Silogismo

Silogismo is a form of deductive argument in logic in which a conclusion follows necessarily from two premises that share a middle term. In the classical syllogistic, the premises and conclusion are categorical propositions of the forms A (All S are P), E (No S are P), I (Some S are P), and O (Some S are not P).

A syllogism uses three terms: the major term (the predicate of the conclusion), the minor term (the subject of the conclusion), and the middle term (the term that appears in both premises but not in the conclusion). There are two premises—the major premise and the minor premise—and a conclusion. Validity is governed by formal rules, such as the middle term being distributed in at least one premise and no term distributed in the conclusion being undistributed in its premise.

Example: All men are mortal. Socrates is a man. Therefore Socrates is mortal. This illustrates a categorical syllogism in standard form. Many valid moods and figures exist, corresponding to different placements of the terms and the A, E, I, O forms.

Beyond categorical syllogisms, there are hypothetical (conditional) syllogisms, where the conclusion follows from linked if-then premises (for example, if P then Q; if Q then R; therefore if P then R), and disjunctive syllogisms, involving either-or premises. Historically, silogismo refers to Aristotle’s syllogistic, the foundation of traditional logic, later developed by medieval scholars. In modern logic, syllogistic is often studied as a precursor to predicate and propositional logic, but it remains a key historical and pedagogical concept.