History of logic

The history of logic traces how people in different cultures developed systems for evaluating reasoning, proof, and inference.

Aristotle: An ancient Greek philosopher whose works established the first systematic formal treatment of deductive logic in the Western tradition. His syllogistic theory became the central framework of European logic for centuries.
Syllogistic: A theory of deductive reasoning in which conclusions follow from relations among terms in categorical premises. Aristotle’s system supplied the dominant formal model of inference in medieval Europe.
Chrysippus: A third-century BCE Stoic philosopher whose works systematized Stoic logic and defended Stoic doctrines. His logical work made the Stoic tradition a major rival to Aristotelian logic.
Principia Mathematica: A three-volume work by Alfred North Whitehead and Bertrand Russell that sought to derive mathematics from logic. It embodied the logicist ambition to ground mathematics in formal logical principles.
Aristotelian logic: A logical tradition centered on categorical propositions, syllogisms, and relations among terms. Its term-based framework contrasts with later systems centered on propositions and quantifiers.
Nyāya: An Indian philosophical tradition that developed theories of knowledge, inference, debate, and liberation. Its analysis of inference grew within an independent Indian tradition of logical inquiry.
Propositional calculus: A formal system that represents propositions and combines them with logical connectives. Its rise shifted attention from terms to relations among whole propositions.
Abelard: A twelfth-century French philosopher and theologian known for work on logic, language, and universals. His treatments of statements and inference helped renew logic in medieval Europe.
Hilbert's program: David Hilbert’s project to formalize mathematics and establish its consistency by finitistic means. Its goals shaped foundational research that Gödel’s results would sharply constrain.
Intuitionistic logic: A nonclassical logic that rejects unrestricted use of the law of excluded middle and interprets proof constructively. Its standards of proof challenge assumptions built into classical logic.

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