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.
- 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.
- 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.
- 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.
- Drinker paradox: 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.
- 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.
- 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.
- Barber paradox: A male barber shaves all and only those men who do not shave themselves. Does he shave himself? (Russell's popularization of his set theoretic paradox.)
- 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.
- Curry's paradox: "If this sentence is true, then Santa Claus exists."
- Epimenides paradox: A Cretan says: "All Cretans are liars". This paradox works in mainly the same way as the liar paradox.
- Grelling–Nelson paradox: Is the word "heterological", meaning "not applicable to itself", a heterological word? (A close relative of Russell's paradox.)
- Hilbert–Bernays paradox: If there was a name for a natural number that is identical to a name of the successor of that number, there would be a natural number equal to its successor.
- Kleene–Rosser paradox: By formulating an equivalent to Richard's paradox, untyped lambda calculus is shown to be inconsistent.
- Knower paradox: "This sentence is not known."
- 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 that each say the other is not true.
- Pinocchio paradox: What would happen if Pinocchio said "My nose grows now"?
- 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.
- Problem of Absolute Generality: It initially appears as if we can quantify over absolutely everything (including the expression itself), but this generates the liar paradox.
- 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?
- I know that I know nothing: Purportedly said by Socrates.
- 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?
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.
- The Antitrust Paradox: A book arguing that antitrust enforcement artificially raised prices by protecting inefficient competitors from competition.
- Arrow information paradox: To sell information you need to give it away before the sale.
- Bertrand paradox: Two players reaching a state of Nash equilibrium both find themselves with no profits gained via exploitation.
- Braess's paradox: Adding extra capacity to a network can reduce overall performance.
- Deaton paradox: Consumption varies surprisingly smoothly despite sharp variations in income.
- 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.
- Downs–Thomson paradox: Increasing road capacity at the expense of investments in public transport can make overall congestion on the road worse.
- Easterlin paradox: For countries with income sufficient to meet basic needs, the reported level of happiness does not correlate with national income per person.
- Edgeworth paradox: With capacity constraints, there may not be an equilibrium.
- European paradox: The perceived failure of European countries to translate scientific advances into marketable innovations.
- Gibson's paradox: Why were interest rates and prices correlated?
- Giffen paradox: Increasing the price of bread makes poor people eat more of it.
- Grossman-Stiglitz paradox: Inability to recoup cost of obtaining market information implies efficient markets cannot exist.
- Icarus paradox: Some businesses bring about their own downfall through their own successes.
- Jevons paradox: Increases in efficiency lead to even larger increases in demand.
- Leontief paradox: Some countries export labor-intensive commodities and import capital-intensive commodities, in contradiction with the Heckscher–Ohlin theorem.
- Louboutin paradox: Paradox of luxury goods. The more expensive some commodity is, the 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.
- Mandeville's paradox: Actions that may be vicious to individuals may benefit society as a whole.
- 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.
- 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.
- 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.
- St. Petersburg paradox: People will only offer a modest fee for a reward of infinite expected value.
- Paradox of plenty: Countries with an abundance of natural resources tend to have less economic growth and worse development outcomes than countries with fewer natural resources.
- Throw away paradox: A trader can gain by throwing away some of his/her initial endowment.
- Tullock paradox: Bribing politicians costs less than one would expect, considering how much profit it can yield.