|
Oskar Becker
Oscar Becker (5 September 1889 – 13 November 1964) was a German philosopher, logician, mathematician, and historian of mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics .... Early life Becker was born in Leipzig, where he studied mathematics. His dissertation under Otto Hölder and Karl Rohn (1914) was ''On the Decomposition of Polygons in non-intersecting triangles on the Basis of the Axioms of Connection and Order.'' He served in World War I and returned to study philosophy with Edmund Husserl, writing his ''Habilitationsschrift'' on ''Investigations of the Phenomenological Foundations of Geometry and their Physical Applications'', (1923). Becker was Husserl's assistant, informally, and then official editor of the ''Yearbook for Phenomenological Research''. Work in p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscar Becker
Oscar, OSCAR, or The Oscar may refer to: People * Oscar (given name), an Irish- and English-language name also used in other languages; the article includes the names Oskar, Oskari, Oszkár, Óscar, and other forms. * Oscar (Irish mythology), legendary figure, son of Oisín and grandson of Finn mac Cumhall Places * Oscar, Kentucky, an unincorporated community * Oscar, Louisiana, an unincorporated community * Oscar, Missouri, an unincorporated community * Oscar, Oklahoma, an unincorporated community * Oscar, Pennsylvania, an unincorporated community * Oscar, Texas, an unincorporated community * Oscar, West Virginia, an unincorporated community * Lake Oscar (other) * Oscar Township, Otter Tail County, Minnesota, a civil township Animals * Oscar (bionic cat), a cat that had implants after losing both hind paws * Oscar (bull), #16, (d. 1983) a ProRodeo Hall of Fame bucking bull * Oscar (fish), ''Astronotus ocellatus'' * Oscar (therapy cat), cat purported to predict ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermeneutics
Hermeneutics () is the theory and methodology of interpretation, especially the interpretation of biblical texts, wisdom literature, and philosophical texts. Hermeneutics is more than interpretative principles or methods used when immediate comprehension fails and includes the art of understanding and communication. Modern hermeneutics includes both verbal and non-verbal communication''The Routledge Companion to Philosophy in Organization Studies'', Routledge, 2015, p. 113.Joann McNamara, ''From Dance to Text and Back to Dance: A Hermeneutics of Dance Interpretive Discourse'', PhD thesis, Texas Woman's University, 1994. as well as semiotics, presuppositions, and pre-understandings. Hermeneutics has been broadly applied in the humanities, especially in law, history and theology. Hermeneutics was initially applied to the interpretation, or exegesis, of scripture, and has been later broadened to questions of general interpretation. p. 2 The terms ''hermeneutics'' and ''exegesi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
African-American Culture
African-American culture refers to the contributions of African Americans to the culture of the United States, either as part of or distinct from mainstream American culture. The culture is both distinct and enormously influential on American and global worldwide culture as a whole. African-American culture is a blend between the native African cultures of West Africa and Central Africa and the European culture that has influenced and modified its development in the American South. Understanding its identity within the culture of the United States, that is, in the anthropological sense, conscious of its origins as largely a blend of West and Central African cultures. Although slavery greatly restricted the ability for Africans to practice their original cultural traditions, many practices, values and beliefs survived, and over time they have modified and/or blended with European cultures and other cultures such as that of Native Americans. African-American identity wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fred Moten
Fred Moten (born 1962) is an American cultural theorist, poet, and scholar whose work explores critical theory, black studies, and performance studies. Moten is Professor of Performance Studies at New York University and Distinguished Professor Emeritus at University of California, Riverside; he previously taught at Duke University, Brown University, and the University of Iowa. His scholarly texts include '' The Undercommons: Fugitive Planning & Black Study'' which was co-authored with Stefano Harney, ''In the Break: The Aesthetics of the Black Radical Tradition'', and ''The Universal Machine'' (Duke University Press, 2018). He has published numerous poetry collections, including ''The Little Edges'', ''The Feel Trio'', ''B Jenkins'', and ''Hughson’s Tavern''. In 2020, Moten was awarded a MacArthur Fellowship for " eating new conceptual spaces to accommodate emerging forms of Black aesthetics, cultural production, and social life." Biography Fred Moten was born in Las Vegas in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nahum Chandler
Nahum ( or ; he, נַחוּם ''Naḥūm'') was a minor prophet whose prophecy is recorded in the ''Tanakh'', also called the Hebrew Bible and The Old Testament. His book comes in chronological order between Micah and Habakkuk in the Bible. He wrote about the end of the Assyrian Empire, and its capital city, Nineveh, in a vivid poetic style. Life Little is known about Nahum's personal history. His name means "comforter," and he was from the town of Alqosh (Nahum 1:1), which scholars have attempted to identify with several cities, including the modern Alqosh in northern Iraq and Capernaum of northern Galilee. He was a very nationalistic Hebrew, however, and lived amongst the Elkoshites in peace. Nahum, called "the Elkoshite", is the seventh in order of the minor prophets. Works Nahum's writings could be taken as prophecy or as history. One account suggests that his writings are a prophecy written in about 615 BC, just before the downfall of Assyria, while another account sugge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universally Quantified
In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation to every member of the domain. It asserts that a predicate within the scope of a universal quantifier is true of every value of a predicate variable. It is usually denoted by the turned A (∀) logical operator symbol, which, when used together with a predicate variable, is called a universal quantifier ("", "", or sometimes by "" alone). Universal quantification is distinct from ''existential'' quantification ("there exists"), which only asserts that the property or relation holds for at least one member of the domain. Quantification in general is covered in the article on quantification (logic). The universal quantifier is encoded as in Unicode, and as \forall in LaTeX and relate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Induction
Mathematical induction is a method for proving that a statement ''P''(''n'') is true for every natural number ''n'', that is, that the infinitely many cases ''P''(0), ''P''(1), ''P''(2), ''P''(3), ... all hold. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: A proof by induction consists of two cases. The first, the base case, proves the statement for ''n'' = 0 without assuming any knowledge of other cases. The second case, the induction step, proves that ''if'' the statement holds for any given case ''n'' = ''k'', ''then'' it must also hold for the next case ''n'' = ''k'' + 1. These two steps establish that the statement holds for every natural number ''n''. The base case does not necessarily begin with ''n'' = 0, but often with ''n'' = 1, and possibly with any fixed natural number ''n'' = ''N'', establishing the truth of the statement for all natu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finitism
Finitism is a philosophy of mathematics that accepts the existence only of finite mathematical objects. It is best understood in comparison to the mainstream philosophy of mathematics where infinite mathematical objects (e.g., infinite sets) are accepted as legitimate. Main idea The main idea of finitistic mathematics is not accepting the existence of infinite objects such as infinite sets. While all natural numbers are accepted as existing, the ''set'' of all natural numbers is not considered to exist as a mathematical object. Therefore quantification over infinite domains is not considered meaningful. The mathematical theory often associated with finitism is Thoralf Skolem's primitive recursive arithmetic. History The introduction of infinite mathematical objects occurred a few centuries ago when the use of infinite objects was already a controversial topic among mathematicians. The issue entered a new phase when Georg Cantor in 1874 introduced what is now called naive set t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metamathematics
Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the term itself) owes itself to David Hilbert's attempt to secure the foundations of mathematics in the early part of the 20th century. Metamathematics provides "a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic" (Kleene 1952, p. 59). An important feature of metamathematics is its emphasis on differentiating between reasoning from inside a system and from outside a system. An informal illustration of this is categorizing the proposition "2+2=4" as belonging to mathematics while categorizing the proposition "'2+2=4' is valid" as belonging to metamathematics. History Metamathematical metatheorems about mathematics itself were originally differentiated from ordinary mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Bernays
Paul Isaac Bernays (17 October 1888 – 18 September 1977) was a Swiss mathematician who made significant contributions to mathematical logic, axiomatic set theory, and the philosophy of mathematics. He was an assistant and close collaborator of David Hilbert. Biography Bernays was born into a distinguished German-Jewish family of scholars and businessmen. His great-grandfather, Isaac ben Jacob Bernays, served as chief rabbi of Hamburg from 1821 to 1849. Bernays spent his childhood in Berlin, and attended the Köllner Gymnasium, 1895–1907. At the University of Berlin, he studied mathematics under Issai Schur, Edmund Landau, Ferdinand Georg Frobenius, and Friedrich Schottky; philosophy under Alois Riehl, Carl Stumpf and Ernst Cassirer; and physics under Max Planck. At the University of Göttingen, he studied mathematics under David Hilbert, Edmund Landau, Hermann Weyl, and Felix Klein; physics under Voigt and Max Born; and philosophy under Leonard Nelson. In 1912, the Unive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory). Hilbert adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set the course for much of the mathematical research of the 20th century. Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Hilbert is known as one of the founders of proof theory and mathematical logic. Life Early life and edu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Foundations Of Mathematics
Foundations of mathematics is the study of the philosophy, philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts (set, function, geometrical figure, number, etc.) and how they form hierarchies of more complex structures and concepts, especially the fundamentally important structures that form the language of mathematics (formulas, theories and their model theory, models giving a meaning to formulas, definitions, proofs, algorithms, etc.) also called metamathematics, metamathematical concepts, with an eye to the philosophical aspects and the unity of mathematics. The search for foundations of mathematics is a cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
