syllogisme

Syllogism, also known as syllogisme in French, is a form of deductive reasoning that uses two premises to derive a conclusion. It asserts that a relation between two terms follows from their relation to a common middle term. In a classical syllogism there are three terms: a major term, a minor term, and a middle term that appears in both premises and links the other two.

The typical structure involves two categorical propositions and a conclusion. Each proposition has a subject term and a predicate term. The middle term connects the major and minor terms, allowing the conclusion to relate the major and minor terms. Terms are arranged into figures, depending on how the middle term is positioned in the premises. The standard notation also uses moods, designated by the letters A (All), E (No), I (Some), and O (Some not).

A simple example is: All men are mortal (A), Socrates is a man (A), therefore Socrates is mortal (A). This illustrates a valid mood in Aristotelian logic. In practice, not all combinations yield a valid inference; the study classifies valid and invalid forms, and identifies rules such as the need for three terms, the distribution of the middle term, and the relation between negative and affirmative premises and conclusions.

Historically, syllogistic was formalized by Aristotle and refined in the medieval period. Modern logic can express these ideas with predicate logic, but syllogisms remain a foundational example of deductive validity and historical approach to reasoning.