Todd (ch.2) – Models of the Undetermined Future

This is part 2 of my ongoing series on Patrick Todd’s recently published book The Open Future: Why Future Contingents are All False (Oxford, 2021). You can find part 1 here.

In chapter 2, Todd compares and contrasts “three models of the undetermined future” and proposes a unified semantics for the future tense. I argue below that one of Todd’s three models (the one he calls “supervaluationism”) is not coherent and that a better breakdown would recognize at least four models, with three of them being versions of open futurism. As for Todd’s semantic proposal, I think it’s very helpful. It allows us to address the key issue dividing open future and settled future models of future contingency—whether there is a unique actual future—in a way that doesn’t beg questions against either side and keeps the semantic and metaphysical issues distinct.

1. Todd’s Three Models

On p. 22, Todd describes three models of the undetermined future. Each model takes for granted that causal indeterminism is true and, therefore, that there are multiple causally possible future histories. A causally possible future history is an extension of the actual past and present that, according to Todd, is “consistent with the past and the laws [of nature]” (p. 21). This way of putting it is not quite right, however. By requiring consistency with the entire past Todd inadvertently begs the question against the Ockhamist model of divine foreknowledge, according to which some past facts are future-dependent and so are compatible with multiple causally possible futures. To avoid begging the question we need to define causally possible futures in terms of consistency with the causal laws and the fixed or future-independent past (i.e., those aspects of the past that are not ontologically dependent on future events).

In any case, here are the three models that Todd delineates:

1. Ockhamism: There are multiple causally possible futures. One of those is the unique actual future, and it is determinate which future that is.
2. “Supervaluationism”: There are multiple causally possible futures. One of those is the unique actual future, but it is indeterminate which future that is.
3. Open Futurism: There are multiple causally possible futures. None of those is the unique actual future.

I put “supervaluationism” in quotes because I think Todd misunderstands what supervaluationism is (see discussion below). As for “open futurism” or model III, that is my term, not Todd’s. I find it amusing that, after noting that model III “doesn’t have a recognized name” (p. 21), Todd doesn’t take advantage of the opportunity to give it a name, as I have done. (How is a model ever supposed to get a recognized name if we don’t start calling it something?)

2. On So-called “Supervaluationism”

On p. 21 Todd admits that he might be “seriously misinformed” about either supervaluationism or Ockhamism or both. I think he’s gets Ockhamism mostly right—I’ll raise a minor issue about his take on it below—but I think he gets supervaluationism wrong. The most obvious reason for saying this is that model II, as Todd explicates it, is incoherent. If precisely one causally possible future is the actual future, then it can’t be indeterminate which future is the actual one—the actual future just is the one that is uniquely actual. Suppose, for example, that futures A, B, C are the only causally possible futures. Suppose we randomly pick one of them as the actual future. Having picked one, it is now determinate that that future, whichever one it is, is the actual future. So how could there be a unique actual future and it be indeterminate which future that is? The only way to make sense of this, it seems to me, is to suppose that there is a different sense—an epistemic sense perhaps—in which it is “indeterminate” which future is the actual one. In any case, I don’t think Todd gets supervaluationism right, and the version he presents is either incoherent or reduces to something like Ockhamism.

Todd’s understanding of what he calls “supervaluationism” seems to come primarily from a 2009 paper by Elizabeth Barnes and Ross Cameron from which he quotes in a footnote on p. 23. In that paper Barnes and Cameron are concerned to oppose John MacFarlane’s 2003 paper “Future contingents and relative truth”, which is largely an updated presentation of Richmond Thomason’s 1970 paper “Indeterminist time and truth-value gaps”. Both Thomason and MacFarlane reject the principle of bivalence, the claim that there are only two truth-values (true, false) and that every proposition determinately has one of those values. Barnes and Cameron don’t like the idea of giving up bivalence, and they don’t like MacFarlane’s relativist semantics, which says that we have to relativize truth-ascriptions to a “context of assessment”. Thomason and MacFarlane adopt a relativist semantics because they want to reconcile (a) future indeterminism, (b) “will excluded middle” (WEM), i.e., Fnp ∨ Fn~p, and (c) “retro-closure” (RC), i.e., p → PnFnp. To preserve these three claims, they must say that future contingent propositions are neither-true-nor-false when evaluated from a context of assessment that lies before the occurrence of the events they describe but also determinately either-true-or-false when evaluated from a context of assessment that lies after the occurrence of those events.

Whatever its merits or demerits, it is the position of Thomason and MacFarlane that most deserves to be called “supervaluationism”, not what Barnes and Cameron serve up it its place. Thomason’s paper, after all, is the original source of the supervaluationist idea among modern discussions of future contingency. And it is core to the supervaluationist idea that “a proposition can have a definite truth value even when its components do not.” That implies a denial of bivalence. Barnes and Cameron even admit in footnote 15 on p. 296 of their paper that their view is a “non-standard” version of supervaluationism and that it is a “departure from the traditional supervaluationist apparatus.” Why then does Todd focus on the non-standard Barnes and Cameron version rather than the standard Thomason version?

Here’s (part of) the quotation from Barnes and Cameron that Todd references in a footnote:

Finally, it’s determinately the case that exactly one of the worlds in {Futures} is actualized. One and only one world matches the complete atemporal state of the actual (concrete) world. It’s just that it’s indeterminate which of the worlds in {Futures} is so actualized.

As already noted, I have a hard time making heads or tails of this. Despite assertions by Barnes and Cameron to the contrary, this strikes me as transparently incoherent. If world A is the unique actual world, the only one that matches the complete atemporal state of the concrete actual world (they seem to assume eternalism), then how can it be “indeterminate” which world is the actual one? They seem to think that coherence can “uncontroversially” (p. 296) be established by distinguishing between “truth” and “determinate truth” so that, for example, there can be a complete, true story of reality (a unique actual world) without it being “determinate” that that story is the true one. I have two theories on how to make this “truth” / “determinate truth” distinction stick. One is to interpret determinacy epistemically—there is a truth, but it’s not knowable and thus not “determinate”. Barnes and Cameron, however, explicitly reject that reading (p. 298). They insist that the type of indeterminacy they have in mind is metaphysical. My other theory is that they are advancing (in apparent ignorance of centuries of theological discussion) something like the Ockhamist soft fact / hard fact distinction. Hard facts are “determinate”; soft facts aren’t. There is a “soft fact” that world A is the actual world, but it’s not yet a “hard fact” because it is metaphysically dependent on the resolution of future contingencies. If that’s what Barnes and Cameron are driving at, then Todd’s model II is really just a repackaged version of model I, i.e., Ockhamism.

In sum, “supervaluationism” as Todd presents it is not a coherent position and is not standard supervaluationism to boot. If interpreted in a way that makes it coherent (or at least not obviously incoherent), then the position arguably collapses into Ockhamism.

3. Revising the Models

Because I don’t think Todd’s way of cashing out “supervaluationism” is either accurate or coherent, I’d like to propose a different breakdown of models based on whether they affirm (a) a unique actual future, (b) bivalence, (c) will excluded middle, (d) retro-closure, and (e) semantic relativism (i.e., that we have to relativize to a “context of assessment”). One advantage of this breakdown is that we don’t need to indulge Todd’s artificial distinction between an “actual” future and a “privileged” future, a distinction he employs simply to accommodate “supervaluationism” falsely so-called.

	Ockhamism	Supervaluationist Open Futurism	Non-Bivalent Open Futurism	Bivalent Open Futurism
unique actual future (UAF)	yes	no	no	no
bivalence (BV)	yes	no	no	yes
will excluded middle (WEM)	yes	yes	yes	no
retro-closure (RC)	yes	yes	no	no
semantic relativism (SR)	no	yes	no	no

All four of these models affirm future contingency, i.e., that there are multiple causally possible futures. Ockhamism is the only one that affirms a UAF (a unique actual future). It also accepts  BV (bivalence), WEM (will excluded middle), and RC (retro-closure). For the Ockhamist there is no need to indulge SR (semantic relativism) because it is at all times determinate which possible future is the actual one. Supervaluationist Open Futurism is the Thomason / MacFarlane view. Because it accepts WEM the view has to deny BV in order to maintain an “open” future. (Given WEM and BV, either Fp or F~p would have to be true at all times in advance, so from the beginning there would have to be a UAF.) Because it also accepts RC, which projects determinacy backward through history and thus threatens to undo the “openness” obtained by denying BV, supervaluationism has to embrace SR in order to maintain consistency. It is thus prospectively indeterminate and retrospectively determinate which future is the actual one. Since the UAF is only fully retrospectively determinate after all future contingencies are resolved, this is an open futurist position. Non-Bivalent Open Futurism also affirms WEM and so has to deny BV, but it doesn’t need to indulge SR because it rejects RC. Bivalent Open-Futurism, in contrast, rejects both WEM and RC, and so has no need to deny BV or to affirm SR.

In terms of this breakdown, we can see that the key issues are UAF, WEM, and RC. Where you stand on those three issues is going to determine whether you have to deny BV or affirm SR. In any case, it’s worth noting that three of these four models are versions of open futurism (Todd’s Model III) and the other is Ockhamism (Todd’s Model I). I will therefore ignore Model II moving forward.

4. Ockhamism and Future-Directed Facts

Before discussing Todd’s semantic proposal, one corrective regarding Ockhamism needs to be mentioned. Todd says on p. 24 that the debate between Ockhamism and Open Futurism turns on the metaphysical question of whether there are “primitive future directed facts”. He then explains that by “primitive” he means merely that these facts are “not grounded in facts about current conditions and laws”. According to Todd, the debate between Ockhamism and Open Futurism turns on the question of whether such facts exist.

I think this way of characterizing the debate is largely correct—Ockhamists and Open Futurists disagree about whether there is such a thing as a unique actual future (UAF). Given indeterminism, if there were a UAF, it couldn’t be grounded in the fixed or future-independent past plus causal laws. So the Ockhamist needs to posit determinate facts about the contingent future that are “primitive” with respect to those potential grounds.

My main qualm with Todd’s way of putting this is that the Ockhamist’s future-directed facts aren’t strictly “primitive”. To call them “primitive”, even with Todd’s qualification in place, misleadingly suggests that Ockhamists view these future-directed facts as though they were simply brute. But that would be incorrect. For the Ockhamist, such facts are ontologically dependent on the actual occurrences of future contingent events. The facts exist because (and only because) the future actually plays out the way it eventually does. So, rather than calling these facts “primitive”, it would be better to drop that adjective and simply describe them as “future-dependent”. Ockhamists affirm the reality of presently (or timelessly) existing future-dependent facts, whereas Open Futurists deny their reality.

5. Todd’s Semantic Proposal

Todd stipulatively defines an available future as a future that is “consistent with the past and the laws and the future directed facts” (p. 25). As I’ve already indicated in sections 1 and 4 above, this isn’t quite right. Reference to “the past” should be restricted to the fixed or future-independent past and “future directed” facts should be replaced with “future-dependent” facts.

Available future (AF) =_def. A complete extension of the actual past and present that is consistent with the causal laws, the future-independent past, and the future-dependent facts.

Given the notion of an available future, Todd proposes a semantics for the future tense “will” that he believes both Ockhamists and Open Futurists can agree on:

All available futures (AAF): It will be in n units of time that p iff in all of the available futures, in n units of time, p.

I think this is a promising semantic proposal. It’s actually very clever. Given a suitable definition of an “available future”, an Ockhamist will say that there is at any point in time exactly one available future and that that future is the unique actual future (UAF). An Open Futurist, in contrast, will deny that there are any future-dependent facts and therefore, given future contingency, will say that there are multiple available futures. The important point is that both sides can agree on AAF even if they disagree on it’s implications because they disagree on whether there are any future-dependent facts. Todd’s semantic proposal, in other words, shifts the terrain of debate from semantics to metaphysics. That is a big plus.

That said, I’m not convinced that AAF accurately represents how all parties actually think about the future tense. In particular, it doesn’t explain why many thinkers from Aristotle on have thought that we need to deny the principle of bivalence with respect to future contingents. As Todd points out on p. 35, Open Futurism (denial of a unique actual future) plus AAF entails a denial of will excluded middle (WEM). But then what are we to make of Supervaluationist and Non-Bivalent Open Futurists? Those views are committed to both WEM and Open Futurism. Given AAF, that’s an impossible combination. So it seems like AAF does not capture how those Open Futurists understand the semantics of the future tense.

Despite the obvious utility of having a unified semantics for the future tense that everyone can agree on, what if there is no such thing? What if there is no unified semantics but rather two or more different and incompatible ways of thinking about the future? This is ultimately an empirical question, not one that can be settled by armchair philosophy. Without going into details, my thinking on the matter is that there are, broadly speaking, two different ways of thinking about the future tense, and about tense in general. One can think of tenses either as directional or as locational. A directional stance looks forward or backward from the perspective of the present. AAF is a directional semantics in this sense because it asks us to quantify over available futures, or possible extensions of the actual past and present. We look forward from the present moment and consider what futures are presently available given our ontological commitments. This yields different answers—Ockhamist or Bivalent Open-Futurist—depending on whether we think future-dependent facts exist or not. A locational stance, in contrast, doesn’t look forward or backwards from the perspective of the present, but rather asks us to shift forward or backward to a different temporal location and to consider that location as if it were present. On this way of thinking to evaluate Fp we don’t quantify over available futures as per AAF; rather, we consider whether it is determinate now that things are a certain way then. Since it must be that either p or ~p obtains then, it is natural on the locational interpretation to think that either Fp or F~p must be true now (we thus get WEM). But if p is a future contingent then it can also seem to be indeterminate now whether Fp obtains then or F~p obtains then. Accordingly, bivalence has to go. In short, while I really like Todd’s proposal of a unified semantics for will, I think the semantic reality is more complicated. If we want to make sense of the full range of positions on future contingents that people actually hold, then AAF is not enough.

6. Peirceanism

Because the Open Futurist denies that there are any future-dependent facts, the available futures just are the causally possible futures. The two groups of “futures” have the same extension. This suggests that Open Futurists should endorse

All possible futures (APF): It will be in n units of time that p iff in all of the causally possible futures, in n units of time, p.

When interpreted as a semantic claim about the meaning of the future tense, APF is known as “Peirceanism” (a label coined by the famous tense logician Arthur Prior). But here Todd makes an important point. He says (p. 36) that even though AAF plus Open Futurism entails APF, this does not require accepting APF as a semantic account of the meaning of will. One can still maintain that AAF gives the right semantics and hold that APF follows as a matter of metaphysics, not semantics. This seem right to me.

Incidentally, Todd cites me (p.37 footnote) as a defender of the claim that Peirceanism or APF is the correct semantics for will. But this is an incorrect attribution. In both of my papers that he references I only argue that Peirceanism is the correct semantics for a special subclass of uses of will. I do not, and never have, defended it as a universal semantics for the future tense. The most I have claimed is that ordinary language, when used predictively, is closer to a Peircean semantics than to an Ockhamist semantics.

7. Metaphysics and Semantics

On p. 40 Todd sums up the “core argument” of his book:

Semantically, will is a universal quantifier over available futures.
Metaphysically, there are no primitive future directed facts, and so the available branches just are the causally possible branches (model (III)).
Result: future contingents are all false.

I think distinguishing clearly between semantic and metaphysical components is a great idea. It’s important to keep questions about meaning distinct from questions about whether future-dependent facts exist.

As argued in section 5 above, though, it’s not obvious to me that Todd’s semantic claim (AAF) is in fact correct. His semantics presupposes a broadly directional stance on the meaning of the future tense, but many people seem to adopt a locational stance instead. I believe that’s how they convince themselves that WEM is true and, in some cases, that bivalence must be denied. To show that future contingents are all false we’re going to need a further semantic argument against WEM. Fortunately, that’s what Todd’s Chapter 3 aims to provide.