Logic Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.Anti-spam check. Do not fill this in! ==Definition== The word "logic" originates from the Greek word "logos", which has a variety of translations, such as [[reason]], [[discourse]], or [[language]].{{sfnm|1a1=PΓ©pin|1loc=Logos|1y=2004|2a1=Online Etymology Staff}} Logic is traditionally defined as the study of the [[laws of thought]] or [[Logical reasoning|correct reasoning]],{{sfn |Hintikka |2019 |loc=lead section, Β§Nature and varieties of logic}} and is usually understood in terms of [[inference]]s or [[argument]]s. Reasoning is the activity of drawing inferences. Arguments are the outward expression of inferences.{{sfnm|1a1=Hintikka|1y=2019|1loc=Β§Nature and varieties of logic|2a1=Haack|2y=1978|2loc=Philosophy of logics|2pp=1β10|3a1=Schlesinger|3a2=Keren-Portnoy|3a3=Parush|3y=2001|3p=220}} An argument is a set of premises together with a conclusion. Logic is interested in whether arguments are correct, i.e. whether their premises support the conclusion.{{sfnm|1a1=Hintikka|1a2=Sandu|1y=2006|1p=13|2a1=Audi|2loc=Philosophy of logic|2y=1999b|3a1=McKeon}} These general characterizations apply to logic in the widest sense, i.e., to both [[Logic#Formal logic|formal]] and [[informal logic]] since they are both concerned with assessing the correctness of arguments.{{sfnm|1a1=Blair|1a2=Johnson|1y=2000|1pp=93β95|2a1=Craig|2y=1996|2loc=Formal and informal logic}} Formal logic is the traditionally dominant field, and some logicians restrict logic to formal logic.{{sfnm|1a1=Craig|1y=1996|1loc=Formal and informal logic|2a1=Barnes|2y=2007|2p=274|3a1=Planty-Bonjour|3y=2012|3p=[https://books.google.com/books?id=0EpFBgAAQBAJ&pg=PA62 62]|4a1=Rini|4y=2010|4p=[https://books.google.com/books?id=vard024vjFgC&pg=PA26 26]}} ===Formal logic=== {{further|Formal system}} Formal logic is also known as symbolic logic and is widely used in [[mathematical logic]]. It uses a [[Formal system|formal]] approach to study reasoning: it replaces concrete expressions with abstract symbols to examine the [[logical form]] of arguments independent of their concrete content. In this sense, it is topic-neutral since it is only concerned with the abstract structure of arguments and not with their concrete content.{{sfnm|1a1=MacFarlane|1y=2017|2a1=Corkum|2y=2015|2pp=753β767|3a1=Blair|3a2=Johnson|3y=2000|3pp=93β95|4a1=Magnus|4y=2005|4loc=1.6 Formal languages|4pp=12-4}} Formal logic is interested in deductively [[Validity (logic)|valid]] arguments, for which the truth of their premises ensures the truth of their conclusion. This means that it is impossible for the premises to be true and the conclusion to be false.{{sfnm|1a1=McKeon|2a1=Craig|2y=1996|2loc=Formal and informal logic}} For valid arguments, the logical structure of the premises and the conclusion follows a pattern called a [[rule of inference]].{{sfn|Hintikka|Sandu|2006|p=13}} For example, [[modus ponens]] is a rule of inference according to which all arguments of the form "(1) ''p'', (2) if ''p'' then ''q'', (3) therefore ''q''" are valid, independent of what the terms ''p'' and ''q'' stand for.{{sfn |Magnus |2005 |loc=Proofs, p. 102}} In this sense, formal logic can be defined as the science of valid inferences. An alternative definition sees logic as the study of [[logical truth]]s.{{sfnm|1a1=Hintikka|1a2=Sandu|1y=2006|1pp=13β16|2a1=Makridis|2y=2022|2pp=1β2|3a1=Runco|3a2=Pritzker|3y=1999|3p=155}} A proposition is logically true if its truth depends only on the logical vocabulary used in it. This means that it is true in all [[possible world]]s and under all [[Interpretation (logic)|interpretations]] of its non-logical terms, like the claim "either it is raining, or it is not".{{sfnm|1a1=GΓ³mez-Torrente|1y=2019|2a1=Magnus|2y=2005|2loc=1.5 Other logical notions, p. 10}} These two definitions of formal logic are not identical, but they are closely related. For example, if the inference from ''p'' to ''q'' is deductively valid then the claim "if ''p'' then ''q''" is a logical truth.{{sfn|Hintikka|Sandu|2006|p=16}} [[File:First-order logic.png|thumb|upright=1.6|alt=Visualization of how to translate an English sentence into first-order logic|Formal logic needs to translate natural language arguments into a formal language, like first-order logic, to assess whether they are valid. In this example, the letter "c" represents Carmen while the letters "M" and "T" stand for "Mexican" and "teacher". The symbol "β§" has the meaning of "and".]] Formal logic uses [[formal language]]s to express and analyze arguments.{{sfnm|1a1=Honderich|1y=2005|1loc=logic, informal|2a1=Craig|2y=1996|2loc=Formal and informal logic|3a1=Johnson|3y=1999|3pp=265β268}} They normally have a very limited vocabulary and exact [[Syntax|syntactic rule]]s. These rules specify how their symbols can be combined to construct sentences, so-called [[well-formed formula]]s.{{sfnm|1a1=Craig|1y=1996|1loc=Formal languages and systems|2a1=Simpson|2y=2008|2p=14}} This simplicity and exactness of formal logic make it capable of formulating precise rules of inference. They determine whether a given argument is valid.{{sfn |Craig |1996 |loc=Formal languages and systems}} Because of the reliance on formal language, natural language arguments cannot be studied directly. Instead, they need to be [[Logic translation#Natural language formalization|translated into formal language]] before their validity can be assessed.{{sfnm|1a1=Hintikka|1a2=Sandu|1y=2006|1pp=22-3|2a1=Magnus|2y=2005|2loc=1.4 Deductive validity|2pp=8β9|3a1=Johnson|3y=1999|3p=267}} The term "logic" can also be used in a slightly different sense as a countable noun. In this sense, ''a logic'' is a logical formal system. Distinct logics differ from each other concerning the rules of inference they accept as valid and the formal languages used to express them.{{sfnm|1a1=Haack|1y=1978|1loc=Philosophy of logics|1pp=1β2, 4|2a1=Hintikka|2a2=Sandu|2y=2006|2pp=16β17|3a1=Jacquette|3y=2006|3loc=Introduction: Philosophy of logic today, pp. 1β12}} Starting in the late 19th century, many new formal systems have been proposed. There are disagreements about what makes a formal system a logic.{{sfnm|1a1=Haack|1y=1978|1loc=Philosophy of logics|1pp=1β2, 4|2a1=Jacquette|2y=2006|2loc=Introduction: Philosophy of logic today|2pp=1β12}} For example, it has been suggested that only [[Completeness (logic)|logically complete]] systems, like [[first-order logic]], qualify as logics. For such reasons, some theorists deny that [[higher-order logic]]s are logics in the strict sense.{{sfnm|1a1=Haack|1y=1978|1loc=Philosophy of logics|1pp=5β7, 9|2a1=Hintikka|2a2=Sandu|2y=2006|2pp=31-2|3a1=Haack|3y=1996|3pp=229β30}} ===Informal logic=== {{Main|Informal logic}} When understood in a wide sense, logic encompasses both formal and informal logic.{{sfnm|1a1=Haack|1y=1978|1loc=Philosophy of logics|1pp=1β10|2a1=Groarke|2y=2021|2loc=lead section; 1.1 Formal and Informal Logic}} Informal logic uses non-formal criteria and standards to analyze and assess the correctness of arguments. Its main focus is on everyday discourse.{{sfn |Johnson |2014 |pp=228β9}} Its development was prompted by difficulties in applying the insights of formal logic to natural language arguments.{{sfnm|1a1=Groarke|1y=2021|1loc=lead section; 1. History|2a1=Audi|2loc=Informal logic|2y=1999a|3a1=Johnson|3y=1999|3pp=265β274}} In this regard, it considers problems that formal logic on its own is unable to address.{{sfnm|1a1=Craig|1y=1996|1loc=Formal and informal logic|2a1=Johnson|2y=1999|2p=267}} Both provide criteria for assessing the correctness of arguments and distinguishing them from fallacies.{{sfnm|1a1=Blair|1a2=Johnson|1y=2000|1pp=93β97|2a1=Craig|2y=1996|2loc=Formal and informal logic}} Many characterizations of informal logic have been suggested but there is no general agreement on its precise definition.{{sfnm|1a1=Johnson|1y=1999|1pp=265β270|2a1=van Eemeren|2a2=Garssen|2a3=Krabbe|2a4=Snoeck Henkemans|2a5=Verheij|2a6=Wagemans|2y=2021|2pp=1β45|2loc=Informal Logic}} The most literal approach sees the terms "formal" and "informal" as applying to the language used to express arguments. On this view, informal logic studies arguments that are in informal or natural language.{{sfnm|1a1=Groarke|1y=2021|1loc=1.1 Formal and Informal Logic|2a1=Audi|2loc=Informal logic|2y=1999a|3a1=Honderich|3y=2005|3loc=logic, informal}} Formal logic can only examine them indirectly by translating them first into a formal language while informal logic investigates them in their original form.{{sfnm|1a1=Blair|1a2=Johnson|1y=2000|1pp=93β107|2a1=Groarke|2y=2021|2loc=lead section; 1.1 Formal and Informal Logic|3a1=van Eemeren|3a2=Grootendorst|3a3=Johnson|3a4=Plantin|3a5=Willard|3y=2013|3p=169}} On this view, the argument "Birds fly. Tweety is a bird. Therefore, Tweety flies." belongs to natural language and is examined by informal logic. But the formal translation "(1) <math>\forall x (Bird(x) \to Flies(x))</math>; (2) <math>Bird(Tweety)</math>; (3) <math>Flies(Tweety)</math>" is studied by formal logic.{{sfn |Oaksford |Chater |2007 |p=47}} The study of natural language arguments comes with various difficulties. For example, natural language expressions are often ambiguous, vague, and context-dependent.{{sfnm|1a1=Craig|1y=1996|1loc=Formal and informal logic|2a1=Walton|2y=1987|2loc=1. A new model of argument|2pp=2β3, 6β8|3a1=Engel|3y=1982|3loc=2. The medium of language|3pp=59β92}} Another approach defines informal logic in a wide sense as the normative study of the standards, criteria, and procedures of argumentation. In this sense, it includes questions about the role of [[rationality]], [[critical thinking]], and the psychology of argumentation.{{sfn |Blair |Johnson |1987 |pp=147β51}} Another characterization identifies informal logic with the study of non-deductive arguments. In this way, it contrasts with deductive reasoning examined by formal logic.{{sfnm|1a1=Falikowski|1a2=Mills|1y=2022|1p=98|2a1=Weddle|2y=2011|2loc=36. Informal logic and the eductive-inductive distinction|2pp=383β8|3a1=Blair|3y=2011|3p=47}} Non-deductive arguments make their conclusion probable but do not ensure that it is true. An example is the [[inductive reasoning|inductive argument]] from the empirical observation that "all ravens I have seen so far are black" to the conclusion "all ravens are black".{{sfnm|1a1=Vickers|1y=2022|2a1=Nunes|2y=2011|2pp=2066β9|2loc=Logical Reasoning and Learning}} A further approach is to define informal logic as the study of [[informal fallacies]].{{sfnm|1a1=Johnson|1y=2014|1p=181|2a1=Johnson|2y=1999|2p=267|3a1=Blair|3a2=Johnson|3y=1987|3pp=147β51}} Informal fallacies are incorrect arguments in which errors are present in the content and the [[Context (language use)|context]] of the argument.{{sfnm|1a1=Vleet|1y=2010|1loc=Introduction|1pp=ixβx|2a1=Dowden|3a1=Stump}} A [[false dilemma]], for example, involves an error of content by excluding viable options. This is the case in the fallacy "you are either with us or against us; you are not with us; therefore, you are against us".{{sfnm|1a1=Maltby|1a2=Day|1a3=Macaskill|1y=2007|2a1=Dowden|1p=564}} Some theorists state that formal logic studies the general form of arguments while informal logic studies particular instances of arguments. Another approach is to hold that formal logic only considers the role of logical constants for correct inferences while informal logic also takes the meaning of substantive [[concept]]s into account. Further approaches focus on the discussion of logical topics with or without formal devices and on the role of [[epistemology]] for the assessment of arguments.{{sfnm|1a1=Craig|1y=1996|1loc=Formal and informal logic|2a1=Johnson|2y=1999|2pp=265β270}} Summary: Please note that all contributions to Christianpedia may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here. 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