When the negative sign is associated with the predicate, so as to make
this an Infinite Term (chap. iv. § 8), the proposition is called an
Infinite Proposition, as _S is not-P_ (or _p), All men are--incapable of
resisting flattery_, or _are--not-proof against flattery_.

Infinite propositions, when the copula is affirmative, are formally,
themselves affirmative, although their force is chiefly negative; for,
as the last example shows, the difference between an infinite and a
negative proposition may depend upon a hyphen. It has been proposed,
indeed, with a view to superficial simplification, to turn all
Negatives into Infinites, and thus render all propositions Affirmative
in Quality. But although every proposition both affirms and denies
something according to the aspect in which you regard it (as _Snow is
white_ denies that it is any other colour, and _Snow is not blue_
affirms that it is some other colour), yet there is a great difference
between the definite affirmation of a genuine affirmative and the vague
affirmation of a negative or infinite; so that materially an affirmative
infinite is the same as a negative.

Generally Mill's remark is true, that affirmation and denial stand for
distinctions of fact that cannot be got rid of by manipulation of words.
Whether granite sinks in water, or not; whether the rook lives a hundred
years, or not; whether a man has a hundred dollars in his pocket, or
not; whether human bones have ever been found in Pliocene strata, or
not; such alternatives require distinct forms of expression. At the same
time, it may be granted that many facts admit of being stated with
nearly equal propriety in either Quality, as _No man is proof against
flattery_, or _All men are open to flattery_.