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The British Journal for the Philosophy of Science Advance Access published online on August 10, 2005
The British Journal for the Philosophy of Science, doi:10.1093/bjps/axi132
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© The Author (2005). Published by Oxford University Press on behalf of British Society for the Philosophy of Science. All rights reserved. For Permissions, please email: journals.permissions@oupjournals.org

Article

Probability Theory and Causation: A Branching Space-Times Analysis

Thomas Müller 1*

1 Philosophisches Seminar, LFB III, Universität Bonn, Lennéstr. 39, 53113 Bonn, Germany

* To whom correspondence should be addressed.
Thomas Müller, E-mail: Thomas.Mueller{at}uni-bonn.de


  Abstract

We provide a formally rigorous framework for integrating singular causation, as understood by Nuel Belnap's theory of causae causantes, and objective single case probabilities. The central notion is that of a causal probability space whose sample space consists of causal alternatives. Such a probability space is generally not isomorphic to a product space. We give a causally motivated statement of the Markov condition and an analysis of the concept of screening-off.

1 Causal dependencies and probabilities

 1.1 Background: causation in branching space-times

 1.2 What are probabilities defined for?

2 Basic transitions

 2.1 Basics of basic transitions

 2.2 Sets of basic transitions

3 Causal probability theory

 3.1 Some simple cases

 3.2 General causal probabilities

 3.3 Application: probability of suprema of a chain


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