D; and, similarly,
grant the premises of a syllogism, and the conclusion follows. Again,
grant that C is not D, and it follows that A is not B; and, similarly,
if the conclusion of a valid syllogism be false, it follows that one, or
other, or both of the premises must be false. But, once more, grant that
C is D, and it does not follow that A is B; so neither, if the
conclusion of a syllogism be true, does it follow that the premises are.
For example:--

Sociology is an exact science;
Mathematics is a branch of Sociology:
.'. Mathematics is an exact science.

Here the conclusion is true although the premises are absurd. Or
again:--

Mathematics is an exact science;
Sociology is a branch of Mathematics:
.'. Sociology is an exact science.

Here the major premise is true, but the minor is false, and the
conclusion is false. In both cases, however, whether the conclusion be
true or false, it equally follows from the premises, if there is any
cogency in Barbara. The explanation of this is, that Barbara has only
formal cogency; and that whether the conclusion of that, or any other
valid mood, shall be true according to fact and experience, depends upon
how the form is filled up. How to establish the premises, then, is a
most important problem; and it still remains to be solved.

Sec. 2. We may begin by recalling the distinction between the denotation
and connotation of a general term: the denotation comprising the things
or events which the term is a name for; the connotation comprising the
common qualities on account of which these things are called by the same
name. Obviously, there are very few general terms whose denotation is
exhaustively known; since the denotation of a general term comprises all
the things that have its connotation, or that ever have had, or that
ever will have it, whether they exist here, or in Australia, or in the
Moon, or in the utmost stars. No one has examined all men, all mammoths,
all crystals, all falling bodies, all cases of fever, all revolutions,
all stars--nor even all planets, since from time to time new ones are
discerned. We have names for animals that existed long before there were
men to observe them, and of which we know only a few bones, the remains
of multitudinous species; and for others that may continue to exist when
men have disappeared from the earth.

If, indeed, we definitely limit the time, or place, or quantity of
matter to be explore