LessonsContraposition: Classical Rules, Validity and the Later ConventionQuiz

“Some humans are learned” asserts only that at least one object is both human and learned. It does not entail “Some nonlearned things are nonhuman.” The chosen universe might contain only humans, some learned.

A particular premise gives information about at least one overlapping instance, not about every complementary class.

Thus the new existential claim about both complements does not follow.

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Why the particular case fails

Contraposition: Classical Rules, Validity and the Later Convention

“Some humans are learned” asserts only that at least one object is both human and learned. It does not entail “Some nonlearned things are nonhuman.” The chosen universe might contain only humans, some learned.

A particular premise gives information about at least one overlapping instance, not about every complementary class.

Thus the new existential claim about both complements does not follow.