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George Spencer-Brown
George Spencer-Brown (2 April 1923 – 25 August 2016) was an English polymath best known as the author of ''Laws of Form''. He described himself as a "mathematician, consulting engineer, psychologist, educational consultant and practitioner, consulting psychotherapist, author, and poet". Life Born in Grimsby, Lincolnshire, England, Spencer-Brown attended Mill Hill School and then passed the First M.B. in 1940 at London Hospital Medical College (now part of Barts and The London School of Medicine and Dentistry). After serving in the Royal Navy (1943–47), he studied at Trinity College, Cambridge, earning Honours in Philosophy (1950) and Psychology (1951), and where he met Bertrand Russell. From 1952 to 1958, he taught philosophy at Christ Church, Oxford, took M.A. degrees in 1954 from both Oxford and Cambridge, and wrote his doctorate thesis ''Probability and Scientific Inference'' under the supervision of William Kneale which was released as a book in 1957. During the 1960s, he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grimsby
Grimsby or Great Grimsby is a port town and the administrative centre of North East Lincolnshire, Lincolnshire, England. Grimsby adjoins the town of Cleethorpes directly to the south-east forming a conurbation. Grimsby is north-east of Lincoln, England, Lincoln, (via the Humber Bridge) south-south-east of Kingston upon Hull, Hull, south-east of Scunthorpe, east of Doncaster and south-east of Leeds. Grimsby is also home to notable landmarks such as Grimsby Minster, Port of Grimsby, Cleethorpes Beach and Grimsby Fishing Heritage Museum. Grimsby was once the home port for the world's largest fishing fleet around the mid-20th century, but fishing then fell sharply. The Cod Wars denied UK access to Icelandic fishing grounds and the European Union used its Common Fisheries Policy to parcel out fishing quotas to other European countries in waters within of the UK coast. Grimsby suffered post-industrial decline like most other post-industrial towns and cities. However, food pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Maryland, College Park
The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public land-grant research university in College Park, Maryland. Founded in 1856, UMD is the flagship institution of the University System of Maryland. It is also the largest university in both the state and the Washington metropolitan area, with more than 41,000 students representing all fifty states and 123 countries, and a global alumni network of over 388,000. Together, its 12 schools and colleges offer over 200 degree-granting programs, including 92 undergraduate majors, 107 master's programs, and 83 doctoral programs. UMD is a member of the Association of American Universities and competes in intercollegiate athletics as a member of the Big Ten Conference. The University of Maryland's proximity to the nation's capital has resulted in many research partnerships with the federal government; faculty receive research funding and institutional support from many agencies, such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis Kauffman
Louis Hirsch Kauffman (born February 3, 1945) is an American mathematician, topologist, and professor of mathematics in the Department of Mathematics, Statistics, and Computer science at the University of Illinois at Chicago. He is known for the introduction and development of the bracket polynomial and the Kauffman polynomial. Biography Kauffman was valedictorian of his graduating class at Norwood Norfolk Central High School in 1962. He received his B.S. at the Massachusetts Institute of Technology in 1966 and his Ph.D. in mathematics from Princeton University in 1972 (with William Browder as thesis advisor). Kauffman has worked at many places as a visiting professor and researcher, including the University of Zaragoza in Spain, the University of Iowa in Iowa City, the Institut des Hautes Études Scientifiques in Bures Sur Yevette, France, the Institut Henri Poincaré in Paris, France, the University of Bologna, Italy, the Federal University of Pernambuco in Recife, Brazil, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heinz Von Foerster
Heinz von Foerster (German spelling: Heinz von Förster; November 13, 1911 – October 2, 2002) was an Austrian American scientist combining physics and philosophy, and widely attributed as the originator of Second-order cybernetics. He was twice a Guggenheim fellow (1956–57 and 1963–64) and also was a fellow of the American Association for the Advancement of Science, 1980. He is well known for his 1960 Doomsday equation formula published in ''Science'' predicting future population growth. As a polymath, he wrote nearly two hundred professional papers, gaining renown in fields from computer science and artificial intelligence to epistemology, and researched high-speed electronics and electro-optics switching devices as a physicist, and in biophysics, the study of memory and knowledge. He worked on cognition based on neurophysiology, mathematics, and philosophy and was called "one of the most consequential thinkers in the history of cybernetics". He came to the United States, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Existential Graph
An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote on logical graph, graphical logic as early as 1882,Peirce, C. S., "[On Junctures and Fractures in Logic]" (editors' title for MS 427 (the new numbering system), Fall–Winter 1882), and "Letter, Peirce to O. H. Mitchell" (L 294, 21 December 1882), ''Charles Sanders Peirce bibliography#W, Writings of Charles S. Peirce'', v. 4, "Junctures" on pp. 391–393 (Googl preview and the letter on pp. 394–399 (Googl preview. See John F. Sowa, Sowa, John F. (1997), "Matching Logical Structure to Linguistic Structure", ''Studies in the Logic of Charles Sanders Peirce'', Nathan Houser, Don D. Roberts, and James Van Evra, editors, Bloomington and Indianopolis: Indiana University Press, pp. 418–444, see 420, 425, 426, 428. and continued to develop the method until his death in 1914. The graphs Peirce proposed three systems of existential graphs: * ''alpha'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entitative Graph
An entitative graph is an element of the diagrammatic syntax for logic that Charles Sanders Peirce developed under the name of qualitative logic beginning in the 1880s, taking the coverage of the formalism only as far as the propositional or sentential aspects of logic are concerned. See 3.468, 4.434, and 4.564 in Peirce's ''Collected Papers''. Peirce wrote of this system in an 1897 ''Monist'' article titled "The Logic of Relatives", although he had mentioned logical graphs in an 1882 letter to O. H. Mitchell. The syntax is: * The blank page; * Single letters, phrases; * Dashes; * Objects (subgraphs) enclosed by a simple closed curve called a ''cut''. A cut can be empty. The semantics are: * The blank page denotes False; * Letters, phrases, subgraphs, and entire graphs can be True or False; * To surround objects with a cut is equivalent to Boolean complementation. Hence an empty cut denotes Truth; * All objects within a given cut are tacitly joined by disjunction. * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Sanders Peirce
Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism". Educated as a chemist and employed as a scientist for thirty years, Peirce made major contributions to logic, a subject that, for him, encompassed much of what is now called epistemology and the philosophy of science. He saw logic as the formal branch of semiotics, of which he is a founder, which foreshadowed the debate among logical positivists and proponents of philosophy of language that dominated 20th-century Western philosophy. Additionally, he defined the concept of abductive reasoning, as well as rigorously formulated mathematical induction and deductive reasoning. As early as 1886, he saw that logic gate, logical operations could be carried out by electrical switching circuits. The same idea was used decades later to produce digital computers. See Also In 1934, the philosopher Paul W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal System
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system". In 1921, David Hilbert proposed to use such a system as the foundation for the knowledge in mathematics. A formal system may represent a well-defined abstraction, system of abstract thought. The term ''formalism'' is sometimes a rough synonym for ''formal system'', but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation. Background Each formal system is described by primitive Symbol (formal), symbols (which collectively form an Alphabet (computer science), alphabet) to finitely construct a formal language from a set of axioms through inferential rules of formation. The system thus consists of valid formulas built up through finite combinations of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-element Boolean Algebra
In mathematics and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose ''underlying set'' (or universe or ''carrier'') ''B'' is the Boolean domain. The elements of the Boolean domain are 1 and 0 by convention, so that ''B'' = . Paul Halmos's name for this algebra "2" has some following in the literature, and will be employed here. Definition ''B'' is a partially ordered set and the elements of ''B'' are also its bounds. An operation of arity ''n'' is a mapping from ''B''n to ''B''. Boolean algebra consists of two binary operations and unary complementation. The binary operations have been named and notated in various ways. Here they are called 'sum' and 'product', and notated by infix '+' and '∙', respectively. Sum and product commute and associate, as in the usual algebra of real numbers. As for the order of operations, brackets are decisive if present. Otherwise '∙' precedes '+'. Hence ''A∙B + C'' is parsed as ''(A∙B)& ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Algebraic Structures
In mathematics, there are many types of algebraic structures which are studied. Abstract algebra is primarily the study of specific algebraic structures and their properties. Algebraic structures may be viewed in different ways, however the common starting point of algebra texts is that an algebraic object incorporates one or more sets with one or more binary operations or unary operations satisfying a collection of axioms. Another branch of mathematics known as universal algebra studies algebraic structures in general. From the universal algebra viewpoint, most structures can be divided into varieties and quasivarieties depending on the axioms used. Some axiomatic formal systems that are neither varieties nor quasivarieties, called ''nonvarieties'', are sometimes included among the algebraic structures by tradition. Concrete examples of each structure will be found in the articles listed. Algebraic structures are so numerous today that this article will inevitably be incompl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daily Express
The ''Daily Express'' is a national daily United Kingdom middle-market newspaper printed in tabloid format. Published in London, it is the flagship of Express Newspapers, owned by publisher Reach plc. It was first published as a broadsheet in 1900 by Sir Arthur Pearson. Its sister paper, the ''Sunday Express'', was launched in 1918. In June 2022, it had an average daily circulation of 201,608. The paper rose to become the largest circulation newspaper in the world under Lord Beaverbrook, going from 2 million in the 1930s to 4 million in the 1940s. It was acquired by Richard Desmond's company Northern & Shell in 2000. Hugh Whittow was the editor from February 2011 until he retired in March 2018. In February 2018 Trinity Mirror acquired the ''Daily Express'', and other publishing assets of Northern & Shell, in a deal worth £126.7 million. To coincide with the purchase the Trinity Mirror group changed the name of the company to ''Reach''. Hugh Whittow resigned as editor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
