Editing Deductive reasoning (section)

== Conceptions of deduction ==
Deductive arguments differ from non-deductive arguments in that the truth of their premises ensures the truth of their conclusion.<ref name="Stump" /><ref name="RoutledgeFormalInformal">{{Cite encyclopedia |year=1996 |title=Formal and informal logic |encyclopedia=Routledge Encyclopedia of Philosophy |publisher=Routledge |url=https://philpapers.org/rec/BEAREO |last1=Craig |first1=Edward}}</ref><ref name="IEPLogical">{{Cite encyclopedia |title=Logical Consequence |encyclopedia=Internet Encyclopedia of Philosophy |url=https://iep.utm.edu/logcon/ |access-date=20 November 2021 |last1=McKeon |first1=Matthew}}</ref> There are two important conceptions of what this exactly means. They are referred to as the [[syntactic]] and the [[semantic]] approach.<ref name="Hintikka">{{Cite book |last1=Jaakko |first1=Hintikka |url=https://philpapers.org/rec/JAAWIL |title=Philosophy of Logic |last2=Sandu |first2=Gabriel |publisher=North Holland |year=2006 |pages=13–39 |chapter=What is Logic?}}</ref><ref name="IEPLogical" /><ref name="Evans" /> According to the syntactic approach, whether an argument is deductively valid depends only on its form, syntax, or structure. Two arguments have the same form if they use the same logical vocabulary in the same arrangement, even if their contents differ.<ref name="Hintikka" /><ref name="IEPLogical" /><ref name="Evans" /> For example, the arguments "if it rains then the street will be wet; it rains; therefore, the street will be wet" and "if the meat is not cooled then it will spoil; the meat is not cooled; therefore, it will spoil" have the same logical form: they follow the [[modus ponens]]. Their form can be expressed more abstractly as "if A then B; A; therefore B" in order to make the common syntax explicit.<ref name="Evans" /> There are various other valid logical forms or [[rules of inference]], like [[modus tollens]] or the [[disjunction elimination]]. The syntactic approach then holds that an argument is deductively valid if and only if its conclusion can be deduced from its premises using a valid rule of inference.<ref name="Hintikka" /><ref name="IEPLogical" /><ref name="Evans" /> One difficulty for the syntactic approach is that it is usually necessary to express the argument in a [[formal language]] in order to assess whether it is valid. This often brings with it the difficulty of translating the [[natural language]] argument into a formal language, a process that comes with various problems of its own.<ref name="Hintikka" /> Another difficulty is due to the fact that the syntactic approach depends on the distinction between formal and non-formal features. While there is a wide agreement concerning the paradigmatic cases, there are also various controversial cases where it is not clear how this distinction is to be drawn.<ref name="MacFarlane">{{Cite encyclopedia |year=2017 |title=Logical Constants |encyclopedia=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/entries/logical-constants/#SynTer |access-date=21 November 2021 |last1=MacFarlane |first1=John}}</ref><ref name="BritannicaPhilosophy">{{Cite encyclopedia |title=Philosophy of logic |encyclopedia=Encyclopædia Britannica |url=https://www.britannica.com/topic/philosophy-of-logic |access-date=21 November 2021}}</ref>

The semantic approach suggests an alternative definition of deductive validity. It is based on the idea that the sentences constituting the premises and conclusions have to be [[Interpretation (logic)|interpreted]] in order to determine whether the argument is valid.<ref name="Hintikka" /><ref name="IEPLogical" /><ref name="Evans" /> This means that one ascribes semantic values to the expressions used in the sentences, such as the reference to an object for [[singular term]]s or to a [[truth-value]] for atomic sentences. The semantic approach is also referred to as the model-theoretic approach since the branch of mathematics known as [[model theory]] is often used to interpret these sentences.<ref name="Hintikka" /><ref name="IEPLogical" /> Usually, many different interpretations are possible, such as whether a singular term refers to one object or to another. According to the semantic approach, an argument is deductively valid if and only if there is no possible interpretation where its premises are true and its conclusion is false.<ref name="Hintikka" /><ref name="IEPLogical" /><ref name="Evans" /> Some objections to the semantic approach are based on the claim that the semantics of a language cannot be expressed in the same language, i.e. that a richer [[metalanguage]] is necessary. This would imply that the semantic approach cannot provide a universal account of deduction for language as an all-encompassing medium.<ref name="Hintikka" /><ref name="BritannicaPhilosophy" />