Abelson's paradox is an applied statistics paradox identified by Robert P. Abelson. The paradox pertains to a possible paradoxical relationship between the magnitude of the r2 (i.e., coefficient of determination) effect size and its practical meaning.
The Abilene paradox is a collective fallacy, in which a group of people collectively decide on a course of action that is counter to the preferences of most or all individuals in the group, while each individual believes it to be aligned with the preferences of most of the others. It involves a breakdown of group communication in which each member mistakenly believes that their own preferences are counter to the grou
The accuracy paradox is the paradoxical finding that accuracy is not a good metric for predictive models when classifying in predictive analytics. This is because a simple model may have a high level of accuracy but too crude to be useful.
Acosmism, held in contrast or equivalent to pantheism, denies the reality of the universe, seeing it as ultimately illusory (the prefix 'ἀ-' in Greek meaning negation; like 'un-' in English), and only the infinite unmanifest Absolute as real. Conceptual versions of Acosmism are found in eastern and western philosophies.
The Aharonov–Bohm effect, sometimes called the Ehrenberg–Siday–Aharonov–Bohm effect, is a quantum-mechanical phenomenon in which an electrically charged particle is affected by an electromagnetic potential ( φ {\\displaystyle \\varphi } , A {\\displaystyle \\mathbf {A} } ), despite being confined to a region in which both the magnetic field B {\\displaystyle \\mathbf {B} } and electric field E {\\displaystyle \\mathbf {E} }
Air conditioning, often abbreviated as A/C (US) or air con (UK), is the process of removing heat from an enclosed space to achieve a more comfortable interior temperature and, in some cases, controlling the humidity of internal air. Air conditioning can be achieved using a mechanical 'air conditioner' or through other methods, such as passive cooling and ventilative cooling.
An apportionment paradox is a situation where an apportionment—a rule for dividing discrete objects according to some proportional relationship—produces results that violate notions of common sense or fairness. Certain quantities, like milk, can be divided in any proportion whatsoever; others, such as horses, cannot—only whole numbers will do.
In stellar astronomy, the Algol paradox is a paradox situation when the two stars of a binary star system appear to act opposite their cycle towards death; one star is more advanced in its stellar evolution than the other despite that star being smaller (less massive) than the other. This paradox is observed when one smaller star has already exited its main sequence form and its larger partner has not.
All horses are the same color is a falsidical paradox that arises from a flawed use of mathematical induction to prove the statement All horses are the same color. There is no actual contradiction, as these arguments have a crucial flaw that makes them incorrect.
The Allais paradox is a choice problem designed by Maurice Allais (1953) to show an inconsistency of actual observed choices with the predictions of expected utility theory. The Allais paradox demonstrates that individuals rarely make rational decisions consistently when required to do so immediately.
The allegory of the cave is an allegory presented by the Greek philosopher Plato in his work Republic (514a–520a, Book VII) to compare 'the effect of education (παιδεία) and the lack of it on our nature'. It is written as a dialogue between Plato's brother Glaucon and his mentor Socrates and is narrated by the latter.
In decision theory and economics, ambiguity aversion (also known as uncertainty aversion) is a preference for known risks over unknown risks. An ambiguity-averse individual would rather choose an alternative where the probability distribution of the outcomes is known over one where the probabilities are unknown.
The ant on a rubber rope is a mathematical puzzle with a solution that appears counterintuitive or paradoxical. It is sometimes given as a worm, or inchworm, on a rubber or elastic band, but the principles of the puzzle remain the same.
High-nutrient, low-chlorophyll (HNLC) regions are regions of the ocean where the abundance of phytoplankton is low and fairly constant despite the availability of macronutrients. Phytoplankton rely on a suite of nutrients for cellular function.
In cosmology and philosophy of science, 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 th
In philosophy, an antinomy (; Ancient Greek: antí 'against' + nómos 'law') is a real or apparent contradiction between two conclusions, both of which seem justified. It is a term used in logic and epistemology, particularly in the philosophy of Immanuel Kant.
In philosophy, an aporia (Ancient Greek: ᾰ̓πορῐ́ᾱ, romanized: aporíā, lit. ''lacking passage', also: 'impasse', 'difficulty in passage', 'puzzlement'') is a conundrum or state of puzzlement. In rhetoric, it is a declaration of doubt, made for rhetorical purpose and often feigned.
An apportionment paradox is a situation where an apportionment—a rule for dividing discrete objects according to some proportional relationship—produces results that violate notions of common sense or fairness. Certain quantities, like milk, can be divided in any proportion whatsoever; others, such as horses, cannot—only whole numbers will do.
The archer's paradox is the phenomenon of an arrow traveling in the direction it is pointed at full draw, when it seems that the arrow would have to pass through the starting position it was in before being drawn, where it was pointed to the side of the target. The bending of the arrow when released is the explanation for why the paradox occurs and should not be confused with the paradox itself.
The argument from free will, also called the paradox of free will or theological fatalism, contends that omniscience and free will are incompatible and that any conception of God that incorporates both properties is therefore inconceivable. See the various controversies over claims of God's omniscience, in particular the critical notion of foreknowledge.
Aristotle's wheel paradox is a paradox or problem appearing in the pseudo-Aristotelian Greek work Mechanica. It states as follows: A wheel is depicted in two-dimensional space as two circles.
The Arrow information paradox (information paradox for short, or AIP), and occasionally referred to as Arrow's disclosure paradox, named after Kenneth Arrow, American economist and joint winner of the Nobel Memorial Prize in Economics with John Hicks, is a problem faced by companies when managing intellectual property across their boundaries. It occurs when they seek external technologies for their business or extern
Arrow's impossibility theorem is a key result in social choice theory showing that no ranked-choice procedure for group decision-making can satisfy the requirements of rational choice. Specifically, American economist Kenneth Arrow showed no such rule can satisfy independence of irrelevant alternatives, the principle that a choice between two alternatives A and B should not depend on the quality of some third, unrela
Artificial intelligence (AI) is the capability of computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of research in computer science that develops and studies methods and software that enable machines to perceive their environment and use learning and intelligence to take actions that maximiz
The ball and shot gun, often also known by the marketing name paradox gun, is a shotgun capable of firing both shot and solid projectiles. First built by Holland and Holland, the term paradox is a proprietary name applied to these guns by Holland and Holland.
The Ross–Littlewood paradox (also known as the balls and vase problem or the ping pong ball problem) is a hypothetical problem in abstract mathematics and logic designed to illustrate the paradoxical, or at least non-intuitive, nature of infinity. More specifically, like the Thomson's lamp paradox, the Ross–Littlewood paradox tries to illustrate the conceptual difficulties with the notion of a supertask, in which an
The Banach–Tarski paradox is a theorem in set-theoretic geometry that states the following: Given a solid ball in three-dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets that can be put back together in a different way to yield two identical copies of the original ball. Indeed, the reassembly process involves only moving the pieces around and rotating them, without c
The barber paradox is a puzzle derived from Russell's paradox. It was suggested to Bertrand Russell as an illustration of the paradox, but he deemed it an invalid modification of his paradox.
The barbershop paradox was proposed by Lewis Carroll in a three-page essay titled 'A Logical Paradox', which appeared in the July 1894 issue of Mind. The name comes from the 'ornamental' short story that Carroll uses in the article to illustrate the paradox.
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement. The first such result was introduced by John Stewart Bell in 1964, building upon the Einstein–Podolsky–Rosen paradox, which had called attention to the phenomenon of quantum
Bell's spaceship paradox is a thought experiment in special relativity. It was first described by E. Dewan and M. Beran in 1959 but became more widely known after John Stewart Bell elaborated the idea further in 1976.
Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement. The first such result was introduced by John Stewart Bell in 1964, building upon the Einstein–Podolsky–Rosen paradox, which had called attention to the phenomenon of quantum
Bellum omnium contra omnes, a Latin phrase meaning 'the war of all against all', is the description that Thomas Hobbes gives to human existence in the state-of-nature thought experiment that he conducts in De Cive (1642) and Leviathan (1651). The common modern English usage is a war of 'each against all' where war is rare and terms such as 'competition' or 'struggle' are more common.
A supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time. Supertasks are called hypertasks when the number of operations is uncountable.
Bentley's paradox (named after Richard Bentley) points to a problem occurring when Newton's theory of gravitation is applied to cosmology. This cosmological paradox states that if all the stars are drawn to each other by gravitation, they should collapse into a single point.
Berkson's paradox, also known as Berkson's bias, collider bias, endogenous selection bias or Berkson's fallacy, is a result in conditional probability and statistics which is often found to be counterintuitive, and hence a veridical paradox. It is a complicating factor arising in statistical tests of proportions.
The Berry paradox is a self-referential paradox arising from an expression like 'The smallest positive integer not definable in under sixty letters' (a phrase with fifty-seven letters). Bertrand Russell, the first to discuss the paradox in print, attributed it to G. G. Berry (1867–1928), a junior librarian at Oxford's Bodleian Library.
In economics and commerce, the Bertrand paradox — named after its creator, Joseph Bertrand — describes a situation in which two players (firms) reach a state of Nash equilibrium where both firms charge a price equal to marginal cost ('MC'). The paradox is that in models such as Cournot competition, an increase in the number of firms is associated with a convergence of prices to marginal costs.
Bertrand's box paradox is a veridical paradox in elementary probability theory. It was first posed by Joseph Bertrand in his 1889 work Calcul des Probabilités.
The Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work Calcul des probabilités (1889) as an example to show that the principle of indifference may not produce definite, well-defined results for probabilities if it is applied uncritically when the domain of possibilities is infinite.
Bhartṛhari (Devanagari: भर्तृहरि; Bhartrihari; fl. c.
The 'Big Book' is a thought experiment developed by Ludwig Wittgenstein about the nature of ethics and the verifiability of ethical knowledge. This account is given by him in an early work, the 1929 Lecture on Ethics, and it matches also his position given in the early Tractatus Logico-Philosophicus (Proposition 6.41).
In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday. The birthday paradox is the counterintuitive fact that only 23 people are needed for that probability to exceed 50%.
The black hole information paradox is an unsolved problem in physics and a paradox that appears when the predictions of quantum mechanics and general relativity are combined. The theory of general relativity predicts the existence of black holes that are regions of spacetime from which nothing—not even light—can escape.
Paul Graham (; born November 13, 1964) is an English-American computer scientist, writer, essayist, entrepreneur and investor. His work includes the programming language Arc, the startup Viaweb (later renamed Yahoo!
The Boltzmann brain thought experiment suggests that it is probably more likely for a brain to spontaneously form, complete with a memory of having existed in our universe, rather than for the entire universe to come about in the manner cosmologists think it actually did. Physicists use the Boltzmann brain thought experiment as a reductio ad absurdum argument for evaluating competing scientific theories.
Bonini's paradox, named after Stanford business professor Charles Bonini, explains the difficulty in constructing models or simulations that fully capture the workings of complex systems (such as the human brain).
A temporal paradox, time paradox, or time travel paradox, is an apparent or actual contradiction associated with the idea of time travel or other foreknowledge of the future. Temporal paradoxes arise from circumstances involving hypothetical time travel to the past.
In probability theory, the Borel–Kolmogorov paradox (sometimes known as Borel's paradox) is a paradox relating to conditional probability with respect to an event of probability zero (also known as a null set). It is named after Émile Borel and Andrey Kolmogorov.
The Boy or Girl paradox surrounds a set of questions in probability theory, which are also known as The Two Child Problem, Mr. Smith's Children and the Mrs.
In linguistic morphology, the bracketing paradox concerns morphologically complex words which have more than one analysis, or bracketing, e.g., one for phonology and one for semantics, and the two are not compatible, or brackets do not align.
Braess's paradox is the observation that adding one or more roads to a road network can slow down overall traffic flow through it. The paradox was first discovered by Arthur Pigou in 1920, and later named after the German mathematician Dietrich Braess in 1968.
Braess's paradox is the observation that adding one or more roads to a road network can slow down overall traffic flow through it. The paradox was first discovered by Arthur Pigou in 1920, and later named after the German mathematician Dietrich Braess in 1968.
In philosophy, the brain in a vat (BIV) is a scenario used in a variety of thought experiments intended to draw out certain features of human conceptions of knowledge, reality, truth, mind, consciousness, and meaning. Gilbert Harman conceived the scenario, which Hilary Putnam turned into a modernized version of René Descartes's evil demon thought experiment.
In the philosophy of mind, the Brainstorm machine is a thought experiment described by Daniel Dennett, to show that it is not possible to intersubjectively compare any two individuals' personal experiences, or qualia, even with perfect technology. It is based on a device described in the film Brainstorm, in which the visual experience of one individual is fed into the brain of another.
A Braitenberg vehicle is a concept presented as a thought experiment by the Italian cyberneticist Valentino Braitenberg in his book Vehicles: Experiments in Synthetic Psychology. The book models the animal world in a minimalistic and constructive way, from simple reactive behaviours (like phototaxis) through the simplest vehicles, to the formation of concepts, spatial behaviour, and generation of ideas.
In the philosophy of thermal and statistical physics, the Brownian ratchet or Feynman–Smoluchowski ratchet is an apparent perpetual motion machine of the second kind (converting thermal energy into mechanical work), first analysed in 1912 as a thought experiment by Polish physicist Marian Smoluchowski. It was popularised by American Nobel laureate physicist Richard Feynman in a physics lecture at the California Insti
Isaac Newton's rotating bucket argument (also known as Newton's bucket) is a thought experiment that was designed to demonstrate that true rotational motion cannot be defined as the relative rotation of the body with respect to the immediately surrounding bodies. It is one of five arguments from the 'properties, causes, and effects' of 'true motion and rest' that support his contention that, in general, true motion a
In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing 'the set of all ordinal numbers' leads to a contradiction and therefore shows an antinomy in a system that allows its construction. It is named after Cesare Burali-Forti, who, in 1897, published a paper proving a theorem which, unknown to him, contradicted a previously proved result by Georg Cantor.
Buridan's ass is an illustration of a paradox in philosophy in the conception of free will. It refers to a hypothetical situation wherein an ass (or donkey) that is equally hungry and thirsty is placed precisely midway between a stack of hay and a pail of water.
Buridan's Bridge (also known as Sophism 17) is described by Jean Buridan, one of the most famous and influential philosophers of the Late Middle Ages, in his book Sophismata. It is a self-referential paradox that involves a proposition pronounced about an event that might or might not happen in the future.
The buttered cat paradox is a common joke based on the combination of two adages: Cats always land on their feet. Buttered toast always lands buttered side down.
Cantor's diagonal argument (among various similar names) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbers – informally, that there are sets which in some sense contain more elements than there are positive integers. Such sets are now called uncountable sets, and the size of infinite sets is treated by the theory of cardina
In set theory, Cantor's paradox states that there is no set of all cardinalities. This is derived from the theorem that there is no greatest cardinal number.
The card paradox is a variant of the liar paradox constructed by Philip Jourdain. It is also known as the postcard paradox, Jourdain paradox or Jourdain's paradox.
In mathematics, cardinality is an inherent property of sets, roughly meaning the number of individual objects they contain, which may be infinite. The concept is understood through one-to-one correspondences between sets.
In physics, Carroll's paradox arises when considering the motion of a falling rigid rod that is specially constrained. Considered one way, the angular momentum stays constant; considered in a different way, it changes.
A catch-22 is a paradoxical situation from which an individual cannot escape because of contradictory rules or limitations. The term was first used by Joseph Heller in his 1961 novel Catch-22.
A temporal paradox, time paradox, or time travel paradox, is an apparent or actual contradiction associated with the idea of time travel or other foreknowledge of the future. Temporal paradoxes arise from circumstances involving hypothetical time travel to the past.
The chain store paradox is a game theory problem that challenges conventional rational choice assumptions about strategic behavior in sequential games. It describes a scenario where an incumbent chain store faces sequential entry threats from multiple potential competitors in different markets.
Charlesworth's Paradox is a paradox related to kin selection, Hamilton's Rule and the evolution of altruism. The paradox was proposed by Brian Charlesworth and is sometimes used as a teaching example to discuss kin selection.
The chicken or the egg causality dilemma is commonly stated as the question, 'which came first: the chicken or the egg?' The dilemma stems from the observation that all chickens hatch from eggs and all chicken eggs are laid by chickens. 'Chicken-and-egg' is a metaphoric adjective describing situations where it is not clear which of two events should be considered the cause and which should be considered the effect, t
In the philosophy of mind, the China brain thought experiment (also known as the Chinese Nation, Chinese Gym, or China-body) considers what would happen if each person in the entire population of China were asked to simulate the action of one neuron in the brain, using telephones or walkie-talkies to simulate the axons and dendrites that connect neurons. The question this thought experiment attempts to answer is whet
The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length or perimeter. This results from the fractal curve–like properties of coastlines, namely the fact that a coastline typically has a fractal dimension.
A code-talker paradox is a situation in which a language prevents communication. As an issue in linguistics, the paradox raises questions about the fundamental nature of languages.
Cognitive psychology is the scientific study of human mental processes such as attention, language use, memory, perception, problem solving, creativity, and reasoning. Cognitive psychology originated in the 1960s in a break from behaviorism, which held from the 1920s to 1950s that unobservable mental processes were outside the realm of empirical science.
Coherence, also called uniformity or consistency, is a criterion for evaluating rules for fair division. Coherence requires that the outcome of a fairness rule is fair not only for the overall problem, but also for each sub-problem.
In decision theory, economics, and probability theory, the Dutch book arguments are a set of results showing that agents must satisfy the axioms of rational choice to avoid a kind of self-contradiction called a Dutch book. A Dutch book, sometimes also called a money pump, is a set of bets that ensures a guaranteed loss, i.e., the gambler will lose money no matter what happens.
The coin rotation paradox is the counter-intuitive mathematical fact that, when one coin is rolled without slipping around the rim of another coin of equal size, the moving coin completes not one but two full rotations after going all the way around the stationary coin, when viewed from an external reference frame. The problem can be further generalized to coins of different radii.
Semelparity and iteroparity are two reproductive strategies available to living organisms. A species is semelparous if it is characterized by a single reproductive episode before death, and iteroparous if it is characterized by multiple reproductive cycles.
In social choice theory, Condorcet's voting paradox (also called Condorcet's paradox or the Condorcet paradox) is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory. The result implies that it is logically impossible for any voting system to guarantee that a winner will have support from a majority of voters; for example, there can be rock-paper-scissors scenarios
In traditional logic, a contradiction involves a proposition conflicting either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias.
The cool tropics paradox is the apparent difference between modeled estimates of tropical temperatures during warm, ice-free periods of the Cretaceous and Eocene, and the colder temperatures which proxies suggested were present. The long-standing paradox was resolved when novel proxy derived temperatures showed significantly warmer tropics during past greenhouse climates.
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may nev
In mathematics, Cramer's paradox or the Cramer–Euler paradox is the statement that the number of points of intersection of two higher-order curves in the plane can be greater than the number of arbitrary points that are usually needed to define one such curve. It is named after the Genevan mathematician Gabriel Cramer.
The crocodile paradox, also known as crocodile sophism, is a paradox in logic in the same family of paradoxes as the liar paradox. The premise states that a crocodile, who has stolen a child, promises the parent that their child will be returned if and only if they correctly predict what the crocodile will do next.
Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself 'If C, then F'. The paradox requires only a few apparently-innocuous logical deduction rules.
In fluid dynamics, d'Alembert's paradox (or the hydrodynamic paradox) is a paradox discovered in 1752 by French mathematician Jean le Rond d'Alembert. D'Alembert proved that – for incompressible and inviscid potential flow – the drag force is zero on a body moving with constant velocity relative to (and simultaneously through) the fluid.
The decision-making paradox is a phenomenon related to decision-making and the quest for determining reliable decision-making methods. It was first described by Triantaphyllou, and has been recognized in the related literature as a fundamental paradox in multi-criteria decision analysis (MCDA), multi-criteria decision making (MCDM) and decision analysis since then.
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false.
There is generally an inverse correlation between monetary income and the total fertility rate within and between nations. The higher the degree of education and GDP per capita of a human population, subpopulation or social stratum, the fewer children are born in any developed country.
In biology, Denny's paradox refers to the apparent impossibility of surface-dwelling animals such as the water strider generating enough propulsive force to move. It is named after biologist Mark Denny, and relates to animal locomotion on the surface layer of water.
In computer science, the dining philosophers problem is an example problem often used in concurrent algorithm design to illustrate synchronization issues and techniques for resolving them. It was originally formulated in 1965 by Edsger Dijkstra as a student exam exercise, presented in terms of computers competing for access to tape drive peripherals.
The Downs–Thomson paradox (named after Anthony Downs and John Michael Thomson), also known as the Pigou–Knight–Downs paradox (after Arthur Cecil Pigou and Frank Knight), states that the equilibrium speed of car traffic on a road network is determined by the average door-to-door speed of equivalent journeys taken by public transport or the next best alternative. Although consistent with economic theory, it is a parado
The drinker paradox (also known as the drinker's theorem, the drinker's principle, or the drinking principle) is a theorem of classical predicate logic that can be stated as 'There is someone in the pub such that, if he or she is drinking, then everyone in the pub is drinking.' It was popularised by the mathematical logician Raymond Smullyan, who called it the 'drinking principle' in his 1978 book What Is the Name of
A Dyson sphere is a hypothetical megastructure that encompasses a star and captures a large percentage of its power output. The concept is a thought experiment that attempts to imagine how a spacefaring civilization would meet its energy requirements once those requirements exceed what can be generated from the home planet's resources alone.
The Easterlin paradox is a finding in happiness economics formulated in 1974 by Richard Easterlin, then professor of economics at the University of Pennsylvania, and the first economist to study happiness data. Easterlin further refined his finding during his subsequent long career at the University of Southern California.
To solve the Bertrand paradox, the Irish economist Francis Ysidro Edgeworth put forward the Edgeworth Paradox in his paper 'The Pure Theory of Monopoly', published in 1897. In economics, the Edgeworth paradox describes a situation in which two players cannot reach a state of equilibrium with pure strategies, i.e.
The Ehrenfest paradox concerns the rotation of a 'rigid' disc in the theory of relativity. In its original 1909 formulation as presented by Paul Ehrenfest in relation to the concept of Born rigidity within special relativity, it discusses an ideally rigid cylinder that is made to rotate about its axis of symmetry.
The Einstein–Podolsky–Rosen (EPR) paradox is a thought experiment proposed by physicists Albert Einstein, Boris Podolsky and Nathan Rosen, which argues that the description of physical reality provided by quantum mechanics is incomplete. In a 1935 paper titled 'Can Quantum-Mechanical Description of Physical Reality be Considered Complete?', they argued for the existence of 'elements of reality' that were not part of
A hallmark of Albert Einstein's career was his use of visualized thought experiments (German: Gedankenexperiment) as a fundamental tool for understanding physical issues and for elucidating his concepts to others. Einstein's thought experiments took diverse forms.
The elevator paradox is a paradox first noted by Marvin Stern and George Gamow, physicists who had offices on different floors of a multi-story building. Gamow, who had an office near the bottom of the building noticed that the first elevator to stop at his floor was most often going down, while Stern, who had an office near the top, noticed that the first elevator to stop at his floor was most often going up.
The elevator paradox relates to a hydrometer placed on an 'elevator' or vertical conveyor that, by moving to different elevations, changes the atmospheric pressure. In this classic demonstration, the floating hydrometer remains at an equilibrium position.
The Elitzur–Vaidman bomb-tester is a quantum mechanics thought experiment that uses interaction-free measurements to verify that a bomb is functional without having to detonate it. It was conceived in 1993 by Avshalom Elitzur and Lev Vaidman.
In decision theory, the Ellsberg paradox (or Ellsberg's paradox) is a paradox in which people's decisions are inconsistent with subjective expected utility theory. John Maynard Keynes published a version of the paradox in 1921.
The Epicurean paradox is a logical dilemma about the problem of evil attributed to the Greek philosopher Epicurus, who argued against the existence of a god who is simultaneously omniscient, omnipotent, and omnibenevolent.
The so-called Epimenides paradox has to do with self-reference in logic. It is named after the Cretan philosopher Epimenides of Knossos (alive circa 600 BC) who said: 'Cretans, liars always, evil beasts, idle bellies'.
Epistemology is the branch of philosophy that examines the nature, origin, and limits of knowledge. Also called the theory of knowledge, it explores different types of knowledge, such as propositional knowledge about facts, practical knowledge in the form of skills, and knowledge by acquaintance as a familiarity through experience.
The Einstein–Podolsky–Rosen (EPR) paradox is a thought experiment proposed by physicists Albert Einstein, Boris Podolsky and Nathan Rosen, which argues that the description of physical reality provided by quantum mechanics is incomplete. In a 1935 paper titled 'Can Quantum-Mechanical Description of Physical Reality be Considered Complete?', they argued for the existence of 'elements of reality' that were not part of
In mathematics, cardinality is an inherent property of sets, roughly meaning the number of individual objects they contain, which may be infinite. The concept is understood through one-to-one correspondences between sets.
The European paradox is the perceived failure of European countries to translate scientific advances into marketable innovations. The term was coined in a European Commission Green Paper in 1995.
The exercise paradox, also known as the workout paradox, refers to the finding that physical activity, while essential for maintaining overall health, does not necessarily lead to significant weight loss or increased calorie expenditure. This paradox challenges the common belief that more exercise equates to more calories burned and consequently, more weight loss.
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes.
The experience machine or pleasure machine is a thought experiment put forward by philosopher Robert Nozick in his 1974 book Anarchy, State, and Utopia. It is an attempt to refute ethical hedonism by imagining a choice between everyday reality and an apparently preferable simulated reality.
In the small wavelength limit, the total scattering cross-section of an impenetrable sphere is twice its geometrical cross-sectional area (which is the value obtained in classical mechanics).
The faint young Sun paradox or faint young Sun problem describes the apparent contradiction between observations of liquid water early in Earth's history and the astrophysical expectation that the Sun's output would have been only 70 percent as intense during that epoch as it is during the modern epoch. The paradox is this: with the young Sun's output at only 70 percent of its current output, early Earth would be exp
The base rate fallacy, also called base rate neglect or base rate bias, is a type of fallacy in which people tend to ignore the base rate (e.g., general prevalence) in favor of the information pertaining only to a specific case. Base rate neglect is a specific form of the more general extension neglect.
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 or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
The Faraday paradox or Faraday's paradox is any experiment in which Michael Faraday's law of electromagnetic induction appears to predict an incorrect result. The paradoxes fall into two classes: Faraday's law appears to predict that there will be zero electromotive force (EMF) but there is a non-zero EMF. Faraday's law appears to predict that there will be a non-zero EMF but there is zero EMF. Faraday deduced his la
The Faraday paradox was a once inexplicable aspect of the reaction between nitric acid and steel. Around 1830, the English scientist Michael Faraday found that diluted nitric acid would attack steel, but concentrated nitric acid would not.
Fenno's paradox is the idea that people generally disapprove of the United States Congress as a whole but often support the congressmen from their own congressional districts. The paradox is named after political scientist Richard Fenno, who discussed this phenomenon in his 1978 book Home Style: House Members in Their Districts.
The Fermi paradox is the discrepancy between the lack of conclusive evidence of advanced extraterrestrial life and the apparently high likelihood of its existence. The paradox is named after physicist Enrico Fermi, who informally posed the question—remembered by Emil Konopinski as 'But where is everybody?'—during a 1950 conversation at Los Alamos with colleagues Konopinski, Edward Teller, and Herbert York.
Fitch's paradox of knowability is a puzzle of epistemic logic. It provides a challenge to the knowability thesis, which states that every truth is, in principle, knowable.
The floating man, flying man, or man suspended in air argument is a thought experiment by the Persian philosopher Ibn Sina (Avicenna) which argues for the existence of the soul. This thought experiment is used to argue in favor of knowledge by presence.
The Flynn effect is the substantial and long-sustained increase in both fluid and crystallized intelligence test scores that were measured in many parts of the world over the 20th century, named after researcher James Flynn (1934–2020). When intelligence quotient (IQ) tests are initially standardized using a sample of test-takers, by convention the average of the test results is set to 100 and their standard deviatio
Fredkin's paradox reads 'The more equally attractive two alternatives seem, the harder it can be to choose between them—no matter that, to the same degree, the choice can only matter less.' Thus, a decision-making agent might spend the most time on the least important decisions. It was proposed by American physicist Edward Fredkin.
In statistical analysis, Freedman's paradox, named after David Freedman, is a problem in model selection whereby predictor variables with no relationship to the dependent variable can pass tests of significance – both individually via a t-test, and jointly via an F-test for the significance of the regression. Freedman demonstrated (through simulation and asymptotic calculation) that this is a common occurrence when t
The French paradox is an apparently paradoxical epidemiological observation that French people have a relatively low incidence of coronary heart disease (CHD), while having a diet relatively rich in saturated fats, in apparent contradiction to the widely held belief that the high consumption of such fats is a risk factor for CHD. The paradox is that if the thesis linking saturated fats to CHD is valid, the French oug
The friendship paradox is the phenomenon first observed by the sociologist Scott L. Feld in 1991 that on average, an individual's friends have more friends than that individual. It can be explained as a form of sampling bias in which people with more friends are more likely to be in one's own friend group.
Gilbert Keith Chesterton (29 May 1874 – 14 June 1936) was an English Christian apologist writer. Chesterton's wit, paradoxical style, and defence of tradition made him a dominant figure in early 20th-century literature.
A Gabriel's horn (also called Torricelli's trumpet) is a type of geometric figure that has infinite surface area but finite volume. The name refers to the Christian idea that the archangel Gabriel will one day blow his horn to announce Judgment Day.
Galileo's paradox is a demonstration of one of the surprising properties of infinite sets. In his final scientific work, Two New Sciences, Galileo Galilei made apparently contradictory statements about the positive integers.
Galileo's ship refers to two physics experiments, a thought experiment and an actual experiment, by Galileo Galilei, the 16th- and 17th-century physicist and astronomer. The experiments were created to argue for the idea of a rotating Earth, as opposed to a stationary Earth around which the Sun, planets, and stars rotate.
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The gender-equality paradox is the disputed finding that various gender differences in personality and occupational choice are larger in more gender equal countries. Larger differences are found in Big Five personality traits, Dark Triad traits, self-esteem, depression, personal values, occupational and educational choices.
The Gettier problem, in the field of epistemology, is a landmark philosophical problem concerning the understanding of descriptive knowledge. Attributed to American philosopher Edmund Gettier, Gettier-type counterexamples (called 'Gettier-cases') challenge the long-held justified true belief (JTB) account of knowledge.
In statistical mechanics, a semi-classical derivation of entropy that does not take into account the indistinguishability of particles yields an expression for entropy which is not extensive (is not proportional to the amount of substance in question). This leads to a paradox known as the Gibbs paradox, after Josiah Willard Gibbs, who proposed this thought experiment in 1874‒1875.
Gibson's paradox is the observation that the rate of interest and the general level of prices under the gold standard are positively correlated. It is named for British economist Alfred Herbert Gibson who noted the correlation in a 1923 article for Banker's Magazine.
In microeconomics and consumer theory, a Giffen good is a product that people consume more of as the price rises and vice versa, violating the law of demand. For ordinary goods, as the price of the good rises, the substitution effect makes consumers purchase less of it, and more of substitute goods; the income effect can either reinforce or weaken this decline in demand, but for an ordinary good never outweighs it.
The glucose paradox was the observation that the large amount of glycogen in the liver was not explained by the small amount of glucose absorbed. The explanation was that the majority of glycogen is made from a number of substances other than glucose.
The new riddle of induction was presented by Nelson Goodman in Fact, Fiction, and Forecast as a successor to Hume's original problem. It presents the logical predicates grue and bleen which are unusual due to their time-dependence.
A temporal paradox, time paradox, or time travel paradox, is an apparent or actual contradiction associated with the idea of time travel or other foreknowledge of the future. Temporal paradoxes arise from circumstances involving hypothetical time travel to the past.
In mathematics, the infinite series 1 − 1 + 1 − 1 + ⋯ is a divergent series, meaning that the sequence of partial sums of the series does not converge. Although it is divergent, it can be manipulated to yield a number of mathematically interesting results.
Gray's Paradox is a paradox posed in 1936 by British zoologist Sir James Gray. The paradox was to figure out how dolphins can obtain such high speeds and accelerations with what appears to be a small muscle mass.
The Green Paradox is a controversial book by German economist, Hans-Werner Sinn, describing the observation that an environmental policy that becomes greener with the passage of time acts like an announced expropriation for the owners of fossil fuel resources, inducing them to accelerate resource extraction and hence to accelerate global warming.
The Grelling–Nelson paradox arises from the question of whether the term 'non-self-descriptive' is self-descriptive. It was formulated in 1908 by Kurt Grelling and Leonard Nelson, and is sometimes mistakenly attributed to the German philosopher and mathematician Hermann Weyl thus occasionally called Weyl's paradox or Grelling's paradox.
Herbert Paul Grice (13 March 1913 – 28 August 1988), usually publishing under the name H. P. Grice, H. Paul Grice, or Paul Grice, was a British philosopher of language who created the theory of implicature and the cooperative principle (with its namesake Gricean maxims), which became foundational concepts in the linguistic field of pragmatics. His work on meaning has also influenced the philosophical study of semanti
In philosophy, the Grim Reaper paradox is a paradox involving an infinite sequence of Grim Reapers, each tasked with killing a person if no reaper has already killed them. The paradox raises questions about the possibility of continuous time and the infinite past (temporal finitism).
The Grossman–Stiglitz Paradox is a paradox introduced by Sanford J. Grossman and Joseph Stiglitz in a joint publication in American Economic Review in 1980 that argues perfectly informationally efficient markets are an impossibility since, if prices perfectly reflected available information, there is no profit to gathering information, in which case there would be little reason to trade and markets would eventually c
The Greisen–Zatsepin–Kuzmin limit (GZK limit or GZK cutoff) is a theoretical upper limit on the energy of cosmic ray protons traveling from other galaxies through the intergalactic medium to our galaxy. The limit is 5×1019 eV (50 EeV), or about 8 joules (the energy of a proton travelling at ≈ 99.99999999999999999998% the speed of light).
Kin selection is a process whereby natural selection favours a trait due to its positive effects on the reproductive success of an organism's relatives, even when at a cost to the organism's own survival and reproduction. Kin selection can lead to the evolution of altruistic behaviour.
Hardy's paradox is a thought experiment in quantum mechanics devised by Lucien Hardy in 1992–1993 in which a particle and its antiparticle may interact without annihilating each other. Experiments using the technique of weak measurement have studied an interaction of polarized photons, and these have demonstrated that the phenomenon does occur.
The Hausdorff paradox is a paradox in mathematics named after Felix Hausdorff. It involves the sphere S 2 {\\displaystyle {S^{2}}} (the surface of a 3-dimensional ball in R 3 {\\displaystyle {\\mathbb {R} ^{3}}} ).
The heat death paradox, also known as thermodynamic paradox, Clausius' paradox, and Kelvin's paradox, is a reductio ad absurdum argument that uses thermodynamics to show the impossibility of an infinitely old universe. It was formulated in February 1862 by Lord Kelvin and expanded upon by Hermann von Helmholtz and William John Macquorn Rankine.
The hedgehog's dilemma, or sometimes the porcupine dilemma, is a metaphor about the challenges of human intimacy. It describes a situation in which a group of hedgehogs seek to move close to one another to share heat during cold weather.
Heisenberg's microscope is a thought experiment proposed by Werner Heisenberg that has served as the nucleus of some commonly held ideas about quantum mechanics. In particular, it provides an argument for the uncertainty principle on the basis of the principles of classical optics.
A heuristic or heuristic technique (problem solving, mental shortcut, rule of thumb) is any approach to problem solving that employs a pragmatic method that is not fully optimized, perfected, or rationalized, but is nevertheless 'good enough' as an approximation or attribute substitution. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a
The Hilbert–Bernays paradox is a distinctive paradox belonging to the family of the paradoxes of reference. It is named after David Hilbert and Paul Bernays.
Hilbert's paradox of the Grand Hotel (colloquially the Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets. It shows that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and this process may be repeated infinitely often.
The Hispanic paradox is an epidemiological finding that Hispanic Americans tend to have health outcomes that paradoxically are comparable to, or in some cases better than, those of their U.S. non-Hispanic White counterparts, even though Hispanics have lower average income and education, higher rates of disability, as well as a higher incidence of various cardiovascular risk factors and metabolic diseases. Low socioec
A temporal paradox, time paradox, or time travel paradox, is an apparent or actual contradiction associated with the idea of time travel or other foreknowledge of the future. Temporal paradoxes arise from circumstances involving hypothetical time travel to the past.
Hooper's paradox is a falsidical paradox based on an optical illusion. A geometric shape with an area of 32 units is dissected into four parts, which afterwards get assembled into a rectangle with an area of only 30 units.
Hormesis is a two-phased dose-response relationship whereby low-dose exposures have a beneficial effect and high-dose amounts are either inhibitory to function or toxic. Within the hormetic zone, the biological response to low-dose amounts of some stressors is generally favorable.
Vertical pressure variation is the variation in pressure as a function of elevation. Depending on the fluid in question and the context being referred to, it may also vary significantly in dimensions perpendicular to elevation as well, and these variations have relevance in the context of pressure gradient force and its effects.
I know that I know nothing' is a saying derived from Plato's account of the Greek philosopher Socrates: 'For I was conscious that I knew practically nothing...' (Plato, Apology 22d, translated by Harold North Fowler, 1966). It is also sometimes called the Socratic paradox, although this name is often instead used to refer to other seemingly paradoxical claims made by Socrates in Plato's dialogues (most notably, Socr
The Icarus paradox is a neologism coined by Danny Miller in his 1990 book by the same name. The term refers to the phenomenon of businesses failing abruptly after a period of apparent success, where this failure is brought about by the very elements that led to their initial success.
What Is Intelligence?: Beyond the Flynn Effect is a book by psychologist James R. Flynn which outlines his model for an explanation of the eponymous Flynn effect. The book summarizes much of the work of Flynn in this area, as well as that of his colleague William Dickens of the Brookings Institution.
In metaphysics, identity (from Latin: identitas, 'sameness') is the relation each thing bears only to itself. The notion of identity gives rise to many philosophical problems, including the identity of indiscernibles (if x and y share all their properties, are they one and the same thing?), and questions about change and personal identity over time (what has to be the case for a person x at one time and a person y at
If a tree falls in a forest and no one is around to hear it, does it make a sound?' is a philosophical thought experiment that raises questions regarding observation and perception.
Ignore all rules' (IAR) is a policy of the English Wikipedia, an online encyclopedia, which reads: 'If a rule prevents you from improving or maintaining Wikipedia, ignore it.' (emphasis and links in original). The rule was proposed by Wikipedia co-founder Larry Sanger to encourage editors to add information without focusing excessively on formatting, though Sanger later criticized the rule's effects on the community
The impossible cube or irrational cube is an impossible object invented by M.C. Escher for his 1958 print Belvedere. It is a two-dimensional figure that superficially resembles a perspective drawing of a three-dimensional cube, with its features drawn inconsistently from the way they would appear in an actual cube.
An impossible object (also known as an impossible figure or an undecidable figure) is a type of optical illusion that consists of a two-dimensional figure which is instantly and naturally understood as representing a projection of a three-dimensional object but cannot exist as a solid object. Impossible objects are of interest to psychologists, mathematicians and artists without falling entirely into any one discipli
Inductive reasoning refers to a variety of methods of reasoning in which the conclusion of an argument is supported not with deductive certainty, but at best with some degree of probability. Unlike deductive reasoning (such as mathematical induction), where the conclusion is certain, given the premises are correct, inductive reasoning produces conclusions that are at best probable, given the evidence provided.
Inferences are steps in logical reasoning, moving from premises to logical consequences; etymologically, the word infer means to 'carry forward'. Inference is theoretically traditionally divided into deduction and induction, a distinction that dates at least to Aristotle (300s BC).
The infinite monkey theorem states that a monkey hitting keys independently and at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, including the complete works of William Shakespeare. More precisely, under the assumption of independence and randomness of each keystroke, the monkey would almost surely type every possible finite text an infinite number of times.
In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable.
In the Middle Ages, variations on the liar paradox were studied under the name of insolubilia ('insolubles').
Renewal theory is the branch of probability theory that generalizes the Poisson process for arbitrary holding times. Instead of exponentially distributed holding times, a renewal process may have any independent and identically distributed (IID) holding times that have finite expectation.
An intentionally blank page is a page that has no content and may be unexpected. Such pages may serve purposes ranging from place-holding to space-filling and content separation.
The interesting number paradox is a humorous paradox which arises from the attempt to classify every natural number as either 'interesting' or 'uninteresting'. The paradox states that every natural number is interesting.
An intuition pump is a type of thought experiment that leads the audience to a specific conclusion through intuition.
The inventor's paradox is a phenomenon that occurs in seeking a solution to a given problem. Instead of solving a specific type of problem, which would seem intuitively easier, it can be easier to solve a more general problem, which covers the specifics of the sought-after solution.
The inverted spectrum is the hypothetical scenario, pertaining to the philosophy of color, of two people sharing their color vocabulary and discriminations, although the colors one sees—that person's qualia—are systematically different from the colors the other person sees.
In psychology, ironic process theory (IPT), also known as the pink elephant paradox or white bear phenomenon, suggests that when an individual intentionally tries to avoid thinking a certain thought or feeling a certain emotion, a paradoxical effect is produced: the attempted avoidance not only fails in its object but in fact causes the thought or emotion to occur more frequently and more intensely. IPT is also known
The irresistible force paradox (also unstoppable force paradox or shield and spear paradox), is a classic paradox formulated as 'What happens when an unstoppable force meets an immovable object?' The immovable object and the unstoppable force are both implicitly assumed to be indestructible, or else the question would have a trivial resolution. Furthermore, it is assumed that they are two entities.
The Israeli paradox was an apparently paradoxical epidemiological observation that Israeli Jews have a relatively high incidence of coronary heart disease (CHD), despite having a diet relatively low in saturated fats, in apparent contradiction to the widely held belief that the high consumption of such fats is a risk factor for CHD. The paradox was that if the thesis linking saturated fats to CHD is valid, the Israel
In economics, the Jevons paradox, or Jevons effect, is said to occur when technological improvements that increase the efficiency of a resource's use lead to a rise, rather than a fall, in total consumption of that resource. Greater efficiency reduces the amount of the resource needed per application, lowering its effective cost; if demand is sufficiently price elastic, this induces demand such that the per-unit savi
Kavka's toxin puzzle is a thought experiment about the possibility of forming an intention to perform an act which, following from reason, is an action one would not actually perform. It was presented by moral and political philosopher Gregory S. Kavka in 'The Toxin Puzzle' (1983), and grew out of his work in deterrence theory and mutual assured destruction.
In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate. John Larry Kelly Jr., a researcher at Bell Labs, described the criterion in 1956.
Kin selection is a process whereby natural selection favours a trait due to its positive effects on the reproductive success of an organism's relatives, even when at a cost to the organism's own survival and reproduction. Kin selection can lead to the evolution of altruistic behaviour.
In mathematics, the Kleene–Rosser paradox is a paradox that shows that certain systems of formal logic are inconsistent, in particular the version of Haskell Curry's combinatory logic introduced in 1930, and Alonzo Church's original lambda calculus, introduced in 1932–1933, both originally intended as systems of formal logic. The paradox was exhibited by Stephen Kleene and J. B. Rosser in 1935.
In relativistic quantum mechanics, the Klein paradox (also known as Klein tunneling) is a quantum phenomenon related to particles encountering high-energy potential barriers. It is named after physicist Oskar Klein who discovered it in 1929.
The knower paradox is a paradox belonging to the family of the paradoxes of self-reference (like the liar paradox). Informally, it consists in considering a sentence saying of itself that it is not known, and apparently deriving the contradiction that such sentence is both not known and known.
The Knudsen paradox has been observed in experiments of channel flow with varying channel width or equivalently different pressures. If the normalized mass flux through the channel is plotted over the Knudsen number based on the channel width a distinct minimum is observed around K n = 0.8 {\\displaystyle Kn=0.8} .
The ladder paradox (or barn-pole paradox) is a thought experiment in special relativity. It involves a ladder, parallel to the ground, travelling horizontally at relativistic speed (near the speed of light) and therefore undergoing a Lorentz length contraction.
In the social sciences, unintended consequences (sometimes unanticipated consequences or unforeseen consequences, more colloquially called knock-on effects) are outcomes of a purposeful action that are not intended or foreseen. The term was popularized in the 20th century by American sociologist Robert K. Merton.
The lek paradox is a conundrum in evolutionary biology that addresses the persistence of genetic variation in male traits within lek mating systems, despite strong sexual selection through female choice. This paradox arises from the expectation that consistent female preference for particular male traits should erode genetic diversity, theoretically leading to a loss of the benefits of choice.
In economics, the Leontief's paradox is that a country with a higher capital per worker has a lower capital/labor ratio in exports than in imports. This econometric finding was the result of Wassily W. Leontief's attempt to test the Heckscher–Ohlin theory ('H–O theory') empirically.
In economics, the Lerner paradox is the theoretical possibility that imposing tariffs raises the world price of the import good, causing a deterioration of the tariff-imposing country's terms of trade. Abba Lerner showed the possibility in his 1936 article.
Levinthal's paradox is a thought experiment in the field of computational protein structure prediction; protein folding is the process by which peptides reach a stable native configuration. In theory, a brute force search, testing all possible conformations, would take longer than the age of the universe to identify this minimum energy configuration (the native state).
In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that 'I am lying'. If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied.
The liberal paradox, also Sen paradox or Sen's paradox, is a logical paradox proposed by Amartya Sen which shows that no means of aggregating individual preferences into a single, social choice, can simultaneously fulfill the following, seemingly mild conditions: The unrestrictedness condition, or U: every possible ranking of each individual's preferences and all outcomes of every possible voting rule will be conside
Lindley's paradox is a counterintuitive situation in statistics in which the Bayesian and frequentist approaches to a hypothesis testing problem give different results for certain choices of the prior distribution. The problem of the disagreement between the two approaches was discussed in Harold Jeffreys' 1939 textbook; it became known as Lindley's paradox after Dennis Lindley called the disagreement a paradox in a
List of unsolved problems may refer to several notable conjectures or open problems in various academic fields:
Lombard's paradox describes a paradoxical muscular contraction in humans. When rising to stand from a sitting or squatting position, both the hamstrings and quadriceps contract at the same time, despite them being antagonists to each other.
In physics, Loschmidt's paradox (named for Josef Loschmidt), also known as the reversibility paradox, irreversibility paradox, or Umkehreinwand (from German 'reversal objection'), is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics. This puts the time reversal symmetry of (almost) all known low-level fundamental physical processes at odds with any attempt to
The lottery paradox arises from Henry E. Kyburg Jr. considering a fair 1,000-ticket lottery that has exactly one winning ticket.
The low birth-weight paradox is an apparently paradoxical observation relating to the birth weights and mortality rate of children born to tobacco smoking mothers. Low birth-weight children born to smoking mothers have a lower infant mortality rate than the low birth weight children of non-smokers.
In economics, the Lucas paradox or the Lucas puzzle is the observation that capital does not flow from developed countries to developing countries despite the fact that developing countries have lower levels of capital per worker. Classical economic theory predicts that capital should flow from rich countries to poor countries, due to the effect of diminishing returns of capital.
Mandeville's paradox is named after Bernard Mandeville (1670–1733), who posits that actions which may be qualified as vicious with regard to individuals have benefits for society as a whole. This is alluded to in the subtitle of his most famous work, The Fable of The Bees: or, Private Vices, Public Benefits.
In philosophy of mind, the knowledge argument (also known as Mary's Room, Mary the Colour Scientist, or Mary the super-scientist) is a thought experiment proposed by Frank Jackson in his article 'Epiphenomenal Qualia' (1982), and extended in 'What Mary Didn't Know' (1986). The thought experiment describes Mary, a scientist who exists in a black-and-white world where she has extensive access to physical descriptions o
Maxwell's demon is a thought experiment that appears to disprove the second law of thermodynamics. It was proposed by the physicist James Clerk Maxwell in 1867.
Mayfield's Paradox states that to keep everyone out of an information system requires an infinite amount of money, and to get everyone onto an information system also requires infinite money, while costs between these extremes are relatively low. The paradox is depicted as a U-curve, where the cost of a system is on the vertical axis, and the percentage of humanity that can access the system is on the horizontal axis
The psychology of eating meat is an area of study seeking to illuminate the confluence of morality, emotions, cognition, and personality characteristics in the phenomenon of the consumption of meat. Research into the psychological and cultural factors of meat-eating suggests correlations with masculinity, support for hierarchical values, and reduced openness to experience.
The median of a set of numbers is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as the “middle' value.
Meno (; Ancient Greek: Μένων, Ménōn) is a Socratic dialogue written by Plato around 385 BC, but set at an earlier date around 402 BC. Meno begins the dialogue by asking Socrates whether virtue (in Ancient Greek: ἀρετή, aretē) can be taught, acquired by practice, or comes by nature. In order to determine whether virtue is teachable or not, Socrates tells Meno that they first need to determine what virtue is.
The mere addition paradox (also known as the repugnant conclusion) is a problem in population ethics identified by Derek Parfit and discussed in his book Reasons and Persons (1984). The paradox identifies the mutual incompatibility of four intuitively compelling assertions about the relative value of populations.
In physics, Mermin's device or Mermin's machine is a thought experiment intended to illustrate the non-classical features of nature without making a direct reference to quantum mechanics. The challenge is to reproduce the results of the thought experiment in terms of classical physics.
The metabasis paradox is an instance in the received text of Aristotle's Poetics where, according to many scholars, he makes two incompatible statements. In chapter 13 of the book, Aristotle states that for tragedy to end in misfortune is 'correct,' yet in chapter 14 he judges a type of plot in tragedy 'best' that does not end in misfortune.
In economics, the Metzler paradox (named after the American economist Lloyd Metzler) is the theoretical possibility that the imposition of a tariff on imports may reduce the relative internal price of that good. It was proposed by Lloyd Metzler in 1949 upon examination of tariffs within the Heckscher–Ohlin model.
The Mexican paradox is the observation that Mexicans exhibit a surprisingly low incidence of low birth weight (especially foreign-born Mexican mothers), contrary to what would be expected from their socioeconomic status (SES). This appears as an outlier in graphs correlating SES with low-birth-weight rates.
In relativistic physics, a velocity-addition formula is an equation that specifies how to combine the velocities of objects in a way that is consistent with the requirement that no object's speed can exceed the speed of light. Such formulas apply to successive Lorentz transformations, so they also relate different frames.
Molyneux's problem is a thought experiment in philosophy concerning immediate recovery from blindness. It was first formulated by William Molyneux, and notably referred to in John Locke's An Essay Concerning Human Understanding (1689).
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975.
Moore's paradox concerns the apparent absurdity involved in asserting a first-person present-tense sentence such as 'It is raining, but I do not believe that it is raining' or 'It is raining, but I believe that it is not raining.' The first author to note this apparent absurdity was George E. Moore. These 'Moorean' sentences, as they have become known, are paradoxical in that while they appear absurd, they neverthele
In philosophy, an ethical dilemma, also called an ethical paradox or moral dilemma, is a situation in which two or more conflicting moral imperatives, none of which overrides the other, confront an agent. A closely related definition characterizes an ethical dilemma as a situation in which every available choice is wrong.
Moravec's paradox is the observation that, as Hans Moravec wrote in 1988, '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'. This counterintuitive pattern may happen because skills that appear effortless to humans, such as recognizing face
A Morton's fork is a type of false dilemma in which contradictory observations lead to the same conclusion. Its name dates back to the rationalising of a benevolence by the 15th century English prelate John Morton.
The Mott problem is an iconic challenge to quantum mechanics theory: how can the prediction of spherically symmetric wave function result in linear tracks seen in a cloud chamber. The problem was first formulated in 1927 by Albert Einstein and Max Born and solved in 1929 by Nevill Francis Mott.
A movement paradox is a phenomenon of grammar that challenges the transformational approach to syntax. The importance of movement paradoxes is emphasized by those theories of syntax (e.g.
The moving magnet and conductor problem is a famous thought experiment, originating in the 19th century, concerning the intersection of classical electromagnetism and special relativity. In it, the current in a conductor moving with constant velocity, v, with respect to a magnet is calculated in the frame of reference of the magnet and in the frame of reference of the conductor.
The Mpemba effect is the observation that very hot liquids or colloids (such as ice cream) can freeze more quickly than colder ones, for similar volumes and surrounding conditions. Physicists remain divided on the effect's reproducibility, precise definition, and underlying mechanisms.
In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both.
In game theory, a Nash equilibrium is a situation where no player could gain more by changing their own strategy (holding all other players' strategies fixed) in a game. A Nash equilibrium is the most commonly used solution concept for non-cooperative games.
The navigation paradox states that increased navigational precision may result in increased collision risk. In the case of ships and aircraft, the advent of Global Positioning System (GPS) navigation has enabled craft to follow navigational paths with such greater precision (often of the order of plus or minus 2 m), that, without better distribution of routes, coordination between neighboring craft and collision avoi
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: 'If P then Q', Q is necessary for P, because the truth of Q is 'necessarily' guaranteed by the truth of P. (Equivalently, it is impossible to have P without Q, or the falsity of Q ensures the falsity of P.) Similarly, P is suffici
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.
The new riddle of induction was presented by Nelson Goodman in Fact, Fiction, and Forecast as a successor to Hume's original problem. It presents the logical predicates grue and bleen which are unusual due to their time-dependence.
Coherence, also called uniformity or consistency, is a criterion for evaluating rules for fair division. Coherence requires that the outcome of a fairness rule is fair not only for the overall problem, but also for each sub-problem.
In philosophy and mathematics, Newcomb's problem, also known as Newcomb's paradox, is a thought experiment involving a decision problem where a player must decide whether to take one or two boxes in conditions where a being, often called the 'predictor', is able to predict his choices with near-certainty. Newcomb's paradox was created by William Newcomb of the University of California's Lawrence Livermore Laboratory.
In philosophy and mathematics, Newcomb's problem, also known as Newcomb's paradox, is a thought experiment involving a decision problem where a player must decide whether to take one or two boxes in conditions where a being, often called the 'predictor', is able to predict his choices with near-certainty. Newcomb's paradox was created by William Newcomb of the University of California's Lawrence Livermore Laboratory.
Newton's cannonball was a thought experiment Isaac Newton used to hypothesize that the force of gravity was universal, and it was the key force for planetary motion. It appeared in his posthumously published 1728 work De mundi systemate (also published in English as A Treatise of the System of the World).
The no–no paradox is a distinctive paradox belonging to the family of the semantic paradoxes (like the Liar paradox). It derives its name from the fact that it consists of two sentences each simply denying what the other says.
The participation criterion is a voting system criterion that says candidates should never lose an election as a result of receiving too many votes in support. More formally, it says that adding more voters who prefer Alice to Bob should not cause Alice to lose the election to Bob.
The no–no paradox is a distinctive paradox belonging to the family of the semantic paradoxes (like the Liar paradox). It derives its name from the fact that it consists of two sentences each simply denying what the other says.
Norton's dome is a thought experiment that exhibits a non-deterministic system within the bounds of Newtonian mechanics. It was devised by John D. Norton in 2003.
The obesity paradox is the finding in some studies of a lower mortality rate for overweight or obese people within certain subpopulations. The paradox has been observed in people with cardiovascular disease and cancer.
In physics, the observer effect is the disturbance of a system by the act of observation. This is often the result of utilising instruments that, by necessity, alter the state of what they measure in some manner.
In the social sciences, the observer's paradox is a situation in which the phenomenon being observed is unwittingly influenced by the presence of the observer/investigator.
Olbers' paradox, also known as the dark night paradox or Olbers and Cheseaux's paradox, is a historical argument in astrophysics and physical cosmology that says the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. If the universe were static, homogeneous at a large scale, and populated by an infinite number of stars, any line of sight from Earth must end at the surf
Olbers' paradox, also known as the dark night paradox or Olbers and Cheseaux's paradox, is a historical argument in astrophysics and physical cosmology that says the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. If the universe were static, homogeneous at a large scale, and populated by an infinite number of stars, any line of sight from Earth must end at the surf
The omnipotence paradox is a family of paradoxes that arise with some understandings of the term omnipotent. The paradox arises, for example, if one assumes that an omnipotent being has no limits and is capable of realizing any outcome, even a logically contradictory one such as creating a square circle.
In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite sets. Usually Greek letters are used for ordinal number variables to help distinguish them from natural number variables.
In philosophy, the original position is a hypothetical position from which members of society would consider which principles they would select for the basic structure of their society if they had no knowledge ahead of time regarding the position which they would end up occupying in that society. The idea of having no such knowledge, because everyone is behind a veil of ignorance, represents a thought experiment ofte
The outcomes paradox (otherwise known as the 'better prognosis hypothesis') is the observation that patients with schizophrenia in developing countries benefit much more from therapy than those in developed countries. This is surprising because the reverse holds for most diseases: 'the richer and more developed the country, the better the patient outcome.' The outcomes paradox came to light in the 1960s due to cross-
In rigid-body dynamics, the Painlevé paradox (also called frictional paroxysms by Jean Jacques Moreau) is the paradox that results from inconsistencies between the contact and Coulomb models of friction. It is named for former French prime minister and mathematician Paul Painlevé.
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 or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
The paradox of analysis (or Langford–Moore paradox) is a paradox that concerns how an analysis can be correct or informative but not both. The problem was formulated by philosopher G. E. Moore in his book Principia Ethica, and first named by C. H. Langford in his article 'The Notion of Analysis in Moore's Philosophy' (in The Philosophy of G. E. Moore, edited by Paul Arthur Schilpp, Northwestern University, 1942, pp.
Paradox of competition in economics names a model of a situation where measures, which offer a competitive advantage to an individual economic entity, lead to nullification of advantage if all others behave in the same way. In some cases the finite state is even more disadvantageous for everybody than before (for the totality as well as for the individual).
The paradox of tolerance is a philosophical concept suggesting that if a society extends tolerance to those who are intolerant, it risks enabling the eventual dominance of intolerance, thereby undermining the very principle of tolerance. This paradox was articulated by philosopher Karl Popper in The Open Society and Its Enemies (1945), where he argued that a truly tolerant society must retain the right to deny tolera
The paradox of enrichment is a term from population ecology coined by Michael Rosenzweig in 1971. He described an effect in six predator–prey models where increasing the food available to the prey caused the predator's population to destabilize.
The paradoxes of material implication are a group of classically true formulae involving material conditionals whose translations into natural language are intuitively false when the conditional is translated with English words such as 'implies' or 'if ... then ...'.
The paradox of fiction, or the paradox of emotional response to fiction, is a philosophical dilemma that questions how people can experience strong emotions to fictional things. The primary question asked is the following: How are people moved by things which do not exist?
Free choice is a phenomenon in natural language where a linguistic disjunction appears to receive a logical conjunctive interpretation when it interacts with a modal operator. For example, the following English sentences can be interpreted to mean that the addressee can watch a movie and that they can also play video games, depending on their preference: You can watch a movie or play video games.
The paradox of tolerance is a philosophical concept suggesting that if a society extends tolerance to those who are intolerant, it risks enabling the eventual dominance of intolerance, thereby undermining the very principle of tolerance. This paradox was articulated by philosopher Karl Popper in The Open Society and Its Enemies (1945), where he argued that a truly tolerant society must retain the right to deny tolera
The paradox of hedonism, also called the pleasure paradox, refers to the practical difficulties encountered in the pursuit of pleasure. For the hedonist, constant pleasure-seeking may not yield the most actual pleasure or happiness in the long term when consciously pursuing pleasure interferes with experiencing it.
The paradox of nihilism is a family of paradoxes regarding the philosophical implications of nihilism, particularly situations contesting nihilist perspectives on the nature and extent of subjectivity within a nihilist framework. There are a number of variations of this paradox.
Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea (c. 490–430 BC), primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia.
The resource curse, also known as the paradox of plenty or the poverty paradox, is the hypothesis that countries with an abundance of natural resources (such as fossil fuels and certain minerals) have lower economic growth, lower rates of democracy, or poorer development outcomes than countries with fewer natural resources. There are many theories and much academic debate about the reasons for and exceptions to the a
Paradox of prosperity is a term used widely in many instances in economics, social theory and general commentary. In inter-generational analysis, Professor Gilbert N. M. O. Morris defines the term through an analysis of the familial dynamics and social proclivities of what Tom Brokaw has called the 'Greatest Generation'.
The paradox of a charge in a gravitational field is an apparent physical paradox in the context of general relativity. A charged particle at rest in a gravitational field, such as on the surface of the Earth, must be supported by a force to prevent it from falling.
Suspense is a state of anxiety or excitement caused by mysteriousness, uncertainty, doubt, or undecidedness. In a narrative work, suspense is the audience's excited anticipation about the plot or conflict (which may be heightened by a violent moment, stressful scene, puzzle, mystery, etc.), particularly as it affects a character for whom the audience feels sympathy.
The Paradox of the Court, also known as the counterdilemma of Euathlus or Protagoras' paradox, is a paradox originating in ancient Greece. The story is related by the Latin author Aulus Gellius in Attic Nights, who says that the famous sophist Protagoras took on a promising pupil, Euathlus, on the understanding that the student pay Protagoras for his instruction after he wins his first court case.
Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea (c. 490–430 BC), primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia.
The sorites paradox (), sometimes known as the paradox of the heap, is a paradox that results from vague predicates. A typical formulation involves a heap of sand, from which grains are removed individually.
The paradox of the pesticides is a paradox that states that applying pesticide to a pest may end up increasing the abundance of the pest or other pests if the pesticide upsets natural predator–prey dynamics in the ecosystem.
In aquatic biology, the paradox of the plankton describes the situation in which a limited range of resources supports an unexpectedly wide range of plankton species, apparently flouting the competitive exclusion principle, which holds that when two species compete for the same resource, one will be driven to extinction.
The paradox of thrift (or paradox of saving) is a paradox of economics. The paradox states that an increase in autonomous saving leads to a decrease in aggregate demand and thus a decrease in gross output which will in turn lower total saving.
The paradox of toil is the economic hypothesis that, under certain conditions, total employment will shrink if there is an increased desire among the population to take on paid work. According to the macroeconomist Gauti Eggertsson, this occurs when 'the short-term nominal interest rate is zero and there are deflationary pressures and output contraction'.
The paradox of tolerance is a philosophical concept suggesting that if a society extends tolerance to those who are intolerant, it risks enabling the eventual dominance of intolerance, thereby undermining the very principle of tolerance. This paradox was articulated by philosopher Karl Popper in The Open Society and Its Enemies (1945), where he argued that a truly tolerant society must retain the right to deny tolera
The paradox of value, also known as the diamond–water paradox, is the paradox that, although water is on the whole more useful in terms of survival than diamonds, diamonds command a higher price in the market. The philosopher Adam Smith is often considered to be the classic presenter of this paradox, although it had already appeared as early as Plato's Euthydemus.
The paradox of voting, also called Downs' paradox, is that for a rational and egoistic voter (Homo economicus), the costs of voting will normally exceed the expected benefits. Because the chance of exercising the pivotal vote is minuscule compared to any realistic estimate of the private individual benefits of the different possible outcomes, the expected benefits of voting are less than the costs.
The paradoxes of material implication are a group of classically true formulae involving material conditionals whose translations into natural language are intuitively false when the conditional is translated with English words such as 'implies' or 'if ... then ...'.
This article contains a discussion of paradoxes of set theory. As with most mathematical paradoxes, they generally reveal surprising and counter-intuitive mathematical results, rather than actual logical contradictions within modern axiomatic set theory.
Paradoxical laughter is an exaggerated expression of humour which is unwarranted by external events. It may be uncontrollable laughter which may be recognised as inappropriate by the person involved.
In set theory, a paradoxical set is a set that has a paradoxical decomposition. A paradoxical decomposition of a set is two families of disjoint subsets, along with appropriate group actions that act on some universe (of which the set in question is a subset), such that each partition can be mapped back onto the entire set using only finitely many distinct functions (or compositions thereof) to accomplish the mapping
Parrondo's paradox, a paradox in game theory, describes how a combination of losing strategies can become a winning strategy. It is named after its creator, Juan Parrondo, who discovered the paradox in 1996.
A perceptual paradox illustrates the failure of a theoretical prediction. Theories of perception are supposed to help a researcher predict what will be perceived when senses are stimulated.
A performative contradiction (German: performativer Widerspruch) arises when the making of an utterance rests on necessary presuppositions that contradict the proposition asserted in the utterance. The term was coined by Jürgen Habermas and Karl-Otto Apel, who attribute the first elaboration of the concept to Jaakko Hintikka, in his analysis of Descartes' cogito ergo sum argument.
Peto's paradox is the observation that, at the species level, the incidence of cancer does not appear to correlate with the number of cells in an organism. For example, the incidence of cancer in humans is much higher than the incidence of cancer in whales, despite a whale having about 1000 times more cells than a human.
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive of philosophical logic in a broader sense as the study of the scope and nature of logic in general.
In philosophy of mind, a philosophical zombie (or 'p-zombie') is a being in a thought experiment that is physically identical to a normal human being but does not have conscious experience. For example, if a philosophical zombie were poked with a sharp object, it would not feel any pain, but it would react exactly the way any conscious human would.
Philosophy of logic is the branch of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application.
Philosophy of mind is a branch of philosophy that deals with the nature of the mind and its relation to the body and the external world. The mind–body problem is a paradigmatic issue in philosophy of mind, although a number of other issues are addressed, such as the hard problem of consciousness and the nature of particular mental states.
A physical paradox is an apparent contradiction in physical descriptions of the universe. While multiple physical paradoxes have accepted resolutions, others defy resolution and may indicate flaws in theory.
The Pinocchio paradox arises in the hypothetical situation when Pinocchio says 'My nose will grow' and is a version of the liar paradox. The liar paradox is defined in philosophy and logic as the statement 'This sentence is false.' Any attempts to assign a classical binary truth value to this statement lead to a contradiction, or paradox.
In ethics, the plank of Carneades is a thought experiment first proposed by the academic skeptic philosopher Carneades of Cyrene. It explores the concept of self-defense in relation to murder.
In metaphysics, Plato's beard is a paradoxical argument dubbed by Willard Van Orman Quine in his 1948 paper 'On What There Is'. The phrase came to be identified as the philosophy of understanding something based on what does not exist.
Polanyi's paradox, named in honour of the British-Hungarian philosopher Michael Polanyi, is the theory that human knowledge of how the world functions and of our own capability are, to a large extent, beyond our explicit understanding. The theory was articulated by Michael Polanyi in his book The Tacit Dimension in 1966, and economist David Autor gave it a name in his 2014 research paper 'Polanyi's Paradox and the Sh
Vote-ratio, weight-ratio, or population-ratio monotonicity is a property of some apportionment methods. It says that if the entitlement for A {\\displaystyle A} grows at a faster rate than B {\\displaystyle B} (i.e.
Postdiction involves explanation after the fact. In skepticism, it is considered an effect of hindsight bias that explains claimed predictions of significant events such as plane crashes and natural disasters.
The potato paradox is a mathematical calculation that has a result which seems counterintuitive to many people. The Universal Book of Mathematics states the problem as such: Fred brings home 100 kg of potatoes, which (being purely mathematical potatoes) consist of 99% water.
The preface paradox, or the paradox of the preface, was introduced by David Makinson in 1965. Similar to the lottery paradox, it presents an argument according to which it can be rational to accept mutually incompatible beliefs.
The preparedness paradox is the proposition that if a society or individual acts effectively to mitigate a potential disaster such as a pandemic, natural disaster or other catastrophe so that it causes less harm, the avoided danger will be perceived as having been much less serious because of the limited damage actually caused. The paradox is the incorrect perception that there had been no need for careful preparatio
The prevention paradox describes the situation where the majority of cases of a disease come from a population at low or moderate risk of that disease, and only a minority of cases come from the high risk population (of the same disease). This is because the number of people at high risk is small.
The prisoner's dilemma is a game theory thought experiment involving two rational agents, each of whom can either cooperate for mutual benefit or betray their partner ('defect') for individual gain. The dilemma arises from the fact that while defecting is rational for each agent, cooperation yields a higher payoff for each.
Probability concerns events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur.
The problem of evil, also known as the problem of suffering, is the philosophical question of how to reconcile the existence of evil and suffering with an omnipotent, omnibenevolent, and omniscient God. There are currently differing definitions of these concepts.
The productivity paradox refers to the slowdown in productivity growth in the United States in the 1970s and 1980s despite rapid development in the field of information technology (IT) over the same period. The term was coined by Erik Brynjolfsson in a 1993 paper ('The Productivity Paradox of IT') inspired by a quip by Nobel Laureate Robert Solow 'You can see the computer age everywhere but in the productivity statis
In probability theory, Proebsting's paradox is an argument that appears to show that the Kelly criterion can lead to ruin. Although it can be resolved mathematically, it raises some interesting issues about the practical application of Kelly, especially in investing.
In logic, reductio ad absurdum (Latin for 'reduction to absurdity'), also known as argumentum ad absurdum, (Latin for 'argument to absurdity') apagogical argument, or proof by contradiction is the form of argument that attempts to establish a claim by showing that following the logic of a contrary proposition or argument would lead to absurdity or contradiction. Although it is quite freely used in mathematical proofs
Pulsus paradoxus, also paradoxic pulse or paradoxical pulse, is an abnormally large decrease in stroke volume, systolic blood pressure (a drop more than 10 mmHg) and pulse wave amplitude during inspiration. Pulsus paradoxus is not related to pulse rate or heart rate, and it is not a paradoxical rise in systolic pressure.
A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together (or take them apart) in a logical way, in order to find the solution of the puzzle.
Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics. Prior to quantum physics, it was thought that Quantum indeterminacy can be quantitatively characterized by a probability distribution on the set of outcomes of measurements of an observable.
Quantum suicide is a thought experiment in quantum mechanics and the philosophy of physics. Purportedly, it can falsify any interpretation of quantum mechanics other than the many-worlds interpretation by means of a variation of the Schrödinger's cat thought experiment from the cat's point of view.
In quantum mechanics, frequent measurements cause the quantum Zeno effect, a reduction in transitions away from the system's initial state, slowing a system's time evolution. Sometimes this effect is interpreted as 'a system cannot change while you are watching it'.
Quine's paradox is a paradox concerning truth values, stated by Willard Van Orman Quine. It is related to the liar paradox as a problem, and it purports to show that a sentence can be paradoxical even if it is not self-referring and does not use demonstratives or indexicals (i.e.
The raven paradox, also known as Hempel's paradox, Hempel's ravens or, rarely, the paradox of indoor ornithology, is a paradox arising from the question of what constitutes evidence for the truth of a statement. Observing objects that are neither black nor ravens may formally increase the likelihood that all ravens are black even though, intuitively, these observations are unrelated.
In logic, reductio ad absurdum (Latin for 'reduction to absurdity'), also known as argumentum ad absurdum, (Latin for 'argument to absurdity') apagogical argument, or proof by contradiction is the form of argument that attempts to establish a claim by showing that following the logic of a contrary proposition or argument would lead to absurdity or contradiction. Although it is quite freely used in mathematical proofs
Reflexive monism is a philosophical position developed by Max Velmans, in his books Understanding Consciousness (2000, 2009) and Toward a Deeper Understanding of Consciousness (2017), to address the problems of consciousness. It is a modern version of an ancient view that the basic stuff of the universe manifests itself both physically and as conscious experience (a dual-aspect theory in the traditions of Spinoza and
The region-beta paradox is the phenomenon that people can sometimes recover more quickly from more distressing experiences than from less distressing ones. The hypothesized reason is that intense states trigger psychological defense processes that reduce the distress, while less intense states do not trigger the same psychological defense processes and, therefore, less effective attenuation of the stress occurs.
In quantum mechanics, the Renninger negative-result experiment is a thought experiment that illustrates some of the difficulties of understanding the nature of wave function collapse and measurement in quantum mechanics. The statement is that a particle need not be detected in order for a quantum measurement to occur, and that the lack of a particle detection can also constitute a measurement.
The resource curse, also known as the paradox of plenty or the poverty paradox, is the hypothesis that countries with an abundance of natural resources (such as fossil fuels and certain minerals) have lower economic growth, lower rates of democracy, or poorer development outcomes than countries with fewer natural resources. There are many theories and much academic debate about the reasons for and exceptions to the a
In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905. The paradox is ordinarily used to motivate the importance of distinguishing carefully between mathematics and metamathematics.
Roko's basilisk is a thought experiment which states that there could be an artificial superintelligence in the future that, while otherwise benevolent, would punish anyone who knew of its potential existence but did not directly contribute to its advancement or development, in order to incentivize that advancement. It originated in a 2010 post at discussion board LessWrong, a rationalist community web forum.
The Ross–Littlewood paradox (also known as the balls and vase problem or the ping pong ball problem) is a hypothetical problem in abstract mathematics and logic designed to illustrate the paradoxical, or at least non-intuitive, nature of infinity. More specifically, like the Thomson's lamp paradox, the Ross–Littlewood paradox tries to illustrate the conceptual difficulties with the notion of a supertask, in which an
Imperative logic is the field of logic concerned with imperatives. In contrast to declaratives, it is not clear whether imperatives denote propositions or more generally what role truth and falsity play in their semantics.
Wittgenstein on Rules and Private Language is a 1982 book by philosopher of language Saul Kripke in which he contends that the central argument of Ludwig Wittgenstein's Philosophical Investigations centers on a skeptical rule-following paradox that undermines the possibility of our ever following rules in our use of language. Kripke writes that this paradox is 'the most radical and original skeptical problem that phi
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician, Bertrand Russell, in 1901. Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions.
The sad clown paradox is the contradictory association, in performers, between comedy and mental disorders such as depression and anxiety. For those affected, early life is characterised by feelings of deprivation and isolation, where comedy evolves as a release for tension, removing feelings of suppressed physical rage through a verbal outlet.
Quantitative structure–activity relationship (QSAR) models are regression or classification models used in the chemical and biological sciences and engineering. In QSAR regression models relate a set of 'predictor' variables (X) to the potency of the response variable (Y), while classification QSAR models relate the predictor variables to a categorical value of the response variable.
Sayre's paradox is a dilemma encountered in the design of automated handwriting recognition systems. A standard statement of the paradox is that a cursively written word cannot be recognized without being segmented and cannot be segmented without being recognized.
Scenario testing is a software testing activity that uses scenarios: hypothetical stories to help the tester work through a complex problem or test system. The ideal scenario test is a credible, complex, compelling or motivating story; the outcome of which is easy to evaluate.
In quantum mechanics, Schrödinger's cat is a thought experiment concerning quantum superposition. In the thought experiment, a hypothetical cat in a closed box may be considered to be simultaneously both alive and dead while it is unobserved, as a result of its fate being linked to a random subatomic event that may or may not occur.
In quantum mechanics, Schrödinger's cat is a thought experiment concerning quantum superposition. In the thought experiment, a hypothetical cat in a closed box may be considered to be simultaneously both alive and dead while it is unobserved, as a result of its fate being linked to a random subatomic event that may or may not occur.
Science fiction (often shortened to sci-fi or abbreviated SF) is the genre of speculative, science-based fiction that imagines advanced and futuristic scientific or technological progress. The elements of science fiction have evolved over time: from space exploration, extraterrestrial life, time travel, and robotics; to parallel universes, dystopian societies, and biological manipulations; and, most lately, to inform
The Scitovsky paradox is a paradox in welfare economics which is resolved by stating that there is no increase in social welfare by a return to the original part of the losers. It is named after the Hungarian born American economist, Tibor Scitovsky.
The self-absorption paradox describes the contradictory association whereby higher levels of self-awareness are simultaneously associated with higher levels of psychological distress and with psychological well-being. In 1999 Trapnell and Campbell explored the self-absorption paradox in relation to private self-consciousness or attention to internal aspects of the self.
Self-reference is a concept that involves referring to oneself or one's own attributes, characteristics, or actions. It can occur in language, logic, mathematics, philosophy, and other fields.
The service recovery paradox (SRP) is a situation in which a customer thinks more highly of a company after the company has corrected a problem with their service, compared to how they would regard the company if non-faulty service had been provided. The main reason behind this thinking is that successful recovery of a faulty service increases the assurance and confidence from the customer.
In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects: numbers, symbols, points in space, lines, geometric shapes, variables, or other sets. A set may be finite or infinite.
The Sherman paradox was a term used to describe the anomalous pattern of inheritance found in fragile X syndrome. The phenomenon is also referred to as anticipation or dynamic mutation.
The Ship of Theseus, also known as Theseus's Paradox, is a paradox and common thought experiment about whether an object (in the most common stating of the paradox, a ship) is the same object after having all of its original components replaced with others over time. In Greek mythology, Theseus, the mythical king of the city of Athens, rescued the children of Athens from King Minos after slaying the Minotaur and then
Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encountered in social-science and medical-science statistics, and is particularly problematic when frequency data are unduly given causal interpretations.
In mathematical logic and philosophy, Skolem's paradox is the apparent contradiction that a countable model of first-order set theory could contain an uncountable set. The paradox arises from part of the Löwenheim–Skolem theorem; Thoralf Skolem was the first to discuss the seemingly contradictory aspects of the theorem, and to discover the relativity of set-theoretic notions now known as non-absoluteness.
Sleep debt or sleep deficit is the cumulative effect of not getting enough sleep. A large sleep debt may lead to mental or physical fatigue, and can adversely affect one's mood, energy, and ability to think clearly.
The Sleeping Beauty problem, also known as the Sleeping Beauty paradox, is a puzzle in decision theory in which an ideally rational epistemic agent is told she will be awoken from sleep either once or twice according to the toss of a coin. Each time she will have no memory of whether she has been awoken before, and is asked what her degree of belief that 'the outcome of the coin toss is Heads' ought to be when she is
The Sleeping Beauty problem, also known as the Sleeping Beauty paradox, is a puzzle in decision theory in which an ideally rational epistemic agent is told she will be awoken from sleep either once or twice according to the toss of a coin. Each time she will have no memory of whether she has been awoken before, and is asked what her degree of belief that 'the outcome of the coin toss is Heads' ought to be when she is
Solomon's paradox is the observation that people can give reasonable advice to others, but fail to apply this advice to their own situation.
The sorites paradox (), sometimes known as the paradox of the heap, is a paradox that results from vague predicates. A typical formulation involves a heap of sand, from which grains are removed individually.
The St. Petersburg paradox or St.
The stability–instability paradox is an international relations theory first developed by Glenn Snyder regarding the effect of nuclear weapons and mutually assured destruction. It states that when two countries each have nuclear weapons, the probability of a direct war between them greatly decreases, but the probability of minor or indirect conflicts between them increases.
A status paradox can be one of several paradoxes involving 'status', in the meaning of either medical state or social status.
In general relativity, the sticky bead argument is a simple thought experiment designed to show that gravitational radiation is indeed predicted by general relativity and can have physical effects. These claims were not widely accepted prior to about 1955, but after the introduction of the bead argument, any remaining doubts soon disappeared from the research literature.
James Bond Stockdale (December 23, 1923 – July 5, 2005) was a U.S. Navy vice admiral, aviator, and Stoic philosopher who received the Medal of Honor in 1976 for his leadership as a POW for more than seven years during the Vietnam War. Stockdale was the most senior naval officer held captive in Hanoi, North Vietnam.
In the science of fluid flow, Stokes' paradox is the phenomenon that there can be no creeping flow of a fluid around a disk in two dimensions; or, equivalently, the fact there is no non-trivial steady-state solution for the Stokes equations around an infinitely long cylinder. This is opposed to the 3-dimensional case, where Stokes' method provides a solution to the problem of flow around a sphere.
A supertask is a countably infinite sequence of operations that occur sequentially within a finite interval of time. Supertasks are called hypertasks when the number of operations is uncountable.
In relativistic physics, Supplee's paradox (also called the submarine paradox) is a physical paradox that arises when considering the buoyant force exerted on a relativistic bullet (or in a submarine) immersed in a fluid subject to an ambient gravitational field. If a bullet has neutral buoyancy when it is at rest in a perfect fluid and then it is launched with a relativistic speed, observers at rest within the fluid
A tachyonic antitelephone is a hypothetical device in theoretical physics that could be used to send signals into one's own past. Albert Einstein in 1907 presented a thought experiment of how faster-than-light signals can lead to a paradox of causality, which was described by Einstein and Arnold Sommerfeld in 1910 as a means 'to telegraph into the past'.
The Taeuber Paradox is a paradox in demography, which results from two seemingly contradictory expectations given a population-wide decrease in mortality, e.g. from curing or reducing the mortality of a disease in a population.
Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that 'arithmetical truth cannot be defined in arithmetic'.
The term boundary paradox refers to the conflict between traditional, rank-based classification of life and evolutionary thinking. In the hierarchy of ranked categories it is implicitly assumed that the morphological gap is growing along with increasing ranks: two species from the same genus are more similar than other two species from different genera in the same family, these latter two species are more similar tha
In fluid dynamics, the tea leaf paradox is a phenomenon where tea leaves in a cup of tea migrate to the center and bottom of the cup after being stirred rather than being forced to the edges of the cup, as would be expected in a spiral centrifuge. The correct physical explanation of the paradox was for the first time given by James Thomson in 1857.
The Temperature paradox or Partee's paradox is a classic puzzle in formal semantics and philosophical logic. Formulated by Barbara Partee in the 1970s, it consists of the following argument, which speakers of English judge as wildly invalid.
A temporal paradox, time paradox, or time travel paradox, is an apparent or actual contradiction associated with the idea of time travel or other foreknowledge of the future. Temporal paradoxes arise from circumstances involving hypothetical time travel to the past.
John Alan Feduccia (born April 25, 1943) is a paleornithologist specializing in the origins and phylogeny of birds. He is S. K. Heninger Distinguished Professor Emeritus at the University of North Carolina.
The Antitrust Paradox is an influential 1978 book by Robert Bork that criticized the state of United States antitrust law in the 1970s. A second edition, updated to reflect substantial changes in the law, was published in 1993.
The beer question is a thought experiment in politics that attempts to measure authenticity and likability in politicians by asking or polling voters about which politicians they would prefer to drink beer with, as in, spending casual time 'hanging out' with. The question has been discussed as far back as the 2000 United States presidential election, as well as in the context of fictional political works such as The
The Green Paradox is a controversial book by German economist, Hans-Werner Sinn, describing the observation that an environmental policy that becomes greener with the passage of time acts like an announced expropriation for the owners of fossil fuel resources, inducing them to accelerate resource extraction and hence to accelerate global warming.
The Lady, or the Tiger?' is a much-anthologized short story written by Frank R. Stockton for publication in the November issue of The Century Magazine in 1882. 'The Lady, or the Tiger?' has entered the English language as an allegorical expression, a shorthand indication or signifier, for a problem that is unsolvable.
In physics, the monkey and hunter is a hypothetical scenario often used to illustrate the effect of gravity on projectile motion. It can be presented as exercise problem or as a demonstration.
Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea (c. 490–430 BC), primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia.
In economics, the paradox of banknotes or cash paradox is the observation that while the share of cash transactions has fallen over the past few decades due to alternative forms of payment such as credit cards and other electronic payment instruments, the demand for physical currency, measured as the ratio of currency in circulation (CIC) to GDP, has been steadily increasing since the early 2000s. This phenomenon con
The Paradox of Choice – Why More Is Less is a book about overchoice written by American psychologist Barry Schwartz and first published in 2004 by Harper Perennial. In the book, Schwartz argues that eliminating consumer choices can greatly reduce anxiety for shoppers.
The survival lottery is a thought experiment, proposed by the philosopher John Harris. The basis of the idea is to ask people to imagine if organ donation were expected to save more individuals than it would kill.
Thomson's lamp is a philosophical thought experiment based on infinites. It was devised in 1954 by British philosopher James F. Thomson, who used it to analyze the possibility of a supertask, which is the completion of an infinite number of tasks.
The three prisoners problem appeared in Martin Gardner's 'Mathematical Games' column in Scientific American in 1959. It is mathematically equivalent to the Monty Hall problem with the car and goat replaced respectively with freedom and execution.
In economics, the throw away paradox is a situation in which a person can gain by throwing away some of his property. It was first described by Robert J. Aumann and B. Peleg as a note on a similar paradox by David Gale.
The ticking time bomb scenario is a thought experiment that has been used in the ethics debate over whether interrogational torture can ever be justified. The scenario can be formulated as follows: Suppose that a person with knowledge of an imminent terrorist attack that will kill many people is in the hands of the authorities, and he will disclose the information needed to prevent the attack only if he is tortured.
Time travel is the hypothetical activity of traveling into the past or future. Time travel is a concept in philosophy, space, time and fiction, particularly science fiction.
A Gabriel's horn (also called Torricelli's trumpet) is a type of geometric figure that has infinite surface area but finite volume. The name refers to the Christian idea that the archangel Gabriel will one day blow his horn to announce Judgment Day.
The transparent eyeball is a philosophical metaphor originated by American transcendentalist philosopher Ralph Waldo Emerson. In his essay Nature, the metaphor stands for a view of life that is absorbent rather than reflective, and therefore takes in all that nature has to offer without bias or contradiction.
The tritone paradox is an auditory illusion in which a sequentially played pair of Shepard tones separated by an interval of a tritone, or half octave, is heard as ascending by some people and as descending by others. Different populations tend to favor one of a limited set of different spots around the chromatic circle as central to the set of 'higher' tones.
The trolley problem is a series of thought experiments in ethics, psychology and artificial intelligence involving stylized ethical dilemmas in a scenario of whether to sacrifice one person to save a larger number. The series usually begins with a scenario in which a runaway trolley (tram) or train is on course to collide with and kill a number of people (traditionally five) down the railway track, but a driver or by
Rent-seeking is the act of growing one's existing wealth by manipulating public policy or economic conditions without creating new wealth. Rent-seeking activities have negative effects on the rest of society.
Twin Earth is a thought experiment proposed by philosopher Hilary Putnam in his papers 'Meaning and Reference' (1973) and 'The Meaning of 'Meaning'' (1975). It is meant to serve as an illustration of his argument for semantic externalism, or the view that the meanings of words are not purely psychological.
In physics, the twin paradox is a thought experiment in special relativity involving twins, one of whom takes a space voyage at relativistic speeds and returns home to find that the twin who remained on Earth has aged more. This result appears puzzling because each twin sees the other twin as moving, and so, as a consequence of an incorrect and naive application of time dilation and the principle of relativity, each
The two capacitor paradox or capacitor paradox is a paradox, or counterintuitive thought experiment, in electric circuit theory. The thought experiment is usually described as follows: Two identical capacitors are connected in parallel with an open switch between them.
In computing, the Two Generals' Problem (or Chinese Generals Problem) is a thought experiment meant to illustrate the pitfalls and design challenges of attempting to coordinate an action by communicating over an unreliable link. In the experiment, two generals are only able to communicate with one another by sending a messenger through enemy territory.
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.
The tzimtzum or tsimtsum (Hebrew: צִמְצוּם, romanized: ṣimṣum, lit. 'contraction, constriction, condensation') is a term used in Lurianic Kabbalah to explain Isaac Luria's doctrine that God began the process of creation by limiting the Ohr Ein Sof (infinite light) of the Godhead in order to allow for a conceptual space in which the Four Worlds, or finite realms, could exist. This primordial initial contraction, formi
In mathematics, an uncountable set, informally, is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related to its cardinal number: a set is uncountable if its cardinal number is larger than aleph-null, the cardinality of the natural numbers.
The unexpected hanging paradox or surprise test paradox is a paradox about a person's expectations about the timing of a future event which they are told will occur at an unexpected time. The paradox is variously applied to a prisoner's hanging or a surprise school test.
Upstream contamination by floating particles is a counterintuitive phenomenon in fluid dynamics. When pouring water from a higher container to a lower one, particles floating in the latter can climb upstream into the upper container.
The utility monster is a thought experiment in the study of ethics created by philosopher Robert Nozick in 1974 as a criticism of utilitarianism.
In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion.
In philosophy, the original position is a hypothetical position from which members of society would consider which principles they would select for the basic structure of their society if they had no knowledge ahead of time regarding the position which they would end up occupying in that society. The idea of having no such knowledge, because everyone is behind a veil of ignorance, represents a thought experiment ofte
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 or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.
A Defense of Abortion' is a moral philosophy essay by Judith Jarvis Thomson first published in Philosophy & Public Affairs in 1971. Granting for the sake of argument that the fetus has a right to life, Thomson uses thought experiments to argue that the right to life does not include, entail, or imply the right to use someone else's body to survive and that induced abortion is therefore morally permissible.
In mathematics, the von Neumann paradox, named after John von Neumann, is the idea that one can break a planar figure such as the unit square into sets of points and subject each set to an area-preserving affine transformation such that the result is two planar figures of the same size as the original. This was proved in 1929 by John von Neumann, assuming the axiom of choice.
In social choice theory, Condorcet's voting paradox (also called Condorcet's paradox or the Condorcet paradox) is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory. The result implies that it is logically impossible for any voting system to guarantee that a winner will have support from a majority of voters; for example, there can be rock-paper-scissors scenarios
Washburn's paradox, Washburn's fallacy or the genetic similarity fallacy is a statement about the genetic relatedness of individuals that is relevant in Hamilton's rule. It is named for American anthropologist Sherwood Washburn, who discussed the issue in his critique of sociobiology and kin selection.
What the Tortoise Said to Achilles', written by Lewis Carroll in 1895 for the philosophical journal Mind, is a brief allegorical dialogue on the foundations of logic. The title alludes to one of Zeno's paradoxes of motion, in which Achilles could never overtake the tortoise in a race.
Wheeler's delayed-choice experiment describes a family of thought experiments in quantum physics proposed by John Archibald Wheeler, with the most prominent among them appearing in 1978 and 1984. These experiments illustrate the central point of quantum theory: 'It is wrong to attribute a tangibility to the photon in all its travel from the point of entry to its last instant of flight.' These experiments close a loop
Wigner's friend is a thought experiment in theoretical quantum physics, first published by the Hungarian-American physicist Eugene Wigner in 1961, and further developed by David Deutsch in 1985. The scenario involves an indirect observation of a quantum measurement: An observer W {\\displaystyle W} observes another observer F {\\displaystyle F} who performs a quantum measurement on a physical system.
The Will Rogers phenomenon, also rarely called the Okie paradox, is when moving an observation from one group to another increases the average of both groups. It is named after a joke attributed to the comedian Will Rogers about Dust Bowl migration during the Great Depression: When the Okies left Oklahoma and moved to California, they raised the average intelligence level in both states.
The willpower paradox is the idea that people may do things better by focusing less directly on doing them, implying that the direct exertion of volition may not always be the most powerful way to accomplish a goal. Research suggests that intrapersonal communication (talking to oneself) and maintaining a questioning mind are more likely to bring change.
Wittgenstein on Rules and Private Language is a 1982 book by philosopher of language Saul Kripke in which he contends that the central argument of Ludwig Wittgenstein's Philosophical Investigations centers on a skeptical rule-following paradox that undermines the possibility of our ever following rules in our use of language. Kripke writes that this paradox is 'the most radical and original skeptical problem that phi
Wollheim's paradox is a problem in political philosophy that points to an inherent contradiction in the concept of democracy. The paradox highlights the fact that a person can simultaneously advocate two conflicting policy options A and B, provided that the person believes that democratic decisions should be followed.
Stephen Yablo (; born 1957) is a Canadian-born American philosopher. He is the Emeritus David W. Skinner Professor of Philosophy at the Massachusetts Institute of Technology (MIT) and taught previously at the University of Michigan, Ann Arbor.
Simpson's paradox is a phenomenon in probability and statistics in which a trend appears in several groups of data but disappears or reverses when the groups are combined. This result is often encountered in social-science and medical-science statistics, and is particularly problematic when frequency data are unduly given causal interpretations.
Zeno of Elea (; Ancient Greek: Ζήνων ὁ Ἐλεᾱ́της; c. 490 – c. 430 BC) was a pre-Socratic Greek philosopher from Elea, in Southern Italy (Magna Graecia). He was a student of Parmenides and one of the Eleatics.
Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea (c. 490–430 BC), primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia.
Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea (c. 490–430 BC), primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia.