Among the following statements two are contradictory to each other. Select the…
2015
Among the following statements two are contradictory to each other. Select the correct code from those given below that represents such a pair of statements :
Statements :
(a) All poets are philosophers.
(b) Some poets are philosophers.
(c) Some poets are not philosophers.
(d) No philosopher is a poet.
Codes :
Answer: C. (a) and (c) — Concept — In the traditional square of opposition every categorical statement takes one of four forms, fixed by its quantity (universal or particular) and its…
- A.
(a) and (b)
- B.
(a) and (d)
- C.
(a) and (c)
- D.
(b) and (c)
Show answer & explanation
Correct answer: C
Concept — In the traditional square of opposition every categorical statement takes one of four forms, fixed by its quantity (universal or particular) and its quality (affirmative or negative): A = "All S are P", E = "No S is P", I = "Some S are P", O = "Some S are not P". Two statements are contradictory when they can neither both be true nor both be false, so exactly one of them must be true. On the square, the contradictory pairs are A with O and E with I. A with E are contraries (never both true, but both can be false), I with O are subcontraries (never both false, but both can be true), and A with I or E with O stand in subalternation.
Application
Fix the two terms for the whole set: subject S = poets, predicate P = philosophers.
(a) "All poets are philosophers" is universal and affirmative, so it is of form A.
(b) "Some poets are philosophers" is particular and affirmative, so it is of form I.
(c) "Some poets are not philosophers" is particular and negative, so it is of form O.
(d) "No philosopher is a poet" is universal and negative. A universal negative converts simply, so it is equivalent to "No poet is a philosopher" and is of form E on the same two terms.
Apply the contradiction rule: A goes with O, which pairs (a) with (c); E goes with I, which pairs (d) with (b). Only the first of those two pairs appears among the codes offered.
Cross-check — the relation each offered code actually names:
Code | Forms | Relation and why |
|---|---|---|
(a) and (b) | A and I | Subalternation: if every poet is a philosopher then certainly some poet is, so both can be true together. |
(a) and (d) | A and E | Contraries: if some but not all poets are philosophers, both statements are false together. |
(a) and (c) | A and O | Contradictories: "all are" and "some are not" cannot both hold, and they cannot both fail, so exactly one is true. |
(b) and (c) | I and O | Subcontraries: if some poets are philosophers and some are not, both statements are true together. |
Hence the two statements contradictory to each other among the codes offered are (a) and (c). The set also contains a second contradictory pair, (b) with (d), that is, I with E, but no code lists it.