Celarent

Celarent is a valid mood in the traditional syllogistic of Aristotelian logic. It belongs to the first figure and follows the EAE form: the major premise is a universal negative (No M are P), the minor premise is a universal affirmative (All S are M), and the conclusion is a universal negative (No S are P). In symbolic terms: No M are P; All S are M; therefore No S are P.

In Figure I, the middle term M serves as the subject of the major premise and the predicate of the minor premise, linking the subject term S with the predicate term P in the conclusion. The pattern demonstrates how the conclusion derives from the two premises while preserving the position of the terms.

Historically, Celarent is one of the standard mnemonic moods used in the medieval and early modern tradition of syllogistic logic. Alongside Barbara (AAA), Darii (AII), and Ferio (EIO), Celarent is listed among the four valid moods of the first figure. The name itself is part of a broader set of Latin-lettered names assigned to syllogistic forms, used to aid memorization of valid patterns.

Example: Major premise: No reptiles are mammals. Minor premise: All snakes are reptiles. Therefore: No snakes are mammals. This illustrates the EAE form of Celarent, showing how a universal negative premise and a universal affirmative premise yield a universal negative conclusion.

Notes: In this context, E stands for universal negative, A for universal affirmative, and I and O for particular affirmative and negative, respectively. Celarent remains a foundational example in discussions of classical syllogistic reasoning.