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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]].  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]].   

===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]]