The Syllogism and the Birth of Formal Logic

Aristotle was the first thinker to study logic systematically as a subject in its own right. His logical works, later grouped together as the Organon ('tool'), analyze how valid arguments work. At their center is the syllogism, an argument in which a conclusion follows necessarily from two premises, as in: all mammals are animals; all whales are mammals; therefore all whales are animals. Aristotle showed that validity depends on the form of an argument, not its subject matter, so the same pattern works for any terms.

He also formulated the principle of non-contradiction, that something cannot both be and not be in the same respect at the same time, and he catalogued fallacies used to mislead. His logic dominated Western and Islamic education for about two thousand years. Modern symbolic logic, developed from the 19th century, goes far beyond it, but Aristotle's insight that reasoning has forms that can be studied remains basic.