LessonsThe Fourth Figure: Productive Conditions, Moods and ProofsQuiz

The move from “All scholars are teachers; all teachers are humans” to “Some humans are scholars” presupposes that scholars exist. Classical categorical logic commonly treats relevant classes as having instances.

If a purely hypothetical kind has no members, two universal statements may be true without yielding a true existential (“some”) conclusion in modern predicate logic.

Diagnostic question: whenever a particular conclusion follows from universals alone, identify the existential commitment that licenses “some.”

Opening interactive controls...

Existence behind a particular conclusion

The Fourth Figure: Productive Conditions, Moods and Proofs

The move from “All scholars are teachers; all teachers are humans” to “Some humans are scholars” presupposes that scholars exist. Classical categorical logic commonly treats relevant classes as having instances.

If a purely hypothetical kind has no members, two universal statements may be true without yielding a true existential (“some”) conclusion in modern predicate logic.

Diagnostic question: whenever a particular conclusion follows from universals alone, identify the existential commitment that licenses “some.”