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Comprehension (logic)
In logic, the comprehension of an object is the totality of intensions, that is, attributes, characters, marks, properties, or qualities, that the object possesses, or else the totality of intensions that are pertinent to the context of a given discussion. This is the correct technical term for the whole collection of intensions of an object, but it is common in less technical usage to see 'intension' used for both the composite and the primitive ideas. See also * Extension Extension, extend or extended may refer to: Mathematics Logic or set theory * Axiom of extensionality * Extensible cardinal * Extension (model theory) * Extension (predicate logic), the set of tuples of values that satisfy the predicate * Ext ... * Extensional definition * Intension * Intensional definition Concepts in logic Definition {{Logic-stub ... [...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 usu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intension
In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — an intension is any property or quality connoted by a word, phrase, or another symbol. In the case of a word, the word's definition often implies an intension. For instance, the intensions of the word ''plant'' include properties such as "being composed of cellulose", "alive", and "organism", among others. A '' comprehension'' is the collection of all such intensions. Overview The meaning of a word can be thought of as the bond between the ''idea the word means'' and the ''physical form of the word''. Swiss linguist Ferdinand de Saussure (1857–1913) contrasts three concepts: # the ''signifier'' – the "sound image" or the string of letters on a page that one recognizes as the form of a sign # the ''signified'' – the meaning, the concept or idea that a sign expresses or evokes # the ''referent'' – the a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relevance
Relevance is the concept of one topic being connected to another topic in a way that makes it useful to consider the second topic when considering the first. The concept of relevance is studied in many different fields, including cognitive sciences, logic, and library and information science. Most fundamentally, however, it is studied in epistemology (the theory of knowledge). Different theories of knowledge have different implications for what is considered relevant and these fundamental views have implications for all other fields as well. Definition "Something (A) is relevant to a task (T) if it increases the likelihood of accomplishing the goal (G), which is implied by T." (Hjørland & Sejer Christensen, 2002). A thing might be relevant, a document or a piece of information may be relevant. The basic understanding of relevance does not depend on whether we speak of "things" or "information". For example, the Gandhian principles are of great relevance in today's world. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extension (semantics)
In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — the extension of a concept, idea, or sign consists of the things to which it applies, in contrast with its comprehension or intension, which consists very roughly of the ideas, properties, or corresponding signs that are implied or suggested by the concept in question. In philosophical semantics or the philosophy of language, the 'extension' of a concept or expression is the set of things it extends to, or applies to, if it is the sort of concept or expression that a single object by itself can satisfy. Concepts and expressions of this sort are monadic or "one-place" concepts and expressions. So the extension of the word "dog" is the set of all (past, present and future) dogs in the world: the set includes Fido, Rover, Lassie, Rex, and so on. The extension of the phrase "Wikipedia reader" includes each person who ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensional Definition
In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They give meaning or denotation to a term. Intensional definition An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. In the case of nouns, this is equivalent to specifying the properties that an object needs to have in order to be counted as a referent of the term. For example, an intensional definition of the word "bachelor" is "unmarried man". This definition is valid because being an unmarried man is both a necessary condition and a sufficient condition for being a bachelor: it is necessary because one cannot be a bachelor without being an unmarried man, and it is sufficient because any unmarried man is a bachelor.Cook, Roy T. "Intensional Definition". In ''A Dictionary of Philosophical Logic''. Edinburgh: Edinburgh University Press, 2009. 155. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intension
In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — an intension is any property or quality connoted by a word, phrase, or another symbol. In the case of a word, the word's definition often implies an intension. For instance, the intensions of the word ''plant'' include properties such as "being composed of cellulose", "alive", and "organism", among others. A '' comprehension'' is the collection of all such intensions. Overview The meaning of a word can be thought of as the bond between the ''idea the word means'' and the ''physical form of the word''. Swiss linguist Ferdinand de Saussure (1857–1913) contrasts three concepts: # the ''signifier'' – the "sound image" or the string of letters on a page that one recognizes as the form of a sign # the ''signified'' – the meaning, the concept or idea that a sign expresses or evokes # the ''referent'' – the a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intensional Definition
In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They give meaning or denotation to a term. Intensional definition An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. In the case of nouns, this is equivalent to specifying the properties that an object needs to have in order to be counted as a referent of the term. For example, an intensional definition of the word "bachelor" is "unmarried man". This definition is valid because being an unmarried man is both a necessary condition and a sufficient condition for being a bachelor: it is necessary because one cannot be a bachelor without being an unmarried man, and it is sufficient because any unmarried man is a bachelor.Cook, Roy T. "Intensional Definition". In ''A Dictionary of Philosophical Logic''. Edinburgh: Edinburgh University Press, 2009. 155. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concepts In Logic
Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by several disciplines, such as linguistics, psychology, and philosophy, and these disciplines are interested in the logical and psychological structure of concepts, and how they are put together to form thoughts and sentences. The study of concepts has served as an important flagship of an emerging interdisciplinary approach called cognitive science. In contemporary philosophy, there are at least three prevailing ways to understand what a concept is: * Concepts as mental representations, where concepts are entities that exist in the mind (mental objects) * Concepts as abilities, where concepts are abilities peculiar to cognitive agents (mental states) * Concepts as Fregean senses, where concepts are abstract objects, as opposed to mental ob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
