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Unknowability
In philosophy, unknowability is the possibility of inherently unaccessible knowledge. It addresses the epistemology of that which we ''cannot'' know. Some related concepts include the halting problem, the limits of knowledge, the unknown unknowns, and chaos theory. Nicholas Rescher provides the most recent focused scholarship for this area in ''Unknowability: An Inquiry into the Limits of Knowledge'', where he offered three high level categories, logical unknowability, conceptual unknowability, and in-principle unknowability. Background Speculation about what is knowable and unknowable has been part of the philosophical tradition since the inception of philosophy. In particular, Baruch Spinoza's Theory of Attributes argues that a human's finite mind cannot understand infinite substance; accordingly, infinite substance, as it is in itself, is in-principle unknowable to the finite mind. Immanuel Kant brought focus to unknowability theory in his use of the noumenon concep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unknowability
In philosophy, unknowability is the possibility of inherently unaccessible knowledge. It addresses the epistemology of that which we ''cannot'' know. Some related concepts include the halting problem, the limits of knowledge, the unknown unknowns, and chaos theory. Nicholas Rescher provides the most recent focused scholarship for this area in ''Unknowability: An Inquiry into the Limits of Knowledge'', where he offered three high level categories, logical unknowability, conceptual unknowability, and in-principle unknowability. Background Speculation about what is knowable and unknowable has been part of the philosophical tradition since the inception of philosophy. In particular, Baruch Spinoza's Theory of Attributes argues that a human's finite mind cannot understand infinite substance; accordingly, infinite substance, as it is in itself, is in-principle unknowable to the finite mind. Immanuel Kant brought focus to unknowability theory in his use of the noumenon concep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicholas Rescher
Nicholas Rescher (; ; born 15 July 1928) is a German-American philosopher, polymath, and author, who has been a professor of philosophy at the University of Pittsburgh since 1961. He is chairman of the Center for Philosophy of Science and was formerly chairman of the philosophy department. Rescher has served as president for the American Catholic Philosophical Association, Leibniz Society of North America, American Metaphysical Society, American Philosophical Association, and Charles S. Peirce Society. He is the founder of ''American Philosophical Quarterly'', '' History of Philosophy Quarterly'', and ''Public Affairs Quarterly''. Early life and education Nicholas Rescher was born in Hagen in the Westphalia region of Germany. In his autobiography he traces his descent to Nehemias Rescher (1735-1801), a founder of the Hochberg-Remseck Jewish community in Swabian Germany. He relocated to the United States when he was 10 and obtained a degree in mathematics at Queens College, New Y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noumenon
In philosophy, a noumenon (, ; ; noumena) is a posited object or an event that exists independently of human sense and/or perception. The term ''noumenon'' is generally used in contrast with, or in relation to, the term ''phenomenon'', which refers to any object of the senses. Immanuel Kant first developed the notion of the noumenon as part of his transcendental idealism, suggesting that while we know the noumenal world to exist because human sensibility is merely receptive, it is not itself sensible and must therefore remain otherwise unknowable to us. In Kantian philosophy, the unknowable noumenon is often identified with or associated with the unknowable "thing-in-itself" (german: Ding an sich). However, the nature of the relationship between the two is not made explicit in Kant's work, and remains a subject of debate among Kant scholars as a result. Etymology The Greek word grc, νοούμενoν, nooúmenon, label=none (plural grc, νοούμενα, nooúmena, label=non ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Undecidable Problems
In computability theory, an undecidable problem is a type of computational problem that requires a yes/no answer, but where there cannot possibly be any computer program that always gives the correct answer; that is, any possible program would sometimes give the wrong answer or run forever without giving any answer. More formally, an undecidable problem is a problem whose language is not a recursive set; see the article Decidable language. There are uncountably many undecidable problems, so the list below is necessarily incomplete. Though undecidable languages are not recursive languages, they may be subsets of Turing recognizable languages: i.e., such undecidable languages may be recursively enumerable. Many, if not most, undecidable problems in mathematics can be posed as word problems: determining when two distinct strings of symbols (encoding some mathematical concept or object) represent the same object or not. For undecidability in axiomatic mathematics, see List of stateme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald Rumsfeld
Donald Henry Rumsfeld (July 9, 1932 – June 29, 2021) was an American politician, government official and businessman who served as Secretary of Defense from 1975 to 1977 under president Gerald Ford, and again from 2001 to 2006 under President George W. Bush. He was both the youngest and the oldest secretary of defense. Additionally, Rumsfeld was a three-term U.S. Congressman from Illinois (1963–1969), director of the Office of Economic Opportunity (1969–1970), counselor to the president (1969–1973), the U.S. Representative to NATO (1973–1974), and the White House Chief of Staff (1974–1975). Between his terms as secretary of defense, he served as the CEO and chairman of several companies. Born in Illinois, Rumsfeld attended Princeton University, graduating in 1954 with a degree in political science. After serving in the Navy for three years, he mounted a campaign for Congress in Illinois's 13th Congressional District, winning in 1962 at the age of 30. Rumsfeld a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States Secretary Of Defense
The United States secretary of defense (SecDef) is the head of the United States Department of Defense, the executive department of the U.S. Armed Forces, and is a high ranking member of the federal cabinet. DoDD 5100.1: Enclosure 2: a The secretary of defense's position of command and authority over the military is second only to that of the president of the United States, who is the commander-in-chief. This position corresponds to what is generally known as a defense minister in many other countries. The secretary of defense is appointed by the president with the advice and consent of the Senate, and is by custom a member of the Cabinet and by law a member of the National Security Council. The secretary of defense is a statutory office, and the general provision in provides that "subject to the direction of the President", its occupant has "authority, direction, and control over the Department of Defense". The same statute further designates the secretary as "the princip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
There Are Unknown Unknowns
"There are unknown unknowns" is a phrase from a response United States Secretary of Defense Donald Rumsfeld gave to a question at a U.S. Department of Defense (DoD) news briefing on February 12, 2002, about the lack of evidence linking the government of Iraq with the supply of weapons of mass destruction to terrorist groups. Rumsfeld stated: The statement became the subject of much commentary. In ''The Decision Book'', author Mikael Krogerus refers to it as the "Rumsfeld matrix". The statement also features in a 2013 documentary film, ''The Unknown Known'', directed by Errol Morris. Known unknowns refers to "risks you are aware of, such as canceled flights," whereas unknown unknowns are risks that come from situations that are so unexpected that they would not be considered. Origins Rumsfeld's statement brought attention to the concepts of known knowns, known unknowns, and unknown unknowns, but national security and intelligence professionals have long used an analysis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gregory Chaitin
Gregory John Chaitin ( ; born 25 June 1947) is an Argentine-American mathematician and computer scientist. Beginning in the late 1960s, Chaitin made contributions to algorithmic information theory and metamathematics, in particular a computer-theoretic result equivalent to Gödel's incompleteness theorem. He is considered to be one of the founders of what is today known as algorithmic (Solomonoff–Kolmogorov–Chaitin, Kolmogorov or program-size) complexity together with Andrei Kolmogorov and Ray Solomonoff. Along with the works of e.g. Solomonoff, Kolmogorov, Martin-Löf, and Leonid Levin, algorithmic information theory became a foundational part of theoretical computer science, information theory, and mathematical logic. It is a common subject in several computer science curricula. Besides computer scientists, Chaitin's work draws attention of many philosophers and mathematicians to fundamental problems in mathematical creativity and digital philosophy. Mathematics and comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Congress Of Mathematicians
The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be renamed as the IMU Abacus Medal), the Carl Friedrich Gauss Prize, Gauss Prize, and the Chern Medal are awarded during the congress's opening ceremony. Each congress is memorialized by a printed set of Proceedings recording academic papers based on invited talks intended to be relevant to current topics of general interest. Being List of International Congresses of Mathematicians Plenary and Invited Speakers, invited to talk at the ICM has been called "the equivalent ... of an induction to a hall of fame". History Felix Klein and Georg Cantor are credited with putting forward the idea of an international congress of mathematicians in the 1890s.A. John Coleman"Mathematics without borders": a book review ''CMS Notes'', vol 31, no. 3, April 1999 ... [...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] |
Emil Du Bois-Reymond
Emil Heinrich du Bois-Reymond (7 November 181826 December 1896) was a German physician and physiologist, the co-discoverer of nerve action potential, and the developer of experimental electrophysiology. Life Du Bois-Reymond was born in Berlin and spent his working life there. One of his younger brothers was the mathematician Paul du Bois-Reymond (1831–1889). His father was from Neuchâtel, and his mother was a Berliner of Huguenot origin. Educated first at the French College in Berlin, du Bois-Reymond enrolled in the University of Berlin in 1838. He seems to have been uncertain at first as to the topic of his studies, for he was a student of the renowned ecclesiastical historian August Neander, and dallied with geology and physics, but eventually began to study medicine with such zeal and success as to attract the notice of Johannes Peter Müller (1801–1858), a well-known professor of anatomy and physiology. Müller's earlier studies had been distinctly physiological, but ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ignoramus Et Ignorabimus
The Latin maxim , meaning "we do not know and will not know", represents the idea that scientific knowledge is limited. It was popularized by Emil du Bois-Reymond, a German physiologist, in his 1872 address ("The Limits of Science"). Seven "World Riddles" Emil du Bois-Reymond first used the words and at the close of his keynote address to the 1872 Congress of German Scientists and Physicians. As he saw it, science was bounded by two limits: the ultimate nature of matter and the enigma of consciousness. Eight years later, in a speech before the Prussian Academy of Sciences, he expanded his list of conundrums to Emil du Bois-Reymond#On epistemology, seven "world riddles" or "shortcomings" of science. Three of these he declared to be "Transcendence (philosophy)#Kant (and modern philosophy), transcendent", or permanently unknowable: "1. the ultimate nature of matter and energy, 2. the origin of motion, ... 5. the origin of simple Sense, sensations." Hilbert's reaction David ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
