Paradox: List of Paradoxes
What is a Paradox
A paradox is a statement or proposition that, despite sound reasoning from acceptable premises, leads to a conclusion that seems senseless, logically unacceptable, or self-contradictory. The logician Willard V. O. Quine distinguishes between two types of paradoxes the first being falsidical paradoxes, which are seemingly valid, logical demonstrations of absurdities, from veridical paradoxes, such as the birthday paradox, which are seeming absurdities that are nevertheless true because they are perfectly logical. The word paradox is often used interchangeably with contradiction. Below is a list of paradoxes that cover categories such as decision theory paradoxes, economic paradoxes, logic paradoxes, math paradoxes, philosophy paradoxes, physics paradoxes, economics paradoxes, and time paradoxes.
List of Paradoxes
What is the 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.
What is the Accuracy paradox: Predictive models with a given level of accuracy may have greater predictive power than models with higher accuracy.
What is the Alabama paradox: Increasing the total number of seats might shrink one block’s seats.
What is the Algol paradox: In some binaries the partners seem to have different ages, even though they’re thought to have formed at the same time.
What is the 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.
What is the Apportionment paradox: Some systems of apportioning representation can have unintuitive results due to rounding.
What is the Archer’s paradox: An archer must, in order to hit his target, not aim directly at it, but slightly to the side.
What is the Archimedes paradox: A massive battleship can float in a few litres of water.
What is the Aristotle’s wheel paradox: Rolling joined concentrical wheels seem to trace the same difference with their circumferences, even though the circumferences are different.
What is the Arrow information paradox: To sell information you need to give it away before the sale.
What is the Arrow’s paradox: Given more than two choices, no system can have all the attributes of an ideal voting system at once.
What is the Banach–Tarski paradox: Cut a ball into 5 pieces, re-assemble the pieces to get two balls, both of equal size to the first. The von Neumann paradox is a two-dimensional analogue.
What is the Barber paradox: An adult male barber shaves all men who do not shave themselves, and no one else. Can he shave himself?
What is the 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.
What is the Bell’s spaceship paradox: Concerning relativity.
What is the Bell’s theorem: Why do measured quantum particles not satisfy mathematical probability theory?
What is the Benford’s law: In lists of numbers from many real-life sources of data, the leading digit 1 occurs much more often than the others.
What is the Bentley’s paradox: In a Newtonian universe, gravitation should pull all matter into a single point.
What is the Berkson’s paradox: A complicating factor arising in statistical tests of proportions.
What is the Berry paradox: The phrase “the first number not nameable in under eleven words” appears to name it in nine words.
What is the Bertrand paradox: Two players reaching a state of Nash equilibrium both find themselves with no profits.
What is the Bertrand’s box paradox: A paradox of conditional probability closely related to the Boy or Girl paradox.
What is the Bertrand’s paradox: Different common-sense definitions of randomness give quite different results.
What is the Birthday paradox: What is the chance that two people in a room have the same birthday?
What is the Black hole information paradox: Black holes violate a commonly assumed tenet of science — that information cannot be destroyed.
What is the 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.
What is the Borel’s paradox: Conditional probability density functions are not invariant under coordinate transformations.
What is the Boy or Girl: A two-child family has at least one boy. What is the probability that it has a girl?
What is the Braess’s paradox: Adding extra capacity to a network can reduce overall performance.
What is the Burali-Forti paradox: If the ordinal numbers formed a set, it would be an ordinal number that is smaller than itself.
What is the Buridan’s ass: How can a rational choice be made between two outcomes of equal value?
What is the Cantor’s paradox: There is no greatest cardinal number.
What is the Card paradox: The next statement is true. The previous statement is false. A variant of the liar paradox that does not use self-reference.
What is the Carroll’s paradox: The angular momentum of a stick should be zero, but is not.
What is the Catch-22 (logic): In need of something which can only be had by not being in need of it.
What is the Chainstore paradox: Even those who know better play the so-called chain store game in an irrational manner
What is the Chicken or the egg: Which came first, the chicken or the egg?
What is the Coastline paradox: The perimeter of a landmass is in general ill-defined.
What is the Code-talker paradox: How can a language both enable communication and block communication?
What is the Cool tropics paradox: A contradiction between modelled estimates of tropical temperatures during warm, ice-free periods of the Cretaceous and Eocene, and the colder temperatures which proxies suggested were present.
What is the Cramer’s paradox: The number of points of intersection of two higher-order curves can be greater than the number of arbitrary points needed to define one such curve.
What is the Crocodile Dilemma: If a crocodile steals a child and promises its return if the father can correctly guess what the crocodile will do, how should the crocodile respond in the case that the father guesses that the child will not be returned?
What is the Curry’s paradox: If this sentence is true, then Santa Claus exists.
What is the D’Alembert’s paradox: An inviscid liquid produces no drag.
What is the Demographic-economic paradox: Nations or subpopulations with higher GDP per capita are observed to have fewer children, even though a richer population can support more children.
What is the Denny’s paradox: Surface-dwelling arthropods (such as the water strider) should not be able to propel themselves horizontally.
What is the Diamond-water paradox(or paradox of value): Water is more useful than diamonds, yet is a lot cheaper.
What is the Downs-Thomson paradox: Increasing road capacity at the expense of investments in public transport can make overall congestion on the road worse.
What is the Drinker paradox: In any pub there is a customer such that, if he or she drinks, everybody in the pub drinks.
What is the Easterlin paradox: For countries with income sufficient to meet basic needs, the reported level of happiness does not correlate with national income per person.
What is the Edgeworth paradox: With capacity constraints, there may not be an equilibrium.
What is the Ehrenfest paradox: On the kinematics of a rigid, rotating disk.
What is the Einstein-Podolsky-Rosen paradox: Can far away events influence each other in quantum mechanics?
What is the Elevator paradox: Elevators can seem to be mostly going in one direction, as if they were being manufactured in the middle of the building and being disassembled on the roof and basement.
What is the Ellsberg paradox: People exhibit ambiguity aversion (as distinct from risk aversion), in contradiction with expected utility theory.
What is the Epimenides paradox: A Cretan says: “All Cretans are liars”.
What is the European paradox: The perceived failure of European countries to translate scientific advances into marketable innovations.
What is the Exception paradox: If there is an exception to every rule, then every rule must have at least one exception; the exception to this one being that it has no exception. “There’s always an exception to the rule, except to the exception of the rule — which is, in of itself, an accepted exception of the rule.”
What is the Faint young Sun paradox: The apparent contradiction between observations of liquid water early in the Earth’s history and the astrophysical expectation that the output of the young sun would have been insufficient to melt ice on earth.
What is the 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.
What is the Faraday paradox: An apparent violation of Faraday’s law of electromagnetic induction.
What is the Faraday paradox (electrochemistry): Dilute nitric acid will corrode steel, while concentrated nitric acid doesn’t.
What is the Fenno’s paradox: The belief that people generally disapprove of the United States Congress as a whole, but support the Congressman from their own Congressional district.
What is the Fermi paradox: If there are, as probability would suggest, many other sentient species in the Universe, then where are they? Shouldn’t their presence be obvious?
What is the Feynman sprinkler: Which way will a sprinkler rotate when it is submerged in a tank and made to suck in the surrounding fluid?
What is the Fitch’s paradox: If all truths are knowable, then all truths must in fact be known.
What is the Freedman’s paradox: It describes a problem in model selection where predictor variables with no explanatory power can appear artificially important.
What is the 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.
What is the Friendship paradox: For almost everyone, their friends have more friends than they do.
What is the 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 shape, 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.
What is the Galileo’s paradox: Though most numbers are not squares, there are no more numbers than squares.
What is the Gibbs paradox: In an ideal gas, is entropy an extensive variable?
What is the Gibson’s paradox: Why were interest rates and prices correlated?
What is the Giffen paradox: Increasing the price of bread makes poor people eat more of it.
What is the Glucose paradox: The large amount of glycogen in the liver cannot be explained by its small glucose absorption.
What is the 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.
What is the Gray’s Paradox: Despite their relatively small muscle mass, dolphins can swim at high speeds and obtain large accelerations.
What is the Green paradox: Policies intending to reduce future CO2 emissions may lead to increased emissions in the present.
What is the Grelling–Nelson paradox: Is the word “heterological”, meaning “not applicable to itself,” a heterological word? (Another close relative of Russell’s paradox.)
What is the GZK paradox: High-energy cosmic rays have been observed that seem to violate the Greisen-Zatsepin-Kuzmin limit, which is a consequence of special relativity.
What is the 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?
What is the Hausdorff paradox: There exists a countable subset C of the sphere S such that SC is equidecomposable with two copies of itself.
What is the Heat death paradox: Since the universe is not infinitely old it can not be infinite in extent.
What is the Hilbert’s paradox of the Grand Hotel: If a hotel with infinitely many rooms is full, it can still take in more guests.
What is the Hispanic Paradox: The finding that Hispanics in the U.S. tend to have substantially better health than the average population in spite of what their aggregate socio-economic indicators predict.
What is the Horse paradox: All horses are the same color.
What is the Hutton’s Paradox: If asking oneself “Am I dreaming?” in a dream proves that one is, what does it prove in waking life?
What is the Icarus paradox: Some businesses bring about their own downfall through their own successes.
What is the Inspection paradox: Why you will wait longer for that bus than you should.
What is the Interesting number paradox: The first number that can be considered “dull” rather than “interesting” becomes interesting because of that fact.
What is the Intransitive dice: You can have three dice, called A, B, and C, such that A is likely to win in a roll against B, B is likely to win in a roll against C, and C is likely to win in a roll against A.
What is the Irresistible force paradox: What would happen if an unstoppable force hit an immovable object?
What is the Jevons paradox: Increases in efficiency lead to even larger increases in demand.
What is the Kavka’s toxin puzzle: Can one intend to drink the non-deadly toxin, if the intention is the only thing needed to get the reward?
What is the Kleene–Rosser paradox: By formulating an equivalent to the liar paradox, untyped lambda calculus is shown to be inconsistent.
What is the Klein paradox: When the potential of a potential barrier becomes similar to the mass of the impinging particle, it becomes transparent.
What is the Ladder paradox: A classic relativity problem
What is the Leontief paradox: Some countries export labor-intensive commodities and import capital-intensive commodities, in contradiction with Heckscher-Ohlin theory.
What is the Levinthal paradox: The length of time in which a protein chain finds its folded state is many orders of magnitude shorter than it would be if it freely searched all possible configurations.
What is the 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.”
What is the Liberal paradox: Minimal Liberty is incompatible with Pareto optimality.
What is the 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.
What is the Lombard’s Paradox: When rising to stand from a sitting or squatting position, both the hamstrings and quadriceps contract at the same time, despite their being antagonists to each other.
What is the Loschmidt’s paradox: Why is there an inevitable increase in entropy when the laws of physics are invariant under time reversal? The time reversal symmetry of physical laws appears to contradict the second law of thermodynamics.
What is the Lottery paradox: It is philosophically justifiable to believe that every individual lottery ticket won’t win, but not justifiable to believe that no lottery ticket will win.
What is the 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. (A special case of Simpson’s paradox.)
What is the 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.
What is the Mandeville’s paradox: Actions which may be qualified as vicious with regard to individuals may have benefits for society as a whole.
What is the Maxwell’s Demon: The second law of thermodynamics seems to be violated by a cleverly operated trapdoor
What is the Mere addition paradox: Also known as Parfit’s paradox Is a large population living a barely tolerable life better than a small, happy population?
What is the Metzler paradox: The imposition of a tariff on imports may reduce the relative internal price of that good.
What is the Mexican paradox: Mexican children tend to have higher birth weights than can be expected from their socio-economic status.
What is the Missing square puzzle: Two similar figures appear to have different areas while built from the same pieces.
What is the Mocanu’s velocity composition paradox: A paradox in special relativity.
What is the Monty Hall problem: An unintuitive consequence of conditional probability.
What is the Moore’s paradox: It’s raining, but I don’t believe that it is.
What is the Morton’s fork: Choosing between unpalatable alternatives.
What is the Mpemba paradox: Hot water can, under certain conditions, freeze faster than cold water, even though it must pass the lower temperature on the way to freezing.
What is the Navigation paradox: Increased navigational precision may result in increased collision risk.
What is the Necktie Paradox: A wager between two people seems to favour them both. Very similar in essence to the Two-envelope paradox.
What is the New states paradox: Adding a new state or voting block might increase the number of votes of another.
What is the Newcomb’s paradox: How do you play a game against an omniscient opponent?
What is the Olbers’ paradox: Why is the night sky black if there is an infinity of stars?
What is the Omnipotence paradox: Can an omnipotent being create a rock too heavy for himself to lift?
What is the Ontological paradox: Can a time traveler send himself information with no outside source?
What is the Opposite Day: It is opposite day today.
What is the Painlevé paradox: Rigid-body dynamics with contact and friction is inconsistent.
What is the Paradox of American Power: At the beginning of the 21st century, the US is as powerful as no nation before it, yet as dependent on the global community as never before.
What is the Paradox of analysis: It seems that no conceptual analysis can both meet the requirement of correctness and of informativeness.
What is the Paradox of enrichment: Increasing the food available to an ecosystem may lead to instability, and even to extinction.
What is the Paradox of entailment: Inconsistent premises always make an argument valid.
What is the Paradox of free will: If God knew how we will decide when he created us, how can there be free will?
What is the Paradox of hedonism: When one pursues happiness itself, one is miserable; but, when one pursues something else, one achieves happiness.
What is the Paradox of nihilism: Several distinct paradoxes share this name.
What is the Paradox of the Court: A law student agrees to pay his teacher after winning his first case. The teacher then sues the student (who has not yet won a case) for payment.
What is the Paradox of the pesticides: Applying pesticide to a pest may increase the pest’s abundance.
What is the Paradox of the plankton: Why are there so many different species of phytoplankton, even though competition for the same resources tends to reduce the number of species?
What is the 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.
What is the Paradox of tolerance: Should one tolerate intolerance; if intolerance would destroy the possibility of tolerance?
What is the Paradox of voting: Also known as the Downs paradox. For a rational, self-interested voter the costs of voting will normally exceed the expected benefits, so why do people keep voting?
What is the Paradoxical set: A set that can be partitioned into two sets, each of which is equivalent to the original.
What is the Parrondo’s paradox: It is possible to play two losing games alternately to eventually win.
What is the Petronius’s Paradox: Practice moderation in all things. Including moderation.
What is the Population paradox: A fast-growing state can lose votes to a slow-growing state.
What is the 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 ontological paradox is closely tied to this, in which as a result of time travel, information or objects appear to have no beginning.
What is the Preface paradox: The author of a book may be justified in believing that all his statements in the book are correct, at the same time believing that at least one of them is incorrect.
What is the Prevention paradox: For one person to benefit, many people have to change their behavior — even though they receive no benefit, or even suffer, from the change.
What is the Prisoner’s dilemma: Two people might not cooperate even if it is in both their best interests to do so.
What is the Problem of evil (Epicurean paradox): The existence of evil seems to be incompatible with the existence of an omnipotent, omniscient, and morally perfect God.
What is the Productivity paradox: Worker productivity may go down, despite technological improvements.
What is the Proebsting’s paradox: The Kelly criterion is an often optimal strategy for maximizing profit in the long run. Proebsting’s paradox apparently shows that the Kelly criterion can lead to ruin.
What is the Pulsus paradoxus: Sometimes, it is possible to detect heartbeats during inhalation using a stethoscope which can’t be felt at the wrist.
What is the Quantum LC circuit paradox: Energies stored on capacitance and inductance are not equal to the ground state energy of the quantum oscillator
What is the Quantum pseudo-telepathy: Two players who can not communicate accomplish tasks that seemingly require direct contact
What is the Quine’s paradox: ‘Yields a falsehood when appended to its own quotation’ yields a falsehood when appended to its own quotation.
What is the Raven paradox (or Hempel’s Ravens): Observing a green apple increases the likelihood of all ravens being black.
What is the Relevance paradox: Sometimes relevant information is not sought out because its relevance only becomes clear after the information is available.
What is the Richard’s paradox: We appear to be able to use simple English to define a decimal expansion in a way that is self-contradictory.
What is the Russell’s paradox: Does the set of all those sets that do not contain themselves contain itself?
What is the SAR paradox: Exceptions to the principle that a small change in a molecule causes a small change in its chemical behaviour are frequently profound.
What is the Schrödinger’s cat paradox: A quantum paradox — Is the cat alive or dead before we look?
What is the Scitovsky paradox: Using the Kaldor-Hicks criterion, an allocation A may be more efficient than allocation B, while at the same time B is more efficient than A.
What is the Service recovery paradox: Successfully fixing a problem with a defective product may lead to higher consumer satisfaction than in the case where no problem occurred at all.
What is the Sherman paradox: An anomalous pattern of inheritance in the fragile X syndrome.
What is the Ship of Theseus: It seems like you can replace any component of a ship, and it will still be the same ship. So you can replace them all, one at a time, and it will still be the same ship. But then you can take all the original pieces, and assemble them into a ship. That, too, is the same ship with which you started.
What is the Simpson’s paradox: An association in sub-populations may be reversed in the population. It appears that two sets of data separately support a certain hypothesis, but, when considered together, they support the opposite hypothesis.
What is the Skolem’s paradox: Countably infinite models of set theory contain uncountably infinite sets.
What is the Sleeping Beauty problem: A probability problem that can be correctly answered as one half or one third depending on how the question is approached.
What is the Smale’s paradox: A sphere can, topologically, be turned inside out.
What is the Socratic paradox: I know that I know nothing at all.
What is the Sorites paradox: One grain of sand is not a heap. If you don’t have a heap, then adding only one grain of sand won’t give you a heap. Then no number of grains of sand will make a heap. Similarly, one hair can’t make the difference between being bald and not being bald. But then if you remove one hair at a time, you will never become bald. Also similar, one dollar will not make you rich, so if you keep this up, one dollar at a time, you will never become rich, no matter how much you obtain.
What is the St. Petersburg paradox: People will only offer a modest fee for a reward of infinite expected value.
What is the 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
What is the Supplee’s paradox: The buoyancy of a relativistic object (such as a bullet) appears to change when the reference frame is changed from one in which the bullet is at rest to one in which the fluid is at rest.
What is the Tea leaf paradox: When a cup of tea is stirred, the leaves assemble in the center, even though centrifugal force pushes them outward.
What is the Temporal paradox: What happens when a time traveler does things in the past that prevent her from doing them in the first place?
What is the Temporal paradox (paleontology): When did the ancestors of birds live?
What is the The holographic principle: The amount of information that can be stored within a given volume is not proportional to the volume but rather to the area bounding that volume.
What is the Three cards problem: When pulling a random card, how do you determine the color of the underside?
What is the Three Prisoners problem: A variation of the Monty Hall problem.
What is the Tritone paradox: An auditory illusion in which a sequentially played pair of Shepard tones is heard as ascending by some people and as descending by others.
What is the Twin paradox: The theory of relativity predicts that a person making a round trip will return younger than his or her identical twin who stayed at home.
What is the Two-envelope paradox: You are given two indistinguishable envelopes and you are told one contains twice as much money as the other. You may open one envelope, examine its contents, and then, without opening the other, choose which envelope to take.
What is the Unexpected hanging paradox: The day of the hanging will be a surprise, so it cannot happen at all, so it will be a surprise. The surprise examination and Bottle Imp paradox use similar logic.
What is the Voting paradox: Also known as Condorcet’s paradox and paradox of voting. A group of separately rational individuals may have preferences that are irrational in the aggregate.
What is the What the Tortoise Said to Achilles: Whatever Logic is good enough to tell me is worth writing down…, also known as Carroll’s paradox, not to be confused with the physical paradox of the same name.
What is the 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.
What is the Yablo’s paradox: An ordered infinite sequence of sentences, each of which says that all following sentences are false. Uses neither self-reference nor circular reference.
What is the Zeno’s paradoxes: You will never reach point B from point A as you must always get half-way there, and half of the half, and half of that half, and so on.
I am an online writer and soon to be published author. I grew up in Southern California, but I currently live in the Bay Area while I work on my books. I enjoy camping and hiking with my dog Max or just relaxing on the back porch while I write. Stay tuned for my first children’s book to be released about Max.
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