Open Futurism, Supervaluationism, and Indeterminacy – A Critique of Barnes and Cameron

In my previous post on Ch. 2 of Patrick Todd’s book The Open Future (Oxford 2021), I criticized Todd for confusing supervaluationism with the view defended by Elizabeth Barnes and Ross Cameron in two influential papers. In this post I want to look more closely at the view of Barnes and Cameron (hereafter B&C). For ease of reference, I’ll refer to B&C’s first paper, “The Open Future: Bivalence, Determinism, and Ontology,” as TOF and their second paper, “Back to the Open Future,” as BTOF. I’m going to explain

• what B&C’s view of the open future is
• why B&C’s view is not “supervaluationist” in any legitimate sense of that word
• why B&C’s view of the open future is inadequate

B&C’s view: Open futurism as metaphysical indeterminacy

In TOF, B&C characterize “the open future thesis” as the view that “contingent facts about how things will be are presently unsettled” (p. 291). In BTOF, they add that “the open future is a matter of it being metaphysically indeterminate what will happen, i.e., that at least some future contingents are metaphysically indeterminate in truth-value” (p. 2). Initially one might be tempted to think that they mean to deny bivalence (the principle that each proposition is either true, or if not true, then false). After all, if some truth-values are “metaphysically indeterminate” then how can they be either true or false? Aren’t truth-values by definition determinate, such that if a proposition is true then it is determinately true? According to B&C, the answer to that is emphatically “no”. In their view, a proposition can be true but not determinately true, in that it can still be indeterminate whether the proposition is true: “every proposition is either true or false, but … for some propositions it is unsettled which truth-value they have” (TOF, p. 294).

In BTOF, after various clarificatory remarks, B&C settle on this as their “final” statement of their view (p. 5):

Openness as Indeterminacy: The future is open with respect to some future contingent p at t if and only if (1) p is, at t, metaphysically indeterminate in truth-value and (2) either it will be the case that, determinately, p was true, or it will be the case that, determinately, p was false. The future is open simpliciter iff there is some future contingent p such that the future is open with respect to p.

That’s a tangled and confusing web of text. Let’s try to unpack it by looking at B&C’s “picture” of the open future:

If the future is open in a world w at time t, then there is a set of complete histories for w representing how w could be atemporally, given what has happened up to t. These atemporal histories all agree on what happens up to t. They disagree on what happens after t. It’s indeterminate which of these histories is the complete atemporal description of w’s history, because it’s indeterminate what will happen in w. But determinately, one and only one of them is the complete atemporal description of w. At the last moment of w’s existence, there will be a single history that ‘gets it right’. But at time t, it’s indeterminate which of the many atemporal world histories compatible with what has happened so far is the right one. (BTOF, pp. 2–3; see also TOF, p. 295)

This is a bit easier to follow. What B&C are saying is that we should consider all of the complete histories that are compatible with how world w is up to time t. The openness of the future, in their minds, just is the thesis that multiple complete histories are compatible with w as of t. So it’s “metaphysically indeterminate” at t which of those histories is w’s actual history. That’s what clause (1) of B&C’s “final” statement is driving at. Now, as time moves forward, fewer and fewer complete histories remain compatible with w’s history up to that point until, “at the last moment of w’s existence”, only one complete history remains. That history is then determinately the history of w. So eventually, looking back, it will be settled which complete history is the actual history of w. That’s what clause (2) of B&C’s “final” statement is saying. Now, say B&C, if we consider the matter atemporally, and not in relation to this or that moment of time, then it is always determinate which history is w’s actual history. But if we consider the matter temporally, in relation to any moment of time but w’s last moment, then is it indeterminate which history is w’s actual history. So it is both determinately either true or false (atemporally considered) whether H is w’s actual history and yet it is presently neither determinately true nor determinately false (temporally considered) whether H is w’s actual history.

I’ll consider the adequacy of B&C’s view below, but first I want to address the relation of their view to supervaluationism properly so-called.

Why this isn’t supervaluationism

B&C compare their view to supervaluationism noting that theirs is a “non-standard” “departure” from “traditional” supervaluationism (TOF, pp. 295–296). While they are right that their view does share some common ground with supervaluationism—in both cases a property is assessed by considering all possible “precisifications” of some general description—their view is not a variant of supervaluationism.

In the case of supervaluationism proper, it is truth-values that are assessed. This is what puts the “value” in super-value-ationism. Standard truth-functional logic is, we might say, “subvaluational” in that the truth-value of a complex proposition is always a function the truth-values of its component propositions. Supervaluationism, in contrast, says that the truth-values of some complex propositions are not a function of the truth-values of their components, but rather of the various ways in which what they assert can be precisified or “fleshed out”. This approach is taken in order to reconcile logically necessary truths like excluded middle with a denial of bivalence. For example, supervaluationists like Richmond Thomason and John MacFarlane say that propositions about future contingents like <There will be a sea battle tomorrow> and <There will not be a sea battle tomorrow> are neither true nor false when evaluated prior to the event in question. They say this because there are precisifications or continuations of actual history up to the present in which a sea battle occurs tomorrow as well as continuations in which no sea battle occurs tomorrow. But Thomason and MacFarlane don’t want to say that the disjunction <Either there will be a sea battle tomorrow or there will not be a sea battle tomorrow> is neither true nor false. Instead, they see it as a necessarily true instance of the law of excluded middle on the grounds that no matter which precisification of history eventuates, it will either include a sea battle tomorrow or it won’t. So the disjunction is not evaluated truth-functionally (i.e., subvaluationally) but rather supervaluationally, that is, in terms of the truth-values the whole disjunction would have given any possible precisification of history as of the present.

B&C’s view isn’t supervaluationist because it is concerned with the assessment of determinacy, not truth. It is, if you will, not super-value-ationist but super-determinacy-ist. Unlike supervaluationists, B&C insist on the principle of bivalence. They don’t evaluate truth by considering precisifications. For them, either <There will be a sea battle tomorrow> or <There will not be a sea battle tomorrow> is true now, and the other is false. But neither proposition is determinately true now or determinately false now because there are continuations of actual history up to the present in which a sea battle occurs tomorrow as well as continuations in which no sea battle occurs tomorrow. Their disjunction, however, is determinately true now because no matter which precisification of history eventuates, it will either include a sea battle tomorrow or it won’t.

In short, while B&C’s view is structurally analogous to supervaluationism, it is not supervaluationist because the latter is definitionally concerned with truth-values, whereas B&C’s view is only concerned with determinacy.

A critique of B&C’s view of open futurism as metaphysical indeterminacy

I have several criticisms of B&C’s version of open futurism.

First, they view future contingency as a matter of metaphysical indeterminacy instead of as a matter of causal indeterminacy, as the notion has traditionally been understood. By a “future contingent”, B&C mean a claim “concerning how things will be such that neither it nor its negation is metaphysically necessary” (TOF, p. 291). This is a much broader notion of future contingency than almost anyone in the long tradition of theological debate over the compatibility of future contingency and creaturely freedom with divine foreknowledge and providence has had in mind. As B&C take pains to point out, not even causal determinism is incompatible with open futurism as they understand it (TOF, pp. 299–305): “The idea of a metaphysically open future is fully compatible with the truth of determinism” (TOF, p. 305).

Second, because they insist that there is a uniquely true history, albeit not one that is determinately true, their view isn’t really a version of open futurism at all, but rather a kind of preventable futurism. In one of my papers, I show that there are two ways of resisting fatalism, the view that the future is exhaustively “fixed” or “now-unpreventable”. The open futurist response denies that there is any uniquely specified future, no unique and complete extension of the actual past and present that is (or that is going to be) the actual future. The preventable futurist response, in contrast, concedes that there is a uniquely specified future but insists that the specified future is nevertheless preventable. It is preventable because the existence of the future specifier is explanatorily dependent on the actual occurrences of the future events it specifies. This is basically the line that B&C take. They are preventable futurists, not open futurists. What puts the “openness” in open futurism is not the indeterminacy of an otherwise uniquely specified future, but the absence of any such specification. For the open futurist, the future is indeterminate (i.e., not unpreventably fixed) because it is not completely specified. For the preventable futurist, the future is indeterminate (i.e., not unpreventably fixed) despite being completely specified. B&C fail to appreciate this distinction.

Third, the distinction between truth and determinate truth is problematic. If it is indeterminate whether future F is the unique actual future, then how can it be true that F is the unique actual future? B&C appeal to an atemporal perspective to maintain that there is a unique actual future. But how can there be such an atemporal fact if it is now indeterminate how the future shall unfold? Given such indeterminacy, it remains an “open question” which future shall come to be the actual future. In other words, the information necessary to specify any one future as “the” actual future doesn’t yet exist and can’t exist until all indeterminacy is exhausted. Since we haven’t yet reached the end of history, the supposedly atemporally specified unique actual future simply doesn’t exist. Thus, B&C’s appeal to an atemporal perspective here is an illegitimate cheat given the indeterminacy that they advocate for.