An Adamite Derivation of the Principles of the Calculus of Probability

  • Abner Shimony
Chapter
Part of the Synthese Library book series (SYLI, volume 192)

Abstract

If Adam was a rational man even before he had garnered much experience of the world, and if the ability to reason probabilistically is an essential part of rationality (as Bishop Butler maintained when he wrote that “But, to us, probability is the very guide of life,”1), then Adam must at least tacitly have known the Principles of the Calculus of Probability. Specifically, Adam must have known that the epistemic concept of probability — probability in the sense of “reasonable degree of belief” — satisfies these Principles, for it is the epistemic concept, rather than the frequency concept or the propensity concept, which enters into rational assessments about uncertain outcomes.2 But what warrant did Adam have for either an explicit or a tacit assertion that epistemic probability satisfies the Principles of the Calculus of Probability?

Keywords

Boolean Algebra Reference Class Countable Sequence Inductive Probability Dutch Book 
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References and Notes

  1. 1.
    Butler, Bishop Joseph, The Analogy of Religion, Natural and Revealed, to the Constitution and Course of Nature, ed. by. G. R. Crooks (Harper: New York, 1868), (originally published in 1736), third paragraph of the Introduction.Google Scholar
  2. 2a.
    Some philosophers have maintained, however, that the frequency concept of probability can be applied epistemically, for example, Hans Reichenbach, The Theory of Probability (U. of California: Berkeley, 1949)Google Scholar
  3. 2b.
    and Wesley C. Salmon, The Foundations of Scientific Inference (U. of Pittsburgh: Pittsburgh, 1966), pp. 83–96Google Scholar
  4. 2c.
    and Wesley C. Salmon, “Statistical Explanation,” in The Nature and Function of Scientific Theories, ed. by R. G. Colodny (U. of Pittsburgh: Pittsburgh, 1970), pp. 173–231.Google Scholar
  5. 3.
    Ramsey, Frank P., “Truth and Probability,” in The Foundations of Mathematics and Other Logical Essays (Routledge and Kegan Paul: London, 1931). Reprinted in Studies in Subjective Probability, ed. by H. Kyburg and H. Smokier (Wiley: New York, 1964).Google Scholar
  6. 4.
    DeFinetti, Bruno, “La prévision: ses lois logiques, ses sources subjectives,” Annales de l’Institut Henri Poincaré 7, 1–68 (1937). Reprinted in English translation in Studies in Subjective Probability, ed. by H. Kyburg and H. Smokier (Wiley: New York, 1964).Google Scholar
  7. 5.
    Shimony, Abner, “Coherence and the Axioms of Confirmation,” Journal of Symbolic Logic 20, 1–28 (1955).CrossRefGoogle Scholar
  8. 6.
    Richard T. Cox, “Probability, Frequency, and Reasonable Expectation,” American Journal of Physics 14, 1–13 (1946).CrossRefGoogle Scholar
  9. 7.
    Good, I. J., Probability and the Weighing of Evidence (C. Griffin: London, 1950).Google Scholar
  10. 8.
    Aczél, J, Lectures on Functional Equations and their Applications (Academic Press: New York, 1966).Google Scholar
  11. 9a.
    Shimony, Abner, “Scientific Inference,” in The Nature and Function of Scientific Theories, ed. by R. G. Colodny (U. of Pittsburgh: Pittsburgh, 1970), 79–172,.Google Scholar
  12. 9b.
    Shimony, Abner, “Scientific Inference,” in The Nature and Function of Scientific Theories, ed. by R. G. Colodny (U. of Pittsburgh: Pittsburgh, 1970), especially pp. 108–110.Google Scholar
  13. 10.
    Carnap, Rudolf, Logical Foundations of Probability (U. of Chicago: Chicago, 1950), pp. 168–175.Google Scholar
  14. 11.
    Only in Principle (ii) has it been explicitly stated that e is not the impossible proposition, but this restriction is a necessary condition for clauses like “P(h/e) is a well defined real number” which occur as antecedents in Principles (i), (iii), and (iv).Google Scholar
  15. 12.
    See Ref. 9, especially Section III Shimony, Abner, “Scientific Inference,” in The Nature and Function of Scientific Theories, ed. by R. G. Colodny (U. of Pittsburgh: Pittsburgh, 1970), especially pp. 108–110.Google Scholar
  16. 13a.
    For a discussion of the effect of correlations on the character of the estimate see Arthur Hobson, “The Interpretation of Inductive Probabilities,” Journal of Statistical Physics 6, 189–193 (1972) andCrossRefGoogle Scholar
  17. 13b.
    Abner Shimony, “Comment on the interpretation of inductive probabilities,” Journal of Statistical Physics 9,187–191 (1973).CrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company 1988

Authors and Affiliations

  • Abner Shimony
    • 1
  1. 1.Boston UniversityUSA

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