Logic (logikê) — The science of the formal laws of correct reasoning and valid argumentation, concerned not with what is thought but with the structure that makes an inference legitimate. The word derives from the Greek logos (reason, word, discourse), and the phrase logikê technê meant the “art of reasoning.” Logic does not assess whether the premises are true, but whether the conclusion follows necessarily from them: it deals with validity, not material truth. Aristotle is regarded as its founder, gathering in the body of treatises later called the Organon the analysis of the syllogism — an inference in which a conclusion is drawn from two premises (for instance: “all men are mortal; Socrates is a man; therefore Socrates is mortal”). The Stoics, above all Chrysippus, then developed propositional logic, focused on the relations between whole statements (if… then, or, and). For centuries Aristotelian logic remained virtually untouched, until, in the late nineteenth century, Gottlob Frege, with the Begriffsschrift (1879), created predicate logic and the theory of quantification, founding modern mathematical logic. Bertrand Russell and Alfred North Whitehead extended it in Principia Mathematica. The young Wittgenstein, in the Tractatus Logico-Philosophicus, held that logic displays the form of the world. Logic is distinct from rhetoric (the art of persuading) and closely related to epistemology, which investigates the justification of knowledge.
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