Logic, Inductive and Deductive

by William Minto

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.