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Probability Assignments and the Principle of Indifference. An Examination of Two Eliminative Strategies

  • Sorin BanguEmail author
Chapter
Part of the Synthese Library book series (SYLI, volume 347)

Abstract

The Principle of Indifference (PI) – roughly, the claim that equipossibility entails equiprobability – has long been regarded with suspicion by philosophers and scientists alike. This hostility has a twofold motivation. On one hand, there are the well-known inconsistencies (Bertrand paradoxes) to which the use of the principle leads. On the other, there are some general metaphysical and epistemological worries regarding the principle’s support for the idea that the occurrence of events in the physical world should follow ‘the directives of human ignorance’, as Reichenbach ([1949]/1971, 354) put it. These concerns naturally led philosophers to design strategies to eliminate PI from probabilistic reasoning. In this paper I examine two such strategies and argue that they are not successful. This conclusion, however, should not count so much as an endorsement of PI, but rather as an indication that another approach to explicating its role in probabilistic reasoning is needed.

Keywords

Statistical Significance Test Outcome Space Smoothness Assumption Probabilistic Hypothesis Epistemic Role 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

I thank Margaret Morrison, Peter Urbach, Colin Howson, Bob Batterman, Anjan Chakravartty, Ranpal Dosanjh and Kaave Lajevardi for discussions and critical comments on earlier versions of this paper. I also thank Mauricio Suarez for encouraging feedback and for stirring up my interest in these issues. Any mistakes that remain are mine. Financial support for working on this paper was kindly provided by the Rotman Postdoctoral Fellowship in Philosophy of Science at the University of Western Ontario.

References

  1. Bangu, S. (2010), On Bertrand’s paradox, Analysis 70, 30–35.Google Scholar
  2. Bartha, P. and Johns, R. (2001), Probability and symmetry, Philosophy of Science 68 (Proceedings), S109–S122.CrossRefGoogle Scholar
  3. Bertrand, J. (1889), Calcul des probabilitiés. Paris: Gauthier-Villars.Google Scholar
  4. Borel, E. (1909), Elements de la Theorie des Probabilites. Paris: Librairie Scientifique.Google Scholar
  5. Castell, P. (1998), A consistent restriction of the principle of indifference, British Journal for the Philosophy of Science 49(3), 387–395.CrossRefGoogle Scholar
  6. Callender, C. (2004), Is there is a puzzle about the low entropy past? In Hitchcock, C. (ed.), Contemporary Debates in the Philosophy of Science, Oxford: Blackwell.Google Scholar
  7. Diaconis, P. and Engel, E. (1986), ‘Comment,’ Statistical Science, 1(2), 171–174.CrossRefGoogle Scholar
  8. Engel, E. (1992), A Road to Randomness in Physical Systems. Springer Lecture Notes in Statistics No. 71, New York, NY: Springer.Google Scholar
  9. Fréchet, M. (1952), Methode des functions arbitraries. Theorie des evenements en chaine dans le cas d’un nombre fini d’etats possibles In E. Borel (ed.), Traite du Calcul des Probabilites et de ses Applications (Tome I, Fascicule III, Second livre). Paris: Gauthier-Villars.Google Scholar
  10. Gillies, D. (2000), Philosophical Theories of Probability. London: Routledge.Google Scholar
  11. Hacking, I. (1975), The Emergence of Probability. Cambridge: Cambridge University Press.Google Scholar
  12. Hajek, A. (1997), ‘Misses Redux’ Redux. Fifteen Arguments Against Finite Frequentism. Erkenntnis 45, 209–227.Google Scholar
  13. Hays, W. and Winkler, R. L. (1971), Statistics: Probability, Inference and Decision. New York, NY: Holt, Rinehart and Winston.Google Scholar
  14. Hopf, E. (1934) On causality, statistics and probability, Journal of Mathematics and Physics 17, 51–102.Google Scholar
  15. Howson, C. and Urbach, P. (2006), Scientific Reasoning. The Bayesian Approach. Chicago, IL: Open Court (3rd edition).Google Scholar
  16. Jaynes, E. T. (1973), The Well-Posed Problem, Foundations of Physics 3, 477–493.CrossRefGoogle Scholar
  17. Kechen, Z. (1990), Uniform distribution of initial states: The physical basis of probability, Physical Review A 41, 1893–1900.CrossRefGoogle Scholar
  18. Kittel, Ch. and Kroemer, H. (1980), Thermal Physics. New York, NY: W. H. Freeman and Company.Google Scholar
  19. Lindley, D. V. and Philips, L. D. (1976), Inference for a Bernoulli process (a Bayesian view) American Statistician, 30, 112–119.CrossRefGoogle Scholar
  20. Marinoff, L. (1994), A Resolution of Bertrand’s Paradox, Philosophy of Science 61, 1–24.CrossRefGoogle Scholar
  21. Mikkelson, J. M. (2004), Dissolving the wine/water Paradox, British Journal for the Philosophy of Science 55, 137–145.CrossRefGoogle Scholar
  22. Norton, J. (2008), Ignorance and indifference, Philosophy of Science 75, 45–68.CrossRefGoogle Scholar
  23. Poincaré, H. (1912), Calcul de probabilités. Paris: Gauthier-Villars (1st edition 1896).Google Scholar
  24. Poincaré, H. (1952a), Science and Hypothesis. Reprint, Dover, New York, NY. Translation of La science et l’hypothèse (1st edition 1902).Google Scholar
  25. Poincaré, H (1952b), Science and Method. Reprint, Dover, New York, NY. Translation of Science et méthode. (1st edition 1908).Google Scholar
  26. Popper, K. R. (1959), The Logic of Scientific Discovery. London: Hutchinson.Google Scholar
  27. Price, H. (2004), On the origins of the arrow of time: why there is still a puzzle about the low entropy past, In C. Hitchcock (ed.), Contemporary Debates in the Philosophy of Science. Oxford: Blackwell.Google Scholar
  28. Reichenbach, H. (1971/[1949]), Theory of Probability. Berkeley, CA: University of California Press.Google Scholar
  29. Reif, F. (1965), Fundamentals of Statistical and Thermal Physics. New York, NY: McGraw-Hill.Google Scholar
  30. Savage, L. J. (1973) Probability in science; a personalistic account In P. Suppes et al. (eds.), Logic, Methodology and Philosophy of Science IV. North Holland: Amsterdam. pp. 467–483.Google Scholar
  31. Shackel, N. (2007), Bertrand Paradox and the principle of indifference Philosophy of Science 74, 150–175.CrossRefGoogle Scholar
  32. Sklar, L. (1993) Physics and Chance. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  33. Strevens, M. (1998), Inferring probabilities from symmetries, Noûs 32, 231–246.Google Scholar
  34. Van Fraassen, B. (1989), Laws and Symmetry. Oxford: Clarendon Press.CrossRefGoogle Scholar
  35. Von Plato, J. (1983), The method of arbitrary functions, British Journal for the Philosophy of Science 34, 37–47.CrossRefGoogle Scholar

Copyright information

© Springer Netherlands 2011

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of Illinois at Urbana-ChampaignChampaignUSA

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