Demonstrative and Empirical

Demonstrative knowl- edge relates ideas to ideas such as in mathematics. Such knowledge is true only by accepted definitions and does not necessarily say anything about facts or objects outside the mind. Demonstrative knowledge is entirely abstract and entirely the product of the imagination. This is not to say that demonstrative knowledge is useless, because the relations gleaned in arithmetic, algebra, and geometry are of this type and represent clear and precise thinking. Such knowledge, however, is based entirely on deduction from one idea to another; therefore, it does not nec- essarily say anything about empirical events. Con- versely, empirical knowledge is based on experience, and it alone can furnish knowledge that can effec- tively guide our conduct in the world. According to Hume, for knowledge to be useful, it must be either demonstrative or empirical; if it is neither, it is not real knowledge and therefore is useless:

When we run over libraries, persuaded of these principles, what havoc must we make? If we take in our hand any vol- ume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or num- ber? No. Does it contain any experimental reasoning concerning matter of fact and exis- tence? No. Commit it then to the flames: