If the statement ‘Some men are honest’ is false, which of the following…
2013
If the statement ‘Some men are honest’ is false, which of the following statements are true? Choose the correct code:
(i) All men are honest.
(ii) No men are honest.
(iii) Some men are not honest.
(iv) All men are dishonest.
Codes:
Answer: B. (ii), (iii) and (iv) — ConceptIn traditional categorical logic, the proposition ‘Some S are P’ and the proposition ‘No S is P’ are contradictories. Exactly one of a contradictory…
- A.
(i), (ii) and (iii)
- B.
(ii), (iii) and (iv)
- C.
(i), (iii) and (iv)
- D.
(ii), (i) and (iv)
Show answer & explanation
Correct answer: B
Concept
In traditional categorical logic, the proposition ‘Some S are P’ and the proposition ‘No S is P’ are contradictories. Exactly one of a contradictory pair is true.
For a nonempty subject class, a true universal negative proposition also supports the corresponding particular negative proposition. If ‘dishonest’ means ‘not honest’, the same predicate complement can be stated in universal form.
Application
Let I denote ‘Some men are honest’. Since I is false, its contradictory E proposition, ‘No men are honest’, is true.
Men form a nonempty class; therefore, from ‘No men are honest’ it follows that ‘Some men are not honest’ is true.
Using ‘dishonest’ as the complement of ‘honest’, ‘No men are honest’ is equivalent here to ‘All men are dishonest’.
‘All men are honest’ is incompatible with ‘No men are honest’, so statement (i) is false.
Cross-check
Statement (i): false — universal affirmation conflicts with the true universal negative.
Statement (ii): true — it is the contradictory of the false particular affirmative.
Statement (iii): true — it follows by subalternation for the nonempty class of men.
Statement (iv): true — it restates the predicate complement in universal form.
Thus the true statements are (ii), (iii) and (iv).