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Symmetry and partial belief geometry

Abstract

When beliefs are quantified as credences, they are related to each other in terms of closeness and accuracy. The “accuracy first” approach in formal epistemology wants to establish a normative account for credences (probabilism, Bayesian conditioning, principle of indifference, and so on) based entirely on the alethic properties of the credence: how close it is to the truth. To pull off this project, there is a need for a scoring rule. There is widespread agreement about some constraints on this scoring rule (for example propriety), but not whether a unique scoring rule stands above the rest. The Brier score equips credences with a structure similar to metric space and induces a “geometry of reason.” It enjoys great popularity in the current debate. I point out many of its weaknesses in this article. An alternative approach is to reject the geometry of reason and accept information theory in its stead. Information theory comes fully equipped with an axiomatic approach which covers probabilism, standard conditioning, and Jeffrey conditioning. It is not based on an underlying topology of a metric space, but uses a non-commutative divergence instead of a symmetric distance measure. I show that information theory, despite initial promise, also fails to accommodate basic epistemic intuitions; and speculate on its remediation.

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Acknowledgments

I want to thank Paul Bartha at the University of British Columbia and Franz Huber at the University of Toronto for their support as I worked on this paper.

Funding

The author received financial support for the research, authorship, and publication of this article from the Social Sciences and Humanities Research Council, SSHRC award 756-2017-0286.

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Correspondence to Stefan Lukits.

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This article belongs to the Topical Collection: EPSA2019: Selected papers from the biennial conference in Geneva

Guest Editors: Anouk Barberousse, Richard Dawid, Marcel Weber

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Lukits, S. Symmetry and partial belief geometry. Euro Jnl Phil Sci 11, 79 (2021). https://doi.org/10.1007/s13194-021-00398-x

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  • DOI: https://doi.org/10.1007/s13194-021-00398-x

Keywords

  • Bayesian conditionalization
  • Epistemic utility
  • Formal epistemology
  • Geometry of reason
  • Gradational accuracy
  • Information theory
  • Jeffrey conditioning
  • Partial beliefs; principle of maximum entropy
  • Probabilism
  • Probability kinematics
  • Probability update
  • Convex analysis
  • Scoring rules
  • Probabilistic forecast