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Calculus Ratiocinator
The ''calculus ratiocinator'' is a theoretical universal logical calculation framework, a concept described in the writings of Gottfried Leibniz, usually paired with his more frequently mentioned ''characteristica universalis'', a universal conceptual language. Two views There are two contrasting points of view on what Leibniz meant by ''calculus ratiocinator''. The first is associated with computer software, the second is associated with computer hardware. Analytic view The received point of view in analytic philosophy and formal logic, is that the ''calculus ratiocinator'' anticipates mathematical logic—an "algebra of logic". The analytic point of view understands that the ''calculus ratiocinator'' is a formal inference engine or computer program, which can be designed so as to grant primacy to calculations. That logic began with Frege's 1879 ''Begriffsschrift'' and C.S. Peirce's writings on logic in the 1880s. Frege intended his "concept script" to be a ''calcul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gottfried Leibniz
Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Isaac Newton, Sir Isaac Newton, with the creation of calculus in addition to many other branches of mathematics, such as binary arithmetic and statistics. Leibniz has been called the "last universal genius" due to his vast expertise across fields, which became a rarity after his lifetime with the coming of the Industrial Revolution and the spread of specialized labor. He is a prominent figure in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history, philology, games, music, and other studies. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science. Leibniz contributed to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Systems Theory
Systems theory is the transdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or artificial. Every system has causal boundaries, is influenced by its context, defined by its structure, function and role, and expressed through its relations with other systems. A system is "more than the sum of its parts" when it expresses synergy or emergent behavior. Changing one component of a system may affect other components or the whole system. It may be possible to predict these changes in patterns of behavior. For systems that learn and adapt, the growth and the degree of adaptation depend upon how well the system is engaged with its environment and other contexts influencing its organization. Some systems support other systems, maintaining the other system to prevent failure. The goals of systems theory are to model a system's dynamics, constraints, conditions, and relations; and to elucidate principles (such as purpose, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Computing
The history of computing is longer than the history of computing hardware and modern computing technology and includes the history of methods intended for pen and paper or for chalk and slate, with or without the aid of tables. Concrete devices Digital computing is intimately tied to the representation of number A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...s. But long before abstractions like ''the number'' arose, there were mathematical concepts to serve the purposes of civilization. These concepts are implicit in concrete practices such as: *''Bijection, One-to-one correspondence'', a rule to counting, count ''how many'' items, e.g. on a tally stick, eventually abstracted into ''numbers''. *''Comparison to a standard'', a method for assuming ''reproducibility'' in a measure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concepts In The Philosophy Of Language
A concept is an abstract idea that serves as a foundation for more concrete principles, thoughts, and beliefs. Concepts play an important role in all aspects of cognition. As such, concepts are studied within such disciplines as linguistics, psychology, and philosophy, and these disciplines are interested in the logical and psychological structure of concepts, and how they are put together to form thoughts and sentences. The study of concepts has served as an important flagship of an emerging interdisciplinary approach, cognitive science. In contemporary philosophy, three understandings of a concept prevail: * mental representations, such that a concept is an entity that exists in the mind (a mental object) * abilities peculiar to cognitive agents (mental states) * Fregean senses, abstract objects rather than a mental object or a mental state Concepts are classified into a hierarchy, higher levels of which are termed "superordinate" and lower levels termed "subordinate". Additi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concepts In Logic
A concept is an abstract idea that serves as a foundation for more concrete principles, thoughts, and beliefs. Concepts play an important role in all aspects of cognition. As such, concepts are studied within such disciplines as linguistics, psychology, and philosophy, and these disciplines are interested in the logical and psychological structure of concepts, and how they are put together to form thoughts and sentences. The study of concepts has served as an important flagship of an emerging interdisciplinary approach, cognitive science. In contemporary philosophy, three understandings of a concept prevail: * mental representations, such that a concept is an entity that exists in the mind (a mental object) * abilities peculiar to cognitive agents (mental states) * Fregean senses, abstract objects rather than a mental object or a mental state Concepts are classified into a hierarchy, higher levels of which are termed "superordinate" and lower levels termed "subordinate". A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The MIT Press
The MIT Press is the university press of the Massachusetts Institute of Technology (MIT), a private research university in Cambridge, Massachusetts. The MIT Press publishes a number of academic journals and has been a pioneer in the Open Access movement in academic publishing. History MIT Press traces its origins back to 1926 when MIT published a lecture series entitled ''Problems of Atomic Dynamics'' given by the visiting German physicist and later Nobel Prize winner, Max Born. In 1932, MIT's publishing operations were first formally instituted by the creation of an imprint called Technology Press. This imprint was founded by James R. Killian, Jr., at the time editor of MIT's alumni magazine and later to become MIT president. Technology Press published eight titles independently, then in 1937 entered into an arrangement with John Wiley & Sons in which Wiley took over marketing and editorial responsibilities. In 1961, the centennial of MIT's founding charter, the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of The New York Academy Of Sciences
The ''Annals of the New York Academy of Sciences'' is an academic journal published by Wiley-Blackwell on behalf of the New York Academy of Sciences. It is one of the oldest science journals still being published, having been founded in 1823. The editor-in-chief is Douglas Braaten. Each issue is of substantial length and explores a single topic with a multidisciplinary approach. A review published on '' Ulrichsweb'' states the scope is enormous and describes the journal as highly respected and the articles as penetrating. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2019 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are considered more prestigious or important within their field. The Impact Factor of a journa ... of 4.728, ranking it 13th out of 71 journals in the categor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The American Mathematical Monthly
''The American Mathematical Monthly'' is a peer-reviewed scientific journal of mathematics. It was established by Benjamin Finkel in 1894 and is published by Taylor & Francis on behalf of the Mathematical Association of America. It is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. The editor-in-chief is Vadim Ponomarenko (San Diego State University). The journal gives the Lester R. Ford Award annually to "authors of articles of expository excellence" published in the journal. Editors-in-chief The following persons are or have been editor-in-chief: See also *''Mathematics Magazine'' *''Notices of the American Mathematical Society ''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathesis Universalis
(from , "science or learning", and "universal") is a hypothetical universal science modelled on mathematics envisaged by René Descartes, Descartes and Gottfried Wilhelm Leibniz, Leibniz, among a number of other 16th- and 17th-century philosophers and mathematicians. For Leibniz, it would be supported by a ''calculus ratiocinator''. John Wallis invokes the name as title in his ''Opera Mathematica'', a textbook on arithmetic, algebra, and Cartesian geometry. History Descartes' most explicit description of ''mathesis universalis'' occurs in ''Rule Four'' of the ''Rules for the Direction of the Mind'', written before 1628. Leibniz attempted to work out the possible connections between mathematical logic, algebra, infinitesimal calculus, combinatorics, and Characteristica universalis, universal characteristics in an incomplete treatise titled "''Mathesis Universalis''" in 1695. Predicate logic could be seen as a modern system with some of these ''universal'' qualities, at least ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Louis Couturat
Louis Couturat (; 17 January 1868 – 3 August 1914) was a French logician, mathematician, philosopher, and linguist. Couturat was a pioneer of the constructed language Ido. Life and education Born in Paris. In 1887 he entered École Normale Supérieure to study philosophy and mathematics. In 1895 he lectured in philosophy at the University of Toulouse and 1897 lectured in philosophy of mathematics at the University of Caen Normandy, taking a stand in favor of transfinite numbers. After a time in Hanover studying the writings of Leibniz, he became an assistant to Henri-Louis Bergson at the Collège de France in 1905. Career He was the French advocate of the symbolic logic that emerged in the years before World War I, thanks to the writings of Charles Sanders Peirce, Giuseppe Peano and his school, and especially to ''The Principles of Mathematics'' by Couturat's friend and correspondent Bertrand Russell. Like Russell, Couturat saw symbolic logic as a tool to advance both ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hartley Rogers
Hartley Rogers Jr. (July 6, 1926 – July 17, 2015) was an American mathematician who worked in computability theory, and was a professor in the Mathematics Department of the Massachusetts Institute of Technology. Biography Born in 1926 in Buffalo, New York, Rogers studied English as an undergraduate at Yale University, graduating in 1946. After visiting the University of Cambridge under a Henry Fellowship, he returned to Yale for a master's degree in physics, which he completed in 1950. He studied mathematics under Alonzo Church at Princeton, earned a second master's degree in 1951, and received his Ph.D. there in 1952. He was a Benjamin Peirce Lecturer at Harvard University from 1952 to 1955. After holding a visiting position at MIT, he became a professor in the MIT Mathematics Department in 1956. His doctoral students included Patrick Fischer, Louis Hodes, Carl Jockusch, Andrew Kahr, David Luckham, Rohit Parikh, David Park, and John Stillwell. He chaired the MIT faculty ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
