Advertisement

Stopping to Reflect

  • Mark J. Schervish
  • Teddy Seidenfeld
  • Joseph B. Kadane
Part of the Springer Graduate Texts in Philosophy book series (SGTP, volume 1)

Abstract

Our note is prompted by a recent article by Frank Arntzenius, “Some Problems for Conditionalization and Reflection,” which appeared in this Journal. Through a sequence of examples, that article purports to show limitations for a combination of two inductive principles that relate current and future rational degrees of belief: Temporal Conditionalization and Reflection:
$${P}_{later}(A) = {P}_{later}\left(A|B\right) = {P}_{now}\left(A|B\right) $$
$$ {P}_{now}\left(A|{P}_{later}(A)=r\right)=r. $$
We will use the expression “Reflection holds with respect to the event A.” to apply to this equality for a specific event A.

Keywords

Local Time Rational Agent Conditional Independence Standard Designator Fair Coin 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Our research was carried out under NSF Grant DMS 0139911. We thank Joseph Halpern for alerting one of us (T.S.) to the Sleeping Beauty problem, independent of Arntzenius’ article.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Mark J. Schervish
    • 1
  • Teddy Seidenfeld
    • 1
  • Joseph B. Kadane
    • 1
  1. 1.Carnegie Mellon UniversityPittsburghUSA

Personalised recommendations