Encyclopedia of Paradoxes

Showing all paradoxes

Paradox Name	Category	Explanation
The Liar Paradox	Logic	"This sentence is false." If it is true, then it is false; if it is false, then it is true. A classic self-referential paradox.
Barber Paradox	Logic	In a village, the barber shaves all those, and those only, who do not shave themselves. Does the barber shave himself?
Russell's Paradox	Logic	Does the set of all sets that do not contain themselves contain itself? It shook the foundations of set theory.
Omnipotence Paradox	Logic	Can an omnipotent being create a rock so heavy that it cannot lift it?
Ship of Theseus	Logic	If every part of a ship is replaced over time, is it still the same ship? Questions identity over time.
Sorites Paradox	Logic	Also known as the Paradox of the Heap. If you remove a single grain of sand from a heap, it remains a heap. When does it stop being a heap?
Catch-22	Logic	A situation where one needs X to get Y, but one needs Y to get X. A no-win dilemma.
Simpson's Paradox	Statistics	A trend appears in several different groups of data but disappears or reverses when these groups are combined.
Monty Hall Problem	Statistics	A counterintuitive probability puzzle: switching your choice after a door is revealed doubles your chances of winning.
Benford's Law	Statistics	In many naturally occurring collections of numbers, the leading significant digit is likely to be small (1 occurs about 30% of the time, 9 less than 5%).
Friendship Paradox	Statistics	On average, your friends have more friends than you do, due to sampling bias.
Parrondo's Paradox	Statistics	Two losing strategies can combine to create a winning strategy.
Will Rogers Phenomenon	Statistics	Moving an element from one set to another raises the average values of both sets.
Fermi Paradox	Physics	The apparent contradiction between the high probability of extraterrestrial civilizations and the lack of evidence for them.
Twin Paradox	Physics	One twin travels at near-light speed, returning younger than the twin who stayed on Earth, despite time dilation applying to both relative to each other.
Olbers' Paradox	Physics	If the universe is infinite and static, the night sky should be bright with starlight.
Ehrenfest Paradox	Physics	A rotating rigid disk in special relativity leads to contradictions about the circumference vs. radius.
Bell's Theorem (EPR Paradox)	Physics	Quantum entanglement implies that either local realism is false or information can travel faster than light.
Schrödinger's Cat	Physics	A cat in a box is simultaneously alive and dead until observed, illustrating the concept of superposition in quantum mechanics.
St. Petersburg Paradox	Economics	A lottery with infinite expected value is only worth a small amount to real people, challenging expected utility theory.
Paradox of Value (Diamond-Water)	Economics	Water is essential but cheap; diamonds are useless but expensive. Explained by marginal utility, not total utility.
Jevons Paradox	Economics	Increases in energy efficiency lead to increases, rather than decreases, in the consumption of that energy.
Paradox of Thrift	Economics	If everyone saves more money during a recession, aggregate demand will fall and lower total savings in the economy.
Leontief Paradox	Economics	The US (capital-abundant) exported labor-intensive commodities and imported capital-intensive commodities, contradicting Heckscher-Ohlin theory.
Grandfather Paradox	Time	A time traveler goes back and kills their grandfather before the traveler's parent is conceived, preventing the traveler from existing.
Bootstrap Paradox	Time	An object or information is sent back in time and becomes the cause of its own existence, having no discernible origin.
Polchinski's Paradox	Time	A billiard ball is sent into a wormhole to knock itself out of the hole, ensuring it never enters the hole.
Prisoner's Dilemma	Decision Theory	Two individuals acting in their own self-interest betray each other, even though cooperation would yield a better result for both.
Newcomb's Paradox	Decision Theory	A highly accurate predictor offers two boxes. Do you take only one box or both? Conflicts between the Dominance Principle and Expected Utility.
Abilene Paradox	Social	A group of people collectively decide on a course of action that none of them individually wants, because they mistakenly believe the others want it.
Buridan's Ass	Decision Theory	A hungry ass placed exactly between two identical haystacks cannot make a rational decision to eat and starves.
Allais Paradox	Decision Theory	Choices people make in gambles contradict the expected utility hypothesis.
Arrow's Paradox	Social	No ranked voting system can convert individual preferences into a community-wide ranking while also meeting basic fairness criteria.
Morton's Fork	Social	A type of false dilemma where two contradictory choices lead to the same (often unpleasant) conclusion.
Stable Marriage Paradox	Decision Theory	While a stable matching always exists, the algorithm used to find it can favor one gender over the other in terms of satisfaction.