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How did Aristotle’s syllogisms work?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — Aristotle Aristotle, detail of a Roman copy (2nd century bce) of a Greek alabaster portrait bust (c. 325 bce); in the Museo Nazionale Romano, Rome.

Aristotle’s syllogisms are a foundational method of logical inference, systematically detailed in his work the Prior Analytics. A syllogism is a form of argument where a conclusion is drawn from two premises.123

Structure and Terms

A categorical syllogism consists of three propositions, each containing two terms. These terms play specific roles:1
* Major term: The predicate of the conclusion.1
* Minor term: The subject of the conclusion.1
* Middle term: The term that appears in both premises, serving to link the major and minor terms.13

Aristotle introduced the use of schematic letters (variables) to represent these terms, allowing him to identify valid patterns of argument regardless of the specific content. For example, the pattern known as Barbara is expressed as: "If A belongs to every B, and B belongs to every C, then A belongs to every C".12

Validity and Classification

Aristotle classified propositions by quantity (universal or particular) and quality (affirmative or negative). He established rules to determine which combinations of these propositions result in valid inferences—arguments where true premises guarantee a true conclusion. By reducing various argument patterns to these valid forms, he created a rigorous system of formal logic.13