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Uniform probability in cosmology.

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  • 1Centre for Logic and Philosophy of Science, Institute of Philosophy, KU Leuven, Belgium.

Studies in History and Philosophy of Science
|September 10, 2023
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Summary
This summary is machine-generated.

The measure problem in cosmology complicates probability assignments for pocket universes. This study clarifies obstacles by examining uniform probabilities on infinite spaces, suggesting multiple consistent mathematical approaches for cosmological theories.

Keywords:
CosmologyInfinityMeasure problemParadoxProbability theory

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Area of Science:

  • Cosmology
  • Probability Theory
  • Inflation Theory

Background:

  • Uniform probabilities on infinite supports present challenges in contemporary cosmology.
  • The measure problem in cosmology complicates probability measure assignments for pocket universes within inflation theory.

Purpose of the Study:

  • Introduce philosophers of probability to recent cosmological discussions.
  • Familiarize cosmologists with foundational probabilistic work.
  • Clarify the origins of obstacles in solving the cosmological measure problem.

Main Methods:

  • Analysis of paradoxes arising from uniform probabilities on infinite sample spaces.
  • Review of foundational work by probabilists like Kolmogorov, de Finetti, and Jaynes.
  • Examination of assumptions underlying probability paradoxes.

Main Results:

  • Identified paradoxes in standard probability theory involving infinite sample spaces.
  • Highlighted the connection between these paradoxes and the cosmological measure problem.
  • Indicated that multiple consistent methods exist for handling uniform probabilities on infinite spaces.

Conclusions:

  • The cosmological measure problem is linked to fundamental issues in probability theory.
  • A pluralist approach to mathematical methods in cosmology can facilitate progress.
  • Further work can build upon foundational probability theory to address cosmological measure challenges.