List of paradoxes

This is a list of paradoxes, grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. Because of varying definitions of the term paradox, some of the following are not considered to be paradoxes by everyone. This list collects only scenarios that have been called a paradox by at least one source and have their own article.

Although considered paradoxes, some of these are based on fallacious reasoning, or incomplete/faulty analysis. Informally, the term is often used to describe a counter-intuitive result.



These paradoxes have in common a contradiction arising from either from self-reference or from 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.



See also: Category:Mathematics paradoxes and Paradoxes of set theory



The Monty Hall problem: which door do you choose?

Infinity and infinitesimals

  • Benardete's paradox: Apparently, a man can be "forced to stay where he is by the mere unfulfilled intentions of the gods".
  • Grandi's series: The sum of 1-1+1-1+1-1... can be either one, zero, or one-half.
  • Ross–Littlewood paradox: After alternatively 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

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

Decision theory


For more details on this topic, see Physical paradox.
A demonstration of the tea leaf paradox


Classical mechanics



Quantum mechanics




Health and nutrition


Time travel

  • 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.
  • Hitler's murder paradox: You travel back in time and kill a famous person in history before they become famous; but if the person had never been famous, then he could not have been targeted as a famous person.

Linguistics and artificial intelligence




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.


For more details on this topic, see Perceptual paradox.


Psychology and sociology


See also


  1. Eldridge-Smith, Peter; Eldridge-Smith, Veronique (13 January 2010). "The Pinocchio paradox". Analysis. 70 (2): 212–215. doi:10.1093/analys/anp173. ISSN 1467-8284. Retrieved 23 July 2010.
    As of 2010, an image of Pinocchio with a speech bubble "My nose will grow now!" has become a minor Internet phenomenon (Google search, Google image search). It seems likely that this paradox has been independently conceived multiple times.
  2. Numberphile (2013-07-15), Infinity Paradoxes - Numberphile, retrieved 2016-05-30
  3. Newton, Roger G. (2002). Scattering Theory of Waves and Particles, second edition. Dover Publications. p. 68. ISBN 0-486-42535-5.
  4. Carnap is quoted as saying in 1977 "... the situation with respect to Maxwell's paradox", in Leff, Harvey S.; Rex, A. F., eds. (2003). Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing (PDF). Institute of Physics. p. 19. ISBN 0-7503-0759-5. Archived from the original (PDF) on 2005-11-09. Retrieved 15 March 2010.
    On page 36, Leff and Rex also quote Goldstein and Goldstein as saying "Smoluchowski fully resolved the paradox of the demon in 1912" in Goldstein, Martin; Goldstein, Inge F. (1993). The Refrigerator and The Universe. Universities Press (India) Pvt. Ltd. p. 228. ISBN 978-81-7371-085-8. OCLC 477206415. Retrieved 15 March 2010.
  5. T.L. Duncan, Phys. Rev. E 61, 4661 (2000).
  6. Sheehan, D.P., D.J. Mallin, J.T. Garamella, and W.F. Sheehan, Found. Phys. 44 235 (2014).
  7. Peng, C.-K; Isaac C Henry; Joseph E Mietus; Jeffrey M Hausdorff; Gurucharan Khalsa; Herbert Benson; Ary L Goldberger (May 2004). "Heart rate dynamics during three forms of meditation". International Journal of Cardiology. 95 (1): 19–27. doi:10.1016/j.ijcard.2003.02.006. PMID 15159033. Retrieved 23 May 2012.
  8. Khasnis, A.; Lokhandwala, Y. (Jan–Mar 2002). "Clinical signs in medicine: pulsus paradoxus". Journal of Postgraduate Medicine. Mumbai – 400 012, India: 49. 48 (1): 46–9. ISSN 0022-3859. PMID 12082330. Retrieved 21 March 2010. The "paradox" refers to the fact that heart sounds may be heard over the precordium when the radial pulse is not felt.
  9. Hidders, J. "Expressive Power of Recursion and Aggregates in XQuery" (PDF). Retrieved 23 May 2012.: Chapter 1, Introduction.
  10. Developing countries: The outcomes paradox
  11. Trapnell, P. D., & Campbell, J. D. (1999). "Private self-consciousness and the Five-Factor Model of Personality: Distinguishing rumination from reflection". Journal of Personality and Social Psychology, 76, 284–304.
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