A categorical term is said to be distributed, if all individual members of that category are accounted for. In a statement like "All A are either B or C", the term A is distributed, because all elements of the set A are pinpointed. The terms B and C are not distributed, because there might be Bs and Cs, that are not A. In a statement like "Some D are E", neither D nor E are distributed, because nothing is said about the remaining Ds (that are not E) and nothing about the Es that are not D. In a categorical syllogism the distribution of terms depends on the quantifier:
- In "All A are B"-propositions the subject (A) is distributed.
- In "No A are B"-propositions both the subject (A) and the predicate (B) are distributed.
- In "Some A are B"-propositions neither the subject nor the predicate are distributed.
- In "Some A are not B"-propositions the predicate is distributed.
Copi and Cohen (see ref.) state two rules about distribution of terms in valid syllogisms:
- 1. The middle term must be distributed in at least one premise.
- 2. If the major term or the minor term is distributed in the conclusion, then it must be distributed in the premises.
When these rules are not followed, a fallacy or sophism can ensue.
References
Irving M. Copi, Carl Cohen: Introduction to Logic. Prentice Hall
