Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-06-04T12:42:22.423Z Has data issue: false hasContentIssue false
  • English
  • Français

A new look at Eddington's liar problem

Published online by Cambridge University Press:  01 August 2016

Michael A. B. Deakin
Michael A. B. Deakin*
Affiliation:
School of Mathematical Sciences, Monash University, Clayton, Australia e-mail: michael.deakin@sci.monash.edu.au
Get access Rights & Permissions [Opens in a new window]

Extract

Eddington's ‘liar problem’ received its first truly public airing in his book New Pathways in Science [1], although it enjoyed a ‘prehistory’ (beginning with a mock examination paper) more fully detailed in his later discussion [7]. As posed, it reads:

If A, B, C and D each speak the truth once in every three times (independently), and A affirms that B denies that C declares that D is a liar, what is the probability that D was speaking the truth?

Type
Articles
Information
The Mathematical Gazette , Volume 93 , Issue 526 , March 2009 , pp. 1 - 9
Copyright
Copyright © The Mathematical Association 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Eddington, A. S., New pathways in science, Cambridge University Press (1934); reprinted Ann Arbor (1959), chapter VI.Google Scholar
2. Dingle, H., Viewpoint and vision (review of [1]), Nature 135 (1935) pp. 451–454.CrossRefGoogle Scholar
3. Sterne, T. E., The solution, by the method of association, of problems in inverse probability, Nature 135 (1935) pp. 1073–1074.Google Scholar
4. Dingle, H., Reply to Sterne, Nature 135 (1935) p. 1074.Google Scholar
5. Sterne, T. E., Inverse probability, Nature 136 (1935) p. 301.CrossRefGoogle Scholar
6. Dingle, H., Further reply to Sterne, Nature 136 (1935) pp. 301–302.CrossRefGoogle Scholar
7. Dingle, H., The meaning of probability, Nature 136 (1935) pp. 423–426.Google Scholar
8. Eddington, A. S., The problem of A, B, C and D, Math, Gaz. 19 (October 1935) pp. 256–257.CrossRefGoogle Scholar
9. Chapman, H. W., Eddington’s probability problem, Math. Gaz. 20 (December 1936) pp. 298–308.Google Scholar
10. Leftwich, H. S., The A, B, C, D problem, Math. Gaz. 20 (December 1936), pp. 309–310.CrossRefGoogle Scholar
11. Campbell, J. W., Problem A4288, Amer. Math. Monthly 55 (1948) p. 165.Google Scholar
12. Park, B., The four liars (Solution I to Problem A4288), Amer. Math. Monthly 57 (1950) p. 43.Google Scholar
13. Garrison, G. N. and Hailperin, T., The four liars (Solution II to Problem A4288), Amer. Math. Monthly 57 (1950) pp. 43–44.Google Scholar
14. Feller, W., The problem of n liars and Markov chains, Amer. Math. Monthly 58 (1951) pp. 606–608.Google Scholar
15. Riordan, J., Note on Problem A4288, Amer. Math. Monthly 57 (1950) pp. 44–45.Google Scholar
16. Gardner, M., Mathematical games column, Scientific American 200(2) (February 1959) p. 140.Google Scholar
17. Gardner, M., Mathematical games column, Scientific American 200(3) (March 1959) p. 152.Google Scholar