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Cognitive biases are systematic patterns of deviation from norm or rationality in judgment, and are often studied in psychology and behavioral economics.

Although the reality of most of these biases is confirmed by reproducible research, there are often controversies about how to classify these biases or how to explain them. Some are effects of information-processing rules (i.e., mental shortcuts), called heuristics, that the brain uses to produce decisions or judgments. Biases have a variety of forms and appear as cognitive ("cold") bias, such as mental noise, or motivational ("hot") bias, such as when beliefs are distorted by wishful thinking. Both effects can be present at the same time.

There are also controversies over some of these biases as to whether they count as useless or irrational, or whether they result in useful attitudes or behavior. For example, when getting to know others, people tend to ask leading questions which seem biased towards confirming their assumptions about the person. However, this kind of confirmation bias has also been argued to be an example of social skill: a way to establish a connection with the other person.

Although this research overwhelmingly involves human subjects, some findings that demonstrate bias have been found in non-human animals as well. For example, loss aversion has been shown in monkeys and hyperbolic discounting has been observed in rats, pigeons, and monkeys.

🔗 Computer science 🔗 Philosophy 🔗 Philosophy/Logic 🔗 Philosophy/Philosophy of science 🔗 Philosophy/Philosophy of mind

Moravec's paradox is the observation by artificial intelligence and robotics researchers that, contrary to traditional assumptions, reasoning (which is high-level in humans) requires very little computation, but sensorimotor skills (comparatively low-level in humans) require enormous computational resources. The principle was articulated by Hans Moravec, Rodney Brooks, Marvin Minsky and others in the 1980s. As Moravec writes, "it is comparatively easy to make computers exhibit adult level performance on intelligence tests or playing checkers, and difficult or impossible to give them the skills of a one-year-old when it comes to perception and mobility".

Similarly, Minsky emphasized that the most difficult human skills to reverse engineer are those that are unconscious. "In general, we're least aware of what our minds do best", he wrote, and added "we're more aware of simple processes that don't work well than of complex ones that work flawlessly".

🔗 Philosophy 🔗 Philosophy/Logic 🔗 Philosophy/Epistemology

In epistemology, the Münchhausen trilemma is a thought experiment used to demonstrate the impossibility of proving any truth, even in the fields of logic and mathematics. If it is asked how any given proposition is known to be true, proof may be provided. Yet that same question can be asked of the proof, and any subsequent proof. The Münchhausen trilemma is that there are only three options when providing further proof in response to further questioning:

• The circular argument, in which the proof of some proposition is supported only by that proposition
• The regressive argument, in which each proof requires a further proof, ad infinitum
• The axiomatic argument, which rests on accepted precepts which are merely asserted rather than defended

The trilemma, then, is the decision among the three equally unsatisfying options.

The name Münchhausen-Trilemma was coined by the German philosopher Hans Albert in 1968 in reference to a trilemma of "dogmatism versus infinite regress versus psychologism" used by Karl Popper. It is a reference to the problem of "bootstrapping", based on the story of Baron Munchausen (in German, "Münchhausen") pulling himself and the horse on which he was sitting out of a mire by his own hair.

It is also known as Agrippa's trilemma or the Agrippan trilemma after a similar argument reported by Sextus Empiricus, which was attributed to Agrippa the Skeptic by Diogenes Laërtius, as well as Fries's trilemma after German philosopher Jakob Friedrich Fries. Sextus' argument, however, consists of five (not three) "modes". Popper in his original 1935 publication mentions neither Sextus nor Agrippa, but attributes his trilemma to Fries.

In contemporary epistemology, advocates of coherentism are supposed to accept the "circular" horn of the trilemma; foundationalists rely on the axiomatic argument. The view that accepts infinite regress is called infinitism.

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Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. Turing is widely considered to be the father of theoretical computer science and artificial intelligence. Despite these accomplishments, he was not fully recognised in his home country during his lifetime, due to his homosexuality, and because much of his work was covered by the Official Secrets Act.

During the Second World War, Turing worked for the Government Code and Cypher School (GC&CS) at Bletchley Park, Britain's codebreaking centre that produced Ultra intelligence. For a time he led Hut 8, the section that was responsible for German naval cryptanalysis. Here, he devised a number of techniques for speeding the breaking of German ciphers, including improvements to the pre-war Polish bombe method, an electromechanical machine that could find settings for the Enigma machine.

Turing played a crucial role in cracking intercepted coded messages that enabled the Allies to defeat the Nazis in many crucial engagements, including the Battle of the Atlantic, and in so doing helped win the war. Due to the problems of counterfactual history, it is hard to estimate the precise effect Ultra intelligence had on the war, but at the upper end it has been estimated that this work shortened the war in Europe by more than two years and saved over 14 million lives.

After the war Turing worked at the National Physical Laboratory, where he designed the Automatic Computing Engine. The Automatic Computing Engine was one of the first designs for a stored-program computer. In 1948 Turing joined Max Newman's Computing Machine Laboratory, at the Victoria University of Manchester, where he helped develop the Manchester computers and became interested in mathematical biology. He wrote a paper on the chemical basis of morphogenesis and predicted oscillating chemical reactions such as the Belousov–Zhabotinsky reaction, first observed in the 1960s.

Turing was prosecuted in 1952 for homosexual acts; the Labouchere Amendment of 1885 had mandated that "gross indecency" was a criminal offence in the UK. He accepted chemical castration treatment, with DES, as an alternative to prison. Turing died in 1954, 16 days before his 42nd birthday, from cyanide poisoning. An inquest determined his death as a suicide, but it has been noted that the known evidence is also consistent with accidental poisoning.

In 2009, following an Internet campaign, British Prime Minister Gordon Brown made an official public apology on behalf of the British government for "the appalling way he was treated". Queen Elizabeth II granted Turing a posthumous pardon in 2013. The Alan Turing law is now an informal term for a 2017 law in the United Kingdom that retroactively pardoned men cautioned or convicted under historical legislation that outlawed homosexual acts.

🔗 Philosophy 🔗 Philosophy/Logic 🔗 Philosophy/Contemporary philosophy 🔗 Philosophy/Philosophy of religion 🔗 Christianity 🔗 Christianity/theology 🔗 Military history/European military history

Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development that goes back to Anselm of Canterbury (1033–1109). St. Anselm's ontological argument, in its most succinct form, is as follows: "God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist." A more elaborate version was given by Gottfried Leibniz (1646–1716); this is the version that Gödel studied and attempted to clarify with his ontological argument.

Gödel left a fourteen-point outline of his philosophical beliefs in his papers. Points relevant to the ontological proof include

4. There are other worlds and rational beings of a different and higher kind.

5. The world in which we live is not the only one in which we shall live or have lived.

13. There is a scientific (exact) philosophy and theology, which deals with concepts of the highest abstractness; and this is also most highly fruitful for science.

14. Religions are, for the most part, bad—but religion is not.

🔗 Philosophy 🔗 Philosophy/Logic

In political discourse, if-by-whiskey is a relativist fallacy in which the speaker's position is contingent on the listener's opinion. An if-by-whiskey argument implemented through doublespeak appears to affirm both sides of an issue, and agrees with whichever side the listener supports, in effect taking a position without taking a position. The statement typically uses words with strongly positive or negative connotations (e.g., terrorist as negative and freedom fighter as positive).

🔗 Mathematics 🔗 Philosophy 🔗 Philosophy/Logic 🔗 Philosophy/Epistemology

In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied, but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possible independent existence in an objective reality.

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Gödel's Loophole is a "inner contradiction" in the Constitution of the United States which Austrian-German-American logician, mathematician, and analytic philosopher Kurt Gödel claimed to have discovered in 1947. The flaw would have allowed the American democracy to be legally turned into a dictatorship. Gödel told his friend Oskar Morgenstern about the existence of the flaw and Morgenstern told Albert Einstein about it at the time, but Morgenstern, in his recollection of the incident in 1971, never mentioned the exact problem as Gödel saw it. This has led to speculation about the precise nature of what has come to be called "Gödel's Loophole". It has been called "one of the great unsolved problems of constitutional law."

🔗 Philosophy 🔗 Philosophy/Logic

The nirvana fallacy is the informal fallacy of comparing actual things with unrealistic, idealized alternatives. It can also refer to the tendency to assume there is a perfect solution to a particular problem. A closely related concept is the "perfect solution fallacy."

By creating a false dichotomy that presents one option which is obviously advantageous—while at the same time being completely implausible—a person using the nirvana fallacy can attack any opposing idea because it is imperfect. Under this fallacy, the choice is not between real world solutions; it is, rather, a choice between one realistic achievable possibility and another unrealistic solution that could in some way be "better".

🔗 Philosophy 🔗 Philosophy/Philosophical literature 🔗 Books 🔗 Philosophy/Logic

Gödel, Escher, Bach: An Eternal Golden Braid, also known as GEB, is a 1979 book by Douglas Hofstadter. By exploring common themes in the lives and works of logician Kurt Gödel, artist M. C. Escher, and composer Johann Sebastian Bach, the book expounds concepts fundamental to mathematics, symmetry, and intelligence. Through illustration and analysis, the book discusses how, through self-reference and formal rules, systems can acquire meaning despite being made of "meaningless" elements. It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of "meaning" itself.

In response to confusion over the book's theme, Hofstadter emphasized that Gödel, Escher, Bach is not about the relationships of mathematics, art, and music—but rather about how cognition emerges from hidden neurological mechanisms. One point in the book presents an analogy about how individual neurons in the brain coordinate to create a unified sense of a coherent mind by comparing it to the social organization displayed in a colony of ants.

The tagline "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll" was used by the publisher to describe the book.