A syllogism (Greek: συλλογισμός – syllogismos – "conclusion," "inference") is a kind of logical argument in which one proposition (the conclusion) is inferred from two or more others (the premises) of a specific form. In antiquity, two rival theories of the syllogism existed: Aristotelian syllogistic and Stoic syllogistic.
Aristotle defines the syllogism as "a discourse in which certain (specific) things having been supposed, something different from the things supposed results of necessity because these things are so."
Despite this very general definition, in the Prior Analytics Aristotle limits himself to categorical syllogisms, which consist of three categorical propositions. These included categorical modal syllogisms. From the Middle Ages onwards, "categorical syllogism" and "syllogism" were mostly used interchangeably, and the present article is concerned with this traditional use of "syllogism" only. The syllogism was at the core of traditional deductive reasoning, where facts are determined by combining existing statements, in contrast to inductive reasoning where facts are determined by repeated observations.
The syllogism was superseded by first-order predicate logic following the work of Gottlob Frege, in particular his Begriffsschrift (Concept Script) (1879), but syllogisms remain useful.
Read more about Syllogism: Basic Structure, Types of Syllogism, Terms in Syllogism, Existential Import, Syllogism in The History of Logic, Syllogistic Fallacies