Under the traditional square of opposition, if the statement “All saints are…

Concept

A universal affirmative proposition has the form “All S are P”: the entire S class is placed within the P class.

In the traditional square of opposition, universal affirmative propositions carry existential import; therefore truth descends by subalternation from A to I, “Some S are P.” Modern Boolean logic does not make this step without assuming that S exists.

Application

Here S = saints and P = materialists. Under the traditional categorical-logic convention used by this item, the given universal affirmative places every saint within the materialist class and presupposes at least one saint.

Contrast

• “No saints are materialists” asserts an empty intersection, contrary to the given class inclusion.

• “Some saints are not materialists” places a saint outside the materialist class, contradicting the universal inclusion.

• “Some materialists are not saints” makes a claim about materialists outside the saint class; the premise gives no information about that remainder.

Result

Thus, by subalternation, “Some saints are materialists” can be inferred under the intended traditional convention.