311. Nay, even when the [upsilon] is an identical proposition,
[omega] will still hold in the same matter. 'All rational animals are
all rational animals': but, for all that, 'Some rational animals are
not some others.' This last form of proposition therefore is almost
wholly devoid of meaning.

312. The chief advantage claimed for the quantification of the
predicate is that it reduces every affirmative proposition to an exact
equation between its subject and predicate. As a consequence every
proposition would admit of simple conversion, that is to say, of
having the subject and predicate transposed without any further change
in the proposition. The forms also of Reduction (a term which will be
explained later on) would be simplified; and generally the
introduction of the quantified predicate into logic might be attended
with certain mechanical advantages. The object of the logician,
however, is not to invent an ingenious system, but to arrive at a true
analysis of thought. Now, if it be admitted that in the ordinary form
of proposition the subject is used in extension and the predicate in
intension, the ground for the doctrine is at once cut away. For, if
the predicate be not used in its extensive capacity at all, we plainly
cannot be called upon to determine whether it is used in its whole
extent or not.




CHAPTER VI.

_Of the Heads of Predicables_.