LessonsContradiction: Definition, Conditions and Application to PropositionsQuiz

The textbook uses the following examples:
“All animals are human” — false.
“No animal is human” — also false, since some animals are human.

Two universal propositions can thus both be false; they are not contradictories.

Likewise:
“Some animals are human” — true.
“Some animals are not human” — also true.

Two particular propositions can thus both be true.

Consequently both quantity and quality must be reversed: universal affirmative pairs with particular negative, and universal negative with particular affirmative.

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Why two universals or two particulars fail

Contradiction: Definition, Conditions and Application to Propositions

The textbook uses the following examples:
“All animals are human” — false.
“No animal is human” — also false, since some animals are human.

Two universal propositions can thus both be false; they are not contradictories.

Likewise:
“Some animals are human” — true.
“Some animals are not human” — also true.

Two particular propositions can thus both be true.

Consequently both quantity and quality must be reversed: universal affirmative pairs with particular negative, and universal negative with particular affirmative.