is an
abbreviation of one additional proposition, viz. We must think of the
two together; while _but_ is an abbreviation of two additional
propositions, viz. We must think of them together, and we must recollect
there is a contrast between them. But hypothetical propositions, i.e.
both disjunctives and conditionals, are true complex propositions, since
with several terms they contain but a single assertion. Thus, in, If the
Koran comes from God, Mahomet is God's prophet, we do not assert the
truth of either of the simple propositions therein contained (viz. the
Koran comes from God, and Mahomet is God's prophet), but only the
inferribility of one from the other. The only difference, then, between
a hypothetical and a categorical proposition, is that the former is
always an assertion about an assertion (though some categoricals are so
likewise; e.g. That the whole is greater than its parts, is an axiom).
Their conspicuous place in treatises on Logic arises from this attribute
which they predicate of a proposition (for a proposition, like other
things, has attributes), viz. its being an inference from something
else, being, with reference to Logic, its chief attribute.

The _third_ common division is into Universal, Particular, Indefinite,
and Singular. A proposition whose subject is an individual name, even if
not a proper name, is singular, e.g. The founder of Rome was killed. In
particular propositions, if the part of the class meant by the _some_
were specified, the proposition would become either singular, or
universal with a different subject including all the part. Indefinite in
Logic is a solecism like _doubtful gender_ in grammar, for the speaker
must mean to make either a particular or a universal assertion.

CHAPTER V.

THE IMPORT OF PROPOSITIONS.

The object of an inquiry into the nature of propositions must be to
analyse, either, 1, the state of mind called belief, or 2, what is
believed. Philosophers have usually, but wrongly, thought the former,
i.e. an analysis of the act of judgment, the chief duty of Logic,
considering a proposition to consist in the denying or affirming one
_idea_ of another. True, we must have the two ideas in the mind
together, in order to believe the assertion about the two _things_; but
so we must also in order to disbelieve it. True also, that besides the
putting the ideas together, there may be a mental process; but this has
nothing to do with the import of propositio