syllogism

A syllogism is a form of deductive reasoning consisting of two premises and a conclusion. In the classic Aristotelian syllogistic, the argument uses three terms: a major term, a minor term, and a middle term. The middle term appears in both premises and serves to link the major and minor terms so that the conclusion follows when the syllogism is valid.

The most common type is the categorical syllogism, which employs categorical propositions of the form All A are B, No A are B, Some A are B, or Some A are not B. A syllogism is valid if the conclusion necessarily follows from the premises; this depends on the arrangement of terms (figure) and the mood (the specific propositions). An everyday example: All humans are mortal. Socrates is a man. Therefore Socrates is mortal.

Historically, Aristotle laid the foundation for syllogistic logic, which influenced medieval and early modern logic. In contemporary logic, syllogisms are understood as special cases of predicate logic and are often analyzed for their validity, not for broader inference beyond the premises. Some caveats include the existential import of universal statements in traditional readings, and the fact that many forms of reasoning require more expressive form than syllogistic notation.