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Admissibility and Bayesian direct inference: no HOPe against ubiquitous defeaters

Gyenis, Zalán and Wronski, Leszek (2020) Admissibility and Bayesian direct inference: no HOPe against ubiquitous defeaters. [Preprint]

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Abstract

In this paper we discuss the ``admissibility troubles'' for Bayesian accounts of direct inference proposed in (Wallmann, 2018), which concern the existence of surprising, unintuitive defeaters even for mundane cases of direct inference. We first show that one could reasonably suspect that the source of these troubles was informal talk about higher-order probabilities: for cardinality-related reasons, classical probability spaces abound in defeaters for direct inference. We proceed to discuss the issues in the context of the rigorous framework of Higher Probability Spaces (Gaifman, 1988). However, we show that the issues persist; we prove a few facts which pertain both to classical probability spaces and to HOPs, in our opinion capturing the essence of the problem. In effect we strengthen the message from the admissibility troubles: they arise not only for approaches using classical probability spaces---which are thus necessarily informal about metaprobabilistic phenomena like agents having credences in propositions about chances---but also for at least one respectable framework specifically tailored for rigorous discussion of higher-order probabilities.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Gyenis, Zalángyz@renyi.hu
Wronski, Leszekleszek.wronski@uj.edu.pl
Keywords: Bayesianism, probabilistic defeaters, Higher order probability
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Probability/Statistics
Depositing User: Zalán Gyenis
Date Deposited: 30 Jan 2020 00:09
Last Modified: 30 Jan 2020 00:09
Item ID: 16860
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Probability/Statistics
Date: 23 January 2020
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/16860

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