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 laws
of number and extension, such as they actually are. The phaenomena of
Astronomy depend on these three classes of laws, and on the law of
gravitation besides; which last has no influence on the truths of
number, geometry, or mechanics. Physics (badly named in common English