Doxastic Indicative Conditionals
Here is a suggestion for a pure doxastic account of indicative conditionals:
‘If A, then C‘ is true iff the most probable world which verifies A also verifies C.
By representing degrees of beliefs or credences by a set of possible worlds, we can determine a closeness relation between worlds directly in terms of credences. By looking at an agent’s actual credences, or a group of agents’ actual credences, we can assign a probability to each possible world w. We can think of this distribution as describing the likelihood of w being the actual world. In this sense, in evaluating an indicative conditional, we hold all those credences fixed that are left untouched by the antecedent A, and this set of credences determines, in a given context, a set of doxastically possible worlds, one (or more) of which gets assigned the highest probability for being actual. In the doxastically speaking most probable world, we then check whether C is verified. If it is, the conditional is true; otherwise false or indeterminate.
The general problem with pure doxastic accounts of indicative conditionals is that the truth-value of a particular indicative conditional is radically relative to a speaker’s, or a group of speakers’, background beliefs. Here are two variations of such a problem.