By which of the following proposition, the proposition ‘some men are not…

Concept — In classical (Aristotelian) categorical logic every standard-form proposition belongs to one of four types: A, the universal affirmative "All S are P"; E, the universal negative "No S are P"; I, the particular affirmative "Some S are P"; and O, the particular negative "Some S are not P". Two propositions are contradictories when they can neither both be true nor both be false — in every situation exactly one of the pair must hold. On the square of opposition the contradictory pairs are A with O, and E with I.

Application — Identify the terms of the given proposition, read off its standard form, and take the proposition at the opposite corner of the square:

1. Given proposition: "Some men are not honest." Subject term S = men, predicate term P = honest.

2. Its shape is "Some S are not P", which is the particular negative — the O proposition.

3. The contradictory of an O proposition sits at the opposite corner of the square: the A proposition, "All S are P".

4. Substituting the terms back in gives "All men are honest", which is therefore the required contradictory.

Cross-check — Apply the defining test of contradictories to the pair "All men are honest" / "Some men are not honest":

• If "All men are honest" is true, then no man falls outside the class of honest people, so "Some men are not honest" must be false.

• If "All men are honest" is false, then at least one man falls outside that class, so "Some men are not honest" must be true.

• Exactly one member of the pair is true in every case, and they can never be true together nor false together — the definition of contradictories is satisfied.

Contrast with the other standard forms —

Result — The proposition that contradicts "Some men are not honest" is "All men are honest".