Conditionals and Probability: A Classical Approach

Intuitively, it seems that both sentences are of the form: it’s likely that x, where, in the first case, x = Georgia will join the E.U. and, in the second case, x = if Russia needs foreign aid, Georgia will join the E.U.. Understanding how these sentences get their meaning as a function of the meaning of both the embedding construction, it’s likely that . . . , and the embedded sentence, x, would seem an easy task. The natural way would be to assume i) that in each case the particular sentence x expresses a proposition, and ii) that sentences of the form it’s likely that x are true iff x expresses a proposition that has a probability greater than one-half. In other words, in general, it’s likely that x is true iff p(x) > .5. This simple proposal leaves various questions unanswered. For instance, what does it mean for x to have a probability greater than one-half? Is it that the speaker has a credal state that assigns a subjective probability of more than one-half to x, or is that there is a more objective or intersubjective probability at stake? I will put this question aside, though, as a more basic problem confronts the proposal. ∗I am grateful to Chris Barker, Brett Sherman, and Philippe Schlenker for comments.