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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 |
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− | 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]]. |
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| ==Nature of logic== | | ==Nature of logic== |
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| ==History of logic== | | ==History of logic== |
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| 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 |
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| ===Logic and computation=== | | ===Logic and computation=== |
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| + | The development of formal logic and its implementation in computing machinery is the foundation of [[computer science]]. |
| 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]]. |
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