A term is distributed in a statement when the statement makes some claim about the entire extension of the term. For the four types of categorical statements, the highlighted terms are distributed, as shown in this simplified square of opposition:
All S is P No S is P
Some S is P Some S is not P
You should discern two patterns to help you remember which terms are distributed:
- The subject of a universal statement is distributed. This is true by the definition of the word “universal”; a universal statement is any statement that makes a claim about the entire extension of the subject. Also, the predicate of negative statements is distributed.
- The distributed terms are opposites in contradictory statements. In the A statement the subject is distributed, in the O statement it is the predicate. In the E statement both terms are distributed, in the I statement neither term is.
The rules for validity that relate to distributed terms are these:
- A valid syllogism must distribute in its premise any term distributed in the conclusion.
- A valid syllogism must distribute the middle term in at least one premise.
In the next two posts, I will explain – from the above understanding of distribution – why these rules distinguish valid from invalid syllogisms.