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 on Wikipedia. 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.

Logic [ edit ]

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.

: 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. What the Tortoise Said to Achilles : If a presumption needs to be made that a specific result can be deduced from premises, then the result can never be deduced. Also known as Carroll's paradox and is not to be confused with the "Achilles and the tortoise" paradox by Zeno of Elea.

: If a presumption needs to be made that a specific result can be deduced from premises, then the result can never be deduced. Also known as and is not to be confused with the "Achilles and the tortoise" paradox by Zeno of Elea. 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 to avoid combat is deemed not insane for that very reason and will therefore not be declared insane.

: 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 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 such that if that customer is drinking, everybody in the pub is drinking.

: In any pub there is a customer such that if that customer is drinking, everybody in the pub is drinking. Paradox of entailment : Inconsistent premises always make an argument valid.

: Inconsistent premises always make an argument valid. 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.

: 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.

: (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.

: Disjunction introduction poses a problem for imperative inference by seemingly permitting arbitrary imperatives to be inferred. 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.

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.

Vagueness [ edit ]

Ship of Theseus: It seems like one can replace any component of a ship, and it is still the same ship. So they can replace them all, one at a time, and it is still the same ship. However, they can then take all the original pieces, and assemble them into a ship. That, too, is the same ship they began with.

See also List of Ship of Theseus examples

Sorites paradox (also known as the paradox of the heap): If one removes a single grain of sand from a heap, they still have a heap. If they keep removing single grains, the heap will disappear. Can a single grain of sand make the difference between heap and non-heap?

Mathematics [ edit ]

All horses are the same color : A fallacious argument by induction that appears to prove that all horses are the same color.

: A fallacious argument by induction that appears to prove that all horses are the same color. Ant on a rubber rope : An ant crawling on a rubber rope can reach the end even when the rope stretches much faster than the ant can crawl.

: An ant crawling on a rubber rope can reach the end even when the rope stretches much faster than the ant can crawl. 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.

: 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. 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.

: 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. Interesting number paradox : The first number that can be considered "dull" rather than "interesting" becomes interesting because of that fact.

: The first number that can be considered "dull" rather than "interesting" becomes interesting because of that fact. Potato paradox : If potatoes consisting of 99% water dry so that they are 98% water, they lose 50% of their weight.

: If potatoes consisting of 99% water dry so that they are 98% water, they lose 50% of their weight. Russell's paradox: Does the set of all those sets that do not contain themselves contain itself?

Statistics [ edit ]

Probability [ edit ]

Infinity and infinitesimals [ edit ]

Benardete's paradox : Apparently, a man can be "forced to stay where he is by the mere unfulfilled intentions of the gods".

: Apparently, a man can be "forced to stay where he is by the mere unfulfilled intentions of the gods". Grim Reaper paradox : An infinite number of assassins can create an explicit self-contradiction by scheduling their assassinations at certain times.

: An infinite number of assassins can create an explicit self-contradiction by scheduling their assassinations at certain times. Grandi's series : The sum of 1-1+1-1+1-1... can be either one, zero, or one-half.

: The sum of 1-1+1-1+1-1... can be either one, zero, or one-half. Ross–Littlewood paradox : After alternately adding and removing balls to a vase infinitely often, how many balls remain?

: After alternately adding and removing balls to a vase infinitely often, how many balls remain? Thomson's lamp: After flicking a lamp on and off infinitely often, is it on or off?

Geometry and topology [ edit ]

The Banach–Tarski paradox : A ball can be decomposed and reassembled into two balls the same size as the original.

Decision theory [ edit ]

Physics [ edit ]

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.

: 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. Irresistible force paradox : What would happen if an unstoppable force hit an immovable object?

: What would happen if an unstoppable force hit an immovable object? Paradox of place : If everything that exists has a place, that place must have a place, and so on ad infinitum.

: If everything that exists has a place, that place must have a place, and so on ad infinitum. Paradox of the grain of millet : When a grain of millet falls it makes no sound, but when a thousand grains fall they do, thus many of nothing become something.

: When a grain of millet falls it makes no sound, but when a thousand grains fall they do, thus many of nothing become something. The moving rows: Suppose two rows are moving past a stationary row in opposite directions. If a member of a moving row moves past a member of the stationary row in an indivisible instant of time, they move past two members of the row that is moving in the other direction in this instant of time.

Astrophysics [ edit ]

Classical mechanics [ edit ]

Cosmology [ edit ]

Bentley's paradox : In a Newtonian universe, gravitation should pull all matter into a single point.

: 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.

: 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? Should not their presence be obvious?

: If there are, as various arguments suggest, many other sentient species in the Universe, then where are they? Should not their presence be obvious? Heat death paradox : If the universe were infinitely old, it would be in thermodynamical equilibrium, which contradicts what we observe.

: If the universe were 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?

Electromagnetism [ edit ]

Faraday paradox: An apparent violation of Faraday's law of electromagnetic induction.

Quantum mechanics [ edit ]

Relativity [ edit ]

Thermodynamics [ edit ]

Biology [ edit ]

Health and nutrition [ edit ]

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.

: 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.

: 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.

: 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.

: 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. Mexican paradox : Mexican children tend to have higher birth weights than can be expected from their socio-economic status.

: Mexican children tend to have higher birth weights than can be expected from their socio-economic status. Obesity paradox : In some medical conditions, obesity is associated with increased survival, although there is a strong association with shortened lifespan in the general population.

: In some medical conditions, obesity is associated with increased survival, although there is a strong association with shortened lifespan in the general population. 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.

: 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. Pulsus paradoxus : A pulsus paradoxus is an exaggerated decrease in systolic blood pressure during inspiration. It can indicate certain medical conditions in which there is reduced cardiac output, such as cardiac tamponade or constrictive pericarditis. Also known as the Pulse Paradox. [5]

: A pulsus paradoxus is an exaggerated decrease in systolic blood pressure during inspiration. It can indicate certain medical conditions in which there is reduced cardiac output, such as cardiac tamponade or constrictive pericarditis. Also known as the Pulse Paradox. 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.

Chemistry [ edit ]

Faraday paradox (electrochemistry) : Diluted nitric acid will corrode steel, while concentrated nitric acid will not.

: Diluted nitric acid will corrode steel, while concentrated nitric acid will not. Levinthal paradox : The length of time that it takes for a protein chain to find its folded state is many orders of magnitude shorter than it would be if it freely searched all possible configurations.

: The length of time that it takes for a protein chain to find its folded state is many orders of magnitude shorter than it would be if it freely searched all possible configurations. SAR paradox: Exceptions to the principle that a small change in a molecule causes a small change in its chemical behavior are frequently profound.

Time travel [ edit ]

Bootstrap paradox (also ontological paradox ): You send information/an object to your past self, but you only have that information/object because in the past, you received it from your future self. This means the information/object was never created, yet still exists.

(also ): You send information/an object to your past self, but you only have that information/object because in the past, you received it from your future self. This means the information/object was never created, yet still exists. 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.

: 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. Temporal paradox: What happens when a time traveler does things in the past that prevent them from doing them in the first place?

Grandfather paradox : If one travels back in time and kill their grandfather before he conceives one of their parents, which precludes their own conception and, therefore, they couldn't go back in time and kill their grandfather.

: If one travels back in time and kill their grandfather before he conceives one of their parents, which precludes their own conception and, therefore, they couldn't go back in time and kill their grandfather. 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.

: 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. Hitler's murder paradox: One can travel back in time and murder Adolf Hitler before he can instigate World War II and the Holocaust; but if he had never been instigated that, then the murder removes any reason for the travel.

Linguistics and artificial intelligence [ edit ]

Bracketing paradox : Is a "historical linguist" a linguist who is historical, or someone who studies "historical linguistics"?

: Is a "historical linguist" a linguist who is historical, or someone who studies "historical linguistics"? Code-talker paradox : How can a language both enable communication and block communication?

: How can a language both enable communication and block communication? Moravec's paradox : Logical thought is hard for humans and easy for computers, but picking a screw from a box of screws is an unsolved problem.

: Logical thought is hard for humans and easy for computers, but picking a screw from a box of screws is an unsolved problem. Movement paradox : In transformational linguistics, there are pairs of sentences in which the sentence without movement is ungrammatical while the sentence with movement is not.

: In transformational linguistics, there are pairs of sentences in which the sentence without movement is ungrammatical while the sentence with movement is not. Sayre's paradox: In automated handwriting recognition, a cursively written word cannot be recognized without being segmented and cannot be segmented without being recognized.

Philosophy [ edit ]

Mysticism [ edit ]

Maya (illusion) : Our illusions are not real, yet it's real that illusion itself exists.

: 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.

Economics [ edit ]

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.

Perception [ edit ]

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.

: An auditory illusion in which a sequentially played pair of Shepard tones is heard as ascending by some people and as descending by others. Blub paradox : Cognitive lock of some experienced programmers that prevents them from properly evaluating the quality of programming languages which they do not know. [7]

: Cognitive lock of some experienced programmers that prevents them from properly evaluating the quality of programming languages which they do not know. Optical illusion: A visual illusion which suggests inconsistency, such as an impossible cube or the vertical-horizontal illusion, where the two lines are exactly the same length but appear to be of different lengths.

Politics [ edit ]

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.

: 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.

Psychology and sociology [ edit ]

Miscellaneous [ edit ]

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.

: 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. Buttered cat paradox : Humorous example of a paradox from contradicting proverbs.

: Humorous example of a paradox from contradicting proverbs. Intentionally blank page : Many documents contain pages on which the text "This page is intentionally left blank" is printed, thereby making the page not blank.

: Many documents contain pages on which the text "This page is intentionally left blank" is printed, thereby making the page not blank. Observer's paradox : The outcome of an event or experiment is influenced by the presence of the observer.

: The outcome of an event or experiment is influenced by the presence of the observer. Taeuber Paradox: A paradox in demography in which lessening mortality for a particular cause results in a surprisingly small increase in life expectancy and no change in overall mortality.

See also [ edit ]