Page:History of Modern Philosophy (Falckenberg).djvu/245

 HUME. 223 the last analysis reduce to three fundamentallaws of associa- tion : Ideas are associated (i) according to their resemblance and contrast ; (2) according to their contiguity in space and time; (3) according to their causal connection. Mathematics is based on the operation of the first of these laws, on the immediate or mediate knowledge of the resemblance, con- trariety, and quantitative relations of ideas; the descriptive and experimental part of the sciences of nature and of man on the second ; religion, metaphysics, and that part of physical and moral science which goes beyond mere obser- vation on the third. The theory of knowledge has to deter- mine the boundaries of human understanding and the degree of credibility to which these sciences are entitled. The objects of human thought and inquiry are either rela- tions of ideas or matters of fact. To the former class belong the objects of mathematics, the truths of which, since they are analytic {i. e., merely explicate in the predicate the characteristics already contained in the subject, and add nothing new to this), and since they concern possible rela- tions only, not reality, possess intuitive or demonstrative certainty. It is only propositions concerning quantity and number that are discoverable a priori by the mere opera- tion of thought, without dependence on real existence, and that can be proved from the impossibility o^ their oppo- sites — mathematics is the only demonstrative science. We reach certainty in matters of fact by direct perception, or by inferences from other facts, when they transcend the testin:>ony of our senses and memory. These arguments from experience are of an entirely different sort from the rational demonstrations of mathematics; as the contrary of a fact is always thinkable (the proposition that the sun will not rise to-morrow implies no logical contradiction), they yield, strictly speaking, probability only, no matter how strong our conviction of their accuracy may be. Never- theless it is advisable to separate this species of inferences from experience — whose certainty is not doubted except by the philosophers — from uncertain probabilities, as a class intermediate between the latter and demonstrative truth (demonstrations — proofs — probabilities). All reason- ings concerning matters of fact are based on the relation of