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Foundations of Probability

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Abstract

The foundations of probability are viewed through the lens of the subjectivist interpretation. This article surveys conditional probability, arguments for probabilism, probability dynamics, and the evidential and subjective interpretations of probability.

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Notes

  1. [71] objects that the constraints are implausible; [49] responds by developing a revised set of constraints.

  2. In decision theoretic representation theorems, the uniqueness component also requires that the utility function be unique up to positive linear transformation, i.e., if both 〈P, U〉 and 〈P ′, U ′〉 represent the same preference ordering, then there exit some positive real number a and real number b such that U = a U ′+b.

    The decision theoretic representation theorem in [45] famously fails to secure the uniqueness half of the theorem; some preference orderings are represented by a 〈P, U〉 and a 〈P ′ U ′〉 where P≠P ′. Joyce [48] shows we can regain uniqueness by supplementing Jeffrey’s constraints on preferences with additional constraints on comparative belief, and on the relationship between comparative belief and preference.

  3. Note, however, that one can to weaken the constraints so that agents are no longer representable as expected utility maximisers, while still allowing that they have a representation that includes a unique credence function [10].

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  1. School of Philosophy, Coombs Building 9, Australian National University, Acton, ACT, Australia

    Rachael Briggs

  2. Department of Philosophy, Stanford University, 450 Serra Mall Main Quad, Building 90, Stanford, CA, 94305, USA

    Rachael Briggs

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Briggs, R. Foundations of Probability. J Philos Logic 44, 625–640 (2015). https://doi.org/10.1007/s10992-015-9377-3

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