mulation 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 ov