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?
This paper is based upon a lecture given at the University of Pittsburgh in January 1982. A similar thesis is developed independently by Bas van Fraassen in “Calibration: A Frequency Justification for Personal Probability,” in Physics, Philosophy, and Psychoanalysis: Essays in Honor of Adolf Grünbaum, ed. by R. S. Cohen and L. Laudan (D. Reidel: Dordrecht and Boston, 1983). I dedicate the paper to Wesley C. Salmon, because he explored with penetration and devotion the epistemic applicability of the frequency concept of probability.
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References and Notes
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.
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)
and Wesley C. Salmon, The Foundations of Scientific Inference (U. of Pittsburgh: Pittsburgh, 1966), pp. 83–96
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.
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).
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).
Shimony, Abner, “Coherence and the Axioms of Confirmation,” Journal of Symbolic Logic 20, 1–28 (1955).
Richard T. Cox, “Probability, Frequency, and Reasonable Expectation,” American Journal of Physics 14, 1–13 (1946).
Good, I. J., Probability and the Weighing of Evidence (C. Griffin: London, 1950).
Aczél, J, Lectures on Functional Equations and their Applications (Academic Press: New York, 1966).
Shimony, Abner, “Scientific Inference,” in The Nature and Function of Scientific Theories, ed. by R. G. Colodny (U. of Pittsburgh: Pittsburgh, 1970), 79–172,.
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.
Carnap, Rudolf, Logical Foundations of Probability (U. of Chicago: Chicago, 1950), pp. 168–175.
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).
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.
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) and
Abner Shimony, “Comment on the interpretation of inductive probabilities,” Journal of Statistical Physics 9,187–191 (1973).
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Shimony, A. (1988). An Adamite Derivation of the Principles of the Calculus of Probability. In: Fetzer, J.H. (eds) Probability and Causality. Synthese Library, vol 192. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3997-4_3
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DOI: https://doi.org/10.1007/978-94-009-3997-4_3
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