This is a list of paradoxes, grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. This list collects only scenarios that have been called a paradox by at least one source and have their own article. Although considered paradoxes, some of these are simply based on fallacious reasoning (falsidical), or an unintuitive solution (veridical). Informally, the term paradox is often used to describe a counter-intuitive result.
However, some of these paradoxes qualify to fit into the mainstream perception of a paradox, which is a self-contradictory result gained even while properly applying accepted ways of reasoning. These paradoxes, often called antinomy, point out genuine problems in our understanding of the ideas of truth and description.
Barbershop paradox: The supposition that if one of two simultaneous assumptions leads to a contradiction, the other assumption is also disproved leads to paradoxical consequences. Not to be confused with the Barber paradox.
Catch-22: A situation in which someone is in need of something that can only be had by not being in need of it. A soldier who wants to be declared insane in order to avoid combat is deemed not insane for that very reason, and will therefore not be declared insane.
Drinker paradox: In any pub there is a customer of whom it is true to say: if that customer drinks, everybody in the pub drinks.
Lottery paradox: If there is one winning ticket in a large lottery, it is reasonable to believe of any particular lottery ticket that it is not the winning ticket, but it is not reasonable to believe that no lottery ticket will win.
Raven paradox: (or Hempel's Ravens): Observing a green apple increases the likelihood of all ravens being black.
Ross' paradox: Disjunction introduction poses a problem for imperative inference by seemingly permitting arbitrary imperatives to be inferred.
These paradoxes have in common a contradiction arising from either self-reference or circular reference, in which several statements refer to each other in a way that following some of the references leads back to the starting point.
Bhartrhari's paradox: The thesis that there are some things which are unnameable conflicts with the notion that something is named by calling it unnameable.
Berry paradox: The phrase "the first number not nameable in under ten words" appears to name it in nine words.
Crocodile dilemma: If a crocodile steals a child and promises its return if the father can correctly guess exactly what the crocodile will do, how should the crocodile respond in the case that the father guesses that the child will not be returned?
Paradox of the Court: A law student agrees to pay his teacher after (and only after) winning his first case. The teacher then sues the student (who has not yet won a case) for payment.
Liar paradox: "This sentence is false." This is the canonical self-referential paradox. Also "Is the answer to this question 'no'?", and "I'm lying."
Card paradox: "The next statement is true. The previous statement is false." A variant of the liar paradox in which neither of the sentences employs (direct) self-reference, instead this is a case of circular reference.
No-no paradox: Two sentences, each saying of the other it is not true.
Quine's paradox: "'Yields a falsehood when appended to its own quotation' yields a falsehood when appended to its own quotation." Shows that a sentence can be paradoxical even if it is not self-referring and does not use demonstratives or indexicals.
Yablo's paradox: An ordered infinite sequence of sentences, each of which says that all following sentences are false. While constructed to avoid self-reference, there is no consensus whether it relies on self-reference or not.
Opposite Day: "It is opposite day today." Therefore, it is not opposite day, but if you say it is a normal day it would be considered a normal day, which contradicts the fact that it has previously been stated that it is an opposite day.
Richard's paradox: We appear to be able to use simple English to define a decimal expansion in a way that is self-contradictory.
Russell's paradox: Does the set of all those sets that do not contain themselves contain itself?
Ship of Theseus: It seems like you can replace any component of a ship, and it is still the same ship. So you can replace them all, one at a time, and it is still the same ship. However, you can then take all the original pieces, and assemble them into a ship. That, too, is the same ship you began with.
Sorites paradox (also known as the paradox of the heap): If you remove a single grain of sand from a heap, you still have a heap. Keep removing single grains, and the heap will disappear. Can a single grain of sand make the difference between heap and non-heap?
Lindley's paradox: Tiny errors in the null hypothesis are magnified when large data sets are analyzed, leading to false but highly statistically significant results.
Low birth weight paradox: Low birth weight and mothers who smoke contribute to a higher mortality rate. Babies of smokers have lower average birth weight, but low birth weight babies born to smokers have a lower mortality rate than other low birth weight babies. This is a special case of Simpson's paradox.
Simpson's paradox, or the Yule–Simpson effect: A trend that appears in different groups of data disappears when these groups are combined, and the reverse trend appears for the aggregate data.
Will Rogers phenomenon: The mathematical concept of an average, whether defined as the mean or median, leads to apparently paradoxical results—for example, it is possible that moving an entry from an encyclopedia to a dictionary would increase the average entry length on both books.
Bertrand's paradox: Different common-sense definitions of randomness give quite different results.
Birthday problem: What is the chance that two people in a room have the same birthday?
Borel's paradox: Conditional probability density functions are not invariant under coordinate transformations.
Boy or Girl paradox: A two-child family has at least one boy. What is the probability that it has a girl?
Dartboard Puzzle: If a dart is guaranteed to hit a dartboard and the probability of hitting a specific point is positive, adding the infinitely many positive chances yields infinity, but the chance of hitting the dartboard is one. If the probability of hitting each point is zero, the probability of hitting anywhere on the dartboard is zero.
False positive paradox: A test that is accurate the vast majority of the time could show you have a disease, but the probability that you actually have it could still be tiny.
Grice's paradox: Shows that the exact meaning of statements involving conditionals and probabilities is more complicated than may be obvious on casual examination.
Two-envelope paradox: You are given two indistinguishable envelopes, each of which contains a positive sum of money. One envelope contains twice as much as the other. You may pick one envelope and keep whatever amount it contains. You pick one envelope at random but before you open it you are given the chance to take the other envelope instead.
Cantor's paradox: The set of all sets would have its own power set as a subset, therefore its cardinality would be at least as great as that of its power set. But Cantor's theorem proves that power sets are strictly greater than the sets they are constructed from. Consequently, the set of all sets would contain a subset greater than itself.
Coin rotation paradox: a coin rotating along the edge of an identical coin will make a full revolution after traversing only half of the stationary coin's circumference.
Gabriel's Horn: or Torricelli's trumpet: A simple object with finite volume but infinite surface area. Also, the Mandelbrot set and various other fractals are covered by a finite area, but have an infinite perimeter (in fact, there are no two distinct points on the boundary of the Mandelbrot set that can be reached from one another by moving a finite distance along that boundary, which also implies that in a sense you go no further if you walk "the wrong way" around the set to reach a nearby point). This can be represented by a Klein bottle.
Hausdorff paradox: There exists a countable subset C of the sphere S such that S\C is equidecomposable with two copies of itself.
Nikodym set: A set contained in and with the same Lebesgue measure as the unit square, yet for every one of its points there is a straight line intersecting the Nikodym set only in that point.
Abilene paradox: People can make decisions based not on what they actually want to do, but on what they think that other people want to do, with the result that everybody decides to do something that nobody really wants to do, but only what they thought that everybody else wanted to do.
Apportionment paradox: Some systems of apportioning representation can have unintuitive results due to rounding
Alabama paradox: Increasing the total number of seats might shrink one block's seats.
New states paradox: Adding a new state or voting block might increase the number of votes of another.
Cool tropics paradox: A contradiction between modelled estimates of tropical temperatures during warm, ice-free periods of the Cretaceous and Eocene, and the lower temperatures that proxies suggest were present.
Algol paradox: In some binaries the partners seem to have different ages, even though they are thought to have formed at the same time.
Faint young Sun paradox: The contradiction between existence of liquid water early in the Earth's history and the expectation that the output of the young Sun would have been insufficient to melt ice on Earth.
Achilles and the tortoise: If the tortoise is ahead of Achilles, by the time Achilles reaches the tortoise's current position, the tortoise will have moved a bit further ahead, which goes on indefinitely.
Archer's paradox: An archer must, in order to hit his target, not aim directly at it, but slightly to the side. Not to be confused with the arrow paradox.
Arrow paradox If we divide time into discrete 0-duration slices, no motion is happening in each of them, so taking them all as a whole, motion is impossible.
Knudsen paradox: Based on the Navier–Stokes equations, one would expect the mass flux in a channel to decrease with increasing Knudsen number, but there is a distinct minimum around Knudsen number 0.8.
Bentley's paradox: In a Newtonian universe, gravitation should pull all matter into a single point.
Boltzmann brain: If the universe we observe resulted from a random thermodynamic fluctuation, it would be vastly more likely to be a simple one than the complex one we observe. The simplest case would be just a brain floating in vacuum, having the thoughts and sensations you have.
Fermi paradox: If there are, as various arguments suggest, many other sentient species in the Universe, then where are they? Shouldn't their presence be obvious?
Heat death paradox: If the universe was infinitely old, it would be in thermodynamical equilibrium, which contradicts what we observe.
Olbers' paradox: Why is the night sky dark if there is an infinity of stars, covering every part of the celestial sphere?
Extinction paradox: 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).
Hardy's paradox: How can we make inferences about past events that we haven't observed while at the same time acknowledge that the act of observing it affects the reality we are inferring to?
Klein paradox: When the potential of a potential barrier becomes similar to the mass of the impinging particle, it becomes transparent.
Mott problem: Spherically symmetric wave functions, when observed, produce linear particle tracks.
Schrödinger's cat paradox: According to the Copenhagen interpretation of quantum mechanics, a cat could be simultaneously alive and dead, as long as it remains unobserved.
Uncertainty principle: There is a fundamental limit to the precision with which certain pairs of physical properties of a particle, known as complementary variables, such as position and momentum can be known. This is often confused with a similar effect in physics called the observer effect
French paradox: The observation that the French suffer a relatively low incidence of coronary heart disease, despite having a diet relatively rich in saturated fats, which are assumed to be the leading dietary cause of such disease.
Glucose paradox: The large amount of glycogen in the liver cannot be explained by its small glucose absorption.
Hispanic paradox: The finding that Hispanics in the United States tend to have substantially better health than the average population in spite of what their aggregate socio-economic indicators predict.
Israeli paradox: The observation that Israelis suffer a relatively high incidence of coronary heart disease, despite having a diet very low in saturated fats, which are assumed to be the leading dietary cause of such disease.
Meditation paradox: The amplitude of heart rate oscillations during meditation was significantly greater than in the pre-meditation control state and also in three non-meditation control groups
Mexican paradox: Mexican children tend to have higher birth weights than can be expected from their socio-economic status.
Obesity survival paradox: Although the negative health consequences of obesity in the general population are well supported by the available evidence, health outcomes in certain subgroups seem to be improved at an increased BMI.
Peto's paradox: Humans and other small-to-medium-sized mammals get cancer with high frequency, while larger mammals, like whales, do not. If cancer is essentially a negative outcome lottery at the cell level, and larger organisms have more cells, and thus more potentially cancerous cell divisions, one would expect larger organisms to be more predisposed to cancer.
Second wind: The "second wind" is a sudden period of increased wakefulness in individuals deprived of sleep that tends to coincide with the individual's circadian rhythm. Although the individual is more wakeful and aware of their surroundings, they are continuing to accrue sleep debt and thus, are actually exacerbating their sleep deprivation.
Bootstrap paradox, (also ontological paradox) Can a time traveler send himself information with no outside source?
Polchinski's paradox: A billiard ball can be thrown into a wormhole in such a way that it would emerge in the past and knock its incoming past self away from the wormhole entrance, creating a variant of the grandfather paradox.
Predestination paradox: A man travels back in time to discover the cause of a famous fire. While in the building where the fire started, he accidentally knocks over a kerosene lantern and causes a fire, the same fire that would inspire him, years later, to travel back in time. The bootstrap paradox is closely tied to this, in which, as a result of time travel, information or objects appear to have no beginning.
Grandfather paradox: You travel back in time and kill your grandfather before he conceives one of your parents, which precludes your own conception and, therefore, you couldn't go back in time and kill your grandfather.
Hitler's murder paradox: You travel back in time and kill a famous person in history before they become famous; but if the person had never been famous, then he could not have been targeted as a famous person.
Maya (illusion): Our illusions are not real, yet it's real that illusion itself exists.
Tzimtzum: In Kabbalah, how to reconcile self-awareness of finite Creation with Infinite Divine source, as an emanated causal chain would seemingly nullify existence. Luria's initial withdrawal of God in Hasidic panentheism involves simultaneous illusionism of Creation (Upper Unity) and self-aware existence (Lower Unity), God encompassing logical opposites.
One class of paradoxes in economics are the paradoxes of competition, in which behavior that benefits a lone actor would leave everyone worse off if everyone did the same. These paradoxes are classified into circuit, classical and Marx paradoxes.
Allais paradox: A change in a possible outcome that is shared by different alternatives affects people's choices among those alternatives, in contradiction with expected utility theory.
Louboutin paradox: Paradox of luxury goods. The more expensive some commodity is, less it is used after acquiring. 
Lucas paradox: Capital is not flowing from developed countries to developing countries despite the fact that developing countries have lower levels of capital per worker, and therefore higher returns to capital.
Mayfield's paradox: Keeping everyone out of an information system is impossible, but so is getting everybody in.
Metzler paradox: The imposition of a tariff on imports may reduce the relative internal price of that good.
Paradox of prosperity: Why do generations that significantly improve the economic climate seem to generally rear a successor generation that consumes rather than produces?
Paradox of thrift: If everyone saves more money during times of recession, then aggregate demand will fall and will in turn lower total savings in the population.
Paradox of toil: If everyone tries to work during times of recession, lower wages will reduce prices, leading to more deflationary expectations, leading to further thrift, reducing demand and thereby reducing employment.
Paradox of value, also known as diamond-water paradox: Water is more useful than diamonds, yet is a lot cheaper.
Productivity paradox: (also known as Solow computer paradox): Worker productivity may go down, despite technological improvements.
Paradox of Plenty: The Paradox of Plenty (resource curse) refers to the paradox that countries and regions with an abundance of natural resources, specifically point-source non-renewable resources like minerals and fuels, tend to have less economic growth and worse development outcomes than countries with fewer natural resources.
Stability–instability paradox: 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.
Wollheim's paradox: A person can simultaneously advocate two conflicting policy options, A and B, provided that the person believes that democratic decisions should be followed.
Ironic process theory: Ironic processing is the psychological process whereby an individual's deliberate attempts to suppress or avoid certain thoughts (thought suppression) renders those thoughts more persistent.
Meat paradox: People care about animals, but embrace diets that involve harming them.
Moral paradox: A situation in which moral imperatives clash without clear resolution.
Outcomes paradox: Schizophrenia patients in developing countries seem to fare better than their Western counterparts.
Paradox of suspense: Sometimes, retelling of familiar stories appears to still induce suspense, despite the fact that the audience already knows how the story will unfold.
Region-beta paradox: People can sometimes recover more quickly from more intense emotions or pain than from less distressing experiences.
Self-absorption paradox: The contradictory association whereby higher levels of self-awareness are simultaneously associated with higher levels of psychological distress and with psychological well-being.
Status paradox: Several paradoxes involve the concept of medical or social status.
Stockdale paradox: "You must never confuse faith that you will prevail in the end—which you can never afford to lose—with the discipline to confront the most brutal facts of your current reality, whatever they might be."
The Paradox of Anti-Semitism: A book arguing that the lack of external persecutions and antagonisms results in the dissolution of Jewish identity, a theory that resonates in works of Dershowitz and Sartre.
Bonini's paradox: Models or simulations that explain the workings of complex systems are seemingly impossible to construct. As a model of a complex system becomes more complete, it becomes less understandable, for it to be more understandable it must be less complete and therefore less accurate. When the model becomes accurate, it is just as difficult to understand as the real-world processes it represents.
^Trapnell, P. D., & Campbell, J. D. (1999). "Private self-consciousness and the Five-Factor Model of Personality: Distinguishing rumination from reflection". Journal of Personality and Social Psychology, 76, 284–304.
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