All horses are the same color

"Horse paradox" redirects here. For a Chinese white horse paradox, see When a white horse is not a horse.

All horses are the same color is a falsidical paradox that arises from a flawed use of mathematical induction to prove the statement All horses are the same color.[1] There is no actual contradiction, as these arguments have a crucial flaw that makes them incorrect. This example was originally raised by George Pólya in a 1954 book in different terms: "Are any n numbers equal?" or "Any n girls have eyes of the same color", as an exercise in mathematical induction.[2] It has also been restated as "All cows have the same color".[3]

The "horses" version of the paradox was presented in 1961 in a satirical article by Joel E. Cohen. It was stated as a lemma, which in particular allowed the author to "prove" that Alexander the Great did not exist, and he had an infinite number of limbs.[4]

  1. ^ Łukowski, Piotr (2011). Paradoxes. Springer. pp. 15.
  2. ^ Pólya, George (1954). Induction and Analogy in Mathematics. Princeton University Press. p. 120.
  3. ^ Thomas VanDrunen, Discrete Mathematics and Functional Programming, Franklin, Beedle and Associates, 2012, Section "Induction Gone Awry"
  4. ^ Cohen, Joel E. (1961), "On the nature of mathematical proofs", Worm Runner's Digest, III (3). Reprinted in A Random Walk in Science (R. L. Weber, ed.), Crane, Russak & Co., 1973, pp. 34-36