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. An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. An extensional definition gives meaning to a term by specifying every object that falls under the definition of the term in question. For example, in set theory one would extensionally define the set of square numbers as , while an intensional definition of the set of the square numbers could be . 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 "bache ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Biology
Biology is the scientific study of life and living organisms. It is a broad natural science that encompasses a wide range of fields and unifying principles that explain the structure, function, growth, History of life, origin, evolution, and distribution of life. Central to biology are five fundamental themes: the cell (biology), cell as the basic unit of life, genes and heredity as the basis of inheritance, evolution as the driver of biological diversity, energy transformation for sustaining life processes, and the maintenance of internal stability (homeostasis). Biology examines life across multiple biological organisation, levels of organization, from molecules and cells to organisms, populations, and ecosystems. Subdisciplines include molecular biology, physiology, ecology, evolutionary biology, developmental biology, and systematics, among others. Each of these fields applies a range of methods to investigate biological phenomena, including scientific method, observation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constance Jones
Emily Elizabeth Constance Jones (19 February 1848 – 9 April 1922), better known as Constance Jones or E. E. Constance Jones, was an English Philosophy, philosopher and educator. She worked in logic and ethics and served as mistress of Girton College, Cambridge from 1903 to 1916. Life and career Emily Elizabeth Constance Jones was born at Langstone Court, Llangarron, Herefordshire, to John Jones and his wife, Emily, daughter of Thomas Oakley JP, of Monmouthshire. She was the eldest of ten children. Constance was mostly tutored at home. She spent her early teenage years with her family in Cape Town, South Africa, and when they returned to England in 1865 she attended a small school, Miss Robinson's, in Cheltenham, for a year. She was coached for the entrance examination for Girton College, Cambridge by Miss Alice Gruner, Alice Grüner, a former student of Newnham College, Cambridge, Newnham College at her home in Sydenham, London, Sydenham, Kent. She went up to Girton in 1875 wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 (not always true)", "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 ''referen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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. An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. An extensional definition gives meaning to a term by specifying every object that falls under the definition of the term in question. For example, in set theory one would extensionally define the set of square numbers as , while an intensional definition of the set of the square numbers could be . 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 "bache ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Ostensive Definition
An ostensive definition conveys the meaning of a term by pointing out examples. This type of definition is often used where the term is difficult to define verbally, either because the words will not be understood (as with children and new speakers of a language) or because of the nature of the term (such as colors or sensations). It is usually accompanied with a gesture pointing to the object serving as an example, and for this reason is also often referred to as " definition by pointing". Overview An ostensive definition assumes the questioner has sufficient understanding to recognize the type of information being given. Ludwig Wittgenstein writes: So one might say: the ostensive definition explains the use—the meaning—of the word when the overall role of the word in language is clear. Thus if I know that someone means to explain a colour-word to me the ostensive definition "That is called 'sepia' " will help me to understand the word.... One has already to know (or be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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. Example 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 * Set notation * 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 element (mathematics), elements of a Set ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Small Set (category Theory)
In category theory, a small set is one in a fixed universe of sets (as the word ''universe'' is used in mathematics in general). Thus, the category of small sets is the category of all sets one cares to consider. This is used when one does not wish to bother with set-theoretic concerns of what is and what is not considered a set, which concerns would arise if one tried to speak of the category of "all sets". A small set is not to be confused with a small category, which is a category in which the collection of arrows (and therefore also the collection of objects) is a set. In other choices of foundations, such as Grothendieck universes, there exist both sets that belong to the universe, called “small sets” and sets that do not, such as the universe itself, “large sets”. We gain an intermediate notion of moderate set: a subset of the universe, which may be small or large. Every small set is moderate, but not conversely. Since in many cases the choice of foundations is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Finite Sets
In mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example, is a finite set with five elements. The number of elements of a finite set is a natural number (possibly zero) and is called the ''cardinality (or the cardinal number)'' of the set. A set that is not a finite set is called an ''infinite set''. For example, the set of all positive integers is infinite: Finite sets are particularly important in combinatorics, the mathematical study of counting. Many arguments involving finite sets rely on the pigeonhole principle, which states that there cannot exist an injective function from a larger finite set to a smaller finite set. Definition and terminology Formally, a set S is called finite if there exists a bijection for some natural number n (natural numbers are defined as sets in Zermelo-Fraenkel set theory). The number n is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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List Of Sovereign States
The following is a list providing an overview of sovereign states around the world with information on their status and recognition of their sovereignty. The 205 listed states can be divided into three categories based on membership within the United Nations System: 193 member states of the United Nations, UN member states, two United Nations General Assembly observers#Current non-member observers, UN General Assembly non-member observer states, and ten other states. The ''sovereignty dispute'' column indicates states having undisputed sovereignty (188 states, of which there are 187 UN member states and one UN General Assembly non-member observer state), states having disputed sovereignty (15 states, of which there are six UN member states, one UN General Assembly non-member observer state, and eight de facto states), and states having a political status of the Cook Islands and Niue, special political status (two states, both in associated state, free association with New ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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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 (logic), 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 monad (Greek philosophy), 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 ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Chess
Chess is a board game for two players. It is an abstract strategy game that involves Perfect information, no hidden information and no elements of game of chance, chance. It is played on a square chessboard, board consisting of 64 squares arranged in an 8×8 grid. The players, referred to as White and Black in chess, "White" and "Black", each control sixteen Chess piece, pieces: one king (chess), king, one queen (chess), queen, two rook (chess), rooks, two bishop (chess), bishops, two knight (chess), knights, and eight pawn (chess), pawns, with each type of piece having a different pattern of movement. An enemy piece may be captured (removed from the board) by moving one's own piece onto the square it occupies. The object of the game is to "checkmate" (threaten with inescapable capture) the enemy king. There are also several ways a game can end in a draw (chess), draw. The recorded history of chess goes back to at least the emergence of chaturanga—also thought to be an ancesto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |