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Philosophical logic

Overview

Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive of philosophical logic in a broader 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 logical 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 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. 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 states. Higher-order logics do not directly apply classical logic to certain new sub-fields within philosophy but generalize it by allowing quantification not just over individuals but also over predicates.

Deviant logics, 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 logics allow additional truth values besides true and false. They thereby reject the principle of bivalence of truth. Paraconsistent logics 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.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

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Toward the composition and structure of which form it is incident to handle the parts thereof, which are propositions, and the parts of propositions, which are simple words. And this is that part of logic which is comprehended in the Analytics. (5) The second method of doctrine was introduced for expedite use and assurance sake, discovering the more subtle forms of sophisms and illaqueations with their redargutions…
Francis Bacon, The Advancement of Learning
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There remains but mere experience, which, when it offers itself, is called chance; when it is sought after, experiment.[47] But this kind of experience is nothing but a loose fagot; and mere groping in the dark, as men at night try all means of discovering the right road, while it would be better and more prudent either to wait for day, or procure a light, and then proceed. On the contrary, the real order of…
Francis Bacon, Novum organum
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But all philosophy is either cognition on the basis of pure reason, or the cognition of reason on the basis of empirical principles. The former is termed pure, the latter empirical philosophy. The philosophy of pure reason is either propædeutic, that is, an inquiry into the powers of reason in regard to pure à priori cognition, and is termed critical philosophy; or it is, secondly, the system of pure…
Immanuel Kant, The Critique of Pure Reason
States what Philosophical logic is.
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Philosophical logic

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