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− | [[Image:Abinitiolongest.jpg|left|"abinitio"]] | + | '''Logic''' (from [[Ancient Greek|Classical Greek]] λόγος [[logos]]; meaning word, thought, idea, argument, account, reason, or principle) is the study of valid [[inference]] and [[demonstration (proof)|demonstration]]. |
− | '''Logic''' (from [[Ancient Greek|Classical Greek]] λόγος [[logos]]; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid [[inference]] and [[demonstration (proof)|demonstration]]. | |
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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 |
− | | + | <center>For lessons on the [[topic]] of '''''Logic''''', follow [https://nordan.daynal.org/wiki/index.php?title=Category:Logic/TeaM this link].</center> |
| 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]]. | | 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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| ===Tolerating the impossible=== | | ===Tolerating the impossible=== |
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− | Closely related to questions arising from the paradoxes of implication comes the radical suggestion that logic ought to tolerate [[inconsistency]]. [[Relevance logic]] and [[paraconsistent logic]] are the most important approaches here, though the concerns are different: a key consequence of [[classical logic]] and some of its rivals, such as [[intuitionistic logic]], is that they respect the [[principle of explosion]], which means that the logic collapses if it is capable of deriving a contradiction. [[Graham Priest]], the main proponent of [[dialetheism]], has argued for paraconsistency on the grounds that there are in fact, true contradictions.[[Graham Priest|Priest, Graham]] (2004), "Dialetheism", ''Stanford Encyclopedia of Philosophy'', Edward N. Zalta (ed.), http://plato.stanford.edu/entries/dialetheism. | + | Closely related to questions arising from the paradoxes of implication comes the radical suggestion that logic ought to tolerate [[inconsistency]]. [[Relevance logic]] and [[paraconsistent logic]] are the most important approaches here, though the concerns are different: a key consequence of [[classical logic]] and some of its rivals, such as [[intuitionistic logic]], is that they respect the [[principle of explosion]], which means that the logic collapses if it is capable of deriving a contradiction. [[Graham Priest]], the main proponent of [[dialetheism]], has argued for paraconsistency on the grounds that there are in fact, true contradictions.[[Graham Priest|Priest, Graham]] (2004), "Dialetheism", ''Stanford Encyclopedia of Philosophy'', Edward N. Zalta (ed.), https://plato.stanford.edu/entries/dialetheism. |
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| ===Is logic empirical?=== | | ===Is logic empirical?=== |
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| * Gabbay, D.M., and Guenthner, F. (eds., 2001-2005), ''Handbook of Philosophical Logic'', 13 vols., 2nd edition, Kluwer Publishers, Dordrecht. | | * Gabbay, D.M., and Guenthner, F. (eds., 2001-2005), ''Handbook of Philosophical Logic'', 13 vols., 2nd edition, Kluwer Publishers, Dordrecht. |
| * [[Vincent F. Hendricks]], ''Thought 2 Talk: A Crash Course in Reflection and Expression'', New York: Automatic Press / VIP, 2005, ISBN 87-991013-7-8. | | * [[Vincent F. Hendricks]], ''Thought 2 Talk: A Crash Course in Reflection and Expression'', New York: Automatic Press / VIP, 2005, ISBN 87-991013-7-8. |
− | * [[David Hilbert|Hilbert, D.]], and [[Wilhelm Ackermann|Ackermann, W]]. (1928), ''Grundzüge der theoretischen Logik'' (''[[Principles of Theoretical Logic]]''), Springer-Verlag. [http://worldcat.org/oclc/2085765 OCLC 2085765] | + | * [[David Hilbert|Hilbert, D.]], and [[Wilhelm Ackermann|Ackermann, W]]. (1928), ''Grundzüge der theoretischen Logik'' (''[[Principles of Theoretical Logic]]''), Springer-Verlag. [https://worldcat.org/oclc/2085765 OCLC 2085765] |
| * Hodges, W. (2001), ''Logic. An introduction to Elementary Logic'', Penguin Books. | | * Hodges, W. (2001), ''Logic. An introduction to Elementary Logic'', Penguin Books. |
− | * Hofweber, T. (2004), "Logic and Ontology", ''[[Stanford Encyclopedia of Philosophy]]'', [[Edward N. Zalta]] (ed.), [http://plato.stanford.edu/entries/logic-ontology/ Eprint]. | + | * Hofweber, T. (2004), "Logic and Ontology", ''[[Stanford Encyclopedia of Philosophy]]'', [[Edward N. Zalta]] (ed.), [https://plato.stanford.edu/entries/logic-ontology/ Eprint]. |
| * Hughes, R.I.G. (ed., 1993), ''A Philosophical Companion to First-Order Logic'', Hackett Publishing. | | * Hughes, R.I.G. (ed., 1993), ''A Philosophical Companion to First-Order Logic'', Hackett Publishing. |
| * [[William Kneale|Kneale, William]], and [[Martha Kneale|Kneale, Martha]], (1962), ''The Development of Logic'', Oxford University Press, London, UK. | | * [[William Kneale|Kneale, William]], and [[Martha Kneale|Kneale, Martha]], (1962), ''The Development of Logic'', Oxford University Press, London, UK. |
− | * Mendelson, Elliott (1964), ''Introduction to Mathematical Logic'', Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, Calif. [http://worldcat.org/oclc/13580200 OCLC 13580200] | + | * Mendelson, Elliott (1964), ''Introduction to Mathematical Logic'', Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, Calif. [https://worldcat.org/oclc/13580200 OCLC 13580200] |
| * [[Barry Smith|Smith, B.]] (1989), "Logic and the Sachverhalt", ''The Monist'' 72(1), 52–69. | | * [[Barry Smith|Smith, B.]] (1989), "Logic and the Sachverhalt", ''The Monist'' 72(1), 52–69. |
− | * [[Alfred North Whitehead|Whitehead, Alfred North]] and [[Bertrand Russell]] (1910), [[Principia Mathematica|''Principia Mathematica'']], The University Press, Cambridge, England. [http://worldcat.org/oclc/1041146 OCLC 1041146] | + | * [[Alfred North Whitehead|Whitehead, Alfred North]] and [[Bertrand Russell]] (1910), [[Principia Mathematica|''Principia Mathematica'']], The University Press, Cambridge, England. [https://worldcat.org/oclc/1041146 OCLC 1041146] |
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| == Further reading == | | == Further reading == |
− | * The [http://www.ucl.ac.uk/philosophy/LPSG/ London Philosophy Study Guide] offers many suggestions on what to read, depending on the student's familiarity with the subject: | + | * The [https://www.ucl.ac.uk/philosophy/LPSG/ London Philosophy Study Guide] offers many suggestions on what to read, depending on the student's familiarity with the subject: |
− | **[http://www.ucl.ac.uk/philosophy/LPSG/L&M.htm Logic & Metaphysics] | + | **[https://www.ucl.ac.uk/philosophy/LPSG/L&M.htm Logic & Metaphysics] |
− | **[http://www.ucl.ac.uk/philosophy/LPSG/SetTheory.htm Set Theory and Further Logic] | + | **[https://www.ucl.ac.uk/philosophy/LPSG/SetTheory.htm Set Theory and Further Logic] |
− | **[http://www.ucl.ac.uk/philosophy/LPSG/MathLogic.htm Mathematical Logic] | + | **[https://www.ucl.ac.uk/philosophy/LPSG/MathLogic.htm Mathematical Logic] |
| *[[Lewis Carroll|Carroll, Lewis]] | | *[[Lewis Carroll|Carroll, Lewis]] |
− | **[http://www.gutenberg.org/etext/4763 "The Game of Logic"], 1886. [http://www.cut-the-knot.org/LewisCarroll/index.shtml] | + | **[https://www.gutenberg.org/etext/4763 "The Game of Logic"], 1886. [https://www.cut-the-knot.org/LewisCarroll/index.shtml] |
− | **[http://durendal.org:8080/lcsl/ "Symbolic Logic"], 1896. | + | **[https://durendal.org:8080/lcsl/ "Symbolic Logic"], 1896. |
| *Samuel D. Guttenplan, Samuel D., Tamny, Martin, "Logic, a Comprehensive Introduction", Basic Books, 1971. | | *Samuel D. Guttenplan, Samuel D., Tamny, Martin, "Logic, a Comprehensive Introduction", Basic Books, 1971. |
| *[[Michael Scriven|Scriven, Michael]], "Reasoning", McGraw-Hill, 1976, ISBN 0-07-055882-5 | | *[[Michael Scriven|Scriven, Michael]], "Reasoning", McGraw-Hill, 1976, ISBN 0-07-055882-5 |
| *[[Susan Haack]]. (1996).'' Deviant Logic, Fuzzy Logic: Beyond the Formalism'', University of Chicago Press. | | *[[Susan Haack]]. (1996).'' Deviant Logic, Fuzzy Logic: Beyond the Formalism'', University of Chicago Press. |
| *Nicolas [[Rescher]]. (1964). ''Introduction to Logic'', St. Martin's Press. | | *Nicolas [[Rescher]]. (1964). ''Introduction to Logic'', St. Martin's Press. |
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− | ==See also==
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− | * [[Artificial intelligence]]
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− | * [[Deductive reasoning]]
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− | * [[Digital logic]]
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− | * [[Indian Logic]]
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− | * [[Inductive reasoning]]
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− | * [[Logical consequence]]
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− | * [[Logic puzzle]]
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− | * [[Mathematical logic]]
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− | * [[Mathematics]]
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− | ** [[List of basic mathematics topics]]
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− | ** [[List of mathematics articles]]
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− |
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− | * [[Philosophy]]
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− | ** [[List of basic philosophy topics]]
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− | ** [[List of philosophy topics]]
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− | * [[Probabilistic logic]]
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− | * [[Propositional logic]]
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− | * [[Reason]]
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− | * [[Table of logic symbols]]
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− | * [[Term logic]]
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− | * [[Truth]]
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− | ** [[Truth theory]]
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| ==External links== | | ==External links== |
− | | + | * ''[https://www.galilean-library.org/int4.html An Introduction to Philosophical Logic]'', by Paul Newall, aimed at beginners |
− | * {{wikia|logic|LogicWiki}}
| + | * ''[https://www.fecundity.com/logic/ forall x: an introduction to formal logic]'', by P.D. Magnus, covers sentential and quantified logic |
− | * ''[http://www.galilean-library.org/int4.html An Introduction to Philosophical Logic]'', by Paul Newall, aimed at beginners | + | * ''[https://www.earlham.edu/~peters/courses/log/transtip.htm Translation Tips]'', by Peter Suber, for translating from English into logical notation |
− | * ''[http://www.fecundity.com/logic/ forall x: an introduction to formal logic]'', by P.D. Magnus, covers sentential and quantified logic | + | * [https://etext.lib.virginia.edu/DicHist/analytic/anaVII.html Math & Logic: The history of formal mathematical, logical, linguistic and methodological ideas.] In ''The Dictionary of the History of Ideas.'' |
− | * ''[http://www.earlham.edu/~peters/courses/log/transtip.htm Translation Tips]'', by Peter Suber, for translating from English into logical notation | + | * ''[https://www.think-logically.co.uk/lt.htm]'' Test your logic skills |
− | * [http://etext.lib.virginia.edu/DicHist/analytic/anaVII.html Math & Logic: The history of formal mathematical, logical, linguistic and methodological ideas.] In ''The Dictionary of the History of Ideas.'' | + | * ''[https://kpaprzycka.swps.edu.pl/xLogicSelfTaught/LogicSelfTaught.html Logic Self-Taught: A Workbook]'' (originally prepared for on-line logic instruction) |
− | * ''[http://www.think-logically.co.uk/lt.htm]'' Test your logic skills | |
− | * ''[http://kpaprzycka.swps.edu.pl/xLogicSelfTaught/LogicSelfTaught.html Logic Self-Taught: A Workbook]'' (originally prepared for on-line logic instruction) | |
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| [[Category: General Reference]] | | [[Category: General Reference]] |
| [[Category: Logic]] | | [[Category: Logic]] |