How did Aristotle help establish the formal study of logic?

Aristotle is widely recognized as the founder of the formal study of logic, a discipline he developed as a rigorous tool for all sciences rather than a theoretical science itself. His foundational work is collected in the Organon, which includes his influential theories on propositions and syllogistic reasoning.123

Key contributions include:

• Invention of Variables: Aristotle was the first logician to use schematic letters (variables) as placeholders for terms. This innovation allowed him to achieve a level of abstraction and generality essential for the systematic study of inference.123
• Theory of the Syllogism: He identified specific patterns of argument, or "moods," and established rules for determining the validity of inferences—ensuring that valid forms never lead from true premises to a false conclusion.3
• Technical Vocabulary: He introduced essential terminology to distinguish between universal and particular propositions, as well as the roles of major, minor, and middle terms within an argument.3
• Systematic Methodology: By analyzing interrogative techniques used in competitive debates, he moved from studying how to "win" arguments to defining the formal relations of logical consequence.12

Through these efforts, Aristotle established a system of rules that defined the landscape of formal logic for centuries.23