Under the intended categorical-logic reading, which of the following…

Concept

A categorical proposition is classified by quantity and quality. A universal affirmative proposition (A: “All S are P”) and a particular negative proposition (O: “Some S are not P”) are contradictories: they cannot both be true and cannot both be false.

An ordinary-language sentence must first be normalized to its intended categorical form; a degree adverb should not be silently turned into a count of people.

Application

“Wise men are hardly afraid of death” is not itself a standard A/E/I/O sentence. In this exam item’s intended categorical reading, “hardly afraid” presents fear as generally absent among wise men and is normalized as the O-form “Some wise men are not afraid of death.”

The contradictory of that O-form is the A-form “All wise men are afraid of death.” The official December 2014 Set-W final key also identifies this proposition as the answer.

Contrast

• “Some wise men are afraid of death” is the I-form; an I-form and an O-form can both be true because different members may have different properties.

• “No wise man is afraid of death” is the E-form; it is a stronger universal-negative claim, not the A-form contradictory of the intended O-form.

• “Some wise men are not afraid of death” is the O-form used to normalize the source statement, so it restates the intended content rather than contradicting it.

Cross-check

Test the A–O pair directly. If every wise man is afraid of death, then “some wise men are not afraid” is false. If “all wise men are afraid” is false in the intended nonempty class, then at least one wise man is not afraid. Thus the A- and O-forms have opposite truth values.

Result

Therefore, the contradictory proposition is “All wise men are afraid of death.”