment of this subject, in the Inquiry, unless possibly the difficulty of giving a satisfactory account of mathematics on his view of space and time, and his desire to satisfy the public. For while he has not much regard for the metaphysicians, or even theologians, he has still some little respect for the mathematicians. And although he is at war with them in the Treatise,[3] he seems desirous of obtaining their favor in the Inquiry.[4]
Among interpreters of Hume there is much confusion as to what his true position is on the question of mathematics. Thus Dr. Gideon Spicker[5] asserts that Hume's view of geometry is the same as that of Kant. But Dr. Spicker quotes from the fourth section of the Inquiry, to the neglect of the twelfth section, and also of the Treatise. Even Kant[6] himself—who was evidently unacquainted with the Treatise[7]—thought that Hume's good sense had kept him from denying the validity of mathematics. Perhaps more unjustifiable is the position of Professor Falckenberg,[8] who asserts that Hume did not impugn the validity of mathematical reasonings, and yet admits, in a note, that in the Treatise he had extended his doubt even to the trustworthiness of geometry. It is a common opinion among the writers on Hume,[9] as well as among the authors of the ordinary histories of modern philosophy,[10] that even if Hume denied the validity of geometry, he still held to that of arithmetic and algebra. But although this view may possibly be
- ↑ Pp. 20-22, 27, 133, 135.
- ↑ Pp. 50, 128, n. 129, n.
- ↑ P. 544.
- ↑ P. 135.
- ↑ Kant, Hume und Berkeley, p. 110.
- ↑ Kritik d. reinen Vernunft, Vorrede.
- ↑ Cf. Adamson, Philosophy of Kant, pp. 30, 202.
- ↑ Geschichte der neueren Philosophie, p. 185.
- ↑ Cf. Huxley, Hume, p. 117; Gordy, Hume as Sceptic, p. 1.
- ↑ Cf. Ueberweg-Heinze, Erdmann, Windelband.
