How did Aristotle use syllogisms to study valid arguments?

Aristotle founded the systematic study of logic by developing the theory of the syllogism, primarily detailed in his work the Prior Analytics. He defined a syllogism as a form of inference where a conclusion necessarily follows from two premises.12

To study valid arguments, Aristotle introduced two revolutionary methods:

• Use of Variables: He was the first to use schematic letters (variables) as placeholders for terms, such as "If A belongs to every B, and B belongs to every C, A belongs to every C". This allowed him to analyze the logical form of arguments independently of their specific content.134
• Categorical Analysis: He classified propositions by their quantity (universal or particular) and quality (affirmative or negative). By identifying the roles of the major, minor, and middle terms, he categorized various "moods" of syllogisms to determine which patterns of inference were consistently valid—meaning they could never lead from true premises to a false conclusion.12

Aristotle’s approach established logic as a rigorous tool for all sciences, focusing on the formal relations between terms to ensure valid reasoning.34