Paradoxes and thought experiments
Each of these is a problem where a confident intuition is wrong, or where two confident intuitions collide. The rule is to commit to an answer before the explanation shows, because an answer you only nodded along to teaches nothing. Where experts genuinely disagree, the entry says so instead of picking a winner.
25 problems · keys 1 to 5 to pick · enter to commit
Probability
The Monty Hall problem
Steve Selvin, in a 1975 letter to The American Statistician; made famous by Marilyn vos Savant's Parade column of September 1990.
Interactive
The birthday paradox
Usually credited to Richard von Mises in 1939; a standard exercise in Feller's 1950 textbook.
Interactive
The two-envelope problem
Traced to Maurice Kraitchik's 1943 necktie puzzle; the envelope form was spread by Barry Nalebuff in 1989 and Martin Gardner in 1982.
Experts disagree
The boy or girl paradox
Martin Gardner, Scientific American, May 1959; in his October 1959 column he admitted the wording was ambiguous.
Settled
The St. Petersburg paradox
Posed by Nicolaus Bernoulli in a 1713 letter; Daniel Bernoulli's resolution appeared in the St. Petersburg Academy's journal in 1738.
Settled
The Sleeping Beauty problem
Circulated by Arnold Zuboff in the 1980s; put into print by Adam Elga in 2000, with David Lewis replying in 2001.
Experts disagree
Bertrand's box paradox
Joseph Bertrand, in the opening pages of Calcul des probabilites (1889).
Settled
Statistics
Simpson's paradox
Described by Karl Pearson, George Udny Yule and others around 1900; named after Edward Simpson's 1951 paper; the Berkeley case is from Bickel, Hammel and O'Connell (1975).
Interactive
Berkson's paradox
Joseph Berkson of the Mayo Clinic, in a 1946 paper on why hospital records mislead about disease associations.
Settled
The friendship paradox
Scott Feld, Why Your Friends Have More Friends Than You Do, American Journal of Sociology, 1991.
Settled
Decision
Newcomb's problem
Devised by the physicist William Newcomb and published by Robert Nozick in 1969.
Experts disagree
The prisoner's dilemma
Merrill Flood and Melvin Dresher at RAND, 1950; the prison story is Albert Tucker's.
Settled
Pascal's mugging
Named by Eliezer Yudkowsky in 2007; set out as a dialogue by Nick Bostrom in Analysis, 2009.
Experts disagree
The Allais paradox
Maurice Allais, 1953, in a paper arguing against the axioms of expected utility.
Settled
Identity and philosophy
The ship of Theseus
Plutarch, Life of Theseus (about AD 100); the rebuilt-ship twist is Thomas Hobbes's, in De Corpore (1655).
Experts disagree
The teleporter problem
Derek Parfit, Reasons and Persons (1984), building on earlier fission cases by David Wiggins and others.
Experts disagree
The Chinese room
John Searle, Minds, Brains, and Programs, Behavioral and Brain Sciences (1980).
Experts disagree
Mary's room
Frank Jackson, Epiphenomenal Qualia, Philosophical Quarterly (1982).
Experts disagree
The trolley problem
Philippa Foot, 1967; the footbridge variant is Judith Jarvis Thomson's, 1976 and 1985.
Experts disagree
Logic and math
Zeno's paradoxes
Zeno of Elea, around 450 BC, as reported and answered by Aristotle in the Physics.
Experts disagree
The liar paradox
Eubulides of the Megarian school, fourth century BC; the modern analysis starts with Tarski (1933) and Kripke (1975).
Experts disagree
Russell's paradox
Bertrand Russell, 1901; sent to Gottlob Frege in a letter of 16 June 1902.
Settled
The unexpected hanging
Circulating since the 1940s; first discussed in print by D. J. O'Connor (1948) and made famous by Martin Gardner.
Experts disagree
Hilbert's hotel
David Hilbert, in a 1924 lecture on the infinite; the set theory behind it is Georg Cantor's, from the 1870s.
Settled
The sorites paradox
Eubulides of Miletus, fourth century BC; the name is from the Greek for heap.
Experts disagree