If the proposition “All men are not mortal” is true then which of the…

Concept. In traditional (Aristotelian) logic every categorical statement takes one of four standard forms, arranged in the square of opposition: the A-form “All S are P” (universal affirmative), the E-form “No S is P” (universal negative), the I-form “Some S are P” (particular affirmative) and the O-form “Some S are not P” (particular negative). A and O are contradictories, and so are E and I: in each pair exactly one member is true. A and E are contraries: they cannot both be true, though both may be false. Calling a form “doubtful” means the given information leaves its truth value undetermined.

Application. The premise “All men are not mortal” denies the A-form “All men are mortal”. English “All S are not P” is read by some logic texts as the E-form (“No men are mortal”) and by others as the O-form (“Some men are not mortal”). On either reading the A-form comes out false: on the E reading because A and E are contraries and E is given as true, and on the O reading because A and O are contradictories and O is given as true.

1. “All men are mortal” is true — cannot hold, since the A-form is false on both readings of the premise.

2. “Some men are mortal” is false — holds on the E reading, because the I-form is the contradictory of the E-form; on the O reading the I-form is left undetermined.

3. “No men are mortal” is doubtful — holds on the O reading, because a true O-form leaves the E-form undetermined; on the E reading the E-form is simply the premise and so is true.

4. “All men are mortal” is false — holds on both readings, exactly as derived above.

Cross-check. Test the four codes against what has just been established. Claim 1 is the only claim that fails on every reading of the premise, so each code containing claim 1 is ruled out, and that removes three of the four codes at a stroke. The single code left standing is the one built from claims 2, 3 and 4, and it is the code recorded in the official UGC answer key for this paper — in the key first issued and again in the revised key released after grievances.

A caveat, stated plainly. This item is logically defective as set, and it is worth knowing why. Claim 2 is secure only on the E reading and claim 3 only on the O reading, so claims 2, 3 and 4 are never all true together under one consistent reading of “All men are not mortal”; on the E reading the sound set would be claims 2 and 4, and on the O reading it would be claims 3 and 4, and neither of those sets is offered. Eliminating claim 1 therefore does not prove the surviving code true — it shows only that this code is the one code free of a claim that is false on every reading, which is why it is the code to mark. The transferable lesson here is the square of opposition itself, together with the habit of disambiguating an “All S are not P” construction before reasoning from it.