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'''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]].

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]].   

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]].   

===Tolerating the impossible===

===Tolerating the impossible===

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.

===Is logic empirical?===

===Is logic empirical?===

* 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]

== 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.

==External links==

==External links==

 

* ''[https://www.galilean-library.org/int4.html An Introduction to Philosophical Logic]'', by Paul Newall, aimed at beginners

* ''[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)

[[Category: General Reference]]

[[Category: General Reference]]

[[Category: Logic]]

[[Category: Logic]]