Distribution of terms

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 (B) 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