Editing Philosophical logic (section)

== Classical logic ==
[[Classical logic]] is the dominant form of logic used in most fields.<ref name="Shapiro">{{cite web |last1=Shapiro |first1=Stewart |last2=Kouri Kissel |first2=Teresa |title=Classical Logic |url=https://plato.stanford.edu/entries/logic-classical/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=4 December 2021 |date=2021}}</ref> The term refers primarily to [[propositional logic]] and [[first-order logic]].<ref name="HaackLogics1"/> Classical logic is not an independent topic within philosophical logic. But a good familiarity with it is still required since many of the logical systems of direct concern to philosophical logic can be understood either as extensions of classical logic, which accept its fundamental principles and build on top of it, or as modifications of it, rejecting some of its core assumptions.<ref name="Burgess1"/><ref name="MacMillanNonClassical"/> Classical logic was initially created in order to analyze mathematical arguments and was applied to various other fields only afterward.<ref name="Burgess1">{{cite book |last1=Burgess |first1=John P. |title=Philosophical Logic |date=2009 |publisher=Princeton, NJ, USA: Princeton University Press |url=https://philpapers.org/rec/BURPL-3 |chapter=1. Classical logic}}</ref> For this reason, it neglects many topics of philosophical importance not relevant to mathematics, like the difference between necessity and possibility, between obligation and permission, or between past, present, and future.<ref name="Burgess1"/> These and similar topics are given a logical treatment in the different philosophical logics extending classical logic.<ref name="MacMillanNonClassical"/><ref name="Jacquette"/><ref name="Goble"/> Classical logic by itself is only concerned with a few basic concepts and the role these concepts play in making valid inferences.<ref name="Magnus3">{{cite book |last1=Magnus |first1=P. D. |title=Forall X: An Introduction to Formal Logic |date=2005 |publisher=Victoria, BC, Canada: State University of New York Oer Services |url=https://philpapers.org/rec/MAGFXI |chapter=1.4 Deductive validity}}</ref> The concepts pertaining to propositional logic include propositional connectives, like "and", "or", and "if-then".<ref name="Hintikka"/> Characteristic of the classical approach to these connectives is that they follow certain laws, like the [[law of excluded middle]], the [[double negation elimination]], the [[principle of explosion]], and the bivalence of truth.<ref name="Shapiro"/> This sets classical logic apart from various deviant logics, which deny one or several of these principles.<ref name="HaackDeviant1"/><ref name="Burgess1"/>

In [[first-order logic]], the [[proposition]]s themselves are made up of subpropositional parts, like [[Predicate (mathematical logic)|predicates]], [[singular term]]s, and [[Quantifier (logic)|quantifiers]].<ref name="Oxford"/><ref name="King">{{cite web |last1=King |first1=Jeffrey C. |title=Structured Propositions |url=https://plato.stanford.edu/entries/propositions-structured/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=4 December 2021 |date=2019}}</ref> Singular terms refer to objects and predicates express properties of objects and relations between them.<ref name="Oxford"/><ref name="Michaelson">{{cite web |last1=Michaelson |first1=Eliot |last2=Reimer |first2=Marga |title=Reference |url=https://plato.stanford.edu/entries/reference/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=4 December 2021 |date=2019}}</ref> Quantifiers constitute a formal treatment of notions like "for some" and "for all". They can be used to express whether predicates have an extension at all or whether their extension includes the whole domain.<ref name="Magnus4">{{cite book |last1=Magnus |first1=P. D. |title=Forall X: An Introduction to Formal Logic |date=2005 |publisher=Victoria, BC, Canada: State University of New York Oer Services |url=https://philpapers.org/rec/MAGFXI |chapter=4. Quantified logic}}</ref> Quantification is only allowed over individual terms but not over predicates, in contrast to higher-order logics.<ref name="Väänänen">{{cite web |last1=Väänänen |first1=Jouko |title=Second-order and Higher-order Logic |url=https://plato.stanford.edu/entries/logic-higher-order/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=23 November 2021 |date=2021}}</ref><ref name="Hintikka"/>