A Problem for Supervaluationism and Relativism?

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?



  1. What about the following:

    When at some time confronted with a sentence like “The coin will come down heads”, we do not aim at supertruth of this sentence at this time, but at supertruth of some other sentence at some other time. In this case: We aim for supertruth of “The coin shows heads” at the time of the coin’s landing. As it should be, this leads us to assign 0.5 as our credence in “The coin will come down heads” at a time before the coin lands: We know that “The coin shows heads” at the time of the landing is either supertrue or superfalse. How likely is it that it is supertrue? 50%!

    I am probably missing something basic. But what?

  2. That’s interesting. I doubt, though, that the supervaluationist or the relativist can avail themselves of your proposal. Here is why:

    Let’s assume that there is to any sentence an earliest point in time at which it gets either verified or falsified, i.e. at which it becomes either supertrue or superfalse. Call this time decision day. Now, the proposal would be that our credences aim at supertruth at decision day.

    First, let us note that the predicate ‘is supertrue at decision day’ applies no longer relative to times. Second, note that any sentence is either supertrue or superfalse at decision day. Hence, ‘is supertrue at decision day’ becomes equivalent to a bivalent truth predicate which is not relativized to times. So, the supervaluationist and the relativist would avail themselves of the very notion they are opposing to. That would strike me as an incoherent position…

  3. Hi there,

    I think this is a really interesting issue.

    There’s also an issue about the connections between logic and credences here. Supervaluational systems are famously revisionary at the level of logic. And if we presuppose standard connections between credences and logic, we can argue directly for (a) a non-classical treatment of degrees of belief; (b) that where we know that p is a truth-value gap, the logic-credence constraints force us to have credence 0 in both p and in ~p.

    (FWIW, some of the details and references are in the blog post here:

    I agree that “belief aims at supertruth” is a way of motivating something similar. Both the “aim of belief” way of getting the result, and the logic-based route are I think resistable, but there may be different costs to resisting in the different cases. E.g. one might claim that the following schematic claim (a rough attempt to explicate the “”aiming” talk) is false:

    one should believe p only if T(p)

    but the following is true:

    one should believe p only if p.

    Now, if someone takes this line, I wonder how to respond (other than say that it deprives truth of an important theoretical role). To me, breaking connections between rational credences and logic is a bigger deal—and then we get a connection with debates about local and global consequence and revisionism. So, even though it’s more long-winded, I reckon the logic stuff may be the way to make most mileage in this area.

    By the way, I totally agree that the future contingents case give far more traction than borderline cases of vague predicates. I also reckon that certain other cases give some mileage… in particular, vague instances of personal identity, and vague indicative conditionals.

  4. Hi Robbie,

    thanks for connecting the issue with the question of how the logic of supervaluationism relates to credences. It took me a while to figure it out, but now I see that given a certain assumption about the logic of supertruth, we can exploit the logic-credence link to generate the very same problem. Pretty cool.

  5. Hi Moritz,

    Your problem is analogous to a problem with probability faced by some defenders of the many-worlds interpretation of QM, because they can’t say prior to a branching event anything corresponding to ‘I’m uncertain what will happen’. The whole system of worlds is deterministic and in principle you could know exactly what happens in both branches resulting from a chancy event. But if you can know everything about the future there’s no room for non-trivial expectations.

    What this problem has in common with yours is that prior to branching / decision day, the subject has no way to express non-trivial expectation – there is (at the time) no relevant fact of the matter for them to be uncertain about.

    In the QM case, some have posited novel principles of rationality. But as Robbie argues, it’s a last resort to modify the connections between logic and rational credence. And if you don’t want to modify logic either, then I think the problem for relativism/supervaluationism about the future is a real one.

    By the way – sorry I’ve taken so long to find your (group’s) blog. And also sorry I missed you in Oxford last week. I also have a blog at mrogblog.wordpress.com which you might like to take a look at.


  6. Hi Al,

    thanks for that comment! About a year or two ago I heard a talk by David Wallace (perhaps you were present too) discussing some aspects of discourse about the future and the many-worlds interpretation of QM which I found very interesting (one can find the corresponding paper here). Due to that talk I had the vague impression that there must be some kind of parallel problem, but I couldn’t see clearly how it would look like.

    One minor point. You say that given the many-worlds interpretation, one could (at least in principle and probably modulo some structural limits of knowldedge in general) know everything about the branches. There is definitely something to that claim, but I wonder whether the following would tell against it. It seems that we cannot have de re knowledge about the branches, because at some present point at some branch, we cannot identify the future branches indexically. Still, I can’t really see whether this would allow us to win back non-trivial expectations (probably not, I guess), but perhaps there is at least some kind of ignorance concerning the branches.

    P.S. Good luck with your blog! We have added it to our list of philosophy blogs.

  7. Al had some problems posing his comment, and we have not yet located the problem. But here is what Al writes:

    There’s a new proposal by Saunders and Wallace which applies a Lewisian analysis of personal identity to allow for indexical de re knowledge at least of the actual future. It’s strongly epistemicist in flavour, in that their is a fact of the matter about which extended cradle-to-grave person we timelessly are, we just can’t know it. See here: http://users.ox.ac.uk/~lina0174/uncertainty.pdf – I’m quite tempted by this line.

    The question of de re knowledge of non-actual branches in the many-worlds interpretation is a tricky one – I think the best thing to say is that we don’t generally have it. We can make true descriptive assertions about other branches, but as we are causally isolated from them we can’t have de re thoughts about them as we have de re thoughts about concrete objects in our own branch. Perhaps there’s a way of having de re knowledge of other-branchly objects through descriptive names – say that Eden is the branch in which most human happiness is instantiated. We can then know of Eden that it contains some humans. But this presumably isn’t what you mean.

    Do you think it’s a problem if a theory says we can’t have the kind of de re knowledge of other-branchly things that we have of ordinary concrete things? The status of de re knowledge of other possible worlds seems questionable on most standard views.

  8. Hi Al,

    I’ll have to check out the Saunders/Wallace account, I didn’t know about that…

    I would agree that we are not in a position to have de re thoughts concerning other-branchly objects (at least if there is no causal chain connecting them with some past node of our actual branch). The exception may be names which we introduce by definite descriptions, as you say, but I am not too sure whether this would constitute the possibility of genuinely de re thoughts.

    Anyway, I don’t think it to be a problem if we can’t have certain kinds of de re knowledge concerning certain objects existing only in other branches; in that respect they may be just like possible worlds of the Lewisian kind.

  9. On the Lewisian semantics I mentioned, causation doesn’t link events in different branches: I don’t think we can sneak in de re thoughts about other-branchly events that way. I suppose someone might think that’s a point against the Lewisian semantics. But I agree with you that it seems OK to deny these kinds of de re thoughts altogether, in which case the Lewisian semantics does fine.

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