Match the column: Square of opposition Result a. if ‘A’ is true i. ‘A’ is…
2024
Match the column:
Square of opposition | Result |
|---|---|
a. if ‘A’ is true | i. ‘A’ is undetermined; ‘I’ is true |
b. if ‘E’ is false | ii. ‘E’ is false, ‘A’ is true |
c. if ‘I’ is true | iii. ‘I’ is true, ‘E’ is false |
d. if ‘O’ is false | iv. ‘O’ is undetermined, ‘E’ is false |
Answer: D. a-iii b-i c-iv d-ii — ConceptThe traditional (Aristotelian) square of opposition arranges the four categorical propositions: A, the universal affirmative (“All S are P”); E, the…
- A.
a-i b-ii c-iii d-iv
- B.
a-iv b-i c-ii d-iii
- C.
a-iv b-iii c-ii d-i
- D.
a-iii b-i c-iv d-ii
Show answer & explanation
Correct answer: D
Concept
The traditional (Aristotelian) square of opposition arranges the four categorical propositions: A, the universal affirmative (“All S are P”); E, the universal negative (“No S is P”); I, the particular affirmative (“Some S are P”); and O, the particular negative (“Some S are not P”).
Four relations hold between them. Contradictories — A with O, and E with I — always take opposite truth values, so each one fixes the other completely. Contraries — A with E — cannot both be true, although both may be false. Subcontraries — I with O — cannot both be false, although both may be true. Subalternation runs A → I and E → O: truth descends from a universal to its particular, and falsity ascends from a particular to its universal.
Anything these relations do not settle is left undetermined; that is the whole content of a match-the-column item built on the square.
Application
Feed each given truth-value into the relations and read off what follows:
‘A’ is true. Its contradictory ‘O’ turns false; its contrary ‘E’ must be false, because two contraries cannot both be true; and subalternation carries the truth down to ‘I’. Every corner is settled, and the pair recorded in the Result column is “‘I’ is true, ‘E’ is false” — entry iii.
‘E’ is false. Its contradictory ‘I’ turns true. ‘A’ is not settled: a false ‘E’ only rules out A and E being true together, and both “All S are P” (A true) and “Some but not all S are P” (A false) make ‘E’ false. The pair recorded is “‘A’ is undetermined; ‘I’ is true” — entry i.
‘I’ is true. Its contradictory ‘E’ turns false. ‘O’ is not settled: subcontraries only forbid both being false, so ‘O’ may be either true or false while ‘I’ is true. The pair recorded is “‘O’ is undetermined, ‘E’ is false” — entry iv.
‘O’ is false. Its contradictory ‘A’ turns true, and because subalternation gives E → O, a false ‘O’ forces ‘E’ false as well; ‘I’ then follows as true. The pair recorded is “‘E’ is false, ‘A’ is true” — entry ii.
Cross-check
Set the four rows side by side and confirm that every Result entry is consumed once:
Given | Forced by the square | Left undetermined | Result entry |
|---|---|---|---|
‘A’ is true | ‘E’ false, ‘I’ true, ‘O’ false | none | iii |
‘E’ is false | ‘I’ true | ‘A’, ‘O’ | i |
‘I’ is true | ‘E’ false | ‘A’, ‘O’ | iv |
‘O’ is false | ‘A’ true, ‘I’ true, ‘E’ false | none | ii |
Entries i, ii, iii and iv are each consumed once, so the matching is one-to-one. The two “undetermined” verdicts land exactly where the square leaves slack — a false universal negative and a true particular affirmative each fix only their contradictory — while the two stronger inputs settle every corner. The match is therefore a–iii, b–i, c–iv, d–ii.