Editing Philosophical logic (section)

== Classification of logics ==
Modern developments in the area of logic have resulted in a great proliferation of logical systems.<ref name="HaackDeviant1">{{cite book |last1=Haack |first1=Susan |title=Deviant Logic, Fuzzy Logic: Beyond the Formalism |date=1996 |publisher=Chicago and London: University of Chicago Press |url=https://philpapers.org/rec/HAADLF |chapter=1. 'Alternative' in 'Alternative Logic'}}</ref> This stands in stark contrast to the historical dominance of [[Aristotelian logic]], which was treated as the one canon of logic for over two thousand years.<ref name="Jacquette"/> Treatises on modern logic often treat these different systems as a list of separate topics without providing a clear classification of them. However, one classification frequently mentioned in the academic literature is due to [[Susan Haack]] and distinguishes between [[classical logic]], extended logics, and [[deviant logic]]s.<ref name="HaackLogics1"/><ref name="HaackDeviant1"/><ref name="Wolf"/> This classification is based on the idea that classical logic, i.e. propositional logic and first-order logic, formalizes some of the most common logical intuitions. In this sense, it constitutes a basic account of the axioms governing valid inference.<ref name="Hintikka"/><ref name="Britannica"/> Extended logics accept this basic account and extend it to additional areas. This usually happens by adding new vocabulary, for example, to express necessity, obligation, or time.<ref name="HaackDeviant1"/><ref name="Jacquette"/><ref name="Hintikka"/><ref name="Britannica"/> These new symbols are then integrated into the logical mechanism by specifying which new rules of inference apply to them, like that possibility follows from necessity.<ref name="Wolf"/><ref name="HaackDeviant1"/> Deviant logics, on the other hand, reject some of the basic assumptions of classical logic. In this sense, they are not mere extensions of it but are often formulated as rival systems that offer a different account of the laws of logic.<ref name="HaackDeviant1"/><ref name="Wolf">{{cite journal |last1=Wolf |first1=Robert G. |title=Are Relevant Logics Deviant? |journal=Philosophia |date=1978 |volume=7 |issue=2 |pages=327–340 |doi=10.1007/BF02378819 |s2cid=143697796 |url=https://philpapers.org/rec/WOLARL}}</ref>

Expressed in a more technical language, the distinction between extended and deviant logics is sometimes drawn in a slightly different manner. On this view, a logic is an extension of classical logic if two conditions are fulfilled: (1) all [[well-formed formula]]s of classical logic are also well-formed formulas in it and (2) all valid inferences in classical logic are also valid inferences in it.<ref name="HaackDeviant1"/><ref name="Wolf"/><ref>{{cite book |last1=Cook |first1=Roy T. |title=A Dictionary of Philosophical Logic |date=2009 |publisher=Edinburgh University Press |url=https://philpapers.org/rec/COOADO |chapter=Extension<sub>2</sub>}}</ref> For a deviant logic, on the other hand, (a) its class of well-formed formulas coincides with that of classical logic, while (b) some valid inferences in classical logic are not valid inferences in it.<ref name="HaackDeviant1"/><ref name="Wolf"/><ref>{{cite book |last1=Cook |first1=Roy T. |title=A Dictionary of Philosophical Logic |date=2009 |publisher=Edinburgh University Press |url=https://philpapers.org/rec/COOADO |chapter=Deviant logic}}</ref> The term quasi-deviant logic is used if (i) it introduces new vocabulary but all well-formed formulas of classical logic are also well-formed formulas in it and (ii) even when it is restricted to inferences using only the vocabulary of classical logic, some valid inferences in classical logic are not valid inferences in it.<ref name="HaackDeviant1"/><ref name="Wolf"/> The term "deviant logic" is often used in a sense that includes quasi-deviant logics as well.<ref name="HaackDeviant1"/>

A philosophical problem raised by this plurality of logics concerns the question of whether there can be more than one true logic.<ref name="HaackDeviant1"/><ref name="Jacquette"/> Some theorists favor a local approach in which different types of logic are applied to different areas. Early intuitionists, for example, saw [[intuitionistic logic]] as the correct logic for mathematics but allowed classical logic in other fields.<ref name="HaackDeviant1"/><ref name="Moschovakis"/> But others, like [[Michael Dummett]], prefer a global approach by holding that intuitionistic logic should replace classical logic in every area.<ref name="HaackDeviant1"/><ref name="Moschovakis"/> Monism is the thesis that there is only one true logic.<ref name="HaackLogics1"/> This can be understood in different ways, for example, that only one of all the suggested logical systems is correct or that the correct logical system is yet to be found as a system underlying and unifying all the different logics.<ref name="Jacquette"/> Pluralists, on the other hand, hold that a variety of different logical systems can all be correct at the same time.<ref>{{cite web |last1=Russell |first1=Gillian |title=Logical Pluralism |url=https://plato.stanford.edu/entries/logical-pluralism/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=14 December 2021 |date=2021}}</ref><ref name="HaackLogics1">{{cite book |last1=Haack |first1=Susan |title=Philosophy of Logics |date=1978 |publisher=London and New York: Cambridge University Press |url=https://philpapers.org/rec/HAAPOL-2 |chapter=1. 'Philosophy of logics'}}</ref><ref name="Jacquette"/>

A closely related problem concerns the question of whether all of these formal systems actually constitute ''logical'' systems.<ref name="Jacquette"/><ref name="Hintikka"/> This is especially relevant for deviant logics that stray very far from the common logical intuitions associated with classical logic. In this sense, it has been argued, for example, that [[fuzzy logic]] is a logic only in name but should be considered a non-logical formal system instead since the idea of [[degrees of truth]] is too far removed from the most fundamental logical intuitions.<ref name="HaackDeviant1"/><ref>{{cite journal |last1=Haack |first1=Susan |title=Do We Need Fuzzy Logic? |journal=International Journal of Man-Machine Studies |date=1979 |volume=11 |issue=1 |pages=437–45 |doi=10.1016/S0020-7373(79)80036-X |url=https://philpapers.org/rec/HAADWN}}</ref><ref name="Hintikka"/> So not everyone agrees that all the formal systems discussed in this article actually constitute ''logics'', when understood in a strict sense.