Mathematical Demonstration. That Mathematics, Astronomy, and Physics
were more perfect Sciences than the others in point of _precision_, he
distinctly affirms, pointing out that 'the relative perfection of the
different Sciences consists in the degree of precision of Knowledge,'
that this degree of precision is in accordance with the extent to which
Mathematical analysis can be applied to the given domain, and that to
the above-mentioned Sciences only is its application possible.
Notwithstanding this apprehension of the different degrees of
_precision_ or _exactitude_ attainable in the various Scientific realms,
he does not seem to have sufficiently understood that there was also a
vast difference in the _nature of the evidence_ which went to prove the
truth of the supposed Principles and ulterior Facts of the various
departments of Thought, and hence variable degrees of _Certainty_ in
regard to the positive bases of the Principles themselves. He thus falls
into the same error which it was one of the main purposes of his
Scientific labors to correct--commingling problematical theories with
Demonstrable Truths, as equally entitled to belief--and ranks Sociology,
including _La Morale_, afterward called a distinct Science, with
Mathematics, Astronomy, and Physics, as domains in which our reasonings,
in the present state of Knowledge, can be equally reliable.

It is barely possible that the purpose and design of Comte's
Classification had, unconsciously, much to do with its really
unscientific and incongruous character. The aim which he had in view was
to construct a Sociology or Science of Society which should be a guide
in the establishment of a new Government, a new Political Economy, a new
Religion, a new Social Life, a new Order of Things, in fine, to take the
place of the decrepit institutions, governmental, ecclesiastical, and
social, which he thought were fast approaching their period of
dissolution. The Generalization which had exhibited to him, that the