Editing Philosophical logic (section)

== Definition and related fields ==
The term "philosophical logic" is used by different theorists in slightly different ways.<ref name="Jacquette"/> When understood in a narrow sense, as discussed in this article, philosophical logic is the area of philosophy that studies the application of logical methods to philosophical problems. This usually happens in the form of developing new logical systems to either extend classical logic to new areas or to modify it to include certain logical intuitions not properly addressed by classical logic.<ref name="BurgessPreface">{{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=Preface}}</ref><ref name="Jacquette">{{cite book |last1=Jacquette |first1=Dale |title=Philosophy of Logic |date=2006 |publisher=North Holland |url=https://philpapers.org/rec/JACPOL |chapter=Introduction: Philosophy of logic today}}</ref><ref name="Goble">{{cite book |last1=Goble |first1=Lou |title=The Blackwell Guide to Philosophical Logic |date=2001 |publisher=Wiley-Blackwell |url=https://philpapers.org/rec/GOBTBG-2 |chapter=Introduction}}</ref><ref name="Hintikka">{{cite book |last1=Jaakko |first1=Hintikka |last2=Sandu |first2=Gabriel |title=Philosophy of Logic |date=2006 |publisher=North Holland |pages=13–39 |url=https://philpapers.org/rec/JAAWIL |chapter=What is Logic?}}</ref> In this sense, philosophical logic studies various forms of non-classical logics, like modal logic and deontic logic. This way, various fundamental philosophical concepts, like possibility, necessity, obligation, permission, and time, are treated in a logically precise manner by formally expressing the inferential roles they play in relation to each other.<ref name="Burgess1"/><ref name="Hintikka"/><ref name="Jacquette"/><ref name="Goble"/> Some theorists understand philosophical logic in a wider sense as the study of the scope and nature of logic in general. On this view, it investigates various philosophical problems raised by logic, including the fundamental concepts of logic. In this wider sense, it can be understood as identical to the [[philosophy of logic]], where these topics are discussed.<ref name="HaackLogics1"/><ref name="Routledge">{{cite book |last1=Craig |first1=Edward |title=Routledge Encyclopedia of Philosophy |date=1996 |publisher=Routledge |url=https://philpapers.org/rec/BEAREO |chapter=Philosophy of logic}}</ref><ref name="Oxford">{{cite book |last1=Honderich |first1=Ted |title=The Oxford Companion to Philosophy |date=2005 |publisher=Oxford University Press |url=https://philpapers.org/rec/HONTOC-2 |chapter=philosophical logic}}</ref><ref name="Jacquette"/> The current article discusses only the narrow conception of philosophical logic. In this sense, it forms one area of the philosophy of logic.<ref name="Jacquette"/>

Central to philosophical logic is an understanding of what logic is and what role philosophical logics play in it. Logic can be defined as the study of valid inferences.<ref name="Hintikka"/><ref name="HaackLogics1"/><ref name="Britannica"/> An inference is the step of reasoning in which it moves from the premises to a conclusion.<ref name="McKeon">{{cite web |last1=McKeon |first1=Matthew |title=Logical Consequence |url=https://iep.utm.edu/logcon/ |website=Internet Encyclopedia of Philosophy |access-date=20 November 2021}}</ref> Often the term "argument" is also used instead. An inference is valid if it is impossible for the premises to be true and the conclusion to be false. In this sense, the truth of the premises ensures the truth of the conclusion.<ref name="RoutledgeFormalInformal">{{cite book |last1=Craig |first1=Edward |title=Routledge Encyclopedia of Philosophy |date=1996 |publisher=Routledge |url=https://philpapers.org/rec/BEAREO |chapter=Formal and informal logic}}</ref><ref name="McKeon"/><ref name="Cambridge">{{cite book |last1=Audi |first1=Robert |title=The Cambridge Dictionary of Philosophy |publisher=Cambridge University Press |url=https://philpapers.org/rec/AUDTCD-2 |chapter=Philosophy of logic|year=1999 }}</ref><ref name="Jacquette"/> This can be expressed in terms of [[rules of inference]]: an inference is valid if its structure, i.e. the way its premises and its conclusion are formed, follows a rule of inference.<ref name="Hintikka"/> Different systems of logic provide different accounts for when an inference is valid. This means that they use different rules of inference. The traditionally dominant approach to validity is called classical logic. But philosophical logic is concerned with non-classical logic: it studies alternative systems of inference.<ref name="BurgessPreface"/><ref name="Jacquette"/><ref name="Goble"/><ref name="Hintikka"/> The motivations for doing so can roughly be divided into two categories. For some, classical logic is too narrow: it leaves out many philosophically interesting issues. This can be solved by extending classical logic with additional symbols to give a logically strict treatment of further areas.<ref name="HaackLogics1"/><ref name="HaackDeviant1"/><ref name="MacMillanNonClassical"/> Others see some flaw with classical logic itself and try to give a rival account of inference. This usually leads to the development of deviant logics, each of which modifies the fundamental principles behind classical logic in order to rectify their alleged flaws.<ref name="HaackLogics1"/><ref name="HaackDeviant1"/><ref name="MacMillanNonClassical">{{cite book |last1=Borchert |first1=Donald |title=Macmillan Encyclopedia of Philosophy, 2nd Edition |date=2006 |publisher=Macmillan |url=https://philpapers.org/rec/BORMEO |chapter=Logic, Non-Classical}}</ref>