Intensional Equality

	Intensional Equality Intensional, related to intension, may refer to: Intensional * in philosophy of language: not extensional. See also intensional definition versus extensional definition * in philosophy of mind: an intensional state is a state which has a propositional content * in mathematical logic: see intensional statement. See also extensionality, and also intensional definition versus extensional definition * Intensional logic embraces the study of intensional languages: at least one of their functors is intensional. It can be contrasted to extensional logic * Intensional fallacy, committed when one makes an illicit use of Leibniz's law in an argument * See also: Musical form In music, ''form'' refers to the structure of a musical composition or musical improvisation, performance. In his book, ''Worlds of Music'', Jeff Todd Titon suggests that a number of organizational elements may determine the formal structure of a ... {{disambiguation ... [...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 (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]
	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]
	Intensional Statement 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 ''referent' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Intensional Logic Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe (''extensions''), by additional quantifiers that range over terms that may have such individuals as their value (''intensions''). The distinction between intensional and extensional entities is parallel to the distinction between sense and reference. Overview Logic is the study of proof and deduction as manifested in language (abstracting from any underlying psychological or biological processes). Logic is not a closed, completed science, and presumably, it will never stop developing: the logical analysis can penetrate into varying depths of the language (sentences regarded as atomic, or splitting them to predicates applied to individual terms, or even revealing such fine logical structures like modal, temporal, dynamic, epistemic ones). In order to achieve its special goal, logic was forced to develop its own formal tools ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Intensional Fallacy In philosophical logic, the masked-man fallacy (also known as the intensional fallacy or epistemic fallacy) is the false assumption that a knowledge or a belief about an object (an intension) can be used to correctly tell it apart from another object (as opposed to facts, that can be used to correctly tell two objects apart). It is committed when one makes an illicit use of Leibniz's law in an argument. Leibniz's law states that if A and B are the same object, then A and B are indiscernible (that is, they have all the same properties). By ''modus tollens'', this means that if one object has a certain property, while another object does not have the same property, the two objects cannot be identical. The fallacy is "epistemic" because it posits an immediate identity between a subject's knowledge of an object with the object itself, failing to recognize that Leibniz's Law is not capable of accounting for intensional contexts. Examples The name of the fallacy comes from the example: * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]