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Comparative infinite lottery logic.

Matthew W Parker1

  • 1Rotman Institute of Philosophy, Western University, Western Interdisciplinary Research Building, 1151 Richmond Street North, London, Ontario, N6A 5B7, Canada.

Studies in History and Philosophy of Science
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A new comparative logic for infinite lotteries addresses limitations in Norton's Material Theory of Induction. This approach offers better guidance for lottery choices but doesn't resolve multiverse model evaluation challenges.

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Area of Science:

  • Philosophy of Science
  • Probability Theory
  • Cosmology

Background:

  • Norton's Material Theory of Induction proposes a novel logic for infinite lotteries and multiverse models.
  • Standard probability theory faces challenges with infinite sets and label independence.

Purpose of the Study:

  • To develop an alternative inductive logic for infinite lotteries that satisfies label independence.
  • To address the limitations of Norton's approach in evaluating multiverse models.

Main Methods:

  • Introduced a purely comparative infinite lottery logic based on 'at most as likely' relations.
  • Avoided primitive chances and reification of inductive support.
  • Ensured label independence and a comparative version of additivity.

Main Results:

  • The proposed logic satisfies label independence and comparative additivity.
  • It provides finer distinctions between events than Norton's logic.
  • The logic offers improved advice for choosing between sets of lottery tickets.

Conclusions:

  • Norton's negative results stem from a fundamental issue in comparing disjoint countably infinite sets.
  • The developed logic, while improving lottery analysis, does not significantly aid multiverse model evaluation.
  • Further research is needed to address the comparison of infinite sets.