Loránd Eötvös University, Budapest, Hungary and

Visiting Scholar, UC Irvine

Reichenbach's Common Cause Principle asserts that if there exists a
statistical correlation between two events then either there is a direct
causal connection between the correlated events or there exists a
(Reichenbachian) common cause that explains the correlation. Assuming
that the Common Cause Principle is valid, one is led to the question of
whether theories that predict probabilistic correlations can be causally
rich enough to contain also the causes of the correlations. The talk
formulates this problem precisely and explicitly in terms of classical
(Kolmogorovian) probability spaces and presents results concerning common
cause completeability and common cause closedness of probabilistic
theories. Specifically, the following statements will be proved and
discussed.
(1) Every classical probability space containing a finite number of
correlations can be extended in such a way that the extension contains a
common cause of each correlation in the finite set.
(2) Different correlations cannot in general have the same common cause;
even two correlations maybe such that they cannot have a common common
cause.
(3) No probability space with a finite number of random events can
contain common causes of all the correlations it predicts; however,
probability spaces even with a finite number of random events can be
common cause closed with respect to a causal independence relation defined
between the random events if this independence relation is stronger than
logical independence.
## Friday, May 9, 2003

SST 777

3 pm

*Refreshments will be served*

©

SST 777

3 pm

©