Syllogism

A deductive argument in which a conclusion follows from two premises, traditionally through relationships among three terms.

Premise: A statement offered as support for a conclusion in an argument. A syllogism’s two premises supply the statements from which its conclusion is meant to follow.
Major term: In a categorical syllogism, the predicate of the conclusion. Its placement in a premise helps define the syllogism’s figure.
Aristotle: An ancient Greek philosopher whose writings shaped logic, metaphysics, ethics, and natural philosophy. His works provide the earliest systematic treatment of syllogistic reasoning.
Propositional logic: A formal system that analyzes compounds of propositions using logical connectives. Unlike term syllogistics, it represents inference through relations among whole propositions.
Conclusion (argumentation): A statement that an argument presents as following from its premises. The syllogism’s third proposition is the conclusion supported by its two premises.
Minor term: In a categorical syllogism, the subject of the conclusion. Its relation to the middle term links the conclusion’s subject to its predicate.
Prior Analytics: Aristotle’s treatise presenting a formal theory of syllogisms and deduction. It develops the central ancient account of syllogistic form and proof.
Predicate logic: A formal system that represents objects, properties, relations, and quantifiers. It expresses quantified arguments beyond the reach of traditional categorical syllogisms.
Categorical proposition: A proposition asserting or denying that all or some members of one class belong to another. Traditional syllogisms connect classes through categorical propositions such as “All A are B.”
Middle term: The term appearing in both premises of a categorical syllogism but not in its conclusion. It connects the major and minor terms across the two premises.

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