The shooting-room paradox and conditionalizing on measurably challenged sets

Synthese 118 (3):403-437 (1999)
  Copy   BIBTEX

Abstract

We provide a solution to the well-known “Shooting-Room” paradox, developed by John Leslie in connection with his Doomsday Argument. In the “Shooting-Room” paradox, the death of an individual is contingent upon an event that has a 1/36 chance of occurring, yet the relative frequency of death in the relevant population is 0.9. There are two intuitively plausible arguments, one concluding that the appropriate subjective probability of death is 1/36, the other that this probability is 0.9. How are these two values to be reconciled? We show that only the first argument is valid for a standard, countably additive probability distribution. However, both lines of reasoning are legitimate if probabilities are non-standard. The subjective probability of death rises from 1/36 to 0.9 by conditionalizing on an event that is not measurable, or whose probability is zero. Thus we can sometimes meaningfully ascribe conditional probabilities even when the event conditionalized upon is not of positive finite (or even infinitesimal) measure.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,322

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Game birds: The ethics of shooting birds for sport.Rebekah Humphreys - 2010 - Sport, Ethics and Philosophy 4 (1):52 – 65.
Conditionalizing on knowledge.Timothy Williamson - 1998 - British Journal for the Philosophy of Science 49 (1):89-121.
Physical probabilities.Peter Milne - 1987 - Synthese 73 (2):329 - 359.
A shooting-room view of doomsday.William Eckhardt - 1997 - Journal of Philosophy 94 (5):244-259.
Countable additivity and the de finetti lottery.Paul Bartha - 2004 - British Journal for the Philosophy of Science 55 (2):301-321.

Analytics

Added to PP
2009-01-28

Downloads
211 (#91,799)

6 months
45 (#87,161)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Christopher Hitchcock
California Institute of Technology
Paul Bartha
University of British Columbia

Citations of this work

Regularity and Hyperreal Credences.Kenny Easwaran - 2014 - Philosophical Review 123 (1):1-41.
Infinitesimal Probabilities.Vieri Benci, Leon Horsten & Sylvia Wenmackers - 2016 - British Journal for the Philosophy of Science 69 (2):509-552.
Symmetry arguments against regular probability: A reply to recent objections.Matthew W. Parker - 2019 - European Journal for Philosophy of Science 9 (1):1-21.

View all 16 citations / Add more citations