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As a [[formal science]], logic investigates and classifies the structure of statements and arguments, both through the study of [[formal system]]s of [[inference]] and through the study of arguments in natural language.  The field of logic ranges from core topics such as the study of [[fallacies]] and [[paradox]]es, to specialized analysis of reasoning using [[probability]] and to arguments involving [[causality]].  Logic is also commonly used today in [[argumentation theory]]. J. Robert Cox and Charles Arthur Willard, eds. ''Advances in Argumentation Theory and Research'', Southern Illinois University Press, 1983 ISBN 0809310503, ISBN-13 978-0809310500  

As a [[formal science]], logic investigates and classifies the structure of statements and arguments, both through the study of [[formal system]]s of [[inference]] and through the study of arguments in natural language.  The field of logic ranges from core topics such as the study of [[fallacies]] and [[paradox]]es, to specialized analysis of reasoning using [[probability]] and to arguments involving [[causality]].  Logic is also commonly used today in [[argumentation theory]]. J. Robert Cox and Charles Arthur Willard, eds. ''Advances in Argumentation Theory and Research'', Southern Illinois University Press, 1983 ISBN 0809310503, ISBN-13 978-0809310500  

Traditionally, logic is studied as a branch of [[philosophy]], one part of the classical [[Trivium (education)|trivium]], which consisted of [[grammar]], logic, and [[rhetoric]].  Since the mid-nineteenth century ''formal logic'' has been studied in the context of [[foundations of mathematics]], where it was often called [[symbolic logic]]. In 1903 [[Alfred North Whitehead]] and [[Bertrand Russell]] attempted to establish logic formally as the cornerstone of mathematics with the publication of [[Principia Mathematica]]."Principia" Alfred North Whitehead and Bertrand Russell, ''Principia Mathematical to *56'', Cambridge University Press, 1967,  ISBN 0-521-62606-4  However, the system of Principia is no longer much used, having been largely supplanted by [[set theory]].  As the study of formal logic expanded, research no longer focused solely on foundational issues, and the study of several resulting areas of mathematics came to be called [[mathematical logic]].  The development of formal logic and its implementation in computing machinery is the foundation of [[computer science]].

Traditionally, logic is studied as a branch of [[philosophy]], one part of the classical [[Trivium (education)|trivium]], which consisted of [[grammar]], logic, and [[rhetoric]].  Since the mid-nineteenth century ''formal logic'' has been studied in the context of [[foundations of mathematics]], where it was often called [[symbolic logic]]. In 1903 [[Alfred North Whitehead]] and [[Bertrand Russell]] attempted to establish logic formally as the cornerstone of mathematics with the publication of [[Principia Mathematica]]."Principia" Alfred North Whitehead and Bertrand Russell, ''Principia Mathematical to *56'', Cambridge University Press, 1967,  ISBN 0-521-62606-4  However, the system of Principia is no longer much used, having been largely supplanted by [[set theory]].  As the study of formal logic expanded, research no longer focused solely on foundational issues, and the study of several resulting areas of mathematics came to be called [[mathematical logic]].   

==Nature of logic==

==Nature of logic==

==History of logic==

==History of logic==

Many cultures have employed intricate systems of reasoning and asked questions about logic or propounded logical paradoxes.  For example, in [[Indian logic|India]], the [[Nasadiya Sukta]] of the [[Rigveda]] ([[RV 10]].129) contains [[ontological]] speculation in terms of various logical divisions that were later recast formally as the four circles of ''[[tetralemma|catuskoti]]'': "A", "not A", "A and not A", and "not A and not not A".[[Subhash Kak|S. Kak]] (2004). ''The Architecture of Knowledge''. CSC, Delhi and the Chinese philosopher '''Gongsun Long''' (ca. [[325 BC|325]]–[[250 BC]]) proposed the paradox "One and one cannot become two, since neither becomes two." McGreal 1995, p. 33

Many cultures have employed intricate systems of reasoning and asked questions about logic or propounded logical paradoxes.  For example, in [[Indian logic|India]], the [[Nasadiya Sukta]] of the [[Rigveda]] ([[RV 10]].129) contains [[ontological]] speculation in terms of various logical divisions that were later recast formally as the four circles of ''[[tetralemma|catuskoti]]'': "A", "not A", "A and not A", and "not A and not not A".[[Subhash Kak|S. Kak]] (2004). ''The Architecture of Knowledge''. CSC, Delhi and the Chinese philosopher '''Gongsun Long''' (ca. [[325 BC|325]]–[[250 BC]]) proposed the paradox "One and one cannot become two, since neither becomes two." McGreal 1995, p. 33

===Logic and computation===

===Logic and computation===

Logic cut to the heart of computer science as it emerged as a discipline: [[Alan Turing]]'s work on the [[Entscheidungsproblem]] followed from [[Kurt Gödel]]'s work on the [[incompleteness theorems]], and the notion of general purpose computers that came from this work was of fundamental importance to the designers of the computer machinery in the [[1940s]].   

Logic cut to the heart of computer science as it emerged as a discipline: [[Alan Turing]]'s work on the [[Entscheidungsproblem]] followed from [[Kurt Gödel]]'s work on the [[incompleteness theorems]], and the notion of general purpose computers that came from this work was of fundamental importance to the designers of the computer machinery in the [[1940s]].