correct, Hume does not always abide by it; and it cannot properly be explicitly stated as his without some considerable modifications. No doubt the Inquiry favors such a view, while the Inquiry concerning Morals[1] goes even farther, so as to extend exactness and certainty to geometry. And in some parts of the Treatise Hume does assert that the sciences of arithmetic and algebra possess perfect exactness and certainty. But in Part IV of the Treatise he denies this. For here, Hume not only attacks the testimony of the senses, but also the trustworthiness of reason, and reduces all knowledge to probability. Also in the "Dialogues concerning Natural Religion,"[2] Philo proclaims: "Let the errors and deceits of our very senses be set before us; the insuperable difficulties which attend first principles in all systems; the contradictions which adhere to the very ideas of matter, cause and effect, extension, space, time, motion; and in one word, quantity of all kinds, the object of the only science, that can fairly pretend to any certainty or evidence." It need scarcely be added that according to Hume's own principles, laid down in the Inquiry as well as in the Treatise, there is no valid ground for asserting the exactness and certainty of any science whatever.[3]
5. Causation and Belief. The doctrine of causation is almost, if not altogether, the same in both works. But there are some differences in the mode of treatment, (1) The treatment in the Inquiry is much briefer, with the exception of the discussion claiming to show that the idea of power or necessary connection is not derived from the energy of the mind. This argument first appears briefly stated in the Appendix[4] (1740), and afterwards more fully expressed in the Inquiry.[5] It was probably called forth by controversy on the subject. (2) There are apparently some slight differences in the treatment of causation, regarded as a philosophical relation; but it is difficult to state precisely how extensive these are. Hume seems to discuss the subject of causation explicitly in the Treatise and implicitly
