Universality, then, of the middle term in one premiss is, by no means, the direct condition that gives us an inference, but only a secondary one. The direct condition is the distribution. Of this, the universality of the middle term is only a sign, and it is the only sign we have, because all and some are the only words we have to choose from. If others were allowed, the appearance which the two words (distributed and universal) have of being synonymous would disappear. And so they do when we abandon the limitations imposed upon us by the words all and some. So they do in the numerically definite syllogism, exemplified in—
More than half Y is X,
More than half Y is Z,
Some Z is X.
So, also, they do when it is assumed that the Y's which are X and the Y's which are Z are identical.
Y is X,
The same Y is Z,
Some Z is X.
In each of these formulæ there is distribution without universality, i. e. there is distribution with a quality other than that of universality as its criterion. The following extract not only explains this, but gives a fresh proof, if fresh proof be needed, that distributed and universal are used synonymously. The "comparison of each of the two terms must be equally with the whole, or with the same part of the third term; and to secure this, (1) either the middle term must be distributed in one premiss at least, or (2) the two terms must be compared with the same specified part of the middle, or (3), in the two premises taken together, the middle must be distributed, and something more, though not distributed in either singly."—Thompson, Outline of the Laws of Thought, § 39.
Here distributed means universal; Mr. Thompson's being the ordinary terminology. In the eyes of the present writer "distributed in one premiss" is a contradiction in terms.
Of the two terms, distributed is the more general; yet it is not the usual one. That it has been avoided by De Morgan has been shown. It may be added, that from the Port Royal Logic it is wholly excluded.
The statement that, in negative propositions, the relation is connective on one side, and disjunctive on the other, requires further notice. It is by no means a matter of indifference on which side the connexion or disjunction lies.
(a.) It is the class denoted by the major, of which the middle term of a negative syllogism is expressly stated to form no part, or from which it is disjoined. (b.) It is the class denoted by the minor, of which the same middle term is expressly stated to form part, or with which it is connected.
No man is perfect—