Page "Transposition (logic)" Paragraph 25

Necessary and sufficient conditions can be explained by analogy in terms of the concepts and the rules of immediate inference of traditional logic.

In the categorical proposition " All S is P ", the subject term ' S ' is said to be distributed, that is, all members of its class are exhausted in its expression.

Conversely, the predicate term ' P ' cannot be said to be distributed, or exhausted in its expression because it is indeterminate whether every instance of a member of ' P ' as a class is also a member of ' S ' as a class.

All that can be validly inferred is that " Some P are S ".

Thus, the type ' A ' proposition " All P is S " cannot be inferred by conversion from the original ' A ' type proposition " All S is P ".

All that can be inferred is the type " A " proposition " All non-P is non-S " ( Note that ( P → Q ) and (~ Q → ~ P ) are both ' A ' type propositions ).

Grammatically, one cannot infer " all mortals are men " from " All men are mortal ".

An ' A ' type proposition can only be immediately inferred by conversion when both the subject and predicate are distributed, as in the inference " All bachelors are unmarried men " from " All unmarried men are bachelors ".