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.

[Footnote 1:  Bacon illustrates the method by the explanation of heat.  The results of experimental observation are to be arranged in three tables.  The table of presence contains many different cases in which heat occurs; the table of absence, those in which, under circumstances otherwise the same, it is wanting; the table of degrees or comparison enumerates phenomena whose increase and decrease accompany similar variations in the degree of heat.  That which remains after the exclusion now to be undertaken (of that which cannot be the nature or cause of heat), yields as a preliminary result or commencement of interpretation (as a “first vintage"), the definition of heat:  “a motion, expansive, restrained, and acting in its strife upon the smaller particles of bodies.”]

[Footnote 2:  This goal of Baconian inquiry is by no means coincident with that of exact natural science.  Law does not mean to him, as to the physical scientist of to-day, a mathematically formulated statement of the course of events, but the nature of the phenomenon, to be expressed in a definition (E.  Koenig, Entwickelung des Causalproblems bis Kant, 1883, pp. 154-156).  Bacon combines in a peculiar manner ancient and modern, Platonic and corpuscular fundamental ideas.  Rejecting final causes with the atomists, yet handing over material and efficient causes (the latter of which sink with him to the level of mere changing occasional causes) to empirical physics, he assigns to metaphysics, as the true science of nature, the search for the “forms” and properties of things.  In this he is guided by the following metaphysical presupposition:  Phenomena, however manifold they may be, are at bottom composed of a few elements, namely, permanent properties, the so-called “simple