Page:History of Modern Philosophy (Falckenberg).djvu/191

 THEORY OF KNOWLEDGE 169 this Being must be omnipotent ; as the cause of beauty and order in the world, and, above all, as the creator of thinking beings, it must be omniscient. But these per- fections are those which we combine in the idea of God. Intuitive knowledge is the highest of the three degrees of knowledge. It is gained when the mind perceives the agreement or disagreement of two ideas at first sight, with- out hesitation, and without the intervention of any third idea. This immediate knowledge is self-evident, irresistible, and exposed to no doubt. Knowledge is demonstrative when the mind perceives the agreement (or disagreement) of two ideas, not by placing them side by side and com- paring them, but through the aid of other ideas. The intermediate links are called proofs ; their discovery is the work of the reason, and quickness in finding them out is termed sagacity. The greater the number of the interme- diate steps, the more the clearness and distinctness of the knowledge decreases, and the more the possibility of error increases. In order for an argument (<?. g., that a = d) to be conclusive, every particular step in it (a = b, b = c, c = d) must possess intuitive certainty. Mathematics is not the only example of demonstrative knowledge, but the most perfect one, since in mathematics, by the aid of visible symbols, the full equality and the least differences amonr: ideas may be exactly measured and sharply determined. Besides real existence Locke, unsystematically enough, enumerates three other sorts of agreement between ideas, — in the perception of which he makes knowledge consist, — viz., identity or diversity (blue is not yellow), relation (when equals are added to equals the results are equal), and co- existence or necessary connexion (gold is fixed). We are best off in regard to the knowledge of the first of these, " identity or diversity," for here our intuition extends as far as our ideas, since we recognize every idea, as soon as it arises, as identical with itself and different from others. We are worst off in regard to " necessary connexion." We know something, indeed, concerning the incompatibility or coexistence of certain properties {e. g., that the same ob- ject cannot have two different sizes or colors at the same time; that figure cannot exist apart from extension): but it