ABSTRACT
Conditionalization (v0) makes reference to three events: the subject having credences cr , the subject receiving evidence E , and the subject adopting new credences cr
E . 5 How are the times of these events – call them t ( cr ), t ( E ) and t(cr
E )
– related? 6 Certain constraints are clear: the time at which a subject adopts cr E
should not be before the time at which she receives E as evidence, and she should adopt cr
E at some point after she has cr . But are there other constraints
on the timing of these events? Let’s focus here on the relation between t ( E ) and t(cr
E ) . (We’ll consider the
relation between these times and t ( cr ) at the end of Section 3.1 .)
Q3. The Time of Evidence Question: How is the time at which the subject receives her evidence related to the time at which she should adopt her new credences? 7
Answers to this question fall into two camps. First, one might hold that subjects should adopt their new credences after they’ve received their new evidence, so that t(E) < t(cr
E ) . Because time is dense – given any two distinct times
there will be some time in-between – it follows that if t(E) < t(cr E ) , there are
times in-between t ( E ) and t(cr E ) . That is, there will be a temporal gap between
t ( E ) and t(cr E ) :
Answer 1 (Posterior). The subject should adopt her new credences some fi nite amount of time after she gets her evidence. We can make this understanding explicit by adding times to our formulation, following the usual convention of using time indices to refl ect the diff erences between these times (e.g. t
1 is one
unit of time after t 0 , according to some linear measure):
Conditionalization (v1.1): If a subject with credences cr gets evidence E at t 0 , she should adopt new credences cr
E at t
1 such that cr
E (⋅) = cr(⋅|E) , if defi ned.
