are B; most
C are B; this is both an A and a C; therefore it is probably a B. On the
other hand, when the subsequent approximation or approximations is or
are applicable only by virtue of the application of the first, this is
joining two (or more) probabilities, _by way of Deduction_, which
produces a _self-infirmative chain_; and the type is: Most A are B; most
C are A; this is a C; therefore it is probably an A; therefore it is
probably a B. As, in the former case, the probability increases at each
step, so, in the latter, it progressively dwindles. It is measured by
the probability arising from the first of the propositions, abated in
the ratio of that arising from the subsequent; and the error of the
conclusion amounts to the aggregate of the errors of all the premisses.

In two classes of cases (exceptions which prove the rule) approximate
can be employed in deduction as usefully as complete generalisations.
Thus, first, we stop at them sometimes, from the inconvenience, not the
impossibility, of going further; and, by adding provisos, we might
change the approximate into an universal proposition; the sum of the
provisos being then the sum of the errors liable to affect the
conclusion. Secondly, they are used in Social Science with reference to
masses with _absolute_ certainty, even without the addition of such
provisos. Although the premisses in the Moral and Social Sciences are
only probable, these sciences differ from the exact only in that we
cannot decipher so many of the laws, and not in the conclusions that we
do arrive at being less scientific or trustworthy.

CHAPTER XXIV.

THE REMAINING LAWS OF NATURE.

There are, we have seen, five facts, one of which every proposition must
assert, viz. Existence, Order in Place, Order in Time, Causation, and
Resemblance. Causation is not fundamentally different from Coexistence
and Sequence, which are the two modes of Order in Time. They have been
already discussed. Of the rest, Existence, if of things in themselves,
is a topic for Metaphysics, Logic regarding the existence of _phenomena_
only; and as this, when it is not perceived directly, is proved by
proving that the unknown phenomenon is connected by _succession or
coexistence_ with some known phenomenon, the fact of Existence is not
amenable to any _peculiar_ inductive principles. There remain
Resemblance and Order in Place.

As for Resemblance, Locke indeed, and, in a more unqualified way, his
scho