universal negative proposition

logic

Also known as: E proposition

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July 14, 2026

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A universal negative proposition is a statement in logic that denies something of all members of a class. For example, "No dogs are cats" is a universal negative proposition. This type of proposition is one of the fundamental forms of categorical propositions, which were systematically studied by Aristotle. These propositions typically involve a quantifier (like "no"), a subject, a copula, and a predicate. The study of logic, including these proposition types, began with Aristotle, who viewed logic as a tool for reasoning across all sciences.12

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history of logic
Categorical forms
” Universal negative: “Every β is not an α,” or equivalently “No β is an α.” Particular affirmative: “Some β is an α.” Particular negative: “Some β is not an α.” Indefinite affirmative: “β is an α.” Indefinite negative: “β is not an α.”
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” Universal negative: “Every β is not an α,” or equivalently “No β is an α.” Particular affirmative: “Some β is an α.” Particular negative: “Some β is not an α.” Indefinite affirmative: “β is an α.” Indefinite negative: “β is not an α.”
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