MARC LANGE
IS JEFFREY CONDITIONALIZATION DEFECTIVE BY VIRTUE OF
BEING NON-COMMUTATIVE? REMARKS ON THE SAMENESS OF
SENSORY EXPERIENCES
1. INTRODUCTION
It has often been held (e.g., by Domotor 1980; Skyrms 1986; van Fraassen
1989; Döring 1999) that Jeffrey’s rule for updating degrees of belief on
the basis of uncertain evidence (“Jeffrey conditionalization”) is defective
by virtue of being non-commutative: if we switch the order in which a
pair of observations is taken into account by the rule, then we may change
the degrees of belief ultimately generated by the rule. I shall argue that
although Jeffrey’s rule is formally noncommutative, this does not represent
a defect in the rule. On the contrary, this kind of non-commutativity is
exactly right. The key point will be that in switching the order in which
numbers are plugged into Jeffrey’s rule, we are not really switching the
order in which the same two sensory experiences are taken into account.
Rather, we are dealing with entirely different pairs of observations. That is
why they should generally yield different final degrees of belief.
2. WHY JEFFREY CONDITIONALIZATION HAS BEEN CONSIDERED
NON- COMMUTATIVE
Bayesian conditionalization is a rule for revising our subjective probability
judgments in light of experience. If the agent learns that e is the case,
and e captures all that the agent has learned from her experience, and
pr
old
(.) is her probability distribution before discovering e, and pr
new
(.)
is her probability distribution after discovering e, and 0 < pr
old
(e) < 1
and 0 < pr
old
(h) < 1, then according to Bayesian conditionalization, the
agent’s pr
new
(h) should equal her pr
old
(h|e).
In his influential (1965; 1983) , Richard Jeffrey proposed a means of
extending Bayesian conditionalization to a case where there is “no propos-
ition e in the agent’s preference ranking of which it can correctly be said
Synthese 123: 393–403, 2000.
© 2000 Kluwer Academic Publishers. Printed in the Netherlands.