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Genus–differentia Definition
A genus–differentia definition is a type of intensional definition, and it is composed of two parts: # a genus (or family): An existing definition that serves as a portion of the new definition; all definitions with the same genus are considered members of that genus. # the differentia: The portion of the definition that is not provided by the genus. For example, consider these two definitions: * ''a triangle'': A plane figure that has 3 straight bounding sides. * ''a quadrilateral'': A plane figure that has 4 straight bounding sides. Those definitions can be expressed as one genus and two ''differentiae'': # ''one genus'': #* ''the genus for both a triangle and a quadrilateral'': "A plane figure" # ''two differentiae'': #* ''the differentia for a triangle'': "that has 3 straight bounding sides." #* ''the differentia for a quadrilateral'': "that has 4 straight bounding sides." The use of genus and differentia in constructing definitions goes back at least as far as Aristotle ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Definition
A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes).Lyons, John. "Semantics, vol. I." Cambridge: Cambridge (1977). p.158 and on. Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions. In mathematics, a definition is used to give a precise meaning to a new term, by describing a condition which unambiguously qualifies what a mathematical term is and is not. Definitions and axioms form the basis on which all of modern mathematics is to be constructed. Basic terminology In modern usage, a definition is something, typically expressed in words, that attac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Directed Graph
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. Definition In formal terms, a directed graph is an ordered pair where * ''V'' is a set whose elements are called '' vertices'', ''nodes'', or ''points''; * ''A'' is a set of ordered pairs of vertices, called ''arcs'', ''directed edges'' (sometimes simply ''edges'' with the corresponding set named ''E'' instead of ''A''), ''arrows'', or ''directed lines''. It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called ''edges'', ''links'' or ''lines''. The aforementioned definition does not allow a directed graph to have multiple arrows with the same source and target nodes, but some authors consider a broader definition that allows directed graphs to have such multiple arcs (namely, they allow the arc set to be a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Difference
Difference, The Difference, Differences or Differently may refer to: Music * ''Difference'' (album), by Dreamtale, 2005 * ''Differently'' (album), by Cassie Davis, 2009 ** "Differently" (song), by Cassie Davis, 2009 * ''The Difference'' (album), Pendleton, 2008 * "The Difference" (The Wallflowers song), 1997 * "The Difference", a song by Westlife from the 2009 album ''Where We Are'' * "The Difference", a song by Nick Jonas from the 2016 album ''Last Year Was Complicated'' * "The Difference", a song by Meek Mill featuring Quavo, from the 2016 mixtape '' DC4'' * "The Difference", a song by Matchbox Twenty from the 2002 album '' More Than You Think You Are'' * "The Difference", a 2020 song by Flume featuring Toro y Moi * "The Difference", a 2022 song by Ni/Co which represented Alabama in the ''American Song Contest'' * "Differences" (song), by Ginuwine, 2001 Science and mathematics * Difference (mathematics), the result of a subtraction * Difference equation, a type of recu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dichotomies
A dichotomy is a partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be * jointly exhaustive: everything must belong to one part or the other, and * mutually exclusive: nothing can belong simultaneously to both parts. If there is a concept A, and it is split into parts B and not-B, then the parts form a dichotomy: they are mutually exclusive, since no part of B is contained in not-B and vice versa, and they are jointly exhaustive, since they cover all of A, and together again give A. Such a partition is also frequently called a bipartition. The two parts thus formed are complements. In logic, the partitions are opposites if there exists a proposition such that it holds over one and not the other. Treating continuous variables or multi categorical variables as binary variables is called dichotomization. The discretization error inherent in dichotomization is temporarily ignored for modeling purposes. Etymology The term '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Definition
A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes).Lyons, John. "Semantics, vol. I." Cambridge: Cambridge (1977). p.158 and on. Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions. In mathematics, a definition is used to give a precise meaning to a new term, by describing a condition which unambiguously qualifies what a mathematical term is and is not. Definitions and axioms form the basis on which all of modern mathematics is to be constructed. Basic terminology In modern usage, a definition is something, typically expressed in words, that attac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstraction
Abstraction in its main sense is a conceptual process wherein general rules and concepts are derived from the usage and classification of specific examples, literal ("real" or "concrete") signifiers, first principles, or other methods. "An abstraction" is the outcome of this process—a concept that acts as a common noun for all subordinate concepts and connects any related concepts as a ''group'', ''field'', or ''category''. Suzanne K. Langer (1953), ''Feeling and Form: a theory of art developed from Philosophy in a New Key'' p. 90: " Sculptural form is a powerful abstraction from actual objects and the three-dimensional space which we construe ... through touch and sight." Conceptual abstractions may be formed by filtering the information content of a concept or an observable phenomenon, selecting only those aspects which are relevant for a particular purpose. For example, abstracting a leather soccer ball to the more general idea of a ball selects only the information on gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synecdoche
Synecdoche ( ) is a type of metonymy: it is a figure of speech in which a term for a part of something is used to refer to the whole (''pars pro toto''), or vice versa (''totum pro parte''). The term comes from Greek . Examples in common English use are ''suits'' for ''businessmen'', ''wheels'' for ''car'', and ''boots'' for ''soldiers''. The use of government buildings to refer to their occupants is metonymy and sometimes also synecdoche. "The Pentagon" for the United States Department of Defense can be considered synecdoche, because the building can be considered part of the bureaucracy. In the same way, using " Number 10" to mean "the Office of the Prime Minister" (of the United Kingdom) is a synecdoche. Definition Synecdoche is a rhetorical trope and a kind of metonymy—a figure of speech using a term to denote one thing to refer to a related thing. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pars Pro Toto
''Pars pro toto'' (, ), , is a figure of speech where the name of a ''portion'' of an object, place, or concept is used or taken to represent its entirety. It is distinct from a merism, which is a reference to a whole by an enumeration of parts; metonymy, where an object, place, or concept is called by something or some place associated with it; or synecdoche, which can refer both to ''pars pro toto'' and its inverse: the whole representing a part. In the context of language, ''pars pro toto'' means that something is named after a part or subset of it, or after a limited characteristic, which in itself is not necessarily representative of the whole. For example, "glasses" is a ''pars pro toto'' name for something that consists of more than literally just two pieces of glass (the frame, nosebridge, temples, etc. as well as the lenses). ''Pars pro toto'' usage is especially common in political geography, with examples including "Russia" or "Russians", used to refer to the entire fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linguistics
Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Linguistics is concerned with both the cognitive and social aspects of language. It is considered a scientific field as well as an academic discipline; it has been classified as a social science, natural science, cognitive science,Thagard, PaulCognitive Science, The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.). or part of the humanities. Traditional areas of linguistic analysis correspond to phenomena found in human linguistic systems, such as syntax (rules governing the structure of sentences); semantics (meaning); morphology (structure of words); phonetics (speech sounds and equivalent gestures in sign languages); phonology (the abstract sound system of a particular language); and pragmatics (how social con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity (philosophy)
In philosophy, identity (from , "sameness") is the relation each thing bears only to itself. The notion of identity gives rise to List of unsolved problems in philosophy, many philosophical problems, including the identity of indiscernibles (if ''x'' and ''y'' share all their properties, are they one and the same thing?), and questions about change and personal identity over time (what has to be the case for a person ''x'' at one time and a person ''y'' at a later time to be one and the same person?). It is important to distinguish between ''qualitative identity'' and ''numerical identity''. For example, consider two children with identical bicycles engaged in a race while their mother is watching. The two children have the ''same'' bicycle in one sense (''qualitative identity'') and the ''same'' mother in another sense (''numerical identity''). This article is mainly concerned with ''numerical identity'', which is the stricter notion. The philosophical concept of identity is dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entity
An entity is something that exists as itself, as a subject or as an object, actually or potentially, concretely or abstractly, physically or not. It need not be of material existence. In particular, abstractions and legal fictions are usually regarded as entities. In general, there is also no presumption that an entity is animate, or present. The term is broad in scope and may refer to animals; natural features such as mountains; inanimate objects such as tables; numbers or sets as symbols written on a paper; human contrivances such as laws, corporations and academic disciplines; or supernatural beings such as gods and spirits. The adjectival form is ''entitative''. Etymology The word ''entity'' is derived from the Latin ''entitas'', which in turn derives from the Latin ''ens'' meaning "being" or "existing" (compare English ''essence''). ''Entity'' may hence literally be taken to mean "thing which exists". In philosophy Ontology is the study of concepts of existence, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Individual
An individual is that which exists as a distinct entity. Individuality (or self-hood) is the state or quality of being an individual; particularly (in the case of humans) of being a person unique from other people and possessing one's own Maslow's hierarchy of needs, needs or goals, rights and moral responsibility, responsibilities. The concept of an individual features in diverse fields, including biology, law, and philosophy. Etymology From the 15th century and earlier (and also today within the fields of statistics and metaphysics) ''individual'' meant "divisible, indivisible", typically describing any numerically singular thing, but sometimes meaning "a person". From the 17th century on, ''individual'' has indicated separateness, as in individualism. Law Although individuality and individualism are commonly considered to mature with age/time and experience/wealth, a sanity, sane adult human, human being is usually considered by the State (polity), state as an "individu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
