Laws and Phenomena of the various departments of investigation were
dependent on each other in a graduated scale, and had thus enabled him
to establish the _Hierarchy of the Sciences_, showed him that Sociology,
including as it does the Principles and Phenomena of the other domains
which he regards as Positive Sciences, must be based upon them.

Hence it became necessary to fix the Scientific character of all these
branches of intelligence, in order to create a Scientific basis for his
Sociology. It was, however, impossible for him to claim that a
Demonstrable or Infallible method of Proof was applicable to Chemistry
and Biology; while, on the other hand, to exhibit such a method as
introducing a certainty into Mathematics, Astronomy, and Physics which
did not appertain to the other so-called Positive Sciences, would have
indicated too plainly the unspanned gulf which yawned between the
indubitable Demonstrations of the Exact Sciences and the merely probable
Generalizations of the others, and have exposed the fallible character
of his Sociological theories.

A Classification was rendered indispensable, therefore, which should
display uniformity in its character, and a sufficiently rigorous mode of
Scientific proof. To fulfil this end, the Inexact Sciences were accorded
a position of _certainty_ in reference to their Principles which does
not in reality belong to them; while the Exact or Infallible Sciences
were degraded from their peculiarly high state, and brought to the new
level of the former on the middle ground of the Positive Philosophy. A
quasi-Scientific basis was thus erected for the Sociological movements
of the French Reformer.

Had he been as _Metaphysically analytical_, _profound_, and
_discriminating_ in his intellectual development, as he was _vigorous_,