Categorical Syllogisms

Rules of Validity
Any syllogism that satisfies all four of the following rules is valid; any syllogism that fails even one of the rules is invalid.

1. In a valid syllogism, the middle term must be distributed in at least one of the premises.
2. If either of the terms in the conclusion is distributed, it must be distributed in the premise in which it occurs.
3. No valid syllogism can have two negative premises.
4. If either premise of a valid syllogism is negative, the conclusion must be negative, and if the conclusion is negative, one premise must be negative.

Venn Diagrams

© Copyright 1998, W.W. Norton & Co.

1.	In a valid syllogism, the middle term must be distributed in at least one of the premises.
2.	If either of the terms in the conclusion is distributed, it must be distributed in the premise in which it occurs.
3.	No valid syllogism can have two negative premises.
4.	If either premise of a valid syllogism is negative, the conclusion must be negative, and if the conclusion is negative, one premise must be negative.