Which of the following propositions is contrary to the proposition ‘All women…

Concept

In the traditional square of opposition, categorical propositions are classified as A (universal affirmative), E (universal negative), I (particular affirmative), and O (particular negative).

A and E are contraries: they cannot both be true, although they can both be false. A and O, and E and I, are contradictory pairs.

Application

1. The proposition “All women are honest” has the A form: All S are P.

2. The contrary of an A proposition is the corresponding E proposition: No S is P.

Contrast

• “Some women are not honest” has the O form and is the contradictory, not the contrary, of the original A proposition.

• “Some women are not dishonest” reduces to a particular affirmative claim about honest women and does not express the E form.

• “No women are dishonest” reduces to the same universal affirmative content as “All women are honest” when honest and dishonest are treated as complements.

Result

Therefore, the contrary proposition is “No women are honest.”