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The frequency interpretation and antecedent probabilities

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Notes

  1. R. Carnap's view that two different concepts of probability are required seems to stem, partly at least, from the view that the frequency interpretation cannot adequately handle the probability of theories. Carnap,Logical Foundations of Probability (Chicago: University of Chicago Press, 1950), Chap. II. Even the frequentist R. von Mises,Positivism (Cambridge, Mass.: Harvard University Press, 1951), pp. 171 ff, believes it is a “transgression of the borderline” to apply the frequency interpretation to the probability of theories.

  2. For example, see H. Reichenbach,Theory of Probability (Berkeley: University of California Press, 1949), pp. 95f and 362.

  3. I am using a notation adopted by Reichenbach, inTheory of Probability. This work contains a derivation of Bayes' theorem and a complete explanation of the notation. [Editors' Note: Limitations in the available type have forced us to replace the overline by which Reichenbach represents negation by a prime.]

  4. Even a theory which we regard as true may suffer disconfirming observations. They are usually explained as errors of observation and measurement.

  5. Of course, the truth of theories used in the lattice may have been established by a previous lattice inference. However, by recursion we would sooner or later arrive at lattices which presuppose no previous lattice inferences, only inductions by enumeration.

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  1. State College of Washington, USA

    Wesley C. Salmon

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  1. Wesley C. Salmon
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Salmon, W.C. The frequency interpretation and antecedent probabilities. Philos Stud 4, 44–48 (1953). https://doi.org/10.1007/BF02292859

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