f Comte's Hierarchy--all other departments of thought other
than those previously excluded from his survey, being regarded as out of
the bounds of human cognition--deals with the still more complicated
problem of the relations of men to each other in society.

This Classification is admirable for the purpose of showing the mutual
interdependence of the branches of Knowledge included in it; but aside
from its covering only a small part of our intellectual domain, it is
also defective in not distinguishing with sufficient clearness that
which is properly Science, from that which is merely Theory or Plausible
Conjecture. Biology and Sociology are classed with Mathematics as
_Positive_ Sciences, as if the Laws or Principles which correlated the
Phenomena of the former were established as certainly and definitely as
those of the latter; while there is no prominence given to the different
nature of _proof_ in Mathematics and that in every other department of
investigation--except in so far as Mathematical Phenomena and Processes
enter into the latter--if, indeed, the founder of Positivism has even
anywhere distinctly stated it. Chemistry, Biology, and Sociology,
leaving Astronomy and Physics aside for the present, are not yet
_Positive_ Sciences, in any such sense as Mathematics. The lack of
_exact_ analysis is apparent in all of Comte's generalizations,
otherwise magnificent and masterly as they undoubtedly are. In respect
to the matter under consideration, it renders his Classification
unavailing for determining with sufficient precision and exactitude the
character of any intellectual domain. History, while it is the source
whence the proof of his fundamental positions is drawn, finds no place
in his Scientific schedule. Even had it been otherwise, the defect just
alluded to would have rendered it useless for our present purposes,
until a prior Classification had first been made, exhibiting the radical
difference between the various domains, which are all indiscriminately
grouped under the name of _Science_. After such a Classification, based
on the nature of _proof_ as involved in Method, the Principle which
guided Comte in the establishment of the Hierarchy of the Sciences will
enable us, in a concluding paper, to estimate with proximate certainty
the character of a possible Science of History, and to ascertain how far
the labors of Mr. Buckle and Professor Draper have aided toward the
creation of such a Science.