Syllogistic

The syllogistic, also known as the Aristotelian syllogistic, is a formal system of deductive reasoning that analyzes categorical propositions to infer conclusions. It treats logic as the study of how two premises about categories relate to a conclusion about related categories.

The basic elements are terms, of which there are three in a syllogism: major, minor, and middle. A syllogism has two premises and a conclusion, each being a categorical proposition in one of four forms: All S are P (A), No S are P (E), Some S are P (I), Some S are not P (O). The major term is the predicate of the conclusion, the minor term is the subject of the conclusion, and the middle term links the two premises.

Syllogisms are traditionally organized into figures, with figure one (the most studied) having premises that relate the middle term to the major and minor terms in a specific order. A classic example is Barbara: All M are P; All S are M; Therefore All S are P. Other moods in figure one include Celarent, Darii, and Ferio, each with a distinct combination of A, E, I, and O forms. In total, Aristotle’s system identifies multiple valid moods across several figures.

Validity is governed by rules about term distribution and premise–conclusion relationships. For example, the middle term must be distributed in at least one premise; a term distributed in the conclusion must be distributed in its corresponding premise; and two negative premises cannot yield a valid conclusion. There is also a standard count of valid moods within the system, typically cited as fourteen in classical accounts.

Historically, the syllogistic dominated ancient and medieval logic, informing scholastic education and philosophical discussions for centuries. In modern logic, it is understood as a historical precursor to predicate logic; while less general than contemporary systems, it remains a foundational study for the history of logical methods.