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[[Aristotle]] was the first to formalize the practice of reasoning.  In particular, Aristotle developed a formalization of the [[syllogism]] and the Square of Opposition.  While Modus ponens and its complement [[Modus tollens]] were known to the Medievals, it is not clear when these central laws of deduction were first formalized.

[[Aristotle]] was the first to formalize the practice of reasoning.  In particular, Aristotle developed a formalization of the [[syllogism]] and the Square of Opposition.  While Modus ponens and its complement [[Modus tollens]] were known to the Medievals, it is not clear when these central laws of deduction were first formalized.

The next easily identifiable major development in logic comes from Boole in 1847 with the creation of [[Boolean algebra]].  In the 1870s, Peirce introduces a logic of quantifiers, followed by [[Gottlob Frege]]'s 1879 ''Begriffsschrift'', which contains the first complete formalization of the propositional calculus.  Frege's work was developed in service of his [[logicism|logicist]] project, which was shown to be inconsistent by [[Bertrand Russell]] in 1903 with what is famously called [[Russell's paradox]].

The next easily identifiable major development in logic comes from Boole in 1847 with the creation of [[Boolean algebra]].  In the 1870s, Peirce introduces a logic of quantifiers, followed by [[Gottlob Frege]]'s 1879 ''Begriffsschrift'', which contains the first complete formalization of the propositional calculus.  Frege's work was developed in service of his logicist project, which was shown to be inconsistent by [[Bertrand Russell]] in 1903 with what is famously called [[Russell's paradox]].

By the 1950s, with the work of many logicians including [[Hilbert]], Emile Post, Alfred Tarski and [[Kurt Godel]], most of the major results in first-order logic had been proved, and in the 1960s Saul Kripke added a completeness proof for modal logic.

By the 1950s, with the work of many logicians including [[Hilbert]], Emile Post, Alfred Tarski and [[Kurt Godel]], most of the major results in first-order logic had been proved, and in the 1960s Saul Kripke added a completeness proof for modal logic.