Supervaluationism and Relativism are popular accounts of future contingents. Even though they differ quite radically, they agree, at least in their most common forms, in how they evaluate present utterances about the future. For instance, consider the sentence A = ‘The coin will come down heads’ as it is evaluated from the present time t. Both the supervaluationist and the relativist will say: A is (a) supertrue at t/(with respect to t) just in case there is no objective chance at t that A is false, (b) superfalse at t/(with respect to t) just in case there is no objective chance at t that A is true, (c) neither supertrue nor superfalse otherwise.
In general, supervaluationism and relativism seem to fare better as accounts of future contingents than as theories of vagueness, since there is no equivalent of the problem of higher-order vagueness for future contingents. In this note, I will try to challenge this assumption by pointing to a problem which seems to arise for supervaluationism and relativism with respect to future contingents without being as problematic in the case of vagueness.
Posted by Moritz.
The problem I have in mind concerns our credences in sentences like ‘The coin will come down heads’. In most situations, it will be the right thing to think that it is roughly 50% likely that the coin will come down heads. The question is whether Supervaluationism and Relativism can explain this kind of epistemic attitude. The corresponding problem in the case of vagueness would concern our credences in statements about borderline cases. But it is less clear whether we should have definite credences with respect to borderline cases. It may well be that we should simply suspend jugdment (or stick with a coarse grained ordering of likelihoods). So, the problem of our epistemic attitudes with respect to sentences which are neither supertrue nor superfalse is less pressing in the case of vagueness than it is in the case of future contingents.
Let’s state the case. Consider a convinced indeterminist who is certain that it is a truely chancy matter whether the coin will come down heads or not. Also, he thinks that there is an objective chance of 50% that the coin will come down heads. Since he has no other relevant information about the future, he assings subjective probability 1/2 to this statement. In this situation, this seems to be the right thing to think. Now given supervaluationist’s and relativist’s views about how to evaluate such statements, it is hard to see how this can be explained. For, our indeterminist has only trivial attitudes towards the sentence’s semantic value as described by supervaluationism and relativism: he can be certain that the sentence is neither supertrue nor superfalse, since he is certain that there is both an objective possibility which would verify the sentence and an objective possibility which would falsify it. Consequently, he can be certain that it is neither supertrue nor superfalse that the coin will come down heads. Hence, his credence in this statement does not aim at supertruth (nor at some weighted average between the three values as is obvious from the fact that supertruth and superfalsity get credence 0). So, how can our non-trivial credences in statements about the future be justified within the framework of supervaluationism and relativism?