The propositions “All Indians eat rice” and “Some Indians eat rice” are an…

In the traditional Square of Opposition, categorical propositions come in four standard forms: A (universal affirmative — "All S are P"), E (universal negative — "No S is P"), I (particular affirmative — "Some S are P"), and O (particular negative — "Some S are not P"). The square names four relations between pairs of these: Contradictories (A-O and E-I) can never both be true and never both be false; Contraries (A-E) cannot both be true but can both be false; Sub-contraries (I-O) cannot both be false but can both be true; and Subalternation (A-I and E-O) links a universal proposition to its particular counterpart of the same quality, where the truth of the universal guarantees the truth of the particular.

1. “All Indians eat rice” has the form “All S are P” — this is the universal affirmative (A) proposition.

2. “Some Indians eat rice” has the form “Some S are P” — this is the particular affirmative (I) proposition, sharing the same subject (Indians), the same predicate (eat rice), and the same affirmative quality as the first.

3. A pair that shares subject, predicate, and quality, but differs only in quantity (universal versus particular), is linked by subalternation — the universal member is the superaltern and the particular member is its subaltern.

4. Since the universal claim “All Indians eat rice” logically guarantees the particular claim “Some Indians eat rice” (what holds for all certainly holds for some), the pair exemplifies subalternation.

• Contraries would need two universal propositions of opposite quality, e.g. “All Indians eat rice” and “No Indians eat rice” — not this pair, since one proposition here is particular, not universal.

• Contradictions would need opposite quantity AND opposite quality, e.g. “All Indians eat rice” and “Some Indians do not eat rice” — not this pair, since both propositions here share the same affirmative quality.

• Sub-contraries would need two particular propositions of opposite quality, e.g. “Some Indians eat rice” and “Some Indians do not eat rice” — not this pair, since one proposition here is universal, not particular.

Hence the relationship exemplified by this pair is Subalternation.