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

Self-reference

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

See also List of Ship of Theseus examples

Mathematics

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

Statistics

See also: Category:Statistical paradoxes

Probability

The Monty Hall problem: which door do you choose?
The Monty Hall problem: which door do you choose?

See also: Category:Probability theory paradoxes

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".
  • Grim Reaper paradox: 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.
  • Ross–Littlewood paradox: 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

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

Decision theory

Physics

Further information: Physical paradox

A demonstration of the tea leaf paradox
A demonstration of the tea leaf paradox

Astrophysics

Classical mechanics

Cosmology

Electromagnetism

Quantum mechanics

Relativity

Thermodynamics

Biology

Health and nutrition

Chemistry

Time travel

  • 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.
  • 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.
  • 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 instigated that, then the murder removes any reason for the travel.

Linguistics and artificial intelligence

Philosophy

Mysticism

Economics

See also: Category:Paradoxes in economics

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

Further information: Perceptual paradox

the vertical–horizontal illusion

Politics

Psychology and sociology

Miscellaneous

See also

References

  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.
    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 (15 July 2013), Infinity Paradoxes - Numberphile, retrieved 30 May 2016
  3. ^ Newton, Roger G. (2002). Scattering Theory of Waves and Particles, second edition. Dover Publications. p. 68. ISBN 978-0-486-42535-1.
  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 978-0-7503-0759-8. Archived from the original (PDF) on 9 November 2005. 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. ^ Khasnis, A.; Lokhandwala, Y. (January–March 2002). "Clinical signs in medicine: pulsus paradoxus". Journal of Postgraduate Medicine. 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.
  6. ^ Mark Skousen, Kenna C. Taylor, Puzzles and paradoxes in economics, (1997), Edward Elgar Publishing, ISBN 978-1858983783
  7. ^ Hidders, J. "Expressive Power of Recursion and Aggregates in XQuery" (PDF). Retrieved 23 May 2012.: Chapter 1, Introduction.
  8. ^ Developing countries: The outcomes paradox Nature.com
  9. ^ 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.