distribution

distribution, in syllogistics, the application of a term of a proposition to the entire class that the term denotes. A term is said to be distributed in a given proposition if that proposition implies all other propositions that differ from it only in having, in place of the original term, any other term whose extension is a part of that of the original term—i.e., if, and only if, the term as it is used in that occurrence covers all the members of the class that it denotes.

Thus, in a proposition of the form “No S is P,” both the subject and the predicate are distributed. In the form “Some S is P,” neither S nor P is distributed. In “Every S is P,” S is distributed, but P is not. Lastly, in “Some S is not P,” S is not distributed, but P is. Briefly, only universal propositions distribute the subject term (S), and only negative propositions distribute their predicate (P). Naturally, singular terms (including proper names used as singular terms) are always distributed, for they refer only to one object and cannot refer to fewer.

The importance of distribution lies in its being a principle of formal inference that no term may be distributed in the conclusion unless it was distributed in the premises.