Syllogismus

Syllogismus, or syllogism, is a form of deductive reasoning in classical logic. It consists of two premises and a conclusion, using three terms. The premises share a middle term that does not appear in the conclusion. If the premises are true and the form is valid, the conclusion must be true.

In the most common type, categorical syllogisms, statements relate terms as All S are P, No S are P, Some S are P, or Some S are not P. For example: All humans are mortal; Socrates is a human; therefore Socrates is mortal. The strength of a syllogism lies in its logical form rather than the factual truth of the premises.

Classical syllogistics categorizes valid forms by mood and figure, using names such as Barbara or Celarent as mnemonics for particular valid patterns. Aristotle’s system, known as the syllogistic, treated terms and their inclusion relations with strict rules of distribution and quantity.

In modern logic, the syllogistic was subsumed by predicate logic, which can express a broader range of inferences. Nevertheless, syllogistic reasoning remains a canonical example of deductive validity and is used to illustrate basic concepts such as validity, soundness, and the difference between form and content. The practical use today is instructional and historical, helping scholars understand how early logicians approached logical consequence.