First principle: “A whole exceeds its proper part”—the understood relation needs no distinct inferential middle.
Innate inference: “Four is even”—the criterion of divisibility into equal integers serves as an ever-present middle.
Ask two different questions:
1. Is the judgment evident from the terms without a distinct middle?
2. Or does an extremely familiar middle already establish it?
Failing to state a readily available proof does not remove the proof. The distinction matters particularly when classifying elementary arithmetic propositions.