Moreover, they acknowledge what must necessarily be admitted: some propositional judgments are self-evident, while others are inferential. They cannot all be inferential, since inferential knowledge depends on what is self-evident. The point previously made concerning conceptions therefore applies here: the distinction between the two is relative, depending on the person. What requires inference for one person may be self-evident to another.

A self-evident propositional judgment is one in which conceiving its two terms—its subject and predicate—is sufficient to assent to it. It does not depend on anything mediating between them, namely, the proof constituted by the middle term. This holds whether or not the conceptions of the two terms are themselves self-evident. It is well known that people differ in mental capacity far more than they differ in physical strength. Some attain such speed and precision in forming conceptions that they far surpass others. Such a person may conceive both terms so fully that this complete conception makes implications apparent which remain unclear to someone who has not conceived them in this way.

It is evident that, for certain propositions, some people may need the mediating term that constitutes the proof, while others do not. Many people know a proposition through sensory perception, experience, demonstration, or mass transmission, whereas someone else comes to know it only through reasoning and inference. Thus, many people need proof that the predicate holds of the subject not for themselves, but for others. They explain this to others using proofs they themselves do not need, even providing illustrative examples.