Mathematics, is in some respects a still sadder picture of intellectual
degeneracy than those which preceded it. After the admirable résumé of
the subject in the first volume of his first great work, we expected
something of the very highest order when he returned to the subject for
a more thorough treatment of it. But, being the commencement of a
Synthèse Subjective, it contains, as might be expected, a great deal
that is much more subjective than mathematical. Nor of this do we
complain: but we little imagined of what nature this subjective matter
was to be. M. Comte here joins together the two ideas, which, of all
that he has put forth, are the most repugnant to the fundamental
principles of Positive Philosophy. One of them is that on which we have
just commented, the assimilation between Positivism and Fetishism. The
other, of which we took notice in a former article, was the "liberté
facultative" of shaping our scientific conceptions to gratify the
demands not solely of objective truth, but of intellectual and aesthetic
suitability. It would be an excellent thing, M. Comte thinks, if science
could be deprived of its _sécheresse_, and directly associated with
sentiment. Now it is impossible to prove that the external world, and
the bodies composing it, are not endowed with feeling, and voluntary
agency. It is therefore highly desirable that we should educate
ourselves into imagining that they are. Intelligence it will not do to
invest them with, for some distinction must be maintained between simple
activity and life. But we may suppose that they feel what is done to
them, and desire and will what they themselves do. Even intelligence,
which we must deny to them in the present, may be attributed to them in
the past. Before man existed, the earth, at that time an intelligent
being, may have exerted "its physico-chemical activity so as to improve
the astronomical order by changing its principal coefficients. Our
planet may be supposed to have rendered its orbit less excentric, and
thereby more habitable, by planning a long series of explosions,