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Enumerative Definition
An enumerative definition of a concept or term is a special type of extensional definition that gives an explicit and exhaustive listing of all the objects that fall under the concept or term in question. Enumerative definitions are only possible for finite sets and only practical for relatively small sets. An example of an enumerative definition for the set ; extant monotreme species (for which the intensional definition is ''species of currently-living mammals that lay eggs'') would be : platypuses : echidnae: :: short-beaked echidna :: long-beaked echidnae: ::: Sir David's long-beaked echidna ::: eastern long-beaked echidna ::: western long-beaked echidna See also * Definition * Extension * 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 give ... * Set ... [...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] |
Eastern Long-beaked Echidna
The eastern long-beaked echidna (''Zaglossus bartoni''), also known as Barton's long-beaked echidna, is one of three species from the genus '' Zaglossus'' to occur in New Guinea. It is found mainly in the eastern half at elevations between . Description The eastern long-beaked echidna can be distinguished from other members of the genus by the number of claws on the fore and hind feet: it has five claws on its fore feet and four on its hind feet. Its weight varies from ; its body length ranges from ; it has no tail. It has dense black fur. It rolls into a spiny ball for defense. They have a lifespan of roughly 30 years. Like the closely related platypus, echidnas have spurs on their hind legs. Unlike the platypus, echidna spurs are not venomous. All eastern long-beaked echidnas start with spurs on their hind feet and spur sheaths that cover them. Females typically lose their spurs later in life while males keep them. Females are also generally larger than males. Body mass tends t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Enumeration
An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the elements of a set. The precise requirements for an enumeration (for example, whether the set must be finite, or whether the list is allowed to contain repetitions) depend on the discipline of study and the context of a given problem. Some sets can be enumerated by means of a natural ordering (such as 1, 2, 3, 4, ... for the set of positive integers), but in other cases it may be necessary to impose a (perhaps arbitrary) ordering. In some contexts, such as enumerative combinatorics, the term ''enumeration'' is used more in the sense of '' counting'' – with emphasis on determination of the number of elements that a set contains, rather than the production of an explicit listing of those elements. Combinatorics In combinatorics, enumeration means counting, i.e., determining the exact number of elem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set Notation
In set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy. Defining sets by properties is also known as set comprehension, set abstraction or as defining a set's intension. Sets defined by enumeration A set can be described directly by enumerating all of its elements between curly brackets, as in the following two examples: * \ is the set containing the four numbers 3, 7, 15, and 31, and nothing else. * \=\ is the set containing , , and , and nothing else (there is no order among the elements of a set). This is sometimes called the "roster method" for specifying a set. When it is desired to denote a set that contains elements from a regular sequence, an ellipses notation may be employed, as shown in the next examples: * \ is the set of integers between 1 and 100 inclusive. * \ is the set of natura ... [...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] |
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] |
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 att ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Western Long-beaked Echidna
The western long-beaked echidna (''Zaglossus bruijnii'') is one of the four extant echidnas and one of three species of '' Zaglossus'' that occurs in New Guinea. Originally described as ''Tachyglossus bruijnii'', this is the type species of ''Zaglossus''. Description The western long-beaked echidna is an egg-laying mammal. Unlike the short-beaked echidna, which eats ants and termites, the long-beaked species eats earthworms. The long-beaked echidna is also larger than the short-beaked species, reaching up to ; the snout is longer and turns downward; and the spines are almost indistinguishable from the long fur. It is distinguished from the other ''Zaglossus'' species by the number of claws on the fore and hind feet: three (rarely four). It is the largest extant monotreme. Distribution and habitat The species is found in the Bird's Head Peninsula and Foja Mountains of West Papua and Papua provinces, Indonesia, respectively, in regions of elevation between ; it is absent f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sir David's Long-beaked Echidna
Sir David's long-beaked echidna (''Zaglossus attenboroughi''), also known as Attenborough's long-beaked echidna or the Cyclops long-beaked echidna, is one of the three species from the genus '' Zaglossus'' that occurs in New Guinea. It is named in honour of Sir David Attenborough, the eminent naturalist. It lives in the Cyclops Mountains, which are near the cities of Sentani and Jayapura in the Indonesian province of Papua. Description It is the smallest member of the genus '' Zaglossus'', being closer in size to the short-beaked echidna (''Tachyglossus aculeatus''). The male is larger than the female, and can be differentiated by the spurs on its hind legs. The echidna is not a social animal, and comes together with its own kind only once a year, in July, to mate. The female will lay the eggs after about eight days, and the babies will stay in the mother's pouch for around eight weeks or until their spines develop. The creature is nocturnal, and can roll up into a spiny bal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Object (philosophy)
An object is a philosophical term often used in contrast to the term '' subject''. A subject is an observer and an object is a thing observed. For modern philosophers like Descartes, consciousness is a state of cognition that includes the subject—which can never be doubted as only it can be the one who doubts—and some object(s) that may be considered as not having real or full existence or value independent of the subject who observes it. Metaphysical frameworks also differ in whether they consider objects existing independently of their properties and, if so, in what way. The pragmatist Charles S. Peirce defines the broad notion of an object as anything that we can think or talk about. In a general sense it is any entity: the pyramids, gods, Socrates, Alpha Centauri, the number seven, a disbelief in predestination or the fear of cats. In a strict sense it refers to any definite being. A related notion is objecthood. Objecthood is the state of being an object. One app ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Short-beaked Echidna
The short-beaked echidna (''Tachyglossus aculeatus''), also called the short-nosed echidna, is one of four living species of echidna and the only member of the genus ''Tachyglossus''. It is covered in fur and spines and has a distinctive snout and a specialized tongue, which it uses to catch its insect prey at a great speed. Like the other extant monotremes, the short-beaked echidna lays eggs; the monotremes are the only living group of mammals to do so. The short-beaked echidna has extremely strong front limbs and claws, which allow it to burrow quickly with great power. As it needs to be able to survive underground, it has a significant tolerance to high levels of carbon dioxide and low levels of oxygen. It has no weapons or fighting ability but repels predators by curling into a ball and deterring them with its spines. It lacks the ability to sweat and cannot deal with heat well, so it tends to avoid daytime activity in hot weather. It can swim if needed. The snout has m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Platypus
The platypus (''Ornithorhynchus anatinus''), sometimes referred to as the duck-billed platypus, is a semiaquatic, egg-laying mammal endemic to eastern Australia, including Tasmania. The platypus is the sole living representative or monotypic taxon of its family ( Ornithorhynchidae) and genus (''Ornithorhynchus''), though a number of related species appear in the fossil record. Together with the four species of echidna, it is one of the five extant species of monotremes, mammals that lay eggs instead of giving birth to live young. Like other monotremes, it senses prey through electrolocation. It is one of the few species of venomous mammals, as the male platypus has a spur on the hind foot that delivers a venom, capable of causing severe pain to humans. The unusual appearance of this egg-laying, duck-billed, beaver-tailed, otter-footed mammal baffled European naturalists when they first encountered it, and the first scientists to examine a preserved platypus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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