Abstract
In this paper, a concept of chance is introduced that is compatible with deterministic physical laws, yet does justice to our use of chance-talk in connection with typical games of chance, and in classical statistical mechanics. We take our cue from what Poincaré called “the method of arbitrary functions,” and elaborate upon a suggestion made by Savage in connection with this. Comparison is made between this notion of chance, and David Lewis’ conception.
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Notes
- 1.
See Hacking [1] for a masterful overview of the history.
- 2.
Poisson says “croix et pile”; heads and tails is our equivalent.
- 3.
Dans la langage ordinaire, les mots chance et probabilité sont á peu prés synonymes. Le plus souvent nous emploierons indifféremment l’un et l’autre; mais lorsqu’il sera nécessaire de mettre une différence entre leurs acceptions, on rapportera, dans cet ouvrage, le mot chances aux événements en eux-mêmes et indépendamment de la connaissance que nous en avons, et l’on conservera au mot probabilité sa définition précédente. Ainsi, un événement aura, par sa nature, une chance plus ou moins grande, connue ou inconnue; et saprobabilité sera relative á nos connaissances, en ce qui le concerne.
Par exemple, au jeu de croix et pile, la chance de l’arrivée de croix et celle de l’arrivée de pile, résultent de la constitution de la pièce que l’on projette ; on peut regarder comme physiquement impossible que l’une de ces chances soit égale à l’autre; cependant, si la constitution du projectile nous est inconnue, et si nous ne l’avons pas déjà soumis à des épreuves, la probabilité de l’arrivée de croix est, pour nous, absolument la même que celle de l’arrivée de pile: nous n’avons, en effet, aucune raison de croire plutôt à l’un qu’à l’autre de ces deux événements. I’l n’en est plus de même, quand la pièce a été projetée plusieurs fois: la chance propre à chaque face ne change pas pendant les épreuves; mais, pour quelqu’un qui en connaît le résultat, la probabilité de l’arrivée future de croix ou de pile, varie avec les nombres de fois ces deux faces se sont déjà présentées.
- 4.
- 5.
Though perhaps this should go without saying, it should be emphasized that taking frequency data as evidence about chances is not tantamount to holding a frequency interpretation of chance.
- 6.
Though, it must be noted, Lewis [13, p. 119] has suggested that this is false.
- 7.
The parenthetical qualification is due to the fact that, though, in some passages de Finetti sounds like a radical subjectivist, there are others that indicate a more moderate position.
- 8.
This example is inspired by the behaviour of the character played by James Garner in the comic western Support Your Local Gunfighter (1971).
- 9.
Quelle est la probabilité pour que cette impulsion ait telle ou telle valeur? Je n’en sais rien, mais il m’est difficile de ne pas admettre que cette probabilité est representée par une fonction analytique continue.
- 10.
Note that there is a shift of notation between Calcul des Probabilités and Science and Hypothesis; φ is here a density function over the final angle, that is, the function we have been calling f.
- 11.
After the ball has been released is another matter.
- 12.
For some references to this literature, and skepticism about the possibility of a cogent justification, see Strevens [21].
- 13.
Once again, these time-evolved credence functions might not be Alice and Bob’s credences about the states of affairs at t 1, if they don’t know the dynamics of the system, or are unable to do the requisite calculation.
- 14.
Note that, without this condition on credences, which Lewis calls regularity, nothing can follow about what chances actually are like from the PP, which is a condition on the credences of a reasonable agent, and hence can only tell us what a reasonable agent must believe.
References
Hacking, I.: The Emergence of Probability. Cambridge University Press, Cambridge (1975)
Poisson, S.-D.: Recherches sur la Probabilité des Jugements en Matiére Criminelle et en Matiére Civile, précédées des régles générales du calcul des probabilités. Bachelier, Imprimeur-Libraire, Paris (1837)
de Finetti, B.: La prevision: ses lois logiques, ses sources subjectives. Ann. Inst. Henri Poincaré 7, 1–68 (1937). English translation in [4]
de Finetti, B.: Foresight: its logical laws, its subjective sources. In: Kyburg, H.E., Smokler, H.E. (eds.) Studies in Subjective Probability. Krieger, Huntington (1980). Translation of [3]
Savage, L.J.: The Foundations of Statistics. Dover, New York ([1954] 1972)
Popper, K.R.: The propensity interpretation of the calculus of probability, and the quantum theory. In: Körner, S. (ed.) Observation and Interpretation: A Symposium of Philosophers and Physicists, pp. 65–70. Butterworths, London (1957)
Popper, K.R.: The propensity interpretation of probability. Br. J. Philos. Sci. 37, 25–42 (1959)
Daston, L.: Classical Probability in the Enlightenment. Princeton University Press, Princeton (1988)
Cournot, A.A.: Exposition de la Théorie des Chances et des Probabilités. Librairie de L. Hachette, Paris (1843)
Howie, D.: Interpreting Probability: Controversies and Developments in the Early Twentieth Century. Cambridge University Press, Cambridge (2002)
Laplace, P.-S.: A Philosophical Essay on Probabilities. Dover, New York ([1902] 1951) [27]
Hacking, I.: Equipossibility theories of probability. Br. J. Philos. Sci. 22, 339–355 (1971)
Lewis, D.: Postscripts to “A subjectivist’s guide to objective chance”. In: Philosophical Papers, IIth edn, Vol. II. Oxford University Press, Oxford (1986)
Schaffer, J.: Deterministic chance? Br. J. Philos. Sci. 58, 113–140 (2007)
von Plato, J.: The method of arbitrary functions. Br. J. Philos. Sci. 34, 37–47 (1983)
Savage, L.J.: Probability in science: a personalistic account. In: Suppes, P. (ed.) Logic Methodology, and Philosophy of Science IV, pp. 417–428. North-Holland, Amsterdam (1973)
Shimony, A.: Scientific inference. In: Colodny, R. (ed.) The Nature and Function of Scientific Theories, pp. 79–172. Pittsburgh University Press, Pittsburgh (1971). Reprinted in [28]
Poincaré, H.: Calcul des probabilités. Gauthier-Villars, Paris (1912)
Poincaré, H.: Science and Hypothesis. Dover, New York ([1905] 1952)
Machina, M.J.: Almost-objective uncertainty. Econ. Theory 24, 1–54 (2004)
Strevens, M.: Objective probability as a guide to the world. Philos. Stud. 95, 243–275 (1999)
Albert, D.: Time and Chance. Harvard University Press, Cambridge (2000)
Jeffrey, R.C.: The Logic of Decision. McGraw-Hill, New York (1965)
Skyrms, B.: Resiliency, propensities, and causal necessity. J. Philos. 74, 704–713 (1977)
Skyrms, B.: Causal Necessity. Yale University Press, New Haven (1980)
Lewis, D.: A subjectivist’s guide to objective chance. In: Jeffrey, R.C. (ed.) Studies in Inductive Logic and Probability, Vol. II, pp. 263–293. University of California Press, Berkeley (1980)
Laplace, P.-S.: Essai Philosophique sur les Probabilités. Courcier, Paris (1814). English translation in Laplace (1951)
Shimony, A.: Search for a Naturalistic World View. Scientific Method and Epistemology, vol. I. Cambridge University Press, Cambridge (1993)
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This work is supported by a grant from the Social Sciences and Humanities Research Council of Canada.
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Myrvold, W.C. (2012). Deterministic Laws and Epistemic Chances. In: Ben-Menahem, Y., Hemmo, M. (eds) Probability in Physics. The Frontiers Collection. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21329-8_5
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