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Jürgen Landes; Jon Williamson (2015)
Publisher: MDPI AG
Journal: Entropy
Languages: English
Types: Article
Subjects: BC, predicate language, Astrophysics, g-entropy, B1, QB460-466, Q, objective Bayesianism, Science, Physics, scoring rule, QA273, QC1-999, minimax
Identifiers:doi:10.3390/e17042459
Objective Bayesianism says that the strengths of one’s beliefs ought to be probabilities, calibrated to physical probabilities insofar as one has evidence of them, and otherwise sufficiently equivocal. These norms of belief are often explicated using the maximum entropy principle. In this paper we investigate the extent to which one can provide a unified justification of the objective Bayesian norms in the case in which the background language is a first-order predicate language, with a view to applying the resulting formalism to inductive logic. We show that the maximum entropy principle can be motivated largely in terms of minimising worst-case expected loss.
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    • 2. There are several alternatives to the objective Bayesian account of strength of belief, including subjective Bayesianism, imprecise probability, the theory of Dempster-Shafer belief functions and related theories. Here we only have the space to motivate objective Bayesianism, not to assess these other views.
    • 3. Taking the convex hull may mean that a calibrated belief function does not satisfy the known constraints on physical probability. For example, if is known to be a statement about the past then it is known that its physical probability is 0 or 1; bel is not constrained to be 0 or 1, however, unless it is also known whether or not is true. Similarly, it may be known that two propositions are probabilistically independent with respect to physical probability; this need not imply that they are probabilistically independent with respect to epistemic probability. See Williamson [1] (pp. 44-45) for further discussion of this point.
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