Which statement best describes the Fourth Law of Opposition?

• A. Subalterns may both be true or both be false.
• B. If the particular is false, the universal is false; if the universal is true, then the particular is true.
• C. Subcontraries may at the same time both be true.
• D. Subalterns may both be true or both be false; if the particular is false, the universal is false; if the universal is true, then the particular is true; otherwise, their status is indeterminate.

Answer: (D)

In traditional syllogistic, the Fourth Law of Opposition governs how a universal proposition and its corresponding particular relate in truth-value. It shows that the universal and the particular can align in different ways, but with clear conditions.

If the particular statement is false, the universal must be false. That is, saying “Some S are P” is false rules out the claim “All S are P.” So a false particular forces the corresponding universal to be false.

If the universal is true, the particular must be true. If “All S are P” holds, then certainly “Some S are P” holds as well, so the universal’s truth guarantees the particular’s truth.

They may both be true (when the universal is true, the particular is true as well) or both be false (in some cases where neither statement can be established, especially under the traditional logic’s existential import). When neither of the above conditions applies, their statuses are indeterminate.

This combination—the entailments in the second and third points plus the possibility of both true or both false and the potential indeterminacy—is captured by the statement describing the Fourth Law.