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Inverse Gambler's Fallacy
The inverse gambler's fallacy, named by philosopher Ian Hacking, is a formal fallacy of Bayesian inference which is an inverse of the better known gambler's fallacy. It is the fallacy of concluding, on the basis of an unlikely outcome of a random process, that the process is likely to have occurred many times before. For example, if one observes a pair of fair dice being rolled and turning up double sixes, it is wrong to suppose that this lends any support to the hypothesis that the dice have been rolled many times before. We can see this from the Bayesian update rule: letting ''U'' denote the unlikely outcome of the random process and ''M'' the proposition that the process has occurred many times before, we have : P(M, U) = P(M) \frac and since ''P''(''U'', ''M'') = ''P''(''U'') (the outcome of the process is unaffected by previous occurrences), it follows that ''P''(''M'', ''U'') = ''P''(''M''); that is, our confidence in ''M'' should be unchanged when we learn ''U''. Real-worl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ian Hacking
Ian MacDougall Hacking (February 18, 1936 – May 10, 2023) was a Canadian philosopher specializing in the philosophy of science. Throughout his career, he won numerous awards, such as the Killam Prize for the Humanities and the Balzan Prize, and was a member of many prestigious groups, including the Order of Canada, the Royal Society of Canada and the British Academy. Life and career Born in Vancouver, British Columbia, he earned undergraduate degrees from the University of British Columbia (1956) and the University of Cambridge (1958), where he was a student at Trinity College, Cambridge, Trinity College. Hacking also earned his PhD at Cambridge (1962) under the direction of Casimir Lewy, a former student of G. E. Moore. Hacking started his teaching career as an instructor at Princeton University in 1960 but, after just one year, moved to the University of Virginia as an assistant professor. After working as a research fellow at Peterhouse, Cambridge from 1962 to 1964, he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Fallacy
In logic and philosophical logic, philosophy, a formal fallacy is a pattern of reasoning rendered validity (logic), invalid by a flaw in its logical structure. propositional calculus, Propositional logic, for example, is concerned with the meanings of sentences and the relationships between them. It focuses on the role of logical operators, called propositional connectives, in determining whether a sentence is true. An error in the sequence will result in a deductive argument that is invalid. The argument itself could have true premises, but still have a false logical consequence, conclusion. Thus, a formal fallacy is a fallacy in which deduction goes wrong, and is no longer a logical process. This may not affect the truth of the conclusion, since validity and truth are separate in formal logic. While a logical argument is a ''non sequitur'' if, and only if, it is invalid, the term "non sequitur" typically refers to those types of invalid arguments which do not constitute formal fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Inference
Bayesian inference ( or ) is a method of statistical inference in which Bayes' theorem is used to calculate a probability of a hypothesis, given prior evidence, and update it as more information becomes available. Fundamentally, Bayesian inference uses a prior distribution to estimate posterior probabilities. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". Introduction to Bayes' rule Formal explanation Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a "likelihood function" derive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gambler's Fallacy
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the belief that, if an event (whose occurrences are Independent and identically distributed random variables, independent and identically distributed) has occurred less frequently than expected, it is more likely to happen again in the future (or vice versa). The fallacy is commonly associated with gambling, where it may be believed, for example, that the next dice roll is more likely to be six than is usually the case because there have recently been fewer than the Expected value, expected number of sixes. The term "Monte Carlo fallacy" originates from an example of the phenomenon, in which the roulette wheel spun black 26 times in succession at the Monte Carlo Casino in 1913. Examples Coin toss The gambler's fallacy can be illustrated by considering the repeated toss of a fair coin. The outcomes in different tosses are statistically independent and the probability of getti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random
In common usage, randomness is the apparent or actual lack of definite pattern or predictability in information. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if there is a known probability distribution, the frequency of different outcomes over repeated events (or "trials") is predictable.Strictly speaking, the frequency of an outcome will converge almost surely to a predictable value as the number of trials becomes arbitrarily large. Non-convergence or convergence to a different value is possible, but has probability zero. Consistent non-convergence is thus evidence of the lack of a fixed probability distribution, as in many evolutionary processes. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will tend to occur twice as often as 4. In this view, randomness is not haphaza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dice
A die (: dice, sometimes also used as ) is a small, throwable object with marked sides that can rest in multiple positions. Dice are used for generating random values, commonly as part of tabletop games, including dice games, board games, role-playing games, and games of chance. A traditional die is a cube with each of its six faces marked with a different number of dots ( pips) from one to six. When thrown or rolled, the die comes to rest showing a random integer from one to six on its upper surface, with each value being equally likely. Dice may also have other polyhedral or irregular shapes, may have faces marked with numerals or symbols instead of pips and may have their numbers carved out from the material of the dice instead of marked on it. Loaded dice are specifically designed or modified to favor some results over others, for cheating or entertainment purposes. History Dice have been used since before recorded history, and their origin is uncertain. It is hypoth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Argument From Design
The teleological argument (from ) also known as physico-theological argument, argument from design, or intelligent design argument, is a rational argument for the existence of God or, more generally, that complex functionality in the natural world, which looks designed, is evidence of an intelligent creator. The earliest recorded versions of this argument are associated with Socrates in ancient Greece, although it has been argued that he was taking up an older argument.Ahbel-Rappe, Sara, and R. Kamtekar. 2009. ''A Companion to Socrates''. John Wiley & Sons. p. 45. "Xenophon attributes to Socrates what is probably the earliest known natural theology, an argument for the existence of the gods from observations of design in the physical world." Later, Plato and Aristotle developed complex approaches to the proposal that the cosmos has an intelligent cause, but it was the Stoics during the Roman era who, under their influence, "developed the battery of creationist arguments broadly kn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mind (journal)
''Mind'' (stylized as ''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 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fine-tuned Universe
The fine-tuned universe is the hypothesis that, because "life as we know it" could not exist if the fundamental physical constants, constants of nature – such as the electron charge, the gravitational constant and others – had been even slightly different, the universe must be tuned specifically for life.Gribbin. J and Rees. M, ''Cosmic Coincidences: Dark Matter, Mankind, and Anthropic Cosmology'' pp. 7, 269, 1989, In practice, this hypothesis is formulated in terms of dimensionless physical constants. History In 1913, chemist Lawrence Joseph Henderson wrote ''The Fitness of the Environment,'' one of the first books to explore fine tuning in the universe. Henderson discusses the importance of water and the environment to living things, pointing out that life as it exists on Earth depends entirely on Earth's very specific environmental conditions, especially the prevalence and properties of water. In 1961, physicist Robert H. Dicke argued that certain forces in physics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John A
Sir John Alexander Macdonald (10 or 11January 18156June 1891) was the first prime minister of Canada, serving from 1867 to 1873 and from 1878 until his death in 1891. He was the Fathers of Confederation, dominant figure of Canadian Confederation, and had a political career that spanned almost half a century. Macdonald was born in Scotland; when he was a boy his family immigrated to Kingston, Ontario, Kingston in the Province of Upper Canada (today in eastern Ontario). As a lawyer, he was involved in several high-profile cases and quickly became prominent in Kingston, which elected him in 1844 to the legislature of the Province of Canada. By 1857, he had become List of Joint Premiers of the Province of Canada, premier under the colony's unstable political system. In 1864, when no party proved capable of governing for long, he agreed to a proposal from his political rival, George Brown (Canadian politician), George Brown, that the parties unite in a Great Coalition to seek fede ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anthropic Principle
In cosmology, the anthropic principle, also known as the observation selection effect, is the proposition that the range of possible observations that could be made about the universe is limited by the fact that observations are only possible in the type of universe that is capable of developing observers in the first place. Proponents of the anthropic principle argue that it explains why the universe has the age and the fundamental physical constants necessary to accommodate intelligent life. If either had been significantly different, no one would have been around to make observations. Anthropic reasoning has been used to address the question as to why certain measured physical constants take the values that they do, rather than some other arbitrary values, and to explain a perception that the universe appears to be finely tuned for the existence of life. There are many different formulations of the anthropic principle. Philosopher Nick Bostrom counts thirty, but the underlying ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotheism
Monotheism is the belief that one God is the only, or at least the dominant deity.F. L. Cross, Cross, F.L.; Livingstone, E.A., eds. (1974). "Monotheism". The Oxford Dictionary of the Christian Church (2 ed.). Oxford: Oxford University Press. A distinction may be made between exclusive monotheism, in which the one God is a singular existence, and both inclusive and pluriform monotheism, in which multiple gods or godly forms are recognized, but each are postulated as extensions of the same God. Monotheism is distinguished from henotheism, a religious system in which the believer worships one god without denying that others may worship different gods with equal validity, and monolatry, monolatrism, the recognition of the existence of many gods but with the consistent worship of only one deity. The term ''monolatry'' was perhaps first used by Julius Wellhausen. Monotheism characterizes the traditions of Abrahamic religions, Abrahamic religions such as Judaism, Samaritanism, Christi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
