A syllogism is a kind of logical argument in which one proposition

Proposition

In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...

 (the conclusion) is inferred

Inference

Inference is the act or process of deriving logical conclusions from premises known or assumed to be true. The conclusion drawn is also called an idiomatic. The laws of valid inference are studied in the field of logic.Human inference Inference is the act or process of deriving logical conclusions...

 from two or more others (the premise

Premise

Premise can refer to:* Premise, a claim that is a reason for, or an objection against, some other claim as part of an argument...

s) of a certain form. In antiquity, there were two rival theories of the syllogism: Aristotelian syllogistic and Stoic syllogistic.

In the Prior Analytics

Prior Analytics

The Prior Analytics is Aristotle's work on deductive reasoning, specifically the syllogism. It is also part of his Organon, which is the instrument or manual of logical and scientific methods....

, Aristotle

Aristotle

Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

 defines the syllogism as "a discourse in which, certain things having been supposed, something different from the things supposed results of necessity because these things are so." (24b18–20)

Despite this very general definition, in the Prior Analytics, Aristotle limits himself to categorical syllogisms, which consist of three categorical proposition

Categorical proposition

A categorical proposition contains two categorical terms, the subject and the predicate, and affirms or denies the latter of the former. Categorical propositions occur in categorical syllogisms and both are discussed in Aristotle's Prior Analytics....

s.