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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.{{fact}}

[[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.{{fact}}

The next easily-identifiable major development in logic comes from [[Boole]] in 1847 with the creation of [[Boolean algebra]].  In the 1870's, Peirce introduces a logic of quantifiers, followed by [[Gottlob Frege]]'s 1879 ''Begriffsschift'', 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 1870's, 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]].

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

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