[7] “Science,” says Mr Spencer in his “Genesis,” “while purely inductive is purely qualitative....  All quantitative prevision is reached deductively; induction can achieve only qualitative prevision.”  Now, if we remember that the very first accurate quantitative law of physical phaenomena ever established, the law of the accelerating force of gravity, was discovered and proved by Galileo partly at least by experiment; that the quantitative laws on which the whole theory of the celestial motions is grounded, were generalized by Kepler from direct comparison of observations; that the quantitative law of the condensation of gases by pressure, the law of Boyle and Mariotte, was arrived at by direct experiment; that the proportional quantities in which every known substance combines chemically with every other, were ascertained by innumerable experiments, from which the general law of chemical equivalents, now the ground of the most exact quantitative previsions, was an inductive generalization; we must conclude that Mr Spencer has committed himself to a general proposition, which a very slight consideration of truths perfectly known to him would have shown to be unsustainable.

Again, in the very pamphlet in which Mr Spencer defends himself against the supposition of being a disciple of M. Comte ("The Classification of the Sciences,” p. 37), he speaks of “M.  Comte’s adherent, Mr Buckle.”  Now, except in the opinion common to both, that history may be made a subject of science, the speculations of these two thinkers are not only different, but run in different channels, M. Comte applying himself principally to the laws of evolution common to all mankind, Mr Buckle almost exclusively to the diversities:  and it may be affirmed without presumption, that they neither saw the same truths, nor fell into the same errors, nor defended their opinions, either true or erroneous, by the same arguments.  Indeed, it is one of the surprising things in the case of Mr Buckle as of Mr Spencer, that being a man of kindred genius, of the same wide range of knowledge, and devoting himself to speculations of the same kind, he profited so little by M. Comte.

These oversights prove nothing against the general accuracy of Mr Spencer’s acquirements.  They are mere lapses of inattention, such as thinkers who attempt speculations requiring that vast multitudes of facts should be kept in recollection at once, can scarcely hope always to avoid.

[8] We refer particularly to the mystical metaphysics connected with the negative sign, imaginary quantities, infinity and infinitesimals, &c, all cleared up and put on a rational footing in the highly philosophical treatises of Professor De Morgan.

[9] Those who wish to see this idea followed out, are referred to “A System of Logic, Ratiocinative and Inductive.”  It is not irrelevant to state that M. Comte, soon after the publication of that work, expressed, both in a letter (published in M. Littre’s volume) and in print, his high approval of it (especially of the Inductive part) as a real contribution to the construction of the Positive Method.  But we cannot discover that he was indebted to it for a single idea, or that it influenced, in the smallest particular, the course of his subsequent speculations.