Under the modern Boolean interpretation, choose the correct answer regarding…

Concept

In a categorical syllogism, the middle term must be distributed in at least one premise, and any term distributed in the conclusion must also be distributed in its corresponding premise.

Under the modern Boolean interpretation, universal E and A propositions do not assert existence, whereas a particular O conclusion asserts that at least one member exists.

Application

1. EAO-3 has the form: No M are P; all M are S; therefore, some S are not P.

2. The E proposition distributes both M and P. The A proposition distributes its subject M. Hence the middle term M is distributed.

3. The O conclusion distributes its predicate P, and P is also distributed in the E premise. The subject S of the conclusion remains undistributed.

4. One premise is negative (E) and the other is affirmative (A), so the premises are not both negative.

5. However, both premises are universal and do not assert existence, while the O conclusion is particular. Thus, under the modern Boolean interpretation, the inference commits the existential fallacy.

Cross-check

If the class M is empty, both universal premises can be true while the conclusion ‘Some S are not P’ need not be true. This countermodel confirms the existential fallacy.

Therefore, the correct answer by value is: Commits the existential fallacy.