Todd on the Open Future

Todd on the Open Future Ryan Wasserman Western Washington University The Open Future is wonderful book, filled with interesting arguments and important contributions to metaphysics, the philosophy of language, and the philosophy of religion. Here, I will limit my attention to what Todd calls the “core argument” of his book: Semantically, will is a universal quantifier over all available branches. Metaphysically, there are no primitive future directed facts, and so the available branches just are the causally possible branches. Result: future contingents are all false. (p.40) In what follows, I will argue that the first premise of this argument is unnecessary (section 1), that the second premise is unsupported (section 2), and that the conclusion overlooks at least one other important view about future contingents (section 3). 1. The First Premise To appreciate Todd’s argument, we first need to understand his terminology. Todd follows the tradition of thinking about the future in terms of “branches”, which he takes to be “abstract representations of total ways things could evolve”. (p.4) In other words, branches are something like complete sets of propositions about the future which are jointly compatible with the current facts and the laws. (p.9) Given indeterminism, there will be many different branches in this sense. Next, Todd introduces the idea of “primitive future-directed facts” which he defines as “facts specifying what is to come, which are primitive solely in the sense that they are not [fully] grounded in facts about current conditions and laws.” 1 (p.24) Suppose, for example, that one is an eternalist who believes that futuredirected facts are grounded (at least in part) in future events. These would then be “primitive” future-directed facts, in Todd’s sense.1 Todd uses the framework of branches and the concept of future-directed facts to introduce the idea of “available futures”—namely, “those futures that are consistent with the past and the laws and the future directed facts.” (p.25, italics mine) In other words, the available futures are those branches which are compatible with all the relevant facts, where this may (or may not) include primitive facts about the future. This concept of available futures is used to characterize three different “models” of the open future: (I) There is only one available future, and it is determinate what it is. (II) There is only one available future, but it is indeterminate what it is. (III) There are exactly as many available futures as there are futures consistent with the past and the laws. (p.25) Since Todd assumes both indeterminism and presentism, he equates (I) with the Ockhamist view that there is a determinate fact about (e.g.) whether there will be a sea battle tomorrow, even though there are no future events to ground this fact (and even though this fact is not determined by the current conditions and the laws). Model (II), meanwhile, is identified with the “supervaluationist” view that there is a fact about whether there will be a sea battle tomorrow, even though it is indeterminate what that fact is.2 Finally, Model (III) is put forward as the view to be defended. On this picture, there are no primitive future-directed facts, so the available futures just are the causally possible ones. Moreover, since 1 Todd is of course free to define his terms, but eternalists will have to continually remind themselves that “primitive”, in this context, does not mean “ungrounded”. 2 It is not entirely clear which views are to be included under this label. Barnes and Cameron (2009) are cited, but what they say about the open future is very different from what a traditional supervaluationist would say about vagueness, for example (cf. Lewis 1986: 212). 2 indeterminism is true, there are many such futures—some of which have sea battles tomorrow and some of which do not.3 We can now turn to the first premise of Todd’s argument: [M]y proposal is that any statement of the form “It will be in n units of time that p” has the same truth-value (whether this is true, false, indeterminate, or something else) as the corresponding statement of the form “In all of the available futures, in n units of time, p”. Will is thus treated as a universal quantifier over all available branches. (p.30)4 It is not immediately clear whether this thesis is about propositions or assertions, and, if assertions, what the truth-value is relative to. (In presenting the argument, Todd does not address the possibility that truth-values are relative to contexts of assessment,5 which would complicate things in various ways.) If we focus just on propositional truth (and ignore assessor-relativism), the idea is fairly straightforward. For the Ockhamist, there is only one available future and there might very well be a sea battle in that future tomorrow. If so, it is now true that there will be a sea battle tomorrow. For the supervaluationist, there is only one available future and it is indeterminate whether there is a sea battle in that future tomorrow. So, it is indeterminate whether there will be a sea battle tomorrow. Finally, on Model III, there are many available futures, some of which include a sea battle tomorrow and some of which do not. So, it is false that there is a sea battle in every available future. Hence, it is false that there will be a sea battle tomorrow, and also false that there will not. The upshot, says Todd, is that all three models can accept the same “neutral semantics” for future contingents. (p.30) 3 As Hud Hudson and Frances Howard-Snyder pointed out to me, these options are not exhaustive. Suppose that it is a primitive future-directed fact that there will be a battle tomorrow, but it is left open whether the battle will be by land or by sea. This view would admit more available futures than the Ockhamist, but fewer than Todd. 4 Todd gives various characterizations of his “semantic” premise. As we’ll see, some of these are too weak to establish his desired conclusion. 5 See MacFarlane (2003) and Todd’s discussion in Chapter 7. 3 We will return to the issue of neutrality below. For now, I want to suggest that Todd’s way of setting up the debate is potentially misleading and also unnecessarily complicated. First, it is potentially misleading because talk about “analyzing” (p.43) will as a quantifier over available futures suggests that facts about what will or will not be the case are grounded in facts about branches. This strikes me as backwards. Like Todd, “I wish to construe the debate between models (I), (II), and (III) as primarily metaphysical—as a debate about the nature and existence of primitive future directed facts.” (pp.23-4) Those views will disagree about which futures are available, but that is only because of their more basic disagreement over tensed facts.6 Suppose, for the sake of argument, that there is only one available future and that it includes a sea battle tomorrow. On the proposed framework, this amounts to the following: (1) there is only one complete set of propositions about the future whose members are jointly compatible with the present state of the universe, the laws, and the primitive future-directed facts (if there are any), and (2) this set includes the proposition that there will be a sea battle tomorrow. But these facts about abstract sets of propositions do not ground the fact that there will be a see battle tomorrow, any more than snow’s membership in the class of white objects is what makes it the case that snow white. Rather, the reason that the relevant proposition is a member of the set satisfying Todd’s condition is that there will in fact be a sea battle tomorrow. Assuming that the laws are indeterministic (and that grounding requires necessitation), this latter fact will count as primitive, in Todd’s sense. So, it is the primitive future-directed facts (or lack thereof) that explain which futures are available, rather than the other way around. Of course, thinking in terms of branches might be a helpful heuristic. And branches certainly have a role to play in model-theoretic semantics. But if what we care about is metaphysics—about what, if anything, grounds facts about the future— then focusing too much on branches is liable to confuse. The focus on branches also strikes me as unnecessary, since there is a simpler argument for Todd’s conclusion. Suppose that his second premise is correct and that there are no primitive future-directed facts. In that case, the only facts there 6 Todd’s own position is unclear. After saying that the basic dispute is about primitive directed facts (pp.23-4) and defining available futures in terms of those facts (p.25), he says that his view is “neutral” on whether future-directed facts explain facts about available futures or vice versa (p.26). 4 are about the future are those which are grounded in current facts and facts about the laws. If we assume that causal indeterminism is true and that grounding requires entailment, it follows immediately that there are no contingent facts about the future. But if there are no contingent facts about the future, then there are no contingent truths about the future. Given bivalence, it follows that all future contingents are false. That is the most direct argument for Todd’s conclusion, and it makes no reference to available branches. 2. The Second Premise Todd’s second claim is that there are no primitive future-directed facts. He suggests that this premise is motivated by the presentist view of time, but this motivation proves difficult to articulate. For example, the presentist might argue that there are no contingent facts about the future because there are no future times or events that could ground such facts. But parallel reasoning would lead the presentist to reject contingent facts about the past—something that Todd is unwilling to do. Todd’s own reasoning goes as follows: When I am having the intuition that there are no facts about the future beyond those determined by the present, I am not having an intuition about truth in general. I am, rather, having an intuition about the future in particular… That there should be such facts about the future— for instance, that there should just be a fact specifying that there will indeed be a sea-battle tomorrow, when everything about the present and the laws is as equally consistent with there being no sea-battle tomorrow—strikes me as mysterious and bizarre. For where would such a fact come from? Not from the future objects and events themselves; on presentist grounds, there just are no such objects and events. And not from facts about what the present and laws require. From where then? From nowhere. And so I am puzzled. (p.18-19) Todd is wary of putting too much weight on this argument (p.19), but I worry that it offers no support at all. 5 First, all parties to the debate can agree that Todd’s example of an alleged fact about the future—that there will be a sea-battle tomorrow—is derivative. That’s because facts about sea-battles—whether past, present, or future—are grounded in more basic facts about ships, cannons, etc. Those facts are grounded— ultimately—in facts about elementary particles and the relationships between them. If there is a sea-battle going on right now, for example, then that is because there are some particles arranged ship-wise and some other particles arranged shipwise and the first particles are related to other particles in the right kind of way. So too, if it is a fact that there will be a sea-battle tomorrow, then that is because there will be some particles arranged ship-wise tomorrow and there will be some other particles arranged ship-wise tomorrow, and… Again, the main point is that Todd’s opponent—the presentist who believes in contingent facts about the future—can agree that his example of a future contingent is derivative. To argue against his opponent, Todd needs to say that the allegedly basic facts about the future—facts about what the elementary particles will be like—are also derivative. But, on the face of it, this seems much less plausible. Facts about ships (past, present, or future) appear derivative; facts about elementary particles (past, present, or future) do not. Or so says the kind of presentist that I am imagining. However, Todd adds the following report: I have the feeling that the present and the laws produce the future— and I have the feeling that, since the present and the laws are all that there is, and since the present and the laws produce the future, there shouldn’t be any facts about the future beyond those the present and the laws produce. (p.18) This is not an intuition about a particular future-directed fact, like the fact that there will be a sea-battle tomorrow. Rather, it is a general intuition about all such facts: facts about the future must be “produced” by the present and the laws. Moreover, Todd says that the same thing is not true for the past: I have no feeling at all—and, I suspect, hardly anyone has any feeling at all— that the past is produced by, or explained by, or otherwise dependent on how things are right now. Indeed, I have precisely the 6 opposite feeling: my feeling instead is that the past is not at all produced or explained or dependent on the present. (p.19) This suggests an argument against primitive future-directed facts that would not extend to facts about the past. The reasoning seems to be this: 1. All facts about the future must be “produced” by the present and the laws. 2. The present and the laws do not determine any contingent facts about the future. C. There are no contingent facts about the future. To this, we should probably add the following unstated premise: 3. If the present and the laws do not determine any contingent facts about the future, then they do not “produce” any contingent facts about the future. The key question here concerns the idea of “production” and its relation to determinism. One way to understand “production” is in terms of metaphysical grounding. On that reading, (3) seems plausible, since the standard view is that grounding requires necessitation. (1), however, seems problematic. To see why, suppose that causal determinism is true and that there is currently a sea-battle taking place. If the world is deterministic, then this fact about the present was (causally) determined by the past and the laws. But it is implausible to think that the relevant fact is grounded in facts about the past and the laws. Rather, it is grounded in more basic facts about the present (e.g., facts about current ships, cannons, etc.). Moreover, the basic facts about the present (e.g., facts about elementary particles) are not grounded in anything. In particular, they are not grounded in facts about the past and the laws, even if they are entailed by those facts. I would think that the same thing is true for facts about the future. If it’s a fact that there will be a sea-battle tomorrow, then that fact is grounded in more basic facts about what the elementary particles will be like tomorrow and how they will be related. It is not grounded in facts about what the elementary particles are like now or how they 7 are currently arranged (even if those latter facts causally necessitate that there will be a sea-battle tomorrow). The other way to think of “production” is in terms of causation. On that reading, (1) seems more plausible: all the facts about the future must be causally explained by the present and the laws. At the same time, (3) seems implausible on this reading. To see this, suppose that a radioactive atom of Thorium has just decayed. If someone wants to know what caused this, the following answer seems perfectly reasonable: the atom was produced over a month ago, and that type of Thorium has a half-life of only 24 days. Of course, these facts about the past and the laws did not determine that the Thorium atom would decay today, but they do give us the best kind of explanation that we can hope for in an indeterministic scenario. I would think that the same is true for the future. Suppose that a new Thorium atom has just been created. And suppose it is a fact that this atom will decay in the next month. If someone wants an explanation for this fact, the following seems perfectly reasonable: the atom was just created, and that kind of atom has a half-life of only 24 days. In this sense, facts about the future could be “produced” by the present and the laws—they could be causally explained by these things—even if they are not determined. In short, if “production” is understood in terms of grounding, (1) is false; if it is understood in terms of causation, (3) is false. Either way, the argument does not give the presentist any reason to reject primitive future-directed facts. 3. The Conclusion Suppose we set aside the preceding worry and grant Todd his second premise. Does it follow that all future contingents are false? Not necessarily. As noted above, if there are no primitive future-directed facts, then the only facts there are about the future are those which are grounded in facts about the present state of the world and the laws. If we assume indeterminism (and that grounding requires entailment), it follows that there are no contingent future-directed facts. So, none of the contingent propositions about the future are true. But to get to the conclusion that they are false, we assumed that the principle of bivalence is correct. And that is precisely what some people want to deny when it comes to future contingents. After all, it is natural to think that it is false that there will be a sea battle 8 tomorrow just in case there will not be a sea battle tomorrow. Since it is not the case that there will not be a sea battle tomorrow (this being a future contingent), it would follow that the relevant proposition is neither true nor false.7 Todd challenges the motivation for the neither-true-nor-false view in various But the view itself seems to fall outside his framework. To see this, consider the following flowchart which Todd uses to summarize his reasoning: ways.8 The top box corresponds to the first premise of Todd’s argument (“will is a universal quantifier over all available branches”). His second premise appears on the righthand side of the chart (“there are no future-directed facts”). And Todd’s conclusion—Model III—is located in the bottom right-hand corner. But again: Model III only says that “there are exactly as many available futures as there are futures consistent with the past and the laws.” (p.25) Given the definition of “available 7 Since this view denies primitive future-directed facts, it is not a version of super- valuationism, as understood by Todd. 8 See Chapters 3 and 4. 9 futures”, this is equivalent to saying there are no primitive future-directed facts. But we have just seen that there are two different ways of developing this idea. If one combines Model III with bivalence, one gets Todd’s view that all future contingents are false. If one combines it with the alternative principle (that it is false that it will be the case that p iff it will not be the case that p), one gets the view that future contingents are neither true nor false. This choice point is conspicuously absent from Todd’s chart. One could address this lacuna by replacing the top box with the following: ‘Fnp’ is true iff in all available future, in n units of time, ‘p’ is true; otherwise, it is false. This would effectively build bivalence into the first premise, and thus rule out the neither-true-nor-false view from the beginning. However, this would no longer be the kind of “neutral” starting point that Todd seems to prefer (p.30). In any case, it seems to me that there is at least one reason to take the alternative view seriously. Suppose that you have just placed a large bet on a coin flip landing heads. You are understandably excited. In fact, you are so excited that you inspect the coin, the flipper, and the surrounding conditions, hoping to determine the results in advance. However, you quickly realize that the system is indeterministic, with a 50% chance either way. So, there is nothing left to do but to wait and wonder. On the neither-true-nor-false view, this makes sense. After all, you have learned all the causally relevant facts, and those facts are consistent with both the proposition that the coin will land heads and the proposition that the coin will land tails. Moreover, on this view, there are no primitive future-directed facts of the sort that one might consult an oracle about. There are simply no facts either way. On the “all false” view, things are different. If your investigation is correct and the coin flip is chancy, then it is straightforwardly false that the coin will land heads. So, it is false that you will win the money. Period. These are additional facts on the “all false” view. Moreover, the defender of that view would presumably be in a position to know those facts. But, in that case, it would no longer make sense to wonder if you will win, since that proposition would be inconsistent with something that you already know—namely, that it is not the case that you will win. The same thing would be true for many other attitudes and intentional states—if you know that it is not the case that the coin will land heads, then it makes no 10 sense to get excited by that prospect, or to be nervous about the possibility, or to plan for what you will do in that scenario. From the practical perspective, every future contingent is an open and shut case, which is just to say that the future does not seem open at all. Consider a parallel. Suppose that you had the opportunity to bet a million dollars on a coin-flip yesterday but chose not to. Afterward, you begin to wonder: would I have won, had I taken the bet? Out of curiosity, you inspect the coinflipping system and determine that it was indeterministic. You conclude that some of the closest worlds where you took the bet are ones in which it comes up heads, while others are ones in which it comes up tails. On the standard approach to counterfactuals, it will then be false that you would have won, had you taken the bet. That is a fact. Moreover, you know it. It would therefore be perverse—if not impossible—to go on wondering if you would have won. The situation with the future is different. While there is (presently) no fact about how the coin will land, there will be such a fact tomorrow. For the presentist (and the growing block theorist), reality is dynamic, with new objects, events, and facts constantly coming into existence. That is why (on these views) the future inspires things like curiosity, fear, and excitement. In the counterfactual case, there is no fact of the matter as to how things would have gone and there will never be such a fact. That is why the relevant attitudes would be out of place. The problem is that Todd would have us treat these cases alike,9 which seems to miss out on at least part of what makes the future so special.10 References Barnes, Elizabeth and Cameron, Ross. 2009. The Open Future: Bivalence, Determinism and Ontology. Philosophical Studies 146: 291-309. 9 See Chapter 4, in which Todd develops an extended analogy between future contingents and counterfactual conditionals. For an indication of how Todd might distinguish between these cases, see his discussion of “tendencies” in Chapter 6 (pp.132-135). 10 For discussion and feedback, I am grateful to Andrew Law, Christian Lee, Daniel Howard-Snyder, Frances Howard-Snyder, Hud Hudson, Patrick Todd, and Neal Tognazzini. 11 Lewis, David. 1986. On the Plurality of Worlds. Oxford: Blackwell. MacFarlane, John. 2003. Future Contingents and Relative Truth. Philosophical Quarterly 53: 321-336. Todd, Patrick. 2021. The Open Future: Why Future Contingents are All False. Oxford: Oxford University Press. 12