Law of
Causation cannot be derived from the Mathematical Axioms, nor these from
the Logical. The kind of evidence upon which Axioms rest, or whether any
evidence can be given for them, is (as before observed) a question for
Metaphysics, not for Logic. Axioms are the upward limit of Logic, which,
like all the special sciences, necessarily takes them for granted, as
the starting point of all deduction and the goal of all generalisation.

Next to Axioms, come Primary Laws of Nature: these are of less
generality than the Axioms, and are subject to the conditions of
methodical proof; being universally true only of certain forces or
properties of matter, or of nature under certain conditions; so that
proof of them by logical or mathematical reasoning is expected, because
they depend upon the Axioms for their formal evidence. Such are the law
of gravitation, in Astronomy; the law of definite proportions, in
Chemistry; the law of heredity, in Biology; and in Psychology, the law
of relativity.

Then, there are Secondary Laws, of still less generality, resulting from
a combination of conditions or forces in given circumstances, and
therefore conceivably derivable from the laws of those conditions or
forces, if we can discover them and compute their united effects.
Accordingly, Secondary Laws are either--(1) Derivative, having been
analysed into, and deduced from, Primary Laws; or (2) Empirical, those
that have not yet been deduced (though from their comparatively special
and complex character, it seems probable they may be, given sufficient
time and ingenuity), and that meanwhile rest upon some unsatisfactory
sort of induction by Agreement or Simple Enumeration.

Whether laws proved only by the canon of Difference are to be considered
Empirical, is perhaps a question: their proof derives them from the
principle of Causation; but, being of narrow scope, some more special
account of them seems requisite in relation to the Primary Laws before
we can call them Derivative in the technical sense.

Many Secondary Laws, again, are partially or imperfectly Derivative; we
can give general reasons for them, without being able to determine
theoretically the precise relations of the phenomena they describe.
Meteorologists can explain the general conditions of all sorts of
weather, but have made little progress toward predicting the actual
course of it (at least, for our island): Geologists know the general
causes of mountain ranges, but