No S is P--
we see at once that "Every war increases taxation" is of the form All
S is M. Does the other sentence yield the Major Premiss No M is P,
when M represents the increasing of taxation, _i.e._, a class bounded
by that attribute? We see that the last sentence of the argument is
equivalent to saying that "Nothing that increases taxation is long
popular"; and this with the Minor yields the conclusion in Celarent.

Nothing that increases taxation is long popular.
Every war increases taxation.
No war is long popular.

Observe, now, what in effect we have done in thus reducing the
argument to the First Figure. In effect, a general principle being
alleged as justifying a certain conclusion, we have put that principle
into such a form that it has the same predicate with the conclusion.
All that we have then to do in order to inspect the validity of the
argument is to see whether the subject of the conclusion is contained
in the subject of the general principle. Is war one of the things that
increase taxation? Is it one of that class? If so, then it cannot long
be popular, long popularity being an attribute that cannot be affirmed
of any of that class.

Reducing to the first figure, then, amounts simply to making the
predication of the proposition alleged as ground uniform with the
conclusion based upon it. The minor premiss or applying proposition
amounts to saying that the subject of the conclusion is contained in
the subject of the general principle. Is the subject of the conclusion
contained in the subject of the general principle when the two have
identical predicates? If so, the argument falls at once under the
_Dictum de Omni et Nullo_.

Two things may be noted concerning an argument thus simplified.

1. It is not necessary, in order to bring an argument under the
_dictum de omni_, to reduce the predicate to the form of an extensive
term. In whatever form, abstract or concrete, the predication is made
of the middle term, it is applicable in the same form to that which is
contained in the middle term.

2. The quantity of the Minor Term does not require special attention,
inasmuch as the argument does not turn upon it. In whatever quantity
it is contained in the Middle, in that quantity is the predicate of
the Middle predicable of it.

These two points being borne in mind, the attention may be
concentrated on the Middle Term and its relations with the extremes.

That the predicate may be left u