Syllogism

Syllogism (from the Greek syllogismós, “reasoning,” “deduction”) — A form of deductive reasoning in which a conclusion follows necessarily from two premises, so that, once the premises are granted, the conclusion cannot be denied without contradiction. The theory was systematized by Aristotle in the Prior Analytics (Analytica Priora), a treatise belonging to the body of logical writings later gathered under the name Organon. In the categorical syllogism, three propositions articulate exactly three terms: the major term (the predicate of the conclusion), the minor term (the subject of the conclusion), and the middle term, which appears in both premises and links them together while never appearing in the conclusion. The canonical instance is the classic example: major premise — “All men are mortal”; minor premise — “Socrates is a man”; conclusion — “Socrates is mortal.” Here “mortal” is the major term, “Socrates” the minor, and “man” the middle. Aristotle distinguished different figures and moods according to the position of the middle term, establishing which combinations yield valid inferences. Validity is purely formal: it depends on structure, not on the material truth of the premises. The syllogism was the core of logic for more than two millennia, dominating medieval and early modern teaching. In the late nineteenth century, Gottlob Frege and later Bertrand Russell subsumed it within more powerful systems — propositional and predicate calculus — capable of handling relations and quantification that Aristotelian syllogistic could not reach. Neighboring concepts are deduction and premise.

← Glossary