we differ from him, we cheerfully bear witness
to the largeness of his views, the clearness of his reasoning, and the
value of his speculations as contributing to intellectual progress. Did
we believe a serial arrangement of the sciences to be possible, that of
M. Comte would certainly be the one we should adopt. His fundamental
propositions are thoroughly intelligible; and if not true, have a great
semblance of truth. His successive steps are logically co-ordinated; and
he supports his conclusions by a considerable amount of
evidence--evidence which, so long as it is not critically examined, or
not met by counter evidence, seems to substantiate his positions. But it
only needs to assume that antagonistic attitude which _ought_ to be
assumed towards new doctrines, in the belief that, if true, they will
prosper by conquering objectors--it needs but to test his leading
doctrines either by other facts than those he cites, or by his own facts
differently applied, to at once show that they will not stand. We will
proceed thus to deal with the general principle on which he bases his
hierarchy of the sciences.

In the second chapter of his _Cours de Philosophic Positive_, M. Comte
says:--"Our problem is, then, to find the one _rational_ order, amongst
a host of possible systems." ... "This order is determined by the degree
of simplicity, or, what comes to the same thing, of generality of their
phenomena." And the arrangement he deduces runs thus: _Mathematics_,
_Astronomy_, _Physics_, _Chemistry_, _Physiology_, _Social Physics_.
This he asserts to be "the true _filiation_ of the sciences." He asserts
further, that the principle of progression from a greater to a less
degree of generality, "which gives this order to the whole body of
science, arranges the parts of each science." And, finally, he asserts
that the gradations thus established _a priori_ among the sciences, and
the parts of each science, "is in essential conformity with the order
which has spontaneously taken place among the branches of natural
philosophy;" or, in other words--corresponds with the order of historic
development.

Let us compare these assertions with the facts. That there may be
perfect fairness, let us make no choice, but take as the field for our
comparison, the succeeding section treating of the first
science--Mathematics; and let us use none but M. Comte's own facts, and
his own admissions. Confining ourselves to this one science, of course
our