### Immediate Inference:Contraposition

The contrapositive of a proposition is formed by two steps:

1. Switching the subject and predicate terms, as in taking the converse

2. Replacing both the subject and the predicate terms with their complements

The quality and quantity of the proposition remain as they were.

It is always legitimate to take the contrapositive of an A proposition. An A proposition says that the class of Ss is included within the class of Ps. So anything outside the class of Ps (i.e., all the non-Ps) must be outside the class of Ss (i.e., it must be a non-S).

Example:

Switzerland is in Europe, so if you're not in Europe, you're not in Switzerland.

Contraposition is not a legitimate operation for I and E propositions.

Example:

The E proposition, "No primate is an aquatic animal," is clearly not equivalent to its contrapositive, "No nonaquatic animal is a nonprimate," because the first is true and the second false (cows are nonaquatic animals but they are nonprimates).

Similarly, the I proposition, "Some soldiers are nonofficers," is clearly not equivalent to its contrapositive, "Some officers are nonsoldiers."

The O proposition is the only one, besides the A, that is equivalent to its contrapositive. Even so, it is rarely used in ordinary speech.

Conversion | Obversion | Contraposition

Immediate Inference