I’ve been thinking what open future (OF) views can say about the modality of statements about the future. There are two OF semantics, which I’ll call N and F. Suppose Curley now exists, and that Curley’s freely taking the bribe is open. On the N semantics, Curley will freely take the bribe is neither true nor false. On the F semantics, it is false that Curley will freely take the bribe. The N semantics requires denial of excluded middle. The F semantics requires denial of the principle that, basically, not(will(p)) iff will(not(p)).
Suppose now that we say that a proposition p possibly/necessarily/impossibly is V iff p is V in some/all/no worlds, where V is a truth value or a logical combination of truth values like “neither true nor false”, which I will abbreviate “ntnf”. Let p be the proposition that Curley will freely take the bribe. On the F semantics, p is false in every world. For in some worlds Curley’s freely taking the bribe is open, and in those worlds p is false by that semantics. And in all other worlds, it is determined that Curley won’t freely take the bribe (e.g., because it is determined that there is no Curley, or that nobody will ever offer Curley a bribe, or whatever). So, in every world, p is false, and so p is necessarily false.
On the N semantics, things are more interesting. In worlds where Curley’s freely taking the bribe is open, p is ntnf. In worlds where Curley’s freely taking the bribe is not open, p is false. Therefore, on the N semantics, p is possibly ntnf and possibly false, and necessarily not true.
So what’s wrong with this? Well, one thing is that as Geoff Pynn pointed out in the previous discussion of open futurism, the open futurist surely wants to say that p is a “future contingent”. But if p is necessarily false, as it is on the F semantics, then that’s endangered. And if p is necessarily not true, then it’s also in a bit of trouble.
On might think this is not a problem for the N semantics. After all, we do have contingency: it is contingent that p is ntnf, since in some worlds p is not ntnf but false. But this is not the kind of contingency in virtue of which we say that p is a “future contingent”. Here’s one way to see this. Suppose q is some kind of a weird paradoxical proposition that is necessarily ntnf (I don’t think there are such, since myself I accept classical logic; but the N-semanticist won’t be credible in saying this) and that has no contingency in it (think of liar sentences and the like; or maybe think of vague modal claims, such as that necessarily anybody with 100 hairs is bald). Now, let r be the proposition q & h, where h is the proposition that there are horses. Then, r is ntnf in those worlds in which there are horses, and is false in those worlds in which there are no horses. (I take it that the conjunction of an ntnf proposition with a false one is false.) So r has exactly the same kind of contingency that p does. But when we call p a contingent, we don’t mean to make p be like r, an unfortunate proposition which in some worlds just manages to rise to the level of ntnf, while being simply false in all the others.
Here’s another way to see that the kind of contingency we get is not the right kind of contingency. Suppose God is a necessary being and is in time, and let s be the proposition that God will freely create a prime number of angels in the future. Then in most worlds, s is ntnf. In some worlds, s may be false, say because in those worlds God has promised something entailing that he won’t create a prime number of angels in the future. So s has a contingency: in some worlds it’s false and in others it’s ntnf. But this contingency tracks not the contingency in God’s choice how many angels to create in the future, but rather it tracks the contingency in what God promises. And that’s the wrong contingency to track. The contingency in s is about the past, while what we want to explain is why s is a future contingent.
Suppose the above is right. Then when we think about open futurism, we think about propositions like p (about Curley) and s (about God). If we find open futurism plausible, we see a kind of contingency or openness in what these propositions claim. So we are drawn to open future views. But then the F theorist comes and tells us that we were wrong to think there was openness there–in fact, the proposition p that led us to open futurism is necessarily false, just like the proposition that 2+2=5. In doing so, the F theorist undercuts the basis of the intuitions that drew us to open futurism in the first place. The N theorist is more subtle, but I think in the end does the same thing. We initially thought there was something possible about p and s–that they described how things might be. But they don’t. The closest to truth that p and s can rise is being ntnf. Their contingency is a contingency of varying in truth value between ntnf and falsity. But if a proposition is necessarily either ntnf or false, how is it that we initially started off with a pretty clear picture of what it would be like for Curley in the future to freely take a bribe or for God to create a prime number of angels, a picture that then led us to open futurism? The N theorist also cuts down the intuition that led to open futurism.
All the above is predicated on the assumption that the modal status of p depends on p’s truth value in different worlds. One might try to work out an alternate account of the modal status of propositions. Here’s one approach that has some hope of working. Allow what time it is to differ between possible worlds (this is a somewhat more ontologically commitive version of talking about temporally centered worlds). Thus, in the actual world, it’s 10:02 am, but in some possible world it’s already noon. Then, in the actual world, p is ntnf (N semantics) or false (F semantics). But there is a world where it’s already noon and Curley is freely accepting a bribe. The proposition p is false or ntnf at that world (since at that world, p says that Curley will freely accept a bribe after noon). But there is an updating of p that is true at that world.
To do this rigorously, we need an updating operator, as I mentioned in a comment on the earlier thread, which given a proposition p and a time-difference delta, generates a proposition U(p,delta). It’s hard to give a precise account of U. But in some cases, it’s pretty easy. Thus, U(that Curley will freely accept a bribe, t), where t is positive, is the proposition that Curley freely accepted a bribe over the last t (units of time) or is freely accepting a bribe or will freely accept a bribe. We also need an operator T which assigns to each world the time which it is at that world.
The semantics now is: possibly(P is V) holds at w0 iff there is a w such that U(p,T(w)-T(w0)) is V at w; necessarily(P is V) holds at w0 iff at every world w, U(p,T(w)-T(w0)) is V at w. Assuming U can be defined, and assuming we’re willing to live with a worlds at which it is a time other than the actual world’s present, this semantics has the right results. Thus, possibly(it is true that Curley will freely accept a bribe). Likewise, possibly(it is false that Curley will freely accept a bribe). Moreover, both claims hold on both F and N semantics. On the N semantics, we further have: possibly(it is ntnf that Curley will freely accept a bribe).
I do not know how plausible this modal semantics is. In particular, I do not know how comfortable the open futurist will be with the idea that at every time, we are in a different world, since right now I am in a world where it’s 10:16, and in four minutes I’ll be in a world where it’s 10:20. But the latter claim is one I think all A-theorists have to make.
Anyway, so it seems that the open futurist can get out of the modal argument. Fortunately for me, there are other, more serious problems with open futurism. 🙂