syllogismos

Syllogismos is the form of deductive reasoning in which a conclusion is inferred from two premises that share a common term, called the middle term. The term comes from Greek syllogismos, meaning a gathering together or reasoning by combining propositions.

Historically, the most influential treatment comes from Aristotle, who systematized syllogismos in the Prior Analytics. Classical syllogismos analyzes categorical propositions and seeks to determine when the conclusion necessarily follows from two premises. Medieval and scholastic logicians expanded the theory; in the modern era, logicians recast syllogistic within predicate logic, where the same reasoning patterns can be expressed in more general form.

In a syllogismos, there are three terms: the major term (the predicate of the conclusion), the minor term (the subject of the conclusion), and the middle term (which appears in both premises but not in the conclusion). The premises are categorical propositions of the form All S are M, No S are M, or Some S are M. A common example is: All humans are mortal; Socrates is a human; therefore Socrates is mortal.

Classical syllogismos also classifies forms by figure, depending on the position of the middle term in the premises, and by mood, indicating the particular forms of the premises. Validity is determined by rules such as proper distribution of terms and the requirement that the conclusion follow from the premises. Not every arrangement yields a valid conclusion.

In contemporary logic, syllogismos is viewed as a restricted fragment of first-order logic. It remains of historical interest and is used as a teaching tool to illustrate deductive structure, while more expressive formalisms handle broader reasoning tasks.