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Function And Concept
"Function and Concept" (German: "Funktion und Begriff", "Function and Concept") is a lecture delivered by Gottlob Frege in 1891. The lecture involves a clarification of his earlier distinction between concepts and objects. It was first published as an article in 1962.G. Patzig (ed.), ''Funktion, Begriff, Bedeutung'', Göttingen: Vandenhoeck & Ruprecht, 1962. Overview In general, a concept is a function whose value is always a truth value (139). A relation is a two place function whose value is always a truth value (146). Frege draws an important distinction between concepts on the basis of their level. Frege tells us that a first-level concept is a one-place function that correlates objects with truth-value In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (''true'' or '' false''). Computing In some progra ...s (147). First level conc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lecture
A lecture (from Latin ''lēctūra'' “reading” ) is an oral presentation intended to present information or teach people about a particular subject, for example by a university or college teacher. Lectures are used to convey critical information, history, background, theories, and equations. A politician's speech, a minister's sermon, or even a business person's sales presentation may be similar in form to a lecture. Usually the lecturer will stand at the front of the room and recite information relevant to the lecture's content. Though lectures are much criticised as a teaching method, universities have not yet found practical alternative teaching methods for the large majority of their courses. Critics point out that lecturing is mainly a one-way method of communication that does not involve significant audience participation but relies upon passive learning. Therefore, lecturing is often contrasted to active learning. Lectures delivered by talented speakers can be high ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gottlob Frege
Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be the greatest logician since Aristotle, and one of the most profound philosophers of mathematics ever. His contributions include the development of modern logic in the ''Begriffsschrift'' and work in the foundations of mathematics. His book the ''Foundations of Arithmetic'' is the seminal text of the logicist project, and is cited by Michael Dummett as where to pinpoint the linguistic turn. His philosophical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function (mathematics)
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth Value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (''true'' or '' false''). Computing In some programming languages, any expression can be evaluated in a context that expects a Boolean data type. Typically (though this varies by programming language) expressions like the number zero, the empty string, empty lists, and null evaluate to false, and strings with content (like "abc"), other numbers, and objects evaluate to true. Sometimes these classes of expressions are called "truthy" and "falsy" / "false". Classical logic In classical logic, with its intended semantics, the truth values are ''true'' (denoted by ''1'' or the verum ⊤), and '' untrue'' or '' false'' (denoted by ''0'' or the falsum ⊥); that is, classical logic is a two-valued logic. This set of two values is also called the Boolean domain. Corresponding semantics of l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth-value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (''true'' or '' false''). Computing In some programming languages, any expression can be evaluated in a context that expects a Boolean data type. Typically (though this varies by programming language) expressions like the number zero, the empty string, empty lists, and null evaluate to false, and strings with content (like "abc"), other numbers, and objects evaluate to true. Sometimes these classes of expressions are called "truthy" and "falsy" / "false". Classical logic In classical logic, with its intended semantics, the truth values are ''true'' (denoted by ''1'' or the verum ⊤), and '' untrue'' or '' false'' (denoted by ''0'' or the falsum ⊥); that is, classical logic is a two-valued logic. This set of two values is also called the Boolean domain. Corresponding semantics of log ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Range Of A Function
In mathematics, the range of a function may refer to either of two closely related concepts: * The codomain of the function * The image of the function Given two sets and , a binary relation between and is a (total) function (from to ) if for every in there is exactly one in such that relates to . The sets and are called domain and codomain of , respectively. The image of is then the subset of consisting of only those elements of such that there is at least one in with . Terminology As the term "range" can have different meanings, it is considered a good practice to define it the first time it is used in a textbook or article. Older books, when they use the word "range", tend to use it to mean what is now called the codomain. More modern books, if they use the word "range" at all, generally use it to mean what is now called the image. To avoid any confusion, a number of modern books don't use the word "range" at all. Elaboration and example Given a functi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1891 Essays
Events January–March * January 1 ** Paying of old age pensions begins in Germany. ** A strike of 500 Hungarian steel workers occurs; 3,000 men are out of work as a consequence. **Germany takes formal possession of its new African territories. * January 2 – A. L. Drummond of New York is appointed Chief of the Treasury Secret Service. * January 4 – The Earl of Zetland issues a declaration regarding the famine in the western counties of Ireland. * January 5 **The Australian shearers' strike, that leads indirectly to the foundation of the Australian Labor Party, begins. **A fight between the United States and Indians breaks out near Pine Ridge agency. **Henry B. Brown, of Michigan, is sworn in as an Associate Justice of the Supreme Court. **A fight between railway strikers and police breaks out at Motherwell, Scotland. * January 6 – Encounters continue, between strikers and the authorities at Glasgow. * January 7 ** General Miles' forces su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Essays
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some sources claim the term was coined by Pythagoras ( BCE), although this theory is disputed by some. Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation. in . Historically, ''philosophy'' encompassed all bodies of knowledge and a practitioner was known as a ''philosopher''."The English word "philosophy" is first attested to , meaning "knowledge, body of knowledge." "natural philosophy," which began as a discipline in ancient India and Ancient Greece, encompasses astronomy, medicine, and physics. For example, Newton's 1687 ''Mathematical Principles of Natural Philosophy'' later became classified as a book of physics. In the 19th century, the growth of modern research universitie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Language
In analytic philosophy, philosophy of language investigates the nature of language and the relations between language, language users, and the world. Investigations may include inquiry into the nature of meaning, intentionality, reference, the constitution of sentences, concepts, learning, and thought. Gottlob Frege and Bertrand Russell were pivotal figures in analytic philosophy's "linguistic turn". These writers were followed by Ludwig Wittgenstein ('' Tractatus Logico-Philosophicus''), the Vienna Circle, logical positivists, and Willard Van Orman Quine. In continental philosophy, language is not studied as a separate discipline. Rather, it is an inextricable part of many other areas of thought, such as phenomenology, structural semiotics, language of mathematics, hermeneutics, existentialism, deconstruction and critical theory. History Ancient philosophy In the West, inquiry into language stretches back to the 5th century BC with Socrates, Plato, Aristotl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Works By Gottlob Frege
Works may refer to: People * Caddy Works (1896–1982), American college sports coach * Samuel Works (c. 1781–1868), New York politician Albums * '' ''Works'' (Pink Floyd album)'', a Pink Floyd album from 1983 * ''Works'', a Gary Burton album from 1972 * ''Works'', a Status Quo album from 1983 * ''Works'', a John Abercrombie album from 1991 * ''Works'', a Pat Metheny album from 1994 * ''Works'', an Alan Parson Project album from 2002 * ''Works Volume 1'', a 1977 Emerson, Lake & Palmer album * ''Works Volume 2'', a 1977 Emerson, Lake & Palmer album * '' The Works'', a 1984 Queen album Other uses * Microsoft Works, a collection of office productivity programs created by Microsoft * IBM Works, an office suite for the IBM OS/2 operating system * Mount Works, Victoria Land, Antarctica See also * The Works (other) * Work (other) Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
