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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.

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 Gödel]], 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.

Most logical systems are bivalent; that is, they admit only two truth-values, true or false. However, there is a fair amount of work done on trivalent systems of logic, specifically paraconsistent logic and relevance logic (a subset of paraconsistent logic). These logics were developed in response to the paradoxes that classical logic can create, namely, that anything can follow from a falsehood and the [[principle of explosion]].

Most logical systems are bivalent; that is, they admit only two truth-values, true or false. However, there is a fair amount of work done on trivalent systems of logic, specifically paraconsistent logic and relevance logic (a subset of paraconsistent logic). These logics were developed in response to the paradoxes that classical logic can create, namely, that anything can follow from a falsehood and the [[principle of explosion]].