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'''Logic''' ([[Greek language|Greek]] ''λογίζω'' – I think, I reason; from ''λόγος'' – reason) refers the patterns in reasoning behind arguments. In [[philosophy]], logic is a sub-branch of [[epistemology]] that deals with and attempts to guide the faculty of human reason. It is often studied alongside [[mathematics]].

'''Logic''' ([[Greek language|Greek]] ''λογίζω'' – I think, I reason; from ''λόγος'' – reason) refers the patterns in reasoning behind arguments. In [[philosophy]], logic is a sub-branch of [[epistemology]] that deals with and attempts to guide the faculty of human reason. It is often studied alongside [[mathematics]].

[[Aristotle]] was the first to formalize the practice of reasoning. In particular, Aristotle developed a formalization of the [[Syllogism|categorical syllogism]], the three laws of logic, and the [[Square of Opposition]]. While [[modus ponens]] and its complement modus tollens were known to the medieval philosophers, 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|categorical syllogism]], the three laws of logic, and the Square of Opposition. While modus ponens and its complement modus tollens were known to the medieval philosophers, 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]] and Boolean logic. 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]]. In 1913 Russell and Whitehead published ''Principia Mathematica'', a landmark work that sought to define mathematics with first-order logic.

The next easily identifiable major development in logic comes from Boole in 1847 with the creation of [[Boolean algebra]] and Boolean logic. 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]]. In 1913 Russell and Whitehead published ''Principia Mathematica'', a landmark work that sought to define mathematics with first-order logic.