λογική

Logic comes from Greek λογική (logikḗ), short for logikḗ téchnē ('the art of reason'), from λόγος (lógos), one of the richest and most contested words in the Greek language. Lógos meant, variously: word, speech, reason, account, proportion, argument, discourse, and (in later philosophy and theology) the divine rational principle that orders the cosmos. The verb from which it derives, λέγω (légō), meant 'to say, to gather, to count.' The entire semantic range of lógos — from the individual utterance to the structure of reality — reflects the Greek conviction that language and reason were not merely connected but identical at the deepest level: to reason was to speak, and to speak truly was to articulate the rational structure of the world.

Aristotle formalized logic as a discipline in his collection of writings known as the Organon ('instrument'), composed in the fourth century BCE. His Prior Analytics developed syllogistic logic: the study of valid inferences in which a conclusion necessarily follows from premises. The famous example — all men are mortal, Socrates is a man, therefore Socrates is mortal — is a syllogism, a form of argument whose validity depends entirely on its structure rather than its content. Aristotle called this the analytics of the syllogism, not yet using the word logikḗ as a discipline name. The systematization of logic as a distinct field with its own name came through the later Stoics, who developed propositional logic and gave the discipline the term logikḗ.

Medieval European universities received Aristotle's logic through Arabic translations and commentaries, particularly those of Avicenna and Averroes, before the Greek originals were recovered in the twelfth and thirteenth centuries. Logic became the cornerstone of the medieval university curriculum — the discipline that trained the mind before it engaged theology, medicine, or law. Thomas Aquinas applied Aristotelian logic to theological questions; the Scholastic method of systematically presenting objections and replies was essentially applied logic. The word 'logic' entered English in the fourteenth century through Old French logique, naming both the formal discipline and the quality of sound reasoning in general usage.

The history of formal logic after Aristotle is a story of progressive formalization and surprising depth. George Boole showed in 1847 that logic could be expressed algebraically. Gottlob Frege, in 1879, created predicate logic, extending Aristotle's syllogistic to handle quantified statements of much greater complexity. Bertrand Russell and Alfred North Whitehead, in Principia Mathematica (1910–1913), attempted to ground all mathematics in logical foundations. Kurt Gödel, in 1931, proved that any sufficiently powerful logical system contains true statements that cannot be proved within that system — the incompleteness theorems that are themselves one of logic's greatest achievements. The discipline that began with Aristotle's syllogisms had become the foundation of computer science, mathematics, and the theory of computation. The lógos that meant 'word' and 'reason' had become the architecture of the digital world.