If the universal is true, what about its subalternate?

• A. It must be false
• B. It must be true
• C. It could be either true or false
• D. It is independent

Answer: (B)

In traditional syllogistic, there is a relation called subalternation: if a universal proposition is true, the corresponding particular must also be true. The reason is existential import: a universal statement like “All S are P” is taken to assert that there is at least one S. If that’s true, that S is also a P, so “Some S are P” is true as well.

For example, if all dogs are mammals, there must be at least one dog, and that dog is a mammal, so some dog is a mammal.

The one-way nature is important: a true particular doesn’t force the universal, so it’s possible that some S are P without all S being P. But when the universal is true, its subalternate must be true.