Which proposition is the contradictory of “No men are mortal”?

Concept

In the traditional square of opposition, contradictory propositions cannot both be true and cannot both be false. The universal negative E-form “No S are P” is contradictory to the particular affirmative I-form “Some S are P”; symbolically, negating ∀x(S→¬P) gives ∃x(S∧P).

Application

1. The given proposition “No men are mortal” has the E-form: No S are P.

2. Its contradictory must reverse both quantity and quality, producing the I-form: Some S are P.

3. Substituting S = men and P = mortal gives “Some men are mortal.”

Cross-check and contrast

• “Some men are not mortal” is an O-form (particular negative), paired contradictorily with an A-form rather than an E-form.

• “All men are mortal” is an A-form (universal affirmative), not the particular affirmative I-form required here.

• “No mortal beings are men” remains an E-form (universal negative) and merely exchanges the subject and predicate terms.

Therefore, the contradictory proposition is “Some men are mortal.”