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Categorical Versus Graded Beliefs.

Franz Dietrich1

  • 1Paris School of Economics, CNRS, Paris, France.

Frontiers in Psychology
|April 7, 2022
PubMed
Summary

This study explores the conflict between categorical (yes/no) and probabilistic (degrees of) beliefs. It examines how the lottery paradox and impossibility theorems challenge the simultaneous use of both belief systems.

Keywords:
belief binarizationbinary beliefcredenceimpossibility theoremlogic vs. rational choice theorylottery paradoxsubjective probabilityyes/no belief vs. graded belief

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Area of Science:

  • Philosophy of Mind
  • Decision Theory
  • Epistemology

Background:

  • Two main paradigms of belief exist: categorical (yes/no) and probabilistic (degrees of).
  • Reconciling these paradigms presents significant theoretical challenges.
  • The lottery paradox highlights issues with categorical beliefs about numerous propositions.

Purpose of the Study:

  • To analyze the inherent tension between categorical and probabilistic belief systems.
  • To assess the implications of recent impossibility theorems on belief reconciliation.
  • To explain the nature and relevance of this philosophical difficulty.

Main Methods:

  • Conceptual analysis of belief paradigms.
  • Examination of the lottery paradox.
  • Discussion of the Dietrich-List impossibility theorem.

Main Results:

  • The simultaneous holding of categorical and probabilistic beliefs is shown to be problematic.
  • Impossibility theorems provide formal challenges to integrating both belief types.
  • The tension between belief systems has significant implications for rational decision-making.

Conclusions:

  • Reconciling categorical and probabilistic beliefs is a complex philosophical problem.
  • The findings challenge existing models of belief representation.
  • Further research is needed to develop coherent theories of belief.