Logic

===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=1–10|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=228–9}} 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=265–274}} 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=93–97|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=265–270|2a1=van Eemeren|2a2=Garssen|2a3=Krabbe|2a4=Snoeck Henkemans|2a5=Verheij|2a6=Wagemans|2y=2021|2pp=1–45|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=93–107|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=2–3, 6–8|3a1=Engel|3y=1982|3loc=2. The medium of language|3pp=59–92}} 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=147–51}}

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=383–8|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=2066–9|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=147–51}} 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=ix–x|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=265–270}}
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