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Philosophical Logic
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 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 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 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permission (philosophy)
Permission, in philosophy, is the attribute of a person whose performance of a specific action, otherwise ethically wrong or dubious, would thereby involve no ethical fault. The term "permission" is more commonly used to refer to consent. Consent is the legal embodiment of the concept, in which approval is given to another party. Permissions depend on norms or institutions. Many permissions and obligations are complementary to each other, and deontic logic Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts. Alternatively, a deontic logic is a formal system that attempts to capture the essential logical features of these concepts. It ... is a tool sometimes used in reasoning about such relationships. Further reading * Alexy, Robert, ''Theorie der Grundrechte'', Suhrkamp, Frankfurt a. M.: 1985. Translation: ''A theory of constitutional rights'', Oxford University Press, Oxford: 2002. * Raz, Joseph, ''Practical reas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relevance Logic
Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural or modal logics. It is generally, but not universally, called ''relevant logic'' by British and, especially, Australian logicians, and ''relevance logic'' by American logicians. Relevance logic aims to capture aspects of implication that are ignored by the " material implication" operator in classical truth-functional logic, namely the notion of relevance between antecedent and conditional of a true implication. This idea is not new: C. I. Lewis was led to invent modal logic, and specifically strict implication, on the grounds that classical logic grants paradoxes of material implication such as the principle that a falsehood implies any proposition. Hence "if I'm a donkey, then two and two is four" is true when translated as a material implication, yet it seems intuitiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Explosion
In classical logic, intuitionistic logic and similar logical systems, the principle of explosion (, 'from falsehood, anything ollows; or ), or the principle of Pseudo-Scotus, is the law according to which any statement can be proven from a contradiction. That is, once a contradiction has been asserted, any proposition (including their negations) can be inferred from it; this is known as deductive explosion. The proof of this principle was first given by 12th-century French philosopher William of Soissons. Priest, Graham. 2011. "What's so bad about contradictions?" In ''The Law of Non-Contradicton'', edited by Priest, Beal, and Armour-Garb. Oxford: Clarendon Press. p. 25. Due to the principle of explosion, the existence of a contradiction ( inconsistency) in a formal axiomatic system is disastrous; since any statement can be proven, it trivializes the concepts of truth and falsity. Around the turn of the 20th century, the discovery of contradictions such as Russell's parado ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paraconsistent Logic
A paraconsistent logic is an attempt at a logical system to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" systems of logic which reject the principle of explosion. Inconsistency-tolerant logics have been discussed since at least 1910 (and arguably much earlier, for example in the writings of Aristotle); however, the term ''paraconsistent'' ("beside the consistent") was first coined in 1976, by the Peruvian philosopher Francisco Miró Quesada Cantuarias. The study of paraconsistent logic has been dubbed paraconsistency, which encompasses the school of dialetheism. Definition In classical logic (as well as intuitionistic logic and most other logics), contradictions entail everything. This feature, known as the principle of explosion or ''ex contradictione sequitur quodlibet'' (Latin, "from a contradiction, anything follows") can be expressed formal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Many-valued Logic
Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false") for any proposition. Classical two-valued logic may be extended to ''n''-valued logic for ''n'' greater than 2. Those most popular in the literature are three-valued (e.g., Łukasiewicz's and Kleene's, which accept the values "true", "false", and "unknown"), four-valued, nine-valued, the finite-valued (finitely-many valued) with more than three values, and the infinite-valued (infinitely-many-valued), such as fuzzy logic and probability logic. History It is wrong that the first known classical logician who did not fully accept the law of excluded middle was Aristotle (who, ironically, is also generally considered to be the first classical logician and the "father of wo-valuedlogic"). In fact, Aristotle did not contest the univer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Logic
A free logic is a logic with fewer existential presuppositions than classical logic. Free logics may allow for terms that do not denote any object. Free logics may also allow models that have an empty domain. A free logic with the latter property is an inclusive logic. Explanation In classical logic there are theorems that clearly presuppose that there is something in the domain of discourse. Consider the following classically valid theorems. :1. \forall xA \Rightarrow \exists xA :2. \forall x \forall rA(x) \Rightarrow \forall rA(r) :3. \forall rA(r) \Rightarrow \exists xA(x) A valid scheme in the theory of equality which exhibits the same feature is :4. \forall x(Fx \rightarrow Gx) \land \exists xFx \rightarrow \exists x(Fx \land Gx) Informally, if F is '=y', G is 'is Pegasus', and we substitute 'Pegasus' for y, then (4) appears to allow us to infer from 'everything identical with Pegasus is Pegasus' that something is identical with Pegasus. The problem comes from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intuitionistic Logic
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems of intuitionistic logic do not assume the law of the excluded middle and double negation elimination, which are fundamental inference rules in classical logic. Formalized intuitionistic logic was originally developed by Arend Heyting to provide a formal basis for L. E. J. Brouwer's programme of intuitionism. From a proof-theoretic perspective, Heyting’s calculus is a restriction of classical logic in which the law of excluded middle and double negation elimination have been removed. Excluded middle and double negation elimination can still be proved for some propositions on a case by case basis, however, but do not hold universally as they do with classical logic. The standard explanation of intuitionistic logic is the BHK interpretati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deviant Logic
Deviant logic is a type of logic incompatible with classical logic. Philosopher Susan Haack uses the term ''deviant logic'' to describe certain non-classical systems of logic. In these logics: * the set of well-formed formulas generated equals the set of well-formed formulas generated by classical logic. * the set of theorems generated is different from the set of theorems generated by classical logic. The set of theorems of a deviant logic can differ in any possible way from classical logic's set of theorems: as a proper subset, superset, or fully exclusive set. A notable example of this is the trivalent logic developed by Polish logician and mathematician Jan Łukasiewicz. Under this system, any theorem necessarily dependent on classical logic's principle of bivalence would fail to be valid. The term ''deviant logic'' first appears in Chapter 6 of Willard Van Orman Quine's ''Philosophy of Logic'', New Jersey: Prentice Hall (1970), which is cited by Haack on p. 15 of her ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantifier (logic)
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier \forall in the first order formula \forall x P(x) expresses that everything in the domain satisfies the property denoted by P. On the other hand, the existential quantifier \exists in the formula \exists x P(x) expresses that there exists something in the domain which satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula. A quantified formula must contain a bound variable and a subformula specifying a property of the referent of that variable. The mostly commonly used quantifiers are \forall and \exists. These quantifiers are standardly defined as duals; in classical logic, they are interdefinable using negation. They can also be used to define more complex quantifiers, as in the formula \neg \exists x P(x) which expresses that nothing has the property P. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Higher-order Logic
mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic properties are less well-behaved than those of first-order logic. The term "higher-order logic", abbreviated as HOL, is commonly used to mean higher-order simple predicate logic. Here "simple" indicates that the underlying type theory is the ''theory of simple types'', also called the ''simple theory of types'' (see Type theory). Leon Chwistek and Frank P. Ramsey proposed this as a simplification of the complicated and clumsy ''ramified theory of types'' specified in the ''Principia Mathematica'' by Alfred North Whitehead and Bertrand Russell. ''Simple types'' is nowadays sometimes also meant to exclude polymorphic and dependent types. Quantification scope First-order logic quantifies only variables th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mental State
A mental state, or a mental property, is a state of mind of a person. Mental states comprise a diverse class, including perception, pain experience, belief, desire, intention, emotion, and memory. There is controversy concerning the exact definition of the term. According to '' epistemic approaches'', the essential mark of mental states is that their subject has privileged epistemic access while others can only infer their existence from outward signs. '' Consciousness-based approaches'' hold that all mental states are either conscious themselves or stand in the right relation to conscious states. '' Intentionality-based approaches'', on the other hand, see the power of minds to refer to objects and represent the world as the mark of the mental. According to '' functionalist approaches'', mental states are defined in terms of their role in the causal network independent of their intrinsic properties. Some philosophers deny all the aforementioned approaches by holding that the term " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
