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In "Prior Analytics" Aristoteles defined the syllogism as "a discourse in which certain (specific) things having been supposed, something different from the things supposed results of necessity because these things are so." Aristotelian syllogistic arguments are usually represented in a three-line form: All men are mortal; Socrates is a man; therefore, Socrates is mortal. But many of Aristoteles' works disappeared after the collapse of the Roman empire in Europe, and "Prior Analytics" did not reappear until the 12th century via a Latin translation by the 6th-century philosopher Boethius. The syllogism became the core of traditional deductive reasoning, where facts are determined by combining existing statements, in contrast to inductive reasoning where facts are determined by repeated observations. In the 17th century, Sir Francis Bacon rejected the syllogism as the best way to draw conclusions in nature amd proposed instead a more inductive approach which involves experimentation and leads to discovering and building on axioms to create a more general conclusion. But in "Logic" (1800) Immanuel Kant claimed that logic was the one completed science since Aristotelian logic essentially included everything about the subject. It was not until 1879, when Gottlob Frege published Begriffsschrift (Concept Script), in which he introduced a calculus, a method of representing categorical statements via the use of quantifiers and variables, leading to the development of sentential logic and first-order predicate logic, which made syllogistic reasoning obsolete (except by the Catholic officials of the Congregation for the Doctrine of the Faith and the Apostolic Tribunal of the Roman Rota, which still require that any arguments crafted by advocates be presented in syllogistic format).
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