If two standard form categorical propositions with the same subject and…
2017
If two standard form categorical propositions with the same subject and predicate are related in such a manner that if one is undetermined the other must be undetermined, what is their relation ?
Answer: C. Contradictory — Concept. In the traditional square of opposition the four standard-form categorical propositions built on the same subject S and the same predicate P are A…
- A.
Contrary
- B.
Subcontrary
- C.
Contradictory
- D.
Sub-altern
Show answer & explanation
Correct answer: C
Concept. In the traditional square of opposition the four standard-form categorical propositions built on the same subject S and the same predicate P are A (All S are P), E (No S is P), I (Some S are P) and O (Some S are not P). Every relation drawn between two of them is an inference rule saying how much of one proposition’s truth value passes across to the other. Call a relation truth-functionally complete when each value of either member fixes its partner’s value, and partial when some values pass across while the remaining ones leave the partner undetermined. Undeterminacy can therefore travel in both directions only across a complete relation.
Application. The relation asked for must satisfy one condition: if either member is undetermined, the other must be undetermined too. Trace the transfer rules of the exclusive-and-exhaustive pairs A–O and E–I:
For A and O (and likewise for E and I) exactly one member of the pair is true and the other is false — they can neither both hold nor both fail.
So a true member yields a false partner, and a false member yields a true partner, in both directions, with no gap in the table.
Read in reverse: no definite value of one member can sit beside an undetermined partner, because a definite value always fixes the partner outright.
Equally, if a member’s own value is unknown, nothing in the pair can pin the partner down, so the partner is undetermined as well.
Undeterminacy therefore passes both ways across this pairing, which is exactly the condition stated in the question.
Cross-check. Set the transfer behaviour of all four relations side by side:
Relation | Values that pass to the partner | Values that leave the partner undetermined |
|---|---|---|
Contrary (A–E) | truth of one member yields falsity of the other | falsity of either member |
Subcontrary (I–O) | falsity of one member yields truth of the other | truth of either member |
Sub-altern (A–I, E–O) | truth of the universal yields truth of the particular; falsity of the particular yields falsity of the universal | falsity of the universal; truth of the particular |
Contradictory (A–O, E–I) | truth yields falsity and falsity yields truth, in both directions | none |
In the first three rows the last column is non-empty, so one member can hold a definite value while its partner stays undetermined — a false E, for instance, is itself determined yet leaves A undetermined, which breaks the stated condition. Only the contradictory relation has an empty last column, so only there does the undeterminacy of one member compel the undeterminacy of the other. The relation described is therefore Contradictory.