To these warnings there are added positive rules. When the investigator, after the removal of prejudices and habitual modes of thought, approaches experience with his senses unperverted and a purified mind, he is to advance from the phenomena given to their conditions. First of all, the facts must be established by observation and experiment, and systematically arranged,[1] then let him go on to causes and laws.[2] The true or scientific induction[3] thus inculcated is quite different from the credulous induction of common life or the unmethodical induction of Aristotle. Bacon emphasizes the fact that hitherto the importance of negative instances, which are to be employed as a kind of counter-proof, has been completely overlooked, and that a substitute for complete induction, which is never attainable, may be found, on the one hand, in the collection of as many cases as possible, and, on the other, by considering the more important or decisive cases, the "prerogative instances." Then the inductive ascent from experiment to axiom is to be followed by a deductive descent from axioms to new experiments and discoveries. Bacon rejects the syllogism on the ground that it fits one to overcome his opponent in disputation, but not to gain an active conquest over nature. In his own application of these principles of method, his procedure was that of a dilettante; the patient, assiduous labor demanded for the successful promotion of the mission of natural investigation was not his forte. His strength lay in the postulation of problems, the stimulation and direction of inquiry, the discovery of lacunae and the throwing out of suggestions; and many ideas incidentally thrown off by him surprise us by their ingenious anticipations of later discoveries. The greatest defect in his theory was his complete failure to recognize the services promised by mathematics to natural science. The charge of utilitarianism, which has been so broadly made, is, on the contrary, unjust. For no matter how strongly he emphasizes the practical value of knowledge, he is still in agreement with those who esteem the godlike condition of calm and cheerful acquaintance with truth more highly than the advantages to be expected from it; he desires science to be used, not as "a courtezan for pleasure," but "as a spouse for generation, fruit and comfort," and--leaving entirely out of view his isolated acknowledgments of the inherent value of knowledge--he conceives its utility wholly in the comprehensive and noble sense that the pursuit of science, from which as such all narrow-minded regard for direct practical application must keep aloof, is the most important lever for the advancement of human culture.