Editing Classical logic (section)

==History==

{{main|History of logic}}

Classical logic is a 19th and 20th-century innovation. The name does not refer to [[classical antiquity]], which used the [[term logic]] of [[Aristotle]]. Classical logic was the reconciliation of Aristotle's logic, which dominated most of the last 2000 years, with the propositional [[Stoic logic]]. The two were sometimes seen as irreconcilable.

[[Leibniz]]'s [[calculus ratiocinator]] can be seen as foreshadowing classical logic. [[Bernard Bolzano]] has the understanding of [[existential import]] found in classical logic and not in Aristotle. Though he never questioned Aristotle, [[George Boole]]'s algebraic reformulation of logic, so-called [[Boolean logic]], was a predecessor of modern [[mathematical logic]] and classical logic. [[William Stanley Jevons]] and [[John Venn]], who also had the modern understanding of existential import, expanded Boole's system.
[[File:Begriffsschrift Titel.png|thumb|180px|Begriffsschrift title page]]
The original [[first-order logic|first-order]], classical logic is found in [[Gottlob Frege]]'s ''[[Begriffsschrift]]''. It has a wider application than Aristotle's logic and is capable of expressing Aristotle's logic as a special case. It explains the [[quantifier (logic)|quantifier]]s in terms of mathematical functions. It was also the first logic capable of dealing with the [[problem of multiple generality]], for which Aristotle's system was impotent. Frege, who is considered the founder of analytic philosophy, invented it to show all of mathematics was derivable from logic, and make [[arithmetic]] rigorous as [[David Hilbert]] had done for [[geometry]], the doctrine is known as [[logicism]] in the [[foundations of mathematics]]. The notation Frege used never much caught on. [[Hugh MacColl]] published a variant of propositional logic two years prior.

The writings of [[Augustus De Morgan]] and [[Charles Sanders Peirce]] also pioneered classical logic with the logic of relations. Peirce influenced [[Giuseppe Peano]] and [[Ernst Schröder (mathematician)|Ernst Schröder]].

Classical logic reached fruition in [[Bertrand Russell]] and [[A. N. Whitehead]]'s ''Principia Mathematica'', and [[Ludwig Wittgenstein]]'s ''[[Tractatus Logico Philosophicus]]''. Russell and Whitehead were influenced by Peano (it uses his notation) and Frege and sought to show mathematics was derived from logic. Wittgenstein was influenced by Frege and Russell and initially considered the ''Tractatus'' to have solved all problems of philosophy.

[[Willard Van Orman Quine]] believed that a formal system that allows quantification over predicates ([[higher-order logic]]) didn't meet the requirements to be a logic, saying that it was "[[set theory]] in disguise".

Classical logic is the standard logic of mathematics. Many mathematical theorems rely on classical rules of inference such as [[disjunctive syllogism]] and the [[double negation elimination]]. The adjective "classical" in logic is not related to the use of the adjective "classical" in physics, which has another meaning. In logic, "classical" simply means "standard". Classical logic should also not be confused with [[term logic]], also known as Aristotelian logic.

[[Jan Łukasiewicz]] pioneered [[non-classical logic]].