INFERENCE, OR REASONING IN GENERAL.

The preceding book treated, not of the proper subject of logic, viz. the
nature of proof, but of assertion. Assertions (as, e.g. definitions)
which relate to the meaning of words, are, since _that_ is arbitrary,
incapable of truth or falsehood, and therefore of proof or disproof. But
there are assertions which are subjects for proof or disproof, viz. the
propositions (the real, and not the verbal) whose subject is some fact
of consciousness, or its hidden cause, about which is predicated, in the
affirmative or negative, one of five things, viz. existence, order in
place, order in time, causation, resemblance: in which, in short, it is
asserted, that some given subject does or does not possess some
attribute, or that two attributes, or sets of attributes, do or do not
(constantly or occasionally) coexist.

A proposition not believed on its own evidence, but inferred from
another, is said to be _proved_; and this process of inferring, whether
syllogistically or not, is _reasoning_. But whenever, as in the
deduction of a particular from a universal, or, in Conversion, the
assertion in the new proposition is the same as the whole or part of
the assertion in the original proposition, the inference is only
apparent; and such processes, however useful for cultivating a habit of
detecting quickly the concealed identity of assertions, are not
reasoning.

Reasoning, or Inference, properly so called, is, 1, Induction, when a
proposition is inferred from another, which, whether particular or
general, is less general than itself; 2, Ratiocination, or Syllogism,
when a proposition is inferred from others equally or more general; 3, a
kind which falls under neither of these descriptions, yet is the basis
of both.

CHAPTER II.

RATIOCINATION, OR SYLLOGISM.

The syllogistic figures are determined by the position of the middle
term. There are four, or, if the fourth be classed under the first,
three. But syllogisms in the other figures can be reduced to the first
by conversion. Such reduction may not indeed be necessary, for different
arguments are suited to different figures; the first figure, says
Lambert, being best adapted to the discovery or proof of the properties
of things; the second, of the distinctions between things; the third, of
instances and exceptions; the fourth, to the discovery or exclusion of
the different species of a genus. Still, as the premisses of the first
f