Syllogistics

Syllogistics is the branch of logic that studies syllogisms, deductive arguments formed from two or more categorical propositions that aim to derive a conclusion about a relation between two terms. In a typical syllogism, three terms appear: a major term (the predicate of the conclusion), a minor term (the subject of the conclusion), and a middle term that links the two. The two premises are categorical statements about inclusion relations between these terms, for example All A are B and No A are C, from which a conclusion about the relation between B and C may be drawn.

A basic structure used in classical syllogistics is the categorical syllogism, which uses forms such as All, No, Some combined with is or are. The mood indicates which types of propositions appear (A: universal affirmative, E: universal negative, I: particular affirmative, O: particular negative), and the figure reflects the arrangement of the middle term in the premises. A standard example is: All humans are mortal; Socrates is a human; therefore Socrates is mortal. Here, human is the minor term, mortal is the major term, and the syllogism asserts a link through inclusion.

Historically, syllogistics traces to Aristotle, who organized logic around the theory of syllogisms and published it in the Organon. Medieval scholastics refined the theory, while later developments in logic expanded beyond syllogistic form to predicate logic. In modern logic, syllogisms are understood as a restricted, class-based fragment that illustrates fundamental deductive reasoning, but they are not as expressive as predicate or sentential logic for more complex arguments.

Syllogistics remains a foundational concept in the study of logical reasoning, illustrating how conclusions can follow from structured, categorical premises, and it provides historical context for the development of formal logic.