All men are mortal,
All heroes are men,
the middle term men forms a part of the class called mortal, by being connected with it in the way that certain contents are connected with the case that contains them; whilst it also stands in connexion with the class of heroes in the way that cases are connected with their contents. In—
No man is perfect,
Heroes are men,
the same double relation occurs. The class man, however, though part of the class hero, is no part of the class perfect but, on the contrary, expressly excluded from it. Now this expression of exclusion constitutes a relation—disjunctive indeed, but still a relation; and this is all that is wanted to give an import to the prefix dis- in distributed.
Wherever there is distribution there is inference, no matter whether the distributed term be universal or not. If the ordinary rules for the structure of the syllogism tell us the contrary to this, they only tell the truth, so far as certain assumptions on which they rest are legitimate. These limit us to the use of three terms expressive of quantity,—all, none, and some; and it is quite true that, with this limitation, universality and distribution coincide.
Say that
Some Y is X,
Some Z is Y,
and the question will arise whether the Y that is X is also the Y that is Z. That some Y belongs to both classes is clear; whether, however, it be the same Y is doubtful. Yet unless it be so, no conclusion can be drawn. And it may easily be different. Hence, as long as we use the word some, we have no assurance that there is any distribution of the middle term.
Instead, however, of some write all, and it is obvious that some Y must be both X and Z; and when such is the case—
Some X must be Z, and
Some Z must be X.