e the abstract
sciences, except those at the very beginning of the scale, have not
attained the degree of perfection necessary to render real concrete
sciences possible.

Postponing, therefore, the concrete sciences, as not yet formed, but
only tending towards formation, the abstract sciences remain to be
classed. These, as marked out by M. Comte, are six in number; and the
principle which he proposes for their classification is admirably in
accordance with the conditions of our study of Nature. It might have
happened that the different classes of phaenomena had depended on laws
altogether distinct; that in changing from one to another subject of
scientific study, the student left behind all the laws he previously
knew, and passed under the dominion of a totally new set of
uniformities. The sciences would then have been wholly independent of
one another; each would have rested entirely on its own inductions, and
if deductive at all, would have drawn its deductions from premises
exclusively furnished by itself. The fact, however, is otherwise. The
relation which really subsists between different kinds of phaenomena,
enables the sciences to be arranged in such an order, that in travelling
through them we do not pass out of the sphere of any laws, but merely
take up additional ones at each step. In this order M. Comte proposes to
arrange them. He classes the sciences in an ascending series, according
to the degree of complexity of their phaenomena; so that each science
depends on the truths of all those which precede it, with the addition
of peculiar truths of its own.

Thus, the truths of number are true of all things, and depend only on
their own laws; the science, therefore, of Number, consisting of
Arithmetic and Algebra, may be studied without reference to any other
science. The truths of Geometry presuppose the laws of Number, and a
more special class of laws peculiar to extended bodies, but require no
others: Geometry, therefore, can be studied independently of all
sciences except that of Number.

Rational Mechanics presupposes, and depends on, the laws of number and
those of extension, and along with them another set of laws, those of
Equilibrium and Motion. The truths of Algebra and Geometry nowise depend
on these last, and would have been true if these had happened to be the
reverse of what we find them: but the phaenomena of equilibrium and
motion cannot be understood, nor even stated, without assuming the la