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Exchange Paradox
The two envelopes problem, also known as the exchange paradox, is a paradox in probability theory. It is of special interest in decision theory, and for the Bayesian interpretation of probability theory. It is a variant of an older problem known as the necktie paradox. The problem is typically introduced by formulating a hypothetical challenge like the following example: Since the situation is symmetric, it seems obvious that there is no point in switching envelopes. On the other hand, a simple calculation using expected values suggests the opposite conclusion, that it is always beneficial to swap envelopes, since the person stands to gain twice as much money if they switch, while the only risk is halving what they currently have. Introduction Problem Basic setup: A person is given two indistinguishable envelopes, each of which contains a sum of money. One envelope contains twice as much as the other. The person may pick one envelope and keep whatever amount it contains. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paradox
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites". In logic, many paradoxes exist that are known to be invalid arguments, yet are nevertheless valuable in promoting critical thinking, while other paradoxes have revealed errors in definitions that were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself, and showed that attempts to found set theory on the identification ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayes' Rule
In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately (by conditioning it on their age) than simply assuming that the individual is typical of the population as a whole. One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference. When applied, the probabilities involved in the theorem may have different probability interpretations. With Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence. Bayesian inference is fundamental to Bayesian s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maurice Kraitchik
Maurice Borisovich Kraitchik (21 April 1882 – 19 August 1957) was a Belgian mathematician and populariser. His main interests were the theory of numbers and recreational mathematics. He was born to a Jewish family in Minsk. He wrote several books on number theory during 1922–1930 and after the war, and from 1931 to 1939 edited ''Sphinx'', a periodical devoted to recreational mathematics. During World War II, he emigrated to the United States, where he taught a course at the New School for Social Research in New York City on the general topic of "mathematical recreations." Kraïtchik was ''agrégé'' of the Free University of Brussels, engineer at the Société Financière de Transports et d'Entreprises Industrielles (Sofina), and director of the Institut des Hautes Etudes de Belgique An institute is an organisational body created for a certain purpose. They are often research organisations (research institutes) created to do research on specific topics, or c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Belgians
Belgians ( nl, Belgen; french: Belges; german: Belgier) are people identified with the Kingdom of Belgium, a federal state in Western Europe. As Belgium is a multinational state, this connection may be residential, legal, historical, or cultural rather than ethnic. The majority of Belgians, however, belong to two distinct ethnic groups or ''communities'' ( nl, gemeenschap, links=no; french: communauté, links=no) native to the country, i.e. its historical regions: Flemings in Flanders, who speak Dutch; and Walloons in Wallonia, who speak French or Walloon. There is also a substantial Belgian diaspora, which has settled primarily in the United States, Canada, France, and the Netherlands. Etymology The 1830 revolution led to the establishment of an independent country under a provisional government and a national congress. The name "Belgium" was adopted for the country, the word being derived from ''Gallia Belgica'', a Roman province in the northernmost part of Gaul that, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mind (journal)
''MIND'' is a quarterly peer-reviewed academic journal published by Oxford University Press on behalf of the Mind Association. Having previously published exclusively philosophy in the analytic tradition, it now "aims to take quality to be the sole criterion of publication, with no area of philosophy, no style of philosophy, and no school of philosophy excluded." Its institutional home is shared between the University of Oxford and University College London. It is considered an important resource for studying philosophy. History and profile The journal was established in 1876 by the Scottish philosopher Alexander Bain (University of Aberdeen) with his colleague and former student George Croom Robertson (University College London) as editor-in-chief. With the death of Robertson in 1891, George Stout took over the editorship and began a 'New Series'. Early on, the journal was dedicated to the question of whether psychology could be a legitimate natural science. In the first issu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Counterfactual Thinking
Counterfactual thinking is a concept in psychology that involves the human tendency to create possible alternatives to life events that have already occurred; something that is contrary to what actually happened. Counterfactual thinking is, as it states: "counter to the facts". These thoughts consist of the "What if?" and the "If only..." that occur when thinking of how things could have turned out differently. Counterfactual thoughts include things that – in the present – now could never happen in reality because they solely pertain to events that have occurred in the past. Overview The term ''"Counterfactual"'' is defined by the Merriam-Webster Dictionary as contrary to the facts. A counterfactual thought occurs when a person modifies a factual prior event and then assesses the consequences of that change. A person may imagine how an outcome could have turned out differently, if the antecedents that led to that event were different. For example, a person may reflect upon h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfred A
Alfred may refer to: Arts and entertainment *''Alfred J. Kwak'', Dutch-German-Japanese anime television series * ''Alfred'' (Arne opera), a 1740 masque by Thomas Arne * ''Alfred'' (Dvořák), an 1870 opera by Antonín Dvořák *"Alfred (Interlude)" and "Alfred (Outro)", songs by Eminem from the 2020 album ''Music to Be Murdered By'' Business and organisations * Alfred, a radio station in Shaftesbury, England *Alfred Music, an American music publisher *Alfred University, New York, U.S. *The Alfred Hospital, a hospital in Melbourne, Australia People * Alfred (name) includes a list of people and fictional characters called Alfred * Alfred the Great (848/49 – 899), or Alfred I, a king of the West Saxons and of the Anglo-Saxons Places Antarctica * Mount Alfred (Antarctica) Australia * Alfredtown, New South Wales * County of Alfred, South Australia Canada * Alfred and Plantagenet, Ontario * Alfred Island, Nunavut * Mount Alfred, British Columbia United States * Alfred, Maine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raymond Smullyan
Raymond Merrill Smullyan (; May 25, 1919 – February 6, 2017) was an American mathematician, magician, concert pianist, logician, Taoist, and philosopher. Born in Far Rockaway, New York, his first career was stage magic. He earned a BSc from the University of Chicago in 1955 and his PhD from Princeton University in 1959. He is one of many logicians to have studied with Alonzo Church. Life He was born on May 25, 1919, in Far Rockaway, Queens, New York, to an Ashkenazi Jewish family. His father was Isidore Smullyan, who was born in Russia but who emigrated to Belgium when young, and whose native language was French. His father was a businessman who graduated from the University of Antwerp. His mother was Rosina Smullyan (née Freeman), who was born and raised in London. She was a painter, who was also an actress. Both parents were musical, his father playing the violin and his mother playing the piano. He was the youngest of three children. His eldest brother, Emile Benoit Smul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael R
Michael may refer to: People * Michael (given name), a given name * Michael (surname), including a list of people with the surname Michael Given name "Michael" * Michael (archangel), ''first'' of God's archangels in the Jewish, Christian and Islamic religions * Michael (bishop elect), English 13th-century Bishop of Hereford elect * Michael (Khoroshy) (1885–1977), cleric of the Ukrainian Orthodox Church of Canada * Michael Donnellan (1915–1985), Irish-born London fashion designer, often referred to simply as "Michael" * Michael (footballer, born 1982), Brazilian footballer * Michael (footballer, born 1983), Brazilian footballer * Michael (footballer, born 1993), Brazilian footballer * Michael (footballer, born February 1996), Brazilian footballer * Michael (footballer, born March 1996), Brazilian footballer * Michael (footballer, born 1999), Brazilian footballer Rulers =Byzantine emperors= *Michael I Rangabe (d. 844), married the daughter of Emperor Nikephoros I * Mi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Utility
The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decisions when the payoff is uncertain. The theory recommends which option rational individuals should choose in a complex situation, based on their risk appetite and preferences. The expected utility hypothesis states an agent chooses between risky prospects by comparing expected utility values (i.e. the weighted sum of adding the respective utility values of payoffs multiplied by their probabilities). The summarised formula for expected utility is U(p)=\sum u(x_k)p_k where p_k is the probability that outcome indexed by k with payoff x_k is realized, and function ''u'' expresses the utility of each respective payoff. On a graph, the curvature of u will explain the agent's risk attitude. For example, if an agent derives 0 utils from 0 apples, 2 utils from one apple, and 3 utils from two apples, their expected utility for a 50–50 gamble between zero apples and two is 0.5''u''(0 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Chalmers
David John Chalmers (; born 20 April 1966) is an Australian philosopher and cognitive scientist specializing in the areas of philosophy of mind and philosophy of language. He is a professor of philosophy and neural science at New York University, as well as co-director of NYU's Center for Mind, Brain and Consciousness (along with Ned Block). In 2006, he was elected a Fellow of the Australian Academy of the Humanities. In 2013, he was elected a Fellow of the American Academy of Arts & Sciences. Chalmers is best known for formulating the hard problem of consciousness. He and David Bourget cofounded PhilPapers, a database of journal articles for philosophers. Early life and education Chalmers was born in Sydney, New South Wales, in 1966, and subsequently grew up in Adelaide, South Australia, where he attended Unley High School. As a child, he experienced synesthesia. He began coding and playing computer games at age 10 on a PDP-10 at a medical center. He also performed excep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Probability
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is and the event is known or assumed to have occurred, "the conditional probability of given ", or "the probability of under the condition ", is usually written as or occasionally . This can also be understood as the fraction of probability B that intersects with A: P(A \mid B) = \frac. For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person is sick, then they are much more likely to be coughing. For example, the conditional probability that someone unwell (sick) is coughing might be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
