Editing Philosophical logic (section)

{{short description|Application of logical methods to philosophical problems}}
{{Distinguish|Philosophy of logic}}
Understood in a narrow sense, '''philosophical logic''' is the area of [[logic]] that studies the application of logical methods to [[philosophy|philosophical]] problems, often in the form of extended logical systems like [[modal logic]]. Some theorists conceive philosophical logic in a wider sense as the study of the scope and nature of [[logic]] in general. In this sense, philosophical logic can be seen as identical to the [[philosophy of logic]], which includes additional topics like how to define logic or a discussion of the fundamental concepts of logic. The current article treats philosophical logic in the narrow sense, in which it forms one field of inquiry within the philosophy of logic.

An important issue for philosophical logic is the question of how to classify the great variety of [[non-classical logic]]al systems, many of which are of rather recent origin. One form of classification often found in the literature is to distinguish between extended logics and deviant logics. Logic itself can be defined as the study of [[Validity (logic)|valid]] [[inference]]. [[Classical logic]] is the dominant form of logic and articulates [[rules of inference]] in accordance with logical intuitions shared by many, like the [[law of excluded middle]], the [[double negation elimination]], and the bivalence of truth. 

Extended logics are logical systems that are based on classical logic and its rules of inference but extend it to new fields by introducing new logical symbols and the corresponding rules of inference governing these symbols. In the case of [[alethic modal logic]], these new symbols are used to express not just what is ''true simpliciter'', but also what is ''possibly'' or ''necessarily true''. It is often combined with possible worlds semantics, which holds that a [[proposition]] is possibly true if it is true in some [[possible world]] while it is necessarily true if it is true in all possible worlds. [[Deontic logic]] pertains to [[ethics]] and provides a formal treatment of ethical notions, such as [[obligation]] and [[Permission (philosophy)|permission]]. [[Temporal logic]] formalizes temporal relations between propositions. This includes ideas like whether something is true at some time or all the time and whether it is true in the future or in the past. [[Epistemic logic]] belongs to [[epistemology]]. It can be used to express not just what is the case but also what someone believes or knows to be the case. Its rules of inference articulate what follows from the fact that someone has these kinds of [[mental state]]s. [[Higher-order logic]]s do not directly apply classical logic to certain new sub-fields within philosophy but generalize it by allowing [[Quantifier (logic)|quantification]] not just over individuals but also over predicates.

[[Deviant logic]]s, in contrast to these forms of extended logics, reject some of the fundamental principles of classical logic and are often seen as its rivals. [[Intuitionistic logic]] is based on the idea that truth depends on verification through a proof. This leads it to reject certain rules of inference found in classical logic that are not compatible with this assumption. [[Free logic]] modifies classical logic in order to avoid existential presuppositions associated with the use of possibly empty singular terms, like names and definite descriptions. [[Many-valued logic]]s allow additional truth values besides ''true'' and ''false''. They thereby reject the principle of bivalence of truth. [[Paraconsistent logic]]s are logical systems able to deal with contradictions. They do so by avoiding the [[principle of explosion]] found in classical logic. [[Relevance logic]] is a prominent form of paraconsistent logic. It rejects the purely truth-functional interpretation of the [[material conditional]] by introducing the additional requirement of relevance: for the conditional to be true, its antecedent has to be relevant to its consequent.