How Is the Asymmetry Between the Open Future and the Fixed Past to Be Characterized?

Abstract

A basic intuition we have regarding the nature of time is that the future is open whereas the past is fixed. However, although this intuition is largely shared, it is not a straightforward matter to determine the nature of the asymmetry it reflects. So, in this chapter, I survey the various philosophical ways of characterizing the asymmetry in openness between the future and the past in order to account for our intuition. In particular, I wonder whether the asymmetry is to be characterized in semantic, epistemic, anthropocentric, physical, modal, metaphysical or ontological terms. I conclude that an ontological characterization of the asymmetry is to be preferred, since it is superior to the alternatives in explanatory power, intelligibility, and in how it coheres with interesting senses of openness.

This chapter is based on Grandjean (2020, 2021a) and Grandjean and Pascucci (2021), but contains new material.

2.1 Introduction

A basic intuition we have regarding the nature of time is that there is a difference between the future and the past: the former appears to be open and the latter appears to be fixed (or closed). This intuition manifests itself in various ways. First, whereas we think of the future as partially unsettled (e.g., it is settled that I will die someday, but it is unsettled whether the first astronaut to go to Mars will be a woman), we think of the past as fully settled (e.g., it is settled that Napoleon lost at Waterloo, that dinosaurs are extinct animals). Second, whereas we think that there are things we can do to affect how the future will unfold (e.g., making a significant donation to an NGO, acting in an environmentally responsible manner), we think that there are not things we can do to affect how the past unfolded (‘what is done is done’).¹ Third, whereas our future experiences are of great concern to us, we attach little importance to our past experiences (e.g., we would prefer, other things being equal, that personal bad events be in the past rather than in the future).² Fourth, and perhaps more radically, whereas we may only wonder how the past unfolded (e.g., ‘What happened to John Kennedy?’), we may wonder whether the future will unfold (e.g., ‘Will reality continue beyond tonight?’).

The intuition of an asymmetry in openness between the future and the past is so deeply ingrained in our manifest image of the world that it seems hopeless to do without. We decide, we create, we remember, we regret. The first two attitudes presuppose an open future, while the two latter ones presuppose a fixed past. For example, when it comes to forming beliefs about what we remember or regret, we explore our mental life, i.e. we consult our memory and records, since these latter attitudes are epistemically constrained by the information we may collect about what happened to us. By contrast, when we want to know what we will decide or create, i.e. when we try to predict the outcomes of such pending processes, we do not gather psychological evidence or records, since any information we might obtain will be overridden by the processes themselves. We rather let these processes run their courses; they are almost guaranteed to produce true beliefs (cf. Ismael, 2016: §6). This suggests that whereas our attitudes towards the past depend on the traces it left on our mental life, the future partially depends (either directly, or in an attenuated manner) on our decisions and our creations. As, for instance, Mauro Dorato puts it: “[o]ur actions can give a (cosmically negligible) contribution to bring [the future] about” (2008: 56). It therefore seems that, unlike the past, the future cannot be regarded as more fixed than the processes in which we are currently engaged.³

However, although the intuition of an open future and a fixed past is largely shared, it is not a straightforward matter to determine the nature of the asymmetry it reflects. So, in this chapter, I survey the various philosophical ways of characterizing the asymmetry in order to account for our intuition. In particular, I discuss the question whether the asymmetry is to be characterized as semantic (the principle of bivalence applies to statements about the past but not to future contingents), epistemic (we can know much more about the past than we can know about the future), anthropocentric (we can affect what will happen, but not what happened), physical (the world is fully deterministic with regard to the past but not to the future), modal (if the present were different, the future would be different, but the past would remain as it in fact is),⁴ metaphysical (whereas the past is singular, there are many alternative future states such that the world fails to specify which ones obtain) or ontological (there being facts of the matter about what happened, but not about what will happen). I conclude that, although many of these characterizations may contribute to a global understanding of the phenomenon, an ontological characterization of the asymmetry is to be preferred, since it is superior to the alternatives in explanatory power, intelligibility, and in how it coheres with interesting senses of openness. Of course, this does not exclude the possibility that other accounts – e.g., those involving epistemic, causal, counterfactual or entropic asymmetries – may (alongside various cognitive mechanisms) shed light on related phenomena such as, for example, our having certain practices regarding the future. But this is not the primary concern of this chapter. What matters here is simply to obtain the best characterization of a crucial aspect of our pre-theoretic representation of the structure of the world, namely our intuition that the future is open and the past fixed.

In this respect, the overall picture is perhaps more fragmented than has been suggested so far. For, the various accounts that will be discussed below do not aim to explain the very same thing. Whereas some of these accounts are explicitly intended to characterize what it is for the future to be open, and the past fixed (i.e. they are attempts to capture our representation of openness and fixity), some others seem better conceived as taking our relevant practices seriously and asking: ‘What could explain our having these practices?’. In particular, the ‘perspectival’ accounts that resort to asymmetries of knowledge (or causation) are clearly of the second kind: they aim less at characterizing the openness of the future than at explaining why we believe the future is open when it is not (or only in a ‘perspectival’ sense). Also, these accounts vindicate our having certain practices (e.g., our deliberating about the future and not the past, and using information about the fixed past in the deliberation), without thereby vindicating that the future is open in some other (more substantial) sense. In this respect, the ‘perspectival’ accounts must crucially be contrasted with the ‘substantial’ accounts (e.g., the metaphysical and ontological accounts) that aim at vindicating the future being open in the sense in which we might have a pre-theoretic representation of its openness.

2.2 The Failure of Bivalence

It has become increasingly popular to claim that the asymmetry in openness between the future and the past is an asymmetry with respect to whether some statements⁵ about the future and the past have a classical truth-value, i.e. are either true or false.⁶ Arguably, this claim is originally to be found in Aristotle’s De Interpretatione, chap. 9. In this book, Aristotle seems to capture the asymmetry between the open future and the fixed past by a semantic claim: future contingents (i.e. statements about the future that, even if they should be either true or false now, their present truth-value would anyway not be predetermined by the present or the past)⁷ are neither true nor false, whereas statements about the past are either true or false.⁸ In other words, it might be argued that, for Aristotle, the ‘open future’ view amounts to the failure of Bivalence (which states that all meaningful statements are either true or false) when applied to future contingents. Aristotle writes:

In the case of that which is or which has taken place, propositions, whether positive or negative, must be true or false. Again, in the case of a pair of contradictories, either when the subject is universal and the propositions are of a universal character, or when it is individual, as has been said, one of the two must be true and the other false; whereas when the subject is universal, but the propositions are not of a universal character, there is no such necessity. […] When the subject, however, is individual, and that which is predicated of it relates to the future, the case is altered (Aristotle, 2014: 31 [my emphasis]).

As an example, Aristotle famously considers the case of a sea-battle, which has since served as the focal point for most of the philosophical discussions concerning the open future. In Aristotle’s picture, a sea-battle “[…] must either take place to-morrow or not, but it is not necessary that it should take place to-morrow, neither is it necessary that it should not take place, yet it is necessary that it either should or should not take place to-morrow”. Now assuming that Bivalence holds unrestrictedly and, therefore, that future contingents, such as ˹There will be a sea-battle tomorrow˺, are either true or false at the time they are asserted, it seems, as Aristotle puts it, that “[...] everything takes place of necessity and is fixed”. In particular, assuming that the statement ˹There will be a sea-battle tomorrow˺ is true now, it seems that tomorrow cannot be peaceful, because “[...] that of which someone has said truly that it will be, cannot fail to take place; and of that which takes place, it was always true to say that it would be” (Aristotle, 2014: 31–32).

Although there are various interpretations of Aristotle’s writing on this and other issues, most commentators⁹ agree that this Aristotelian argument – commonly referred to as ‘the fatalist argument’ – can be reconstructed as follows:¹⁰

• 1. Either it is true that there will be a sea-battle tomorrow or it is false that there will be a sea-battle tomorrow.

• 2. If it is true that there will be a sea-battle tomorrow, then it is true now that there will be a sea-battle tomorrow, and likewise, if it is false that there will be a sea-battle tomorrow, then it is false now that there will be a sea-battle tomorrow.

• 3. If it is true now that there will be a sea-battle tomorrow, or false now that there will be a sea-battle tomorrow, then how tomorrow is (at least with respect to sea-battles) is settled by how the present is.

• 4. Therefore, how tomorrow is (at least with respect to sea-battles) is settled by how the present is.

• 5. Since we were dealing with an arbitrary event at an arbitrary future time, how the future is in all respects is settled by how the present is.

Given that step (5) is the denial of the claim that the future is open in any respect whatsoever, the fatalist argument leads Aristotle to conclude that the openness of the future¹¹ cannot be preserved without excluding future contingents from the scope of Bivalence, i.e. without denying (1). That is presumably why some philosophers¹² go a step further by identifying the ‘open future’ view with the claim that Bivalence does not hold for future contingents. In this sense, these philosophers do not consider the failure of Bivalence as merely implied by the openness of the future (if the future is open, then future contingents are neither true nor false), but claim that the openness of the future is nothing but the non-bivalence of future contingents (the future is open iff future contingents are neither true nor false). Here is, for example, what Markosian writes about the open future:

Let us agree on some terminology. To say, with regard to some time, t, that the future is open at t is to say that there are some propositions about the future relative to t that are, at t, neither true nor false. To say that the future is closed at t is to deny this, i.e., to say that every proposition about the future relative to t is, at t, either true or else false (1995: 96).¹³

So, according to Markosian, tomorrow is open (at least with respect to sea-battles) iff (i) it is not true now that there will be a sea-battle tomorrow and (ii) it is not false now that there will be a sea-battle tomorrow. And, of course, since the openness of the future is not confined to potential sea-battles, those who adopt Markosian’s terminology will typically claim that all future contingents (at least as defined above) are neither true nor false. For example, as I write these lines, it may be claimed that it is neither true nor false that the first astronaut to go to Mars will be a woman, a cure for cancer will be discovered by the year 2115, and Federer’s grandson will also become a famous tennis player. Of course, everyone is free to define the openness of the future as they want, especially in such a way that it is analytic that the future is only open if future contingents are non-bivalent. But such a definition might appear unsatisfying for at least three reasons that I present now.

First of all, the claim that the future is open is meant to capture some basic intuitions we have regarding the nature of time (partial unsettledness of the future, power over what will happen, etc.), and if we identify the ‘open future’ view with the claim that Bivalence does not hold for future contingents then we risk simply missing the point. The non-bivalence of future contingents has indeed nothing to do with the way we commonly think of time. That may in particular be revealed by our pragmatic assessments concerning the correctness and the incorrectness of statements about how things would turn out (cf. Besson & Hattiangadi, 2013).

As a first example, consider our current assertions of future contingents; it seems natural to regard some of them as correct. There would, for instance, be nothing prima facie problematic in someone’s asserting that ˹I will brush my teeth tonight˺. However, it is generally taken to be a necessary condition of an assertion’s being correct that it is true; so that if an assertion of a proposition is believed to be not true, it will not be assessed as correct (cf. Grice, 1989). Given this, Markosian seems compelled to conclude either that the future is fixed (at least with respect to assertions of future contingents that are assessed as correct), or that we are massively mistaken when we feel pragmatically justified in asserting future contingents. Neither of these options is acceptable.

As a second example, consider our past predictions about how things would turn out; it seems natural to regard some of them as correct retrospectively. For instance, while we may think that it is now open whether or not there will be a sea-battle tomorrow, once tomorrow comes and there is indeed a sea-battle, we are not only inclined to think that it is true now that there is a sea-battle, but we are also inclined to think that this reveals that yesterday’s prediction that there would be a sea-battle was correct. However, it is hard for anyone who takes openness to consist in (or even to imply) the non-bivalence of future contingents to agree with this. In particular, when Markosian considers predictions made in the past about how things would be at a time that is now the present, he seems forced into saying that they were neither true nor false and – given the orthodox account of assertion – that they could not have been correct. After all, assuming that the openness of the future consists in the failure of Bivalence for future contingents, it must be concluded that while there is now a sea-battle, yesterday’s prediction that there would be a sea-battle today was not correct, because it was open how things would turn out (cf. Macfarlane, 2003: 324–325). That is unacceptable. As Gilbert Ryle writes: “[i]t is an unquestionable and very dull truth that for anything that happens, if anyone had at any previous time made the guess that it would happen, his guess would have turned out correct” ([1953] 2015: 19).

A possible answer to this objection lies in adopting a relativist semantics whereby tensed claims have a truth-value only relative to a context of assessment (cf. Macfarlane, 2003, 2008). The main idea is that the very same claim – the prediction made on Monday that there will be a sea-battle on Tuesday, say – lacks a truth-value when assessed relative to the time of utterance (Monday), but is either true or false when assessed relative to the time whose goings on the claim is making a prediction about (Tuesday). However, although this answer seems to reconcile the openness of the future with our intuition about retrospective assessments, it has an important theoretical cost: the rejection of the absoluteness of utterance-truth (i.e. the orthodox assumption according to which the truth-value of an utterance does not depend on some context of assessment) (cf. Evans, 1985: 349–350).

A second reason why we might think that identifying the ‘open future’ view with the failure of Bivalence for future contingents is unsatisfying has to do with the fatalist argument. Although this argument seems to be valid, some of its steps – especially (3) – can be disputed. It is not clear whether the bivalence of future contingents rules out the openness of the future. Many philosophers¹⁴ defend the view that the openness of the future is compatible with the bivalence of future contingents and, therefore, that the statement ˹There will be a sea-battle tomorrow˺ can be either true or false now without settling how the future will be. For example, Barnes and Cameron (2009, 2011) reject step (3) of the fatalist argument. They claim that the move from ‘if it is either true or false now that p’ to ‘it is now settled that p’ relies on a mistaken assumption, namely that if a statement has a truth-value then it is settled that it has that truth-value. For Barnes and Cameron, it can be settled that a statement has a truth-value (either truth or falsity), without it being settled which truth-value this statement has. Specifically, it is settled that ˹There will be a sea-battle tomorrow˺ is either true or false, but it is neither settled that this statement is true nor that it is false. This claim leads Barnes and Cameron to conclude that the bivalence of future contingents can be reconciled with a peculiar kind of open future (expressed in terms of metaphysical indeterminacy) and, therefore, that the fatalist argument must be rejected.

Likewise, Correia and Rosenkranz (2018) reject step (3) of the fatalist argument. They argue that it rests on too strong a conception of the so-called ‘grounding requirement on tensed truths’ (i.e. the requirement according to which tensed truths do not ‘float free’, but are grounded in reality). Their idea is that, although the truth-value of a future contingent must be grounded in reality (i.e. in what exists and how things that exist are), it does not need to be grounded in how things located in the present or past (of now) are or have been. In particular, “[…] the present truth of a statement about how, at some future time, things will be, might well be said to be, at that future time, going to be grounded by things being that way” (2018: 108). For instance, supposing that ˹There will be a sea-battle tomorrow˺ is true now, there will be a sea-battle tomorrow such that it will explain why, one day before, the statement ˹There will be a sea-battle tomorrow˺ was true. Now, since tomorrow’s sea-battle is not predetermined (nothing there is or was, in conjunction with how it is or was makes it inevitable), Correia and Rosenkranz conclude that future contingents can now have a truth-value without the future being bound to be a certain way; so they reject step (3) of the fatalist argument.

A last example is given by Todd’s Russellian approach to future contingents. According to Todd (2016), there is a crucial connection between the debate about ‘The present King of France’ (cf. Russell, 1905, 1957; Strawson, 1950) and the debate about the open future: just as everyone denies that there exists ‘the present King of France’, so the open futurist denies that there exists an actual future. Taking this parallel seriously, the Strawsonian view of statements such as ˹The present King of France is bald˺ and the Aristotelian view of future contingents look very similar: they both take the relevant statements to be neither true nor false. Therefore, just as there is a Russellian alternative to the Strawsonian view, according to which statements such as ˹The present King of France is bald˺ are all simply false, so there must be a Russellian alternative to the Aristotelian view, according to which future contingents are all simply false. Todd develops this latter alternative, which rests on a very simple principle: a future tensed-statement is true iff what it says happens in the actual future. But given that there is no actual future (as open futurists contend), then nothing happens in the actual future and any future-tensed statement is false. Now, since a statement such as ˹There will be a sea-battle tomorrow, or there will not be a sea-battle tomorrow˺ is not an instance of p v ¬p (even if it can easily seem that it could not fail to be true, at least if the ‘open future’ view is false),¹⁵ Todd concludes that the ‘open future’ view can be endorsed without any violation of the classical logical principles of bivalence and Excluded Middle; so he also rejects step (3) of the fatalist argument.¹⁶

Finally, a third reason why Markosian’s attempt to define the openness of the future seems flawed relates to the important costs generated by the denial of Bivalence. In particular, future contingents cannot be presented as counterexamples to Bivalence without specifying what logic and semantics one ought to assume when reasoning about the open future. Two options are generally retained to model truth-value gaps: (i) assuming a three-valued treatment of truth-functional connectives, (ii) assuming supervaluationism. However, both of these options have well-known drawbacks.

For example, on either Kleene’s or Łukasiewicz’s three-valued logics, Fφ ∨ ¬Fφ is neither true nor false when Fφ is a future contingent, which is clearly undesirable: even if it may be now unsettled whether or not there will be a sea-battle tomorrow, it should anyway be settled that either there will be, or there will not be a sea-battle tomorrow (cf. Aristotle, 2014: 32, Prior, 1953). This problem cannot be solved in terms of three-valued semantics if the logic is truth-functional, i.e. if the truth-value of any proposition always depends entirely on the truth-values of its parts. As has been argued by Arthur Prior (1953: 326), changing the truth-tables to something different from Łukasiewicz’s model would be useless. As long as the model is truth-functional, it is clear that the two disjunctions Fφ ∨ ¬Fφ and Fφ ∨ Fφ will have the same truth-value (cf. Øhrstrøm & Hasle, 2020: §4.1). This is not satisfactory, since Fφ ∨ ¬Fφ is clearly true, whereas Fφ ∨ Fφ is undetermined, given that Fφ is undetermined.

With supervaluationism no comparable problem arises. The non-bivalent semantics it affords underwrites all theorems of classical logic, including every instance of Fφ ∨ ¬Fφ. According to this theory, a statement is true at a time t just in case it is supertrue at t, i.e. just in case it is true at t on all histories that include t. Likewise, a statement is false at t just in case it is superfalse at t, i.e. just in case it is false at t on all histories that include t. In all other cases, a statement is neither true nor false. In particular, future contingents – that are true on some future histories, false on others – are neither true nor false, where this must be understood not in the sense that future contingents have a third truth-value (as in Kleene’s or Łukasiewicz’s logics), but that they lack a truth-value. It is thus common to define future contingents as ‘gappy’ because supervaluationism, contrary to Kleene’s or Łukasiewicz’s three-valued logics, allows for truth-value gaps. However, since supervaluationism retains the Excluded-middle while it rejects Bivalence, it has to abandon the Tarski biconditional (‘φ’ is true iff φ)¹⁷ and, therefore, the disquotational property of truth, which could turn out to be unacceptable. Tim Williamson, for instance, writes that “[h]ow much more there is to the concept of truth than the disquotational property is far from clear, but in most contexts truth is assumed to be at least disquotational, whatever else it is or is not” (1994: 162).¹⁸

Moreover, as Williamson (1994: 151) points out, the following rules of inference are classically valid, yet they may fail in a language with a supervaluational semantics:¹⁹

[1]	From Σ, φ ⊨ ψ infer Σ ⊨ φ → ψ	Conditional proof
[2]	From Σ, φ ⊨ ψ infer Σ, ¬ψ ⊨ ¬φ	Contraposition
[3]	From Σ, φ ⊨ ψ ∧ ¬ψ infer Σ ⊨ ¬φ	Indirect proof
[4]	From Σ, φ ⊨ σ and Σ, ψ ⊨ σ infer Σ, φ ∨ ψ ⊨ σ)	Proof by cases

It might therefore be argued that, since classical logic and semantics are vastly superior to the alternatives required by the denial of bivalence in “[…] simplicity, power, past success and integration with theories in other domains” (Williamson, 1994: 186), they should as far as possible be preserved, and so Markosian’s characterization of the asymmetry – which leads to non-classicality – should be rejected.

In a nutshell, since we aim (i) to capture some basic intuitions about the nature of time, (ii) to question the fatalist argument, and (iii) to possibly retain classical logic and semantics, it seems wrong to begin with the supposition that the ‘open future’ view amounts to the failure of Bivalence for future contingents. Rather, we should ask how best to understand our basic intuitions regarding the nature of time, while leaving open the possibility that the failure of Bivalence may end up being a non-logical consequence of the ‘open future’ view. In other words, it seems that the costly rejection of Bivalence is not definitional of the open future and, if needed, should only be motivated by our best understanding of our intuitions about time. For these reasons, it seems preferable to look for another, presumably non-semantic, way of characterizing the asymmetry, and ultimately assess whether it might be reconciled with an unrestricted application of Bivalence.

2.3 A Reflection of Our Ignorance

It is often assumed that the asymmetry between the open future and the fixed past is merely an epistemic phenomenon: we can know much more about the past than we can know about the future. For example, if we want to know who won the Nobel Prize for literature last year, or whether John Kennedy was killed on a Tuesday, we can consult our memory or look it up in a book. After all, we find ourselves in a world with plenty of information about the past. By contrast, we have no records of who will win the Nobel Prize for literature next year, no books in which we can look up whether the first astronaut to go to Mars will be a woman. Of course, we can make guesses about how the future will be, but our guesses are “spotty” and “provisional” (Ismael, 2016: 140). In this sense, the asymmetry in openness between the future and the past is not among the ‘fundamental features’ of reality. It only reflects the fact that whereas we are in a position to gain a wide knowledge of the past, the future remains largely unknowable to us.

At first sight, this understanding of the asymmetry as an epistemic and therefore non-fundamental feature of reality accords well with important results of contemporary physics. For example, the theory of relativity seems to imply a ‘block universe’ view of time,²⁰ in which the asymmetry does not arise. According to this view, the block universe extends from the Big Bang to the end of time if there is one, or indefinitely, if there is not. It represents all times as equal parts of reality, i.e. without making any fundamental asymmetric distinction between them. Just as spatial places (e.g., Greenwich Village, Plaça de Catalunya) exist, despite not being here (in Switzerland), so too past and future times exist, despite not being now (in 2022).²¹ In other words, the spatiotemporal model favored by contemporary physics does not seem to reflect any difference between space and time that somehow accounts for the fact that whereas there is no here-there space-asymmetry, there should be a past-future time asymmetry.

Likewise, the fundamental laws of physics, which are time-reversal invariant (insofar as the positions of particles are concerned),²² do not underpin any asymmetry regarding the nature of time. For example, the laws of classical electrodynamics – since they entail that whatever motions particles can execute, they can execute backward – fail to capture any temporal asymmetry: “[...] the unbreaking of glass can be no less in accord with the laws of Maxwellian electrodynamics than the breaking of glass is, and the spontaneous heating of soup can be no less in accord with Maxwellian electrodynamics than its spontaneous cooling is, and the coming of youth can be no less in accord with Maxwellian electrodynamics than its passing is” (Albert, 2000: 15). After all, for a glass to break, or for a soup to be spontaneously heated is just for their constitutive particles to assume certain particular sequences of positions. And, since every sequence of positions S₁…S_F (which is in accord with the laws of classical electrodynamics) admits the inverse sequence of time-reversed positions S_F’…S_1’ (which is also in accord with these laws), it turns out that classical electrodynamics (as well as most post-Newtonian theories, such as the Special and General theory of relativity, and the standard interpretations of quantum mechanics) makes no significant difference between the future and the past (at least with respect to their fundamental laws).²³

Of course, one might emphasize that there are exceptions. In particular, one might claim that classical thermodynamics is partially governed by its Second Law, which states that the total entropy of any isolated system (i.e. no outside influences and no leakage) tends to increase with time, and therefore indicates the irreversibility of natural processes.²⁴ For instance, Lawrence Sklar claims that “[w]here there is no local entropic asymmetry, there is no future-past of time” (1992: 149). This claim will later be considered in greater detail, but I can already mention the main reason why it seems flawed: even if thermodynamics could yield the desired asymmetry, which is doubtful (cf. Uffink, 2001, Brown & Uffink, 2001, but also Poincaré’s ‘recurrence theorem’), this would not provide a fundamental explanation as to why the past appears to be fixed and the future open. Classical thermodynamics postulates both physical magnitudes – such as temperature, pressure, volume, entropy and heat – and laws stated in terms of these magnitudes, such as the Second Law. But these features are not believed to be fundamental. Many of them arise at a macroscopic level from the collective behavior of many microscopic entities. In general, quantum mechanics deals with the behavior of such microscopic entities, while its laws are – at least on the standard views – time-reversal invariant. So, even assuming that thermodynamics encodes a time asymmetry, it seems that this would at best postpone the problem: if there is no directedness in fundamental physics, then where does the thermodynamic asymmetry in time come from?

It might therefore be tempting for philosophers of physics to conclude that the asymmetry in openness between the future and the past is some sort of non-fundamental phenomenon, especially an epistemic phenomenon²⁵ (perhaps an artifact of the peculiar way our minds interact with the world). The main virtue of such a conclusion is a dialectical one: it explains away the awkward fact that the asymmetry has not yet been captured by our best physical theories and, therefore, preserves the reach of our understanding. This dialectical move is, by the way, pretty common in philosophy. There is indeed a fine tradition of dismissing awkward facts as non-fundamental features of reality. Kant ([1787] 1998: B51/A35), for example, argues that the Euclidean structure of space and time is not among the fundamental features of reality, but arises from the interaction of our sensory apparatus with the things in themselves. This idealist thesis has been explicitly developed to protect our knowledge of geometric truths from Hume’s arguments that highlighted the fallibility of our epistemic devices. In brief, assuming that Euclidean geometry does not exist independently of us and, therefore, is not inferred from our ordinary inductive exploration of the world, it does not fall under Hume’s skepticism.

Another example is given by the Everett, or ‘many-worlds’, interpretation of quantum mechanics. Some many-worlds theorists protect the possibility of some superpositions of systems at the macroscopic level by claiming that “[…] the most basic fact of laboratory experience – that experiments have unique outcomes – is an illusion” (Norton, 2010: 24). According to them, every time a quantum experiment with different possible outcomes is performed, all outcomes are obtained, each in a different world. For instance, many-worlds theorists affirm that Schrödinger’s cat is both dead and alive, even before the box is opened. But since we do not see this macroscopic superposition – the cat is just dead, say, when we check – they conclude that there is another alive cat we cannot see, so that the definiteness of its death is an illusion. Here again, this theory requires us to dismiss some fact of experience as an illusion: we are actually deceived when we see just a dead cat. This dialectical move allows preserving the linearity of quantum mechanics (which states that objects can evolve into superpositions) without admitting that observation puts an end to this linearity.

However, it might seem that failing to capture particular phenomena, facts or entities is not sufficient grounds to doubt their fundamentality. For centuries physical models have not made any reference to quarks, but that did not prevent some ancient philosophers (e.g., Leucippus, Democritus, Epicurus) from rightly defending (supposing that it is right)²⁶ the view that the world is fundamentally composed of elementary particles.²⁷ Moreover, there are dozens of natural phenomena (e.g., northern lights, will-o’-the-wisps) that, although science had for long regarded them as subject-dependent, turn out to be objective features of reality. When impressed by the tremendous results obtained by physics through the last century, we get used to the idea that our best theories of space and time are telling us all that can be said about the nature of time, we just start to invert the reasoning. This is sometimes called ‘the exclusivity dogma’, namely the view that physics is an infallible guide to ontology, against which Yuval Dolev (2006: 189), for instance, warns us. If a phenomenon has all the marks of a fundamental and therefore non-epistemic one (like elementary particles in constitution processes), then it can legitimately be expected that physics must somehow characterize it. This leads to a principle, sometimes referred to as ‘the principle of credulity’ that seems reasonable to accept: intuitions must be preserved as long as science has not shown them to be wrong. Of course, this principle does not exclude that intuitions can be revised, but it states that they must be retained until they should be revised.

Moreover, assuming that the asymmetry is merely an epistemic phenomenon, the mechanism through which this phenomenon arises must be identified. There is a need to explain why – though the asymmetry has allegedly nothing to do with the nature of time – we have privileged epistemic access to the past rather than to the future. But such an explanation is rarely found in the literature. Most of the time, philosophers of science avoid the problem by claiming that potential solutions to this issue are to be found outside their field of expertise. For example, Rudolph Carnap invokes here the role of psychology: “[...] all that occurs objectively can be described in science; on the one hand the temporal sequence of events is described in physics; and, on the other hand, the peculiarities of man’s experiences with respect to time, including his different attitude towards past, present, and future, can be described and (in principle) explained in psychology” (1963: 37–38). In a similar vein, Paul Davies argues that “[t]he flow of time is an illusion. […] And presumably the explanation for this illusion has to do with something up here (in your head) and is connected with memories […]. So it’s a feeling we have, but it’s not a property of time itself […]. Time doesn’t flow. That’s part of psychology” (cf. Dowker, 2020: 144). These kinds of buck-passing answers are, however, clearly unsatisfying. The issue raised by the origins of our intuitions regarding the nature of time cannot be skipped under the pretense that it could hypothetically be solved by psychologists (or other scientists). As, for instance, Mauro Dorato puts it: “[i]f a physical theory were in radical conflict with our experience of the world, and it could not give any explanation of the origin of such contrast, we should not invoke the illusoriness of our experience, but we would rather have good reasons to reformulate or even abandon the physical theory” (2008: 54).

Nonetheless, it must be acknowledged that there are projects that aim to explain the epistemic difference between the future and the past in certain physical facts (cf. Reichenbach [1956] 1971; Butterfield, 1984; Horwich, 1987; Craig 2001a, b; Callender, 2008). Apart from the details, all these projects involve the notion of causation, by appealing either to the unidirectionality of causation (causes occur prior to their effects), or to the causal independence of the past to the present (nothing that can now happen could have any effect on the past). However, although it is natural to associate temporal asymmetries with the idea that anything that can now happen can only have effects in the future (there is no backwards causation), there are reasons to doubt whether causation is the key of the mystery. For, unidirectional causation and causal independence appear to be neither necessary nor sufficient for fixity and openness. Consider the two following arguments.

First, reflection on permanentist thinking (always, everything always exists)²⁸ suggests that the causal independence of the past to the present is not necessary for the fixity of the past – or, to put it another way, the thesis that the future is fixed is compatible with the causal dependence of the future to the present. Consider the following case: by killing Archduke Franz Ferdinand of Austria, Gavrilo Princip (we may suppose) led to the outbreak of World War I. The latter event was causally dependent on the former. Yet, assuming that WWI has always existed (permanentism), it seems that one can still accept the causal claim that ‘the outbreak of WWI is causally dependent on Gavrilo Princip’s previous act of murder’, without doubting that WWI could not have failed to take place. In other words, assuming that permanentism is true, one can question whether Gavrilo Princip had before him, at any time in his existence, a future that was ‘open’ rather than ‘fixed’ (without denying the causal role he played in the outbreak of WWI). Moreover, it seems that causal independence is not sufficient for fixity. A future that is a completely random continuation of the present is surely a future that is causally independent of the present. Yet such a ‘random’ future, far from being a ‘fixed’ future, might seem to be “[…] a paradigm of one type of openness (even if it represents a type of openness that brings with it no prospect of control over the course of events)” (Mackie 2014: 415).

Second, the unidirectionality of causation is not sufficient for openness. Consider the Gödel spacetime that admits closed time-like curves: “[…] if P, Q are any two points on a world line of matter, and P precedes Q on this line, there exists a time-like line connecting P and Q on which Q precedes P” (Gödel 1949a, b: 447).²⁹ In such a theoretical option, the future is clearly fixed (the sequence is closed and composed of a finite numbers of events), in spite of causation being unidirectional. The planting of a seed leads to the growing of a tree, which leads to the shading of a bench. Events causally related continue in the same way they would do in linear time. Of course, since the sequence of events is circular, one could theoretically plant a tree tomorrow in order to provide shade for a bench yesterday. But this is clearly not a case of backwards causation, since the shading at t₂ continues from the planting at t₄ in the forward direction, i.e. not through t₃, but through t₅, t₆, … t₁ (cf. Diekemper, 2005: 232). For these reasons, the question of causation appears to be largely independent of the question of temporal asymmetries and, therefore, fails to explain the asymmetry between what we can know about the past and what we can know about the future.

Finally, claiming that the asymmetry is merely an epistemic phenomenon betrays our intuitions. Although everybody agrees that we can know much more about the past than we can know about the future, it cannot be the whole story. We think of the open future and the fixed past in a much stronger sense. Unlike the spatial parts of which we have no memories and only few records (e.g., a distant planet, the center of the Earth), we do not think of the future as out there, waiting to be experienced. We rather think of it as partially unsettled until it has been made available to experience. This can be revealed by ordinary language: if I say that it is open whether my favorite football team (viz. Neuchâtel Xamax) will win the match tomorrow, I do not mean that the result is settled even though I don’t know it yet. I rather mean that everything about tomorrow’s match is still possible: perhaps my favorite team will win, or perhaps it will not. Our intuitions of openness seem thus to relate to worldly unsettledness regarding the future, rather than to our lack of epistemic access to what will happen. Of course, proponents of the epistemic approach might reply that the fact that their characterization is counterintuitive is of no consequence, since scientists have shown on many occasions that our intuitions (and especially our intuitions about time) are misleading. For example, it seems to us that ‘our present’ extends throughout the universe, while this intuition requires an objective notion of absolute simultaneity, which has been banned by Special Relativity (cf. Bourne, 2006). To that, two comments can be made.

First, all our intuitions are not equally important. Admittedly, our intuition of a common present has been denied by science (this will nonetheless be discussed in Sect. 4.6), but this intuition has come very late in human history. For centuries – as long as travel was on horseback, on foot, or in carriages – every village had its own peculiar time based on natural phenomena; there was then no reason to synchronize clocks between one place and another. It is only in the nineteenth century, with the development of the rail network, that the problem arose of properly synchronized clocks between different cities, and that the intuition of a universal ‘now’ emerged (cf. Rovelli, 2018: 47; Stephens, 1989). By contrast, the intuition of a fixed past and an open future has always been part of our manifest image of the world. At least, as long as we have viewed ourselves as agents capable of influencing the world in various ways, we have presupposed that the future was somehow open.³⁰ Therefore, it may not be as easy to deny the intuition of an open future than the intuition of a universal ‘now’, since these two intuitions play roles of varying levels of importance in our relationship to the world.

Second, an important consequence of the epistemic approach must be highlighted. If the openness of the future is merely to be explained by our great ignorance about what will happen, then, strictly speaking, the future is fixed. For example, the possibilities to act otherwise than how we actually act are not genuine possibilities, but merely epistemic ones. In such a picture (as in any other), there are two ways of seeing things: either humans can act freely, or they cannot. Assuming that human freedom should be preserved, the proponents of the epistemic approach have no choice but to accept a compatibilist theory (where the fixity of the future is not a threat to human freedom). As we will see in the next section, there are good reasons to believe that compatibilism is true, but – as compatibilists must themselves admit – even if this theory is true, it is not trivially true. Incompatibilists also provide powerful arguments to show that, when the future is fixed, no human act is free (precisely because, in such a picture, the possibilities to act otherwise are merely epistemic). So, since compatibilism is not trivially true (incompatibilists might be right, after all), there is a sense in which proponents of the epistemic approach endanger human freedom: they make it dependent on the non-trivial truth of compatibilism. By contrast, although substantial approaches to the open future (according to which the open future is not merely an epistemic phenomenon) do not ensure that some human acts are free, they do not make human freedom dependent on the non-trivial truth of compatibilism (nor on the non-trivial truth of incompatibilism). As a result, substantial approaches may seem more hospitable to human freedom than the epistemic approach. To be sure, this point is not against compatibilism; it merely highlights the fact that, assuming that human freedom should be preserved, proponents of the epistemic approach are forced to accept compatibilism, while this theory is, at best, non-trivially true.

Thus, although the asymmetry between what we can know about the past and what we can know about the future may, here again, end up being a consequence of the nature of time, it seems wrong to reduce the issue to its epistemic aspect. First, there are no good grounds for dismissing the asymmetry as an epistemic phenomenon (but mainly dialectical grounds). Second, there are no (or very few) satisfying attempts to identify the mechanism through which the epistemic asymmetry arises, if not grounded in the nature of time. And, finally, such an epistemic account betrays our basic intuitions that relate to the world itself (and not to the limits of our knowledge). For these reasons, it seems preferable to look for a more fundamental way of characterizing the asymmetry, which may ultimately explain why our knowledge of the future is not as vast as our knowledge of the past.

2.4 The Anthropocentric Attempt

Some philosophers tend to reduce the open future debate to the question of human abilities. They take the claim that ‘the future is open while the past is fixed’ to express the idea that ‘humans can affect what will happen, but not what happened’. This move is natural, since our beliefs about our powers with respect to the future contrast sharply with our beliefs about our lack of power with respect to the past: whereas we do not deliberate about the past, our beliefs about opportunities, possibilities, alternatives, and so on, are all future-oriented. For instance, whereas there is no use crying over a broken window because once it has happened there is nothing we can do about it (except fixing it of course), we take to be (partially) within our power whether or not a future window is broken. Such an ‘anthropocentric view’ is, for example, defended by Stephan Torre who argues that “[t]he fact that so many [philosophers] have considered arguments against the open future by considering arguments that threaten our power over future events strongly suggests that […] our notion of an asymmetry in openness between the past and the future is tied to an asymmetry in what we can affect or have power over” (2011: 361–362). In the same vein, Jenann Ismael claims that “[t]he future is as open as you are free to change your mind. And so understanding the sense in which the future is open really turns out to hinge on a proper understanding of the sense in which deliberation is unfixed by prior belief” (2016: 153). However, as we will see, it is one thing to say that the question of our abilities may inform us on the asymmetry between the open future and the fixed past; it is another to say that this asymmetry is nothing but an asymmetry in our abilities. This will become clear when we will consider senses in which the future and the past may respectively be said to be open and fixed in a world without humans (or before humanity emerged).

Another ‘anthropocentric view’ is endorsed by John Martin Fischer (1994, 2011) and Wesley Holliday (2012), who use the expression ‘The Principle of the Fixity of the Past’ to describe a thesis about a limitation on our abilities. More specifically, Fischer (2011) focuses on the thesis, commonly referred to as ‘theological fatalism’, according to which God’s foreknowledge and human freedom are incompatible: if there is a God who knows the entire future infallibly, then no human act is free. This thesis is generally motivated by the following line of reasoning: for any future act you will perform, if God infallibly believed in the past that the act would occur,³¹ there is nothing you can do now about the fact that he believed what he believed, since (i) nobody has any control over past events (fixity of the past), and (ii) you cannot make God mistaken in his belief (infallible foreknowledge).³² Therefore, “[…] there is nothing you can do now about the fact that he believed in a way that cannot be mistaken that you would do what you will do. But if so, you cannot do otherwise than what he believed you would do. And if you cannot do otherwise, you will not perform the act freely” (Zagzebski, 2017, cf. also Pike, 1965).

Although both incompatibilist and compatibilist replies can be made to this seemingly valid argument, Fischer’s point is rather to reinforce it by clarifying premise (i), i.e. by providing an accurate characterization of the fixity of the past. As Fischer puts it: “[…] it is really unsatisfying simply to assert this [principle] as an a priori truth” (2011: 467); he therefore proposes to characterize the fixity of the past in terms of a limitation on our abilities, to the effect that we cannot do anything such that, were we to do it, the past would have been (or have had to be) different. According to Fischer, an agent cannot perform any action, the performance of which would require the past to have unfolded differently than it actually did. This characterization of (i) is meant to undermine any attempt to reject theological fatalism: if there is a God who knows the entire future infallibly, then you cannot do otherwise than what he believed you would do, since any different action would require a different past (in particular, any different action would require that God would have had a different belief), which is impossible. God’s foreknowledge and human freedom are therefore incompatible.

Faced with this argument, compatibilists – who aim to reconcile God’s foreknowledge with human freedom – must reject Fischer’s characterization of the fixity of the past. In that respect, they might argue that, although nobody has an incredible power to change the past (i.e. to undo events that had already occurred in history), one has a more modest power, a power to do things at t such that certain events that actually occurred before t would never have occurred at all. For example, even if it is true that if I had visited my parents yesterday, the past would have (to have) been different (e.g., God would have had a different belief), I could have done so, provided I was under no coercion or compulsion to not visit my parents. Of course, in such a case, different events would have occurred instead, but no event would have both occurred and then been undone by my action. Thus, once one realizes that compatibilism does not involve any commitment to a power of undoing the past, it seems that Fischer’s characterization of (i) fails to undermine any attempt to reject theological fatalism. From a compatibilist point of view, what is right about the Principle of the Fixity of the Past is that we cannot undo the past; what is wrong about Fischer’s characterization of this principle is that it goes further, stating that we cannot do anything that requires a different past. In short, compatibilists believe that one can perform an action that is inconsistent with the actual past (and so Fischer is wrong), even though one will not.³³

The question as to whether God’s foreknowledge can be reconciled with human freedom is somehow similar to a more general and well-known question in the history of philosophy, ‘the free will problem’, which concerns a disputed incompatibility between free will (i.e. the ability of persons to make decisions of the sort for which one can be morally responsible) and determinism (i.e. the thesis that at any time the world has exactly one possible future, given the past and the laws of nature).³⁴ Unfortunately, despite all of the work philosophers have devoted to it, there is no single specification of the free will problem. Part of the reason is that a completely neutral formulation of the problem can hardly be found. So, although I doubt that what follows will meet general approval, here is how Robert Kane introduces the problem:

[…] suppose Jane has just graduated from law school and she has a choice between joining a law firm in Chicago or a different firm in New York. If Jane believes her choice is a free choice (made “of her own free will”), she must believe both options are “open” to her while she is deliberating. She could choose either one. (If she did not believe this, what would be the point of deliberating?) But that means she believes there is more than one possible path into the future available to her and it is “up to her” which of these paths will be taken. [However] if determinism is true, it seems there would not be more than one possible path into the future available to Jane, but only one. It would not be “up to her” what she chose from an array of alternative possibilities, since only one alternative would be possible (2007: 6).

One reason to complain about Kane’s formulation of the ‘free will problem’ is its use of the locution “it is up to her”. For, both incompatibilists and compatibilists agree that human actions are not epiphenomenal. Therefore, even if determinism is true, compatibilists will claim that “it is up to Jane” whether she will work in Chicago or New York (at least as long as her choice is made for her own reasons).

As in the previous debate, there is a long-standing tradition of dividing up the conceptual terrain in two families of positions. Traditionally, incompatibilists are those who think that free will is incompatible with the world being deterministic, while compatibilists reject this thought. To return to Kane’s example, an incompatibilist will typically claim that, if determinism is true, Jane has no ability to choose how her own future will unfold (she has no control over the past or the laws of nature), while a compatibilist will argue that, although there might be only one possible way the future might unfold, Jane still has the ability to choose to work in Chicago or New York (she is under no coercion or compulsion, after all). It is worth noting that neither incompatibilists nor compatibilists are committed to the further claim that Jane does, in fact, have free will. However, as Michael McKenna and Justin Coates make clear: “[…] many compatibilists (but by no means all) do think that we are sometimes free. And though some incompatibilists remain agnostic as to whether persons have free will, most take a further stand regarding the reality or unreality of free will” (2015: §1.4). In the philosophical literature, libertarians are the incompatibilists who argue that at least some persons have free will (and, therefore, that determinism is false), while hard incompatibilists (or hard determinists) have a less optimistic view, holding that determinism is true and, therefore, that no persons have free will.

From a contemporary perspective, the conflict between incompatibilists and compatibilists lies, at least partially, in a disagreement over the meaning of ‘can’ (or ‘have the power’) and related expressions, such as ‘could have done otherwise’ (which does not imply that the conflict is merely verbal). According to incompatibilists, we are able to do otherwise only if our doing otherwise is a possible continuation of the past consistent with the laws. It thus appears that, if determinism is true, there is only one possible continuation of the past consistent with the laws, and so no human action is free. As Kadri Vihvelin puts it: “[w]hat we actually do is the only thing we are able to do” (2003: §5). By contrast, compatibilists insist that ‘can’ (or ‘have the power’) should be understood as a counterfactual expression: when someone says ‘you can (or have the power) to do something’, it simply means that ‘if you want (or try) to do it, you shall do it’. For example, saying that ‘you can jump over this fence’ means that ‘you will jump over it, if you want to or try to’. It is therefore wrong to claim that, if determinism is true, no human action is free, since our actions counterfactually depend on our choices, which in turn depend on the reasons we take ourselves to have (at least in the normal case, where there is no coercion or compulsion). If our reasons were different, we would choose otherwise, and if we chose otherwise, we would do otherwise. And, it seems that our reasons can be different, at least in the sense that we, unlike animals or young children, have (i) the ability to critically evaluate our reasons (beliefs, desires, values, principles, etc.) and (ii) the ability to change them (this is sometimes called the ‘can’ of freedom and choice).

Of course, this is not the place to settle these debates, even if I am inclined to think, as Fischer does, that the compatibilist interpretation of ‘can’ (or ‘have the power to’) is contextually inappropriate. After all, it is uncontentious that I have the general ability and ‘know-how’ to refrain from visiting my parents (even in the scenario in which God has foreknowledge that I will in fact not visit them), just as it is uncontentious that Jane has the general ability and ‘know-how’ to accept a position in Chicago or New York (even in a scenario in which determinism is true). But this does not seem to be the conception of ability in question. The whole point of the human freedom debate is to question whether, in some specific contexts (e.g., there is an omniscient God, determinism is true), we have the ability to do otherwise with respect to ordinary actions. Having a general capacity (relevant skills and know-how) is not sufficient for the ability in question, since one might have the general capacity while being blocked from exercising it in various ways! So, it does not seem ‘dialectically kosher’ simply to assume, in these two examples, that Jane and I have the ability to do so and so. As Fischer puts it: “[…] one cannot simply import ordinary views about our powers into the philosophical context of an evaluation of the argument for the incompatibility of God’s foreknowledge [or determinism] and human freedom – a skeptical argument that explicitly challenges these ordinary views about powers” (2011: 471).³⁵

Anyway, despite what Fischer suggests, what incompatibilists and compatibilists seem to agree upon is that nobody can perform an action that changes the past (which does not imply, according to compatibilists, that nobody can perform an action that is inconsistent with the past), not even time-travelers, contrary to what many Hollywood movies suggest. In a model with a single past, changing the past clearly involves contradictions: e.g., the time-traveler bets on the victory of his favorite team in 1976, and does not bet on the victory of his favorite team in 1976. It is not as if there were two versions of the past: the original one, and a second version with the time-traveler playing a role. There is only one past and two perspectives on it: the perspective of the younger self, and the perspective of the older time-traveler. If these perspectives are inconsistent (e.g., if an event occurs in one but not in the other), then the time-travel scenario is incoherent.³⁶ However, although time-travelers cannot make the past different from the way it was, this does not mean that they must be entirely powerless in the past: they can participate in it, in particular they can do anything that happened. For example, if tomorrow Sam travels back to 1976, then the past already contains Sam appearing out of nowhere in 1976, as well as it contains all the actions Sam performed there and all the consequences of his actions. Sam will be causally effective in the past, but he will not bring about any change: before he travels what will happen to him happened in the past (cf. Andreoletti, 2020 and Lewis, 1976).³⁷

Now the central question is the following: is it a good suggestion to reduce the open future debate to the question of human abilities? Although I must acknowledge that our power and lack of power over certain events is constitutive of our pre-theoretic understanding of openness and fixity (cf. Torre, 2011: 361), I think that it is a bad suggestion. First, unless we find some common ground between incompatibilists and compatibilists on what the expression ‘can’ (or ‘have the power’) means (which seems hopeless – the free will debate has been raging since Plato and Aristotle, cf. Irwin, 1992), the risk is to privilege one or the other of these positions. For example, supposing that there is an omniscient God or that determinism is true, can humans choose how their own future will unfold? As has been shown, the answer depends on whether we adopt an incompatibilist or a compatibilist point of view: if ‘can’ means that humans have the freedom to do otherwise, incompatibilists immediately answer ‘no’, while at least some compatibilists might answer ‘yes’ (there is at least one counterfactual conception of ‘can’ according to which humans can choose how their own future will unfold). Therefore, since we do not want our characterization of the temporal asymmetry to presuppose the truth (or the falsity) of incompatibilism or compatibilism – two venerable positions in the history of philosophy – it seems preferable to look for another option. It is worth noting that, although the failure of determinism will be introduced in the next section as a necessary condition for the future being open, this does not preclude compatibilism, since this does not preclude the possibility for humans to act freely when the future is fixed; in such a case, humans remain causally efficient, after all.

Second, reducing the open future debate to the question of human abilities is objectionably agent-centered. It might indeed seem that the asymmetry between the open future and the fixed past was prior to the existence of any agent. For example, it might be argued that, 100 million years ago, it was open whether dinosaurs would disappear and humanity would emerge. Moreover, there is at least one sense in which the future may be said to be open that does not involve any agent: time could come to an end, with no ontological commitment to future things standing in the way (cf. Correia & Rosenkranz, 2018: 99). It indeed seems possible that the future is open not simply in terms of how it will unfold, but also in terms of whether it will unfold (this will be discussed at length in Sects. 2.7, 2.8 and 2.9). Taking this possibility seriously (as a number of physicists and theologians do), while it obviously exceeds anything humans may claim to have power on (no matter what we mean by ‘power’ here), it must be concluded that the question of the open future should not be reduced to the question of our abilities. After all, there is nothing strange in supposing that there are senses in which the future may be said to be open in a world without humans (especially if determinism is false and there being no fact about what will happen, cf. Sect. 2.9).

The point of this section was not to minimize the importance of the human freedom debate (even if determinism and God’s foreknowledge are no longer at the heart of our highest concerns – most physicists think that the world is not deterministic (at least with respect to quantum mechanics) and theological questions have progressively been banned from scientific inquiry). This debate is crucial, especially with regard to moral responsibility, because it is generally agreed that having free will is a necessary condition of being morally responsible, so that if determinism precludes free will, it also precludes moral responsibility. The idea was rather to show that, although a reflection on our abilities (what we can or cannot do, what ‘can’ truly means, etc.) contributes to the understanding of the openness and fixity phenomena, the asymmetry between the open future and the fixed past should not be reduced to an asymmetry of mutability. As Penelope Mackie puts it: “[…] Fischer’s principle seems more appropriately regarded as a (controversial) claim about a consequence of the fixity of the past, rather than an expression of what it means to say that the past is fixed” (Mackie, 2014: 414). One should therefore look for a less anthropocentric characterization of the temporal asymmetry, and ultimately assess whether it is compatible with human freedom.

2.5 Physical Indeterminism

Suppose that the world is physically indeterministic in the sense that its future history is not nomologically necessitated by its current history: “[t]o say that the future is open might only be to say that the future is not nomologically determined in this sense” (Pooley, 2013: 337). In other words, the way the world is, up to a certain time t, together with the laws of nature, does not necessitate the way it is at any future time t*. Of course, there can only be a unique and actual way the world is at t*, but, assuming physical indeterminism, this way “[…] need not be the only one compatible with the actual laws and the way the world is up to and including t” (Pooley id). According to this understanding, the future is open at a certain time t only if, given how the world is up to t and what laws obtain, there are several possible ways the world might be at some future time t*.³⁸

There are at least three scenarios in which indeterminism might be the case. First, following Nancy Cartwright (2008), it could be that there are not any laws of nature, such that the world is a disordered jumbled place of random facts. Second, it could be that there are laws of nature, but they do not cover all types of situations that may arise in our universe. For example, perhaps what we call ‘laws of nature’ are local laws that only describe what happens in the part of the universe we can observe, but there are other parts of the universe for which there are not even local laws that apply. Third, and this is what many physicists think follows from quantum mechanics, it could be that there are laws of nature that govern what happens in all types of situations, but these laws do not describe what will happen as a matter of necessity; they only describe what will happen as a matter of chance. Specifically, although the central dynamical law of quantum mechanics – Schrödinger’s equation – is purely deterministic (it does not make any reference to chances), many physicists think that there must be some additional laws describing the chances that there will be a collapse of the wave function (cf. Albert, 1994: 80). If this is true, i.e. if there must be probabilistic laws governing the wave function, then the laws of the universe will turn out to be indeterministic.

The claim that the ‘open future’ view is nothing but the view that ‘there are various futures that can nomologically issue from the current history’ sounds plausible. A reason is that physical determinism, which is correspondingly understood as the negation of physical indeterminism (once you have fixed the world history up to a certain time t and the laws of nature, you have fixed the world history at any future time t*), seems to commit to the fixity of the future. After all, if physical determinism is true and, therefore, if there is only one possible way the world history can unfold, then it is unclear how the future could still be called open. Specifically, if it is necessary, given the facts about how things are up to t and what laws obtain, that the world will be a certain way at t*, then it seems settled that it will be that way, which is just to say that the future is fully settled at t, and hence that the future is fixed. This point may, in particular, be illustrated by Laplace’s intelligence (or demon as it is often called). Assuming determinism, if a demon (which should be construed as a ‘super-scientist’, cf. Popper 1988: 34) knows the precise location and momentum (i.e. the product of the mass and velocity) of every particle of the universe, i.e. has an access to the complete specification of past and present world-states, he can predict their future locations and momenta from the laws of nature. Although Laplace seems to have another kind of determinism in mind (expressed in terms of predictability) and only the laws of classical mechanics, his thought experiment tends to show that if determinism is true, then the future is predictable and hence fully fixed (cf. Laplace [1814] 1951).

John Mackie, for example, endorses such a physical characterization of the open future when he claims that the laws of nature³⁹ cover the ways in which things become fixed or remain open. As he puts it, “[…] the universe needs to know where to go next” and the laws of nature cater to this need (1974: 225). For instance, if two electrons collide, then the laws of quantum mechanics dictate what the future possibilities are: they fix that whereas none of these electrons will turn into a proton or into a water molecule, there is a probability that these electrons will deflect at this or that angle. According to Mackie’s view, the current world history and the laws of nature are thus together both necessary and sufficient to establish whether the future is open or not. If there is only one way the future can nomologically issue from the current world history, then the future is fixed (physical determinism) and, conversely, if there is more than one way the future can nomologically issue from the current world history, then the future is open (physical indeterminism).⁴⁰

However, physical indeterminism is often deemed insufficient for characterizing the openness of the future. For example, Peter Geach argues that if there is a current world history from which the future can nomologically issue only in one way, then the future is fixed, but the converse does not hold. As he metaphorically puts it, considering a book, “[…] even if the text of later pages is not determined by the text of earlier pages, there may nevertheless be a completely fixed text on those pages which we have not yet turned over” (1973: 208). Although the relevance of this metaphor might be questioned, the idea it expresses is quite clear: the future may be fixed without being nomologically necessitated by the current world history. In particular, it appears that in a permanentist picture of the world (where always, what exists always exists), the future might be regarded as fixed in spite of the world being indeterministic with regard to what will happen. As Jiri Benovsky puts it: “[…] if the inventory of all there exists in the universe includes all past and future times and entities as well as present ones, then the future is, metaphorically speaking, ‘already there’ (as well as the past and the present). […] No surprise, then, that under such a view the future is already fixed, in a metaphysical way” (2013: 160). For example, it seems reasonable to think that the existence of my grand-son (which is not located in the current world history) fully settles that I will have children in the future, no matter whether the world is indeterministic (or not), at least assuming that Kripkean necessity of origin holds.⁴¹

More controversially, it has been argued that physical indeterminism is not even necessary for the future being open. After all, assuming physical determinism, what is necessary is not, strictly speaking, the way the world is at any future time t* (nor the way it has been up to t), but rather the conditional that if the world has been a certain way up to a certain time t and has certain laws L, then it will be a certain way at any future time t*. Both the antecedent and the consequent of the conditional are contingent in this picture. It might then appear that all that we are entitled to say is that “[…] the consequent of the conditional is settled if the antecedent is; if there is any unsettledness in the antecedent, this may bleed over into the consequent” (Barnes & Cameron, 2009: 300). Following this line of reasoning, Barnes and Cameron conclude that it is wrong to claim that physical determinism commits to the fixity of the future, since all that this thesis entails is that the future is only open if there is unsettledness in the antecedent of the conditional (i.e. either in the world history up to t, or in the laws of nature which obtain). If both the laws and the history are settled, then the future is fixed, but if either the laws or the history is unsettled, then the future might be open. In other words, the future could be called open even if indeterminism is false.

However, as suggested above, this latter argument is highly controversial. For example, Sven Rosenkranz (2013) points out that, by Barnes and Cameron’s own view, the sense in which the current world history might be unsettled is not the sense in which the future is said to be unsettled by being open. In particular, the current world history might be said to be unsettled in the sense that, prior to opening the box, Schrödinger’s cat is neither determinately alive nor dead. But this is clearly not a case of the world being unsettled about which range of completely determinate options obtains, as the openness of the future is meant to be.⁴² According to Calosi and Wilson (2019), for example, the superposition of states (as a source of quantum metaphysical indeterminacy), must rather be seen as involving a state of affairs whose constitutive entity (Schrödinger’s cat) has a determinable property (having a certain life status), but no unique determinate of that determinable (being alive and being dead). Therefore, it is hard to make sense of the claim that the unsettledness in the antecedent can “bleed” into the consequent, since Barnes and Cameron are dealing with at least two different kinds of unsettledness: one that concerns the current world history and the laws of nature (and that may include quantum metaphysical indeterminacy), the other that concerns the plurality of ways the future might develop. To be sure, the claim is not that it is impossible to provide a unified account of both quantum and future unsettledness, but only that if the openness of the future is defined as Barnes and Cameron do, i.e. as the world’s being unsettled about what range of completely determinate options obtains, then it radically differs (by their own view) from the unsettledness that lies in the superposition of quantum states.

In a nutshell, the first reason why physical indeterminism does not appear to be appropriate for characterizing the asymmetry in openness between the future and the past is that, although this thesis seems to be necessary for the future being open (the future is intuitively fixed in a fully deterministic world), it does not seem to be sufficient. Since physical indeterminism is available to permanentists who can clearly deny that the future is genuinely open (although they might not be forced to), it appears that something more than physical indeterminism is required to fully characterize the asymmetric nature of time. That is all the more evident as there are interesting senses in which the future may be said to be open that are not constrained by the current world history and the laws of nature (at least assuming that the world is not fully deterministic). After all, the facts about how the future might unfold need not be fully grounded in physical facts. Perhaps the only sense in which the future turns out to be open is that time will come to an end within 1 s. This logical possibility should not be ruled out on the grounds that it does not exclusively rest on a naturalistic assumption, or so it could be argued (cf. Barnes & Cameron, 2011: §3).

A second, and perhaps more fundamental, reason why physical indeterminism (alone) does not appear to be appropriate for accommodating the asymmetry has to do with the symmetric nature of physical laws. As a reminder, for every physically allowable sequence of states, the inverse sequence of time-reversed states is also physically allowable (cf. Sect. 2.3). Roughly speaking, given that the laws of nature are time-reversal invariant, it seems that the world cannot be considered as physically indeterministic with regard to the future without being considered as physically indeterministic with regard to the past.⁴³ It would indeed be arbitrary to claim that the current world history up to a certain time t, together with the time-reversal invariant laws of nature, is compatible with various alternative futures, but not with various alternative pasts. Hence, any good argument from physical indeterminism in support of the open future seems to be, at the same time, an equally good argument with regard to the open past (cf. Markosian, 1995). Therefore, since physical indeterminism entails that if the future is open, so must be the past; it clearly fails to accommodate any asymmetry in openness between the future and the past. For these reasons, it seems preferable to look for another notion that may ultimately be combined with physical indeterminism in order to provide an accurate characterization of the asymmetry.

2.6 Counterfactual Dependence

The most famous example of an account using modal resources in order to characterize the asymmetry between the open future and the fixed past has been provided by David K. Lewis:

I suggest that the mysterious asymmetry between open future and fixed past is nothing else than the asymmetry of counterfactual dependence. The forking paths into the future – the actual one and all the rest – are the many alternative futures that would come about under various counterfactual suppositions about the present. The one actual, fixed past is the one past that would remain actual under this same range of suppositions (1979a: 462).⁴⁴

Basically, “[…] the future is open because if the present were different the future would be different, whereas the past is fixed because if the present were different the past would remain as it in fact is” (Barnes & Cameron, 2011: 7). For example, suppose that I were watching a movie instead of writing these lines. Then clearly tomorrow would be different also; e.g., I would fall behind in writing this section and presumably feel guilty about this. By contrast, it might seem that there is no true counterfactual about how the past would be different if the present were somehow different. Intuitively, if I were watching a movie instead of writing these lines, what I wrote yesterday would not be affected. As Lewis puts it, “[i]t is at best doubtful whether the past depends counterfactually on the present, whether the present depends on the future, and in general whether the way things are earlier depends on the way things will be later” (1979a: 455).

Of course, counterfactuals are context-sensitive. Given that present conditions have their past causes, one can, as Lewis acknowledges – in atypical contexts – set things up to accept as true that, had the present been different, the past would have been as well. This is commonly called a back-tracking argument. For example, suppose that Jim and Jack quarreled yesterday, and that Jim is a prideful fellow who would never ask someone he quarreled with the day before for help (cf. Downing, 1959). One can easily accept the truth of ˹If Jim asked Jack for help today, there would have been no quarrel between the two men yesterday˺. It thus seems that whether or not an assertion of a counterfactual claim is true depends on what facts do matter in the context of assertion. After all, there is no absolute evaluation of counterfactual claims; the evaluation is always relative to a preselection in the kind of facts that serve as points of reference. Therefore, in order to invalidate back-tracking arguments, and hence yield the desired temporal asymmetry of counterfactual dependence, proponents of the modal approach must explain what facts do matter for the evaluation of counterfactual claims.

In that respect, Lewis (1973a, b, 1979a) provides (i) an analysis of counterfactuals based on comparative similarity of possible worlds and (ii) an account of what kind of facts do matter when comparing possible worlds. Basically, his idea is to take what is open to be what could happen under various counterfactual assumptions concerning the present given a metric of similarity for possible worlds. The evaluation of counterfactuals thus requires the comparison of worlds for similarity to the actual world. According to Lewis’s analysis, “[…] a counterfactual ‘If it were that A, then it would be that C’ is (non-vacuously) true if and only if some (accessible) world where A and C are true is more similar to our actual world, overall, than is any world where A is true but C is false” (1979a: 465). For instance, the counterfactual ˹If Jim swallowed his pride, he would ask Jack for help˺ is true iff every world that makes the antecedent true (Jim swallowed his pride) without a great divergence with actuality is a world that also makes the consequent true (Jim would ask Jack for help).

Then, given that similarities and differences among worlds are not all equal (some of them have more ‘weight’ than others), Lewis provides further rules of how to order worlds for similarity. Specifically, he states that physical facts (e.g., the laws of nature) are the facts that matter when comparing worlds. In general, the less a world violates the laws of nature, the more similar it is to our world. Arguably, this account invalidates back-tracking arguments: the counterfactual ˹If Jim asked Jack for help today, there would have been no quarrel yesterday˺ is usually false because the consequences of supposing that there was no quarrel would make more difference (from a physical point of view) to the world than those of supposing that somehow Jim swallowed his pride. In Lewis’s terms, the world (or, more precisely, the type of worlds) in which Jim somehow swallowed his pride is closer to ours (physical laws are not violated) than the world in which there was no quarrel. Accordingly, if the present were different the past would be the same (e.g., if Jim asked Jack for help today, the quarrel would nevertheless have taken place yesterday), but the same causes would somehow fail to cause the same present effect (e.g., Jim would somehow have swallowed his pride and asked Jack for help despite yesterday’s quarrel).

At first sight, Lewis’s account does display the desired temporal asymmetry of counterfactual dependence, but a closer look reveals important difficulties. First, on Lewis’s view, the facts about what is open depend on the physical facts that determine the similarity metric for possible worlds, while it has been shown that such naturalistic resources cannot do the job. In particular, it is hard to see how Lewis could get an asymmetry in counterfactuals out of physical laws that are time-reversal invariant. At the end of his paper, Lewis suggests that thermodynamics might play a crucial role in his metric: the Second Law, when extended from isolated systems to the whole universe, indicates that a given event tends to have an isolated cause but many spread-out effects (it leaves an enormous multitude of traces into the future). As a result, “[…] only a small miracle is needed to allow an event that did happen not to have happened, keeping the past of that event fixed. But a gigantic one would be needed to allow that event to have happened keeping the future exactly the same” (cf. Sklar, 1993: 403). It can therefore be supposed that the more a possible world avoids ‘big, widespread, diverse’ violations of the Second Law (i.e. the more it preserves the entropic spreading situations), the more it is similar to our world.

However, this Reichenbach-inspired strategy, which has already been encountered in Sect. 2.3, seems to fail. First, as John Earman (1974) points out, applying the thermodynamic concept to systems as diverse as decks of playing cards, human beings, printed records, and so on, involves a considerable extension of the concept beyond its established range of legitimacy, and there is no guarantee that the extension is legitimate. Second, if Harvey Brown and Jos Uffink (2001) are correct, then the Second Law of thermodynamics does not presuppose any time asymmetry at all; it is simply a relation between a few variables at equilibrium. And there is no question that thermodynamics, if not its Second Law, makes time-asymmetric claims (cf. Callender, 2001). Henry Poincaré reaches a similar conclusion when he introduces his ‘recurrence theorem’ (against Boltzmann’s view), according to which the particles in any energetically isolated state will, given enough time, return to a state that is arbitrarily analogous to their initial state: the entropic asymmetry may break. Finally, even if thermodynamics could yield the desired asymmetry, this would not provide a fundamental explanation as to why the past appears to be fixed and the future open. As has previously been argued (cf. Sect. 2.3), thermodynamics is a ‘phenomenal’ science; that means that its variables range over macroscopic magnitudes, such as temperature, pressure, volume, heat, and entropy. These magnitudes arise from the collective behavior of many microscopic entities, which is governed by the time-reversal invariant laws of quantum mechanics. Therefore, claiming that the asymmetry in time is to be grounded in the increase of entropy (i.e. in the spread-out effects of events) simply postpones the problem: if there is no directedness in fundamental physics, what then grounds the entropic asymmetry in time?⁴⁵

Of course, as Barnes and Cameron suggest, one can in principle “[…] agree with Lewis that openness is to be analyzed in terms of counterfactual dependence on the present and disagree with his account of what facts get fixed for the evaluation of counterfactuals” (2011: 7). But this option leads to a dilemma. Either there is something special about the facts that matter (that get held fixed) in the evaluation of counterfactuals, or there is not. If there is, then extra non-naturalistic resources are to be found in order to say what is special about these facts; we are back to square one. If there is not, then Lewis’s attempt is completely irrelevant to the explanatory project: “[t]here needs to be something special about the facts to be held fixed that explains why holding them fixed is relevant to openness” (2011: 8). After all, supposing that some facts are arbitrarily held fixed, why should it matter what would have happened given these facts rather than others?

Penelope Mackie (2014) also provides several objections against Lewis’s account, and especially against his characterization of the fixity of the past in terms of counterfactual dependence. In particular, she argues that there is an ambiguity in the claim that we usually take the past to be counterfactually independent of the present. Let me explain. Lewis explicitly endorses the thesis that backward counterfactuals are, as well as forward counterfactuals, usually assessed in a way that keeps the past (relative to the time of the antecedent) fixed (cf. Lewis, 1979a: 458).⁴⁶ For example, when we assess the backward counterfactual ˹If Jane had handed in her essay on Monday, she would have revised it properly first˺, we assume that the past (relative to the antecedent, i.e. the past until Monday) in the counterfactual situation is exactly the same as the actual past. That is why Lewis takes his conclusion that there is no true backward counterfactual (unless the consequent is true, i.e. unless Jane’s essay has indeed been revised properly) to be in line with usual practice.

However, as Penelope Mackie points out, this is “[…] plainly false as a description of the way in which we usually evaluate counterfactuals” (2014: 403).⁴⁷ There are dozens of examples in which we naturally suppose that if the situation had been different at a time t, then some features of the past relative to t would have been different also, otherwise the situation would not have been thus. Downing’s case involving prideful Jim and angry Jack may obviously serve as a good example, but Mackie imagines many different cases: (i) ˹If there had been ice on the pond this morning, the temperature last night would have been lower than it actually was˺; (ii) ˹If the roof had been intact today, it would not have been hit by a falling tree yesterday˺; etc. In this way, Mackie shows that back-tracking cases (which are a kind of backward cases) are much more common than Lewis claims and, therefore, that they do not require atypical contexts.

As we have seen, Lewis resolves backward cases by keeping the past relative to the time of the antecedent fixed, with the result that all backward counterfactuals (including back-tracking ones) usually come out false. But this solution is only one among others and, as Mackie puts it, Lewis has no right to “[…] call this (non-back-tracking) resolution ‘the standard resolution’” (2014: 404), especially considering that it outlaws back-tracking cases which are, as indicated above, very common. According to Mackie, Lewis has taken a feature (the ‘keeping fixed’ of the past relative to the time of the antecedent) that may with some plausibility be regarded as a feature of the resolution of forward cases, and has extended it, quite implausibly, to the resolution of backward cases. Therefore, since Lewis’s resolution of backward cases is insufficient – sometimes we keep the past fixed, but sometimes we do not (especially in back-tracking cases) – it appears to be incapable of yielding a satisfactory characterization of the fixity of the past.

It can therefore be concluded that (i) Lewis cannot get an asymmetry in counterfactuals out of only physical facts, and (ii) even if he could, his account would fail to describe the way we usually evaluate backward counterfactuals. There are many examples in which we naturally suppose that if the present had been different, then the past would have been different also (cf. back-tracking cases). As a consequence, Lewis’s account fails to display a temporal asymmetry of counterfactual dependence that accounts for the asymmetry in openness between the future and the past, and must as such be rejected. Of course, there is no certainty that these criticisms of Lewis’s account can be extended to any modal account. After all, there might be some modification of Lewis’s attempt that would escape these criticisms – Mackie expresses serious doubts about this (cf. 2014: 413). One thing is certain: contrary to what Barnes and Cameron (2011) suggest, it is not enough to supplement Lewis’s counterfactual analysis with the right (non-naturalistic) ideology to ground the desired asymmetry between what is open and what is fixed. The modification has indeed to be more radical, insofar as the past does sometimes counterfactually depend on the present.

2.7 Metaphysical Indeterminacy

A position that is in the minority, perhaps, but deserves ever greater attention is the claim that the fixity of the past and the openness of the future must be characterized in terms of metaphysical determinacy and indeterminacy, respectively. The main idea is that whereas it is fully determinate how the past did turn out, it is partially indeterminate how the future will turn out. The way in which how the future will turn out fails to be fully determinate is to be understood as a brute fact: sometimes it is simply unsettled how the world is at its most fundamental level. At this point, it is worth noting that among the various phenomena that may be thought of as types of worldly unsettledness, the one we are concerned with here is a matter of the world being poised between various determinate states. In that sense, there are multiple determinate (precise) states between which the world is unsettled, such that it fails to specify which one obtains. For instance, Cameron (2015: 196) argues that the openness of the future consists in such brute unsettledness. He claims that if we think that the future is open with respect to whether or not there will be a sea-battle tomorrow, we ought to think that this is a matter of the world being unsettled as to which relevant state obtains.

From a semantic perspective, it is determinately the case that either a future contingent or its negation is true, but it is indeterminate which (where this indeterminacy is a brute unsettledness between ways the world could be), so that future contingents are said to be metaphysically indeterminate in truth-value (cf. Barnes & Cameron, 2009: 294). This is not to say that the worldly conditions required for the truth (or the falsity) of future contingents are absent, but rather that there is a ‘lack of specificity’ concerning what worldly conditions obtain. As an analogy, Barnes and Cameron take the borderline case of being bald: it might be indeterminate whether this person is bald or not, but it is determinate that either he is bald or he is not. Just as in the case of future contingents, it is determinate that the statement ˹This person is bald˺ is either true or false (those are the only two options), but it is indeterminate which of the two options is in fact the case (cf. Barnes & Cameron, 2009: 294).

The immediate benefit of such a characterization of the asymmetry is that it allows one to accept Bivalence without restriction and, therefore, to resist the non-classical logic and semantics introduced in Sect. 2.2 (three-valued treatment of truth-functional connectives, supervaluationism). Indeed, assuming that the indeterminacy in truth-value of future contingents results from the world being unsettled in this respect (one way or another, there is a fact of the matter), the world always speaks to the truth or falsity of any claim about how things will be. This allows one, for example, to assess as correct (or incorrect) some of our current and past assertions of statements about how things would turn out (assuming the orthodox account of assertion, cf. Sect. 2.2).⁴⁸ Moreover, since this characterization provides a robust understanding of the asymmetry as a genuine feature of how the world is, it avoids the main pitfalls encountered by the theories addressed so far. For example, it provides an explanation as to why our knowledge of the future is not as vast as our knowledge of the past: we cannot know more about the future than what determinately will be the case.

However, despite the non-negligible benefits this characterization offers, there are some reasons to complain. First, this characterization faces difficulties in interpretation that render it less than metaphysically illuminating. It is unclear, for example, how metaphysical indeterminacy might involve an indeterminate degree of obtaining: whether or not a state obtains seems to be an all-or-nothing situation – either a state obtains or it does not. In particular, if the future is genuinely open, then intuitively, none of the relevant states ‘obtain’ – the future has not yet happened, after all. To clarify further, the ‘metaphysical indeterminacy’ account, since it analyses the openness of the future in terms of the world being ‘stuck’ between various states, presupposes that these states exist, while it is clear that all of them cannot share the same ontological status. After all, even assuming that both tomorrow’s sea-battle and its peaceful alternative exist, only one of these states will be actualized. There must therefore be a difference between these two states: one must ‘less obtain’ than the other. As Barnes and Cameron recognize, the indeterminate degree of obtaining to which their account is committed covers two possibilities: “[…] perhaps the state of an object indeterminately instantiating a familiar property, or perhaps the state of an object instantiating the non-familiar property of being indeterminately F” (2017: 123). In other words, either the indeterminate degree of obtaining concerns the instantiation of the property, or the property itself. However, both possibilities are mysterious. Furthermore, whereas it is clear what it means for human beings to be undecided between various possibilities (e.g., to go, or not to go to the cinema), it is unclear what it means for the world to be undecided about, for example, what will happen tomorrow (e.g., there will be, or there will not be a sea-battle). Admittedly, there have been courageous attempts to make sense of this claim, as reflecting, for example, that it may be ‘indeterminate which world is actualized’ (Barnes & Cameron, 2011), or that there may be multiple ‘actual worlds’ (Williams, 2008a). But even if such attempts are coherent, they occupy, as Jessica Wilson says, “[…] a metaphysically tenuous region of logical space” (2013: 364).

Moreover, there are cases of future contingents lacking determinate truth-value that are not cases of the future being open. According to Barnes (2010), the conditions of being bald are such that there can be people for whom it is unsettled whether they are bald or not. If so, the future contingent ˹This person will be bald tomorrow˺ might now be metaphysically indeterminate in truth-value. But this does not necessarily seem like a case of the future being open. After all, what is going to happen could be perfectly settled. Perhaps the person in question will undergo a chemotherapy session tomorrow, which has been scheduled for months and which will inevitably make him lose a lot of hair (to such an extent that it will be unsettled whether he is bald or not). There are not different ways the future might develop here; there is only one settled future, but it is unsettled whether it will include an additional bald head. The analysis of the openness of the future as metaphysical indeterminacy might thus appear insufficient, since it fails to delineate cases of open future indeterminacy from other cases (e.g., cases of ontic vagueness). Admittedly, this objection could be prevented by denying that openness and vagueness are two phenomena of the same kind. After all, perhaps vagueness is merely a semantic deficiency of language that can be treated with, for example, a supervaluationist account of truth and validity (cf. Fine, 1975b). In other words, the above objection does not rule out the possibility that Barnes and Cameron might be wrong about vagueness, but right about the openness of the future.

However, it must be acknowledged that Barnes and Cameron (2011: 3) outline a solution to the latter issue. They claim that there is a clear delineation between cases of open future indeterminacy and other cases: the former cases will be resolved as time passes, while the latter will never be resolved. For example, while it might now be open whether or not there will be a sea-battle tomorrow, once tomorrow comes the situation will be resolved: depending on how the future unfolds, it will be determinate that there is a sea-battle or that there is not. By contrast, if it is now indeterminate whether or not a person will be bald tomorrow (assuming that the future is perfectly settled), once tomorrow comes it will still be indeterminate whether or not this person is bald. Indeed, assuming that it is indeterminate whether a person who has, say, 200 hairs on his head is bald or not, the passage of time does not help clear up the matter: tomorrow and the following days, it will still be indeterminate whether having 200 hairs is to be bald or not.

Yet, this solution may not appear very attractive, since it includes exceptions: (i) there are cases of open future indeterminacy that will never be resolved; (ii) there are cases of other sorts of indeterminacy that will be resolved. As a first example, consider the prediction ˹Jesus will return someday˺ and suppose for the sake of argument that it is open whether he will.⁴⁹ Suppose further that this prediction is uttered in a world where time never ends, and where, at any given moment, Jesus has not yet shown up. If time does in fact unfold this way then, it seems that the indeterminacy in ‘Jesus will return’ will never be resolved: for at all times, there will still be a future in which he might still return. After all, we could wait for the return of Jesus forever! According to Wilson, this kind of possibility is not straightforwardly handled on Barnes and Cameron’s account, since in supposing that openness consists in the matter of the world being unsettled as to which relevant state obtains, “[…] it is presupposed that the future gets settled, one way or another” (2013: 381).

As a second example, consider the prediction ˹Schrödinger’s cat will be alive˺ and suppose that it is uttered 5 min before opening the box. This prediction is now indeterminate in truth-value (the world fails to settle a unique determinate of the cat’s life status). But, 5 min hence, when opening the box, ˹Schrödinger’s cat is alive˺ will be determinately true or determinately false. This case will thus be resolved as time passes. However, it might be argued (although it is controversial) that this is not a case of the future being open. The indeterminacy is indeed to be explained by the weirdness of quantum mechanics, not by the passage of time. After all, one can easily imagine an alternative case in which, 5 min hence, the box will remain closed, so that the indeterminacy will not be resolved as time passes. Since the second case, which arguably has nothing to do with the openness of the future, is of the same sort as the first one, it seems that the first case has nothing to do with the openness of the future either. It therefore appears that Barnes and Cameron fail to provide an absolute criterion to separate cases of the future being open from other cases and, therefore, that their account of openness in terms of metaphysical indeterminacy is insufficient (cf. also Wilson, 2016: 110–111).

Finally, there is an important sense in which the future may be said to be open but that the ‘metaphysical indeterminacy’ account fails to capture: time could come to an end, with no ontological commitment to future things standing in the way (cf. Correia & Rosenkranz, 2018: 99). Taking seriously the ‘doomsday scenario’ as it is described, for instance, in the cosmological ‘Big Crunch’ scenario (cf. Misner et al., 1973: 771), or in the eschatologies of the three major monotheisms (Judaism, Christianism, Islam), it could be that time does not go on indefinitely and, possibly, that there will be a last moment of time. In other words, it seems possible that the future is open not simply in terms of how it will unfold, but also in terms of whether it will unfold. However, Barnes and Cameron’s account, in taking openness to be unsettledness between determinate states, presupposes that there are determinate states, and so cannot accommodate the possibility of radical openness, where more determinate states are simply not available because time has ended. To say that time could come to an end is to say that there could be no more determinate states for the world to be in, so that if the future may be said to be open in this radical sense, then Barnes and Cameron’s account – which presupposes that there are determinate states – cannot accommodate it. By assuming that, one way or another, the future gets fixed, Barnes and Cameron rule out the possibility of radical openness.⁵⁰

Of course, it might be argued that this latter objection only concerns Barnes and Cameron’s account, and not all attempts to characterize the openness of the future in terms of metaphysical indeterminacy. After all, it seems intuitively possible to claim that in the same way that it is metaphysically indeterminate whether or not there will be a sea-battle tomorrow, it is indeterminate whether or not time will unfold. It might therefore be argued that another account of the openness of the future in terms of metaphysical indeterminacy could be better equipped to respond to the above objections. In particular, it might seem that abandoning the conception of time as being linear in favor of a conception of time as forward-branching could express the idea of the metaphysically indeterminate future in a more appropriate way. Therefore, before taking up a final position on the ‘metaphysical indeterminacy’ accounts of openness, it is worth checking whether another type of worldly indeterminacy could meet the challenges presented so far.

2.8 The Branching Future

The idea of a non-linear time has been developed in various ways, but all the most plausible ones are based on the same principle: the past is actual and unique, while the future comprises many possibilities.⁵¹ Intuitively, the temporal order of the world has the shape of a tree: the past constitutes a single trunk and the future a multiplicity of branches (each bearing the relation is later than to the present time). This difference in the topological structure of the future with respect to the past is meant to spell out the intuition that the future is open while the past is fixed. Indeed, whereas the linear conception of time admits at most one possible future for each time t, non-linear time permits instances in which a time t has many possible alternative futures. In that sense, non-linear time puts possible alternative futures into the topological structure of time, so that they must be considered in reckoning the truth-values of tensed statements (with the costly consequence that future contingents are neither true nor false) (cf. Thomason, 1970: 265).

For instance, ‘the sea-battle case’ can be sketched with such a tree model. It would comprise a trunk (C₀) and two branches, one representing the possibility that there will be a sea-battle tomorrow (C₁), the other representing the possibility that there will not be a sea-battle tomorrow (C₂). It would then be said to be open at (C₀) whether there will be a sea-battle, since a sea-battle occurs at (C₁) but not at (C₂). In other words, assuming that (C₁) and (C₂) are two genuine possibilities (neither is privileged over the other), it appears to be metaphysically indeterminate which of these two possibilities will be actualized and, therefore, how the future will unfold. Moreover, forward-branching time is arguably able to make sense of the radical possibility that time could come to an end by representing it by an absence of further branches from a node. But this is highly controversial. As, for instance, Ross Cameron claims: “[…] the absence of further branches from a node does not represent the further possibility that nothing will happen beyond that node, it simply represents the absence of further open possibilities” (2015: 179). Indeed, considering Fig. 2.1, two branches diverge from (C₀), thus signifying that there are two ways the future might unfold from (C₀). The absence of a third branch signifies that there are only two ways the future might unfold from (C₀), not that it might not unfold any way from (C₀) because (C₀) could be the last moment of time (cf. also Pooley, 2013: 340).

Fig. 2.1

Basic branching structure of time

Although branching time provides a forceful metaphor to picture the openness of the future, it might be denied that it captures a genuine notion of it. In particular, branching time appears like a “[…] a metaphysic on which it is perfectly settled how things will be, you just do not know whereabouts you will be within reality” (Cameron, 2015: 175). After all, at (C₀) it is perfectly settled that there is a sea-battle temporally beyond us. It only seems unsettled as to whether or not there will be a sea-battle because it is unsettled which of the two branches, (C₁) or (C₂), will be ours. But that is not a case of reality being unsettled; it is simply that, when we talk of the future, we commonly privilege a small portion of it, which corresponds to “[…] the branch we happen to find ourselves upon” (Cameron id). From a metaphysical point of view, there is thus nothing special about that branch; it is merely that it is our branch. It might thus be argued that genuine openness should not only arise as a result of our non-neutral perspective on time, but also requires reality to be truly unsettled (cf. Lewis, 1986: 207, Rosenkranz, 2013).

Of course, one might respond that our branch is metaphysically different from the others, e.g., by adding to the view a specification that determines our branch as the unique history of the world. This option may, in particular, come in two flavors: static and dynamic. According to the static option, it is not only true that either there will be, or there will not be a sea-battle tomorrow, but also that there is a present specification (commonly referred to as ‘the thin red line’) of what is actually going to happen (cf. Fig. 2.2). This specification breaks the symmetry between the two ways the future might develop, privileging the one that is actually going to be actualized. As a consequence, statements like ˹There will be a sea-battle tomorrow˺ are not exceptions to Bivalence: they now have a classical truth-value, albeit our limited minds keep us from knowing which (cf. Belnap & Green, 1994; Borghini & Torrengo, 2013; Burgess, 1979; Thomason, 1970). Although the specification is to be taken as an objective feature of reality, it is not epistemically accessible: there is no way to know which possible future will be actualized, except by waiting. Arguably, this option is compatible with believing that the future is open, since it retains the crucial idea that even if there will in fact be a sea-battle tomorrow, there need not be: even though one of two possibilities (either there will be, or there will not be a sea-battle tomorrow) is already the one which is going to be actualized (we cannot know which one), it could have been the other.

Fig. 2.2

Branching structure of time with a specification

However, many philosophers reject the idea that a privileged future possibility is compatible with the open future. For example, Belnap and Green (1994), MacFarlane (2003), and Barnes and Cameron (2011) argue that if one wants to hang on to genuine openness regarding the future, it is problematic to give one future possibility a special status. It might indeed seem that the intuition of the open future is more radical than what is supposed in the static option. As Barnes and Cameron write: “[i]t’s not that there is a way our future actually is but that there are different ways it could have been […]; it’s that there actually are now multiple possible ways our future could turn out to be” (2011: 2). After all, from a God’s eye point of view, looking down on the tree and seeing that only one possibility remains in play (i.e. the branch singled out as that which is going to happen), the other possibilities are not genuine possibilities. They merely represent possibilities in an epistemic sense: we do not know which one will be actualized.

By contrast, the dynamic option seems to capture a genuine notion of openness. The idea is to claim that the tree changes as time progresses, e.g., by adding to the view a process of ‘branch attrition’ – the branches which are ruled out as being part of history cease to exist (cf. Fig. 2.3). This idea has, in particular, been defended by Storrs McCall (1994). According to his view, the passage of time is represented by the vanishing or ‘falling off’ of branches; the one branch remaining being the ‘actual’ one that becomes part of the trunk. The probability of any future event (e.g., tomorrow’s sea-battle) is specified by the proportion of future branches on which that event occurs. However, although this view pictures a genuine notion of openness (branch attrition depicts the past-future asymmetry in an objective, observer-independent way), it is unsatisfying. First, ‘branch attrition’ is not a physical mechanism and, as far as I know, there is no physical mechanism that can account for it (but see quantum decoherence). It therefore seems that McCall’s model fails to explain why, for example, we cannot climb down the tree trunk and return to the past. Second, contrary to what is entailed by McCall’s view (that there is no branch that used to diverge from earlier times, since these branches ceased to exist when those times became past), we do not think of the present as the first time from which there is branching. We rather think that in the past there were multiple ways history could have gone but did not.

Fig. 2.3

McCall’s dynamic branching structure of time

But if reality was indeed open prior to now, despite the fact it is not branching before now, what allows us to exclude the possibility that reality might be closed in the future, despite the fact that it is branching from now on? It seems that as soon as McCall admits that there are resources (e.g., brute tensed facts about how the tree used to be) to say how the branching reality was, he has to allow the possibility that there are resources about which branch our history will be and, therefore, that the future is perhaps not open after all (despite the multiplicity of branches).⁵² Thus, although branching trees might seem convenient as long as we are concerned with the semantics of future contingents (cf. Belnap, 1992; Belnap et al., 2001; Prior, 1967; Thomason, 1970, 1984), they fail to provide a perspicuous picture of the metaphysics underlying the asymmetry in openness between the future and the past.

Another reason why dynamic branching-tree models do not seem appropriate to account for the asymmetry between the open future and the fixed past has to do with the logical possibility of time-travel. Specifically, as soon as time-travel enters the picture, it seems that the openness of the future cannot be characterized by means of alternative future branches. To illustrate this point, consider the following scenario. Suppose that t₁ is the objective present and that only two future branches stem from t₁: (C₁) and (C₂). Max is born at t₂ on (C₁), whereas Mary is born at t₂ on (C₂). Assuming that time-travel is possible, we can imagine that both Max and Mary have a time-machine, and hence that both of them can travel to the past. Now, suppose that both Max and Mary travel back in time to t₁ from their respective locations. According to the dynamic branching-tree model, time moves forward and only one of the two branches, (C₁) or (C₂), becomes actual. Let us suppose that (C₁) is the branch that becomes actual, and thus that (C₂) drops off. The branch where Mary is born and activates her time-machine does no longer exist. What happens at t₁ then?

There are only two possibilities which both lead to difficulties: either (i) Mary exists at t₁ when t₁ is present, but does not exist at t₁ when t₂ is present, or (ii) Mary tenselessly exists at t₁. The first possibility contradicts the principle according to which it is not possible to change the past (t₁ change from containing Mary (when t₁ is present) to not containing her (when t₂ is present)); the second possibility contradicts (at least when t₂ is present) the Lewisian principle according to which P is a time-traveler only if all P’s temporal stages are united by some causal relation (since Mary’s t₁ person-stage is not causally related to any person-stages in the future) (cf. Lewis, 1976: 148).⁵³ Since we might not want to give up any of these two plausible principles, we might conclude that dynamic branching-tree models of time are incompatible with time-travel (cf. Andreoletti, 2020; Miller, 2005; Norton, 2018). However, as we will see in the fourth chapter (Sect. 4.7), a natural way to resist this kind of objection is to accept, for instance, a revised conception of perdurantism.

This new failure in properly characterizing the asymmetry between the open future and the fixed past leads us to think that this requires another type of worldly unsettledness that is not to be expressed in terms of the world being indeterminate whether something is the case (neither by postulating multiple states that the world is unsettled between, nor by postulating multiple forward branches), but rather in terms of there being no fact of the matter whether something is the case. Before introducing this last characterization, I would like to address an objection that might be raised against both the ‘metaphysical indeterminacy’ and the ‘no fact of the matter’ account. This objection relies on the thought that worldly unsettledness may not be a fundamental phenomenon, but merely a derivative one (cf. Bacon, 2019; Eva, 2018; Sattig, 2014). At first sight, this objection seems absurd: if there is no unsettledness in fundamentals, there is nowhere for unsettledness to come from. As Elizabeth Barnes puts it: “[…] if you combine a bunch of determinate things, you won’t (no matter how you combine them) be able to get any (genuine) indeterminacy” (2014: 341). However, the thought that ‘if reality is really unsettled, then it must be in virtue of unsettledness in fundamentals’ rests on two principles that can be disputed: (i) fundamental facts ground the derivative, (ii) grounding is determinacy-preserving. In particular, it might be argued that grounding (or the link between the fundamental and derivative, whatever it is) can itself be unsettled. For example, one might think that the fundamental facts do indeed ground the derivative ones, but since it can be unsettled what derivative facts the fundamental facts ground, the facts about what grounds what are themselves unsettled. An immediate reply to this objection, however, is that the facts about what grounds what belong to the fundamentals. After all, if these facts were not fundamental, they would in turn be grounded in some other facts in a way that seems to involve a vicious regress.⁵⁴ So, even if principle (ii) is false (which is doubtful), then – given that the facts about what grounds what are fundamental – the fundamental level is the source of unsettledness.

2.9 No Future!

When Johnny Rotten of the Sex Pistols shouts “No future!” (in the closing refrain of the controversial song “God Save the Queen”), what he probably intended to say is that the future will certainly be unfair for the English working class. Nonetheless, this slogan (which has since become emblematic of the punk rock movement) might be interpreted in a more literal and, therefore, radical sense: the future is simply nothing at all. This is precisely what C. D. Broad defended, long before the advent of punk rock music. According to his doctrine, “[n]othing has happened to the present by becoming past except that fresh slices of existence have been added to the total history of the world. The past is thus as real as the present. On the other hand, the essence of a present event is, not that it precedes future events, but that there is quite literally nothing to which it has the relation of precedence. The sum total of existence is always increasing, and it is this which gives the time-series a sense as well as an order” (1923: 66–67). In Broad’s view, the present is thus a kind of ‘ontological gateway’ through which events have to pass on their way to become real and always remain so.

Although going beyond Broad’s view is surprisingly difficult (this will occupy us throughout the next chapter), his intuitions may provide decisive insights into the temporal asymmetry we are concerned with. Indeed, perhaps the asymmetry between the open future and the fixed past is to be characterized by an ontological difference: the past and the present exist, while the future does not exist. In that sense, the openness of the future (as a kind of worldly unsettledness) should perhaps not be regarded as a matter of the world being poised between various determinate states (as Barnes & Cameron suggest), but rather as there being no state that the world is in with respect to what will happen. For example, if we think the future is open with respect to whether or not there will be a sea-battle tomorrow, we ought to think that reality simply lacks the relevant ontology: there is no fact of the matter whether a sea-battle will take place tomorrow. Mauro Dorato comes to similar conclusions when he comments on this passage from Broad’s book. He writes: “[t]he main thought here seems to be that by leaving the future wholly empty, we make sense both of the fact that our actions can give a (cosmically negligible) contribution to bring it about, and of our closely related intuition, hard to explicate in a clear way, that at any instant of time, there is a part of the history of the universe that is ‘fixed’ and ‘definite’, and a part that isn’t” (2008: 56). Besides metaphysical indeterminacy, there is thus another way in which reality may fail to settle some future facts: there may be no fact of the matter whether these facts obtain.⁵⁵

These two types of worldly unsettledness seem to be very different by nature: the first type is a case of overdetermination (there are too many states, such that the world is unsettled as to which one obtains), while the second type is a case of underdetermination (there is no state, such that the world is unsettled as to whether something obtains). As an analogy, consider two teenagers – one rich, the other poor – getting ready for a party. In front of their closets, they might both be ‘unsettled’ as to what to wear for the evening: the rich teenager because she is spoiled for choice (e.g., she has too many dresses suitable for the occasion), and the poor teenager because he has literally nothing to wear. In such a case, although the two teenagers are equally unsettled as to what to wear for the party, it clearly appears that this reflects two different phenomena.

The second kind of unsettledness, by the way, is commonly invoked in many different contexts. In the philosophy of quantum physics, for example, the superposition of states as a source of metaphysical indeterminacy can successfully be accommodated by a so-called determinable-based account, which treats certain sources via a gappy implementation. For example, as has already been mentioned, Calosi and Wilson (2019) argue that the case of Schrödinger’s cat suggests a metaphysical indeterminacy that must be seen as involving that there is no (determinate) fact of the matter whether the cat is or is not alive. Specifically, there is no fact such that the property of having a certain life status of Schrödinger’s cat has a unique determinate (being alive or being dead). Thus, as in the case of the open future, the determinable-based account of quantum indeterminacy does not involve that it is indeterminate which of various determinate facts obtain (metaphysical indeterminacy), but rather that it is determinate that no determinate fact obtains (no fact of the matter).

Of course, this account is insufficient to accommodate the open future, since the future is intuitively fixed in a fully deterministic world (where the state of the world at a time nomologically necessitates the state of the world at any later time). As has previously been argued, if it is necessary, given the facts about how things are up to a time t and what laws obtain, that the world will be a certain way at any later time, then it seems settled that it will be that way, which is just to say that the future is fully settled at t and, therefore, that the future is fixed. However, assuming that all that will happen is not made inevitable by how the world currently is (together with the laws of nature) – which sounds quite plausible in regard of important results of contemporary physics (especially quantum mechanics) – the ‘no fact of the matter’ account provides a powerful characterization of the openness of the future, understood as a kind of worldly unsettledness.

From a semantic point of view, it is not that there is a ‘lack of specificity’ concerning which worldly conditions for future contingents obtain, but rather that worldly conditions are absent: there is no fact that speaks to the truth or falsity of ˹There will be a sea-battle tomorrow˺. This kind of unsettledness might thus seem to be incompatible with Bivalence. This is, at least, what Broad himself contends when he claims that future contingents are without exception neither true nor false (cf. 1923: 70–73). After all, if there is no fact of the matter as to whether Fφ (where ‘Fφ’ stands for ‘It will be the case that φ’), i.e. if nothing worldly answers to whether or not Fφ, it might seem that Fφ should be neither true nor false. In particular, Fφ should not be true, because the worldly conditions required for its truth are absent, but nor should it be false, because the worldly conditions required for its falsity are also absent. It might thus be concluded that if there are some statements concerning which there is no fact of the matter, Bivalence must be rejected (cf. Cameron, 2015: 181).

This conclusion is clearly problematic. As has already been said, most philosophers believe that “[...] classical semantics and logic are vastly superior to the alternatives in simplicity, power, past success, and integration with theories in other domains” (Williamson, 1994: 186). However, it is not clear that this has to be accepted. According to Correia and Rosenkranz (2018), this conclusion is driven by too strong a conception of the ‘grounding requirement on tensed truths’ (i.e. the requirement according to which tensed truths do not ‘float free’, but are grounded in reality).⁵⁶ They argue that the present truth of a given statement does not require it to be grounded in how things located in the present are, but that it might well be grounded, at some future time, by things whose future existence and future ways of being are such as the statement claims. For example, the statement ˹There will be a sea-battle tomorrow˺ might well be true now, provided that, 1 day hence, there will be a sea-battle the existence of which will explain why, 1 day before, the statement was true.

This theoretical option allows Correia and Rosenkranz to affirm that future contingents are not exceptions to Bivalence – they now have a classical truth-value – while keeping the future open. Indeed, assuming that there will be things whose existence is not rendered inevitable by how things located in the present or past of now are or were, the present truth of a statement that will be grounded by how matters are going to stand does not undermine its status as a future contingent. In other words, the bivalence of statements about the future that will be grounded by what there will be and how it will be does not threaten the open future as long as “[…] nothing there is or was, in conjunction with how it is or was, makes it inevitable that, in the future, there will be such grounds” (2018: 110). Thus, through a weaker (and more plausible) conception of the grounding requirement on tensed truths – “[t]he truth of a given tensed statement at most requires that it sometimes be grounded in what then is something and a certain way” (2018: 108) – Correia and Rosenkranz’s option allows one to reconcile the bivalence of future contingents with the ‘no fact of the matter’ account of openness: assuming physical indeterminism, the future may be said to be open in the sense that there is no fact of the matter regarding the grounds of some present truths about the future, without future contingents lacking a classical truth-value.

Conversely, this weaker conception of the ‘grounding requirement on tensed truths’ allows one to account for the truth of statements about the past, without committing to the existence of the past. Indeed, since the truth-value of a tensed statement does not need to be grounded in how things located in the present are (e.g., a future contingent might well be said to be true now in virtue of how, at some future time, things will be), a past-tensed statement might well be said to be true now in virtue of how, at some past time, things have been. For example, the truth of the statement ˹Napoleon lost at Waterloo˺ merely requires that things have been that way, i.e. that Napoleon has actually been defeated by the Seventh Coalition. The weaker conception of the ‘grounding requirement on tensed truths’ therefore renders the existence of the past superfluous to ground present truths about it: that the Battle of Waterloo, located in the past, still exists, is superfluous to ground the present truth of ˹Napoleon lost at Waterloo˺. As a consequence, the metaphysicians who deny the existence of the past (e.g., the presentists) are in no worse position than those who do not (e.g., the growing blockers) to provide present grounds for truths about the past. To put it another way, since the weaker conception of the ‘grounding requirement on tensed truths’ is available to both presentists and growing blockers, they are equally well positioned to account for truths about the past. Resorting to the existence of the past to obtain grounds (truthmakers) for present truths about the past (as, for instance, some growing blockers do) is therefore useless. Thus, while one might have various independent reasons to defend the existence of the past (e.g., to ensure its fixity), the semantics of tensed statements should not count as one of them.

However, it must be acknowledged that this weaker conception of the grounding requirement on tensed truths is often regarded with suspicion. In particular, a question that constantly recurs is: ‘How can a statement that has not yet been made true be true?’ What lies behind this question is presumably the belief that at least some statements have no truth-value until they are made true (or false) by actions and other events. It is indeed often assumed that many of our statements about the future express propositions that are neither true nor false when they are made, but become true or false when events make them so in the future (cf. Broad, 1923: 70–73). For example, it might seem that the statement ˹Switzerland is the next champion of the football world cup˺ is not true (or false) until the events of the next world cup (e.g., until the delivery of the cup). In the next few lines, I will argue that this belief rests on a confusion between two different properties having to do with truth – being true, and being made true – and should therefore be abandoned.⁵⁷

First, it is worth noting that the converse of the belief in question does not hold: it is not true that if a statement is true, then some events either have made, are making, or will make it true. There are important statements whose truth-value is established not by being made true by events, but in some other way. For example, consider Pythagoras’s theorem: no event has ever made true the statement ˹The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides˺, and none ever will. It is not like the statement ˹Biden won the 2020 election˺. There is no sequence of events, ending at a certain time, the occurrence of which makes Pythagoras’s theorem true. Perhaps it would be correct to say that, although Pythagoras’s theorem is independent of events, events do conform to it. But, if so, events do not make this theorem true; they merely reflect its truth (cf. Perry, 2004: 235–236).

Second, suppose that the laws of nature are not made true by events, and that these laws, together with statements made true by events that have already happened, entail that Sam will not go to the cinema at some future time t.⁵⁸ It seems that, although the statement ˹Sam will not go to the cinema at t˺ has not yet been made true, its truth-value has been settled. Of course, the statement will not be made true until the events that are determined by the laws of nature and the past have actually occurred, i.e. until Sam goes to bed instead of going to the cinema at time t. But, as Perry puts it: “[…] these events were already entailed by a combination of propositions some of which were already made true and the rest of which aren’t made true by events at all” (2004: 236). Therefore, against what skepticism about the weaker conception of the grounding requirement suggests, it clearly seems that the truth-value of the statement ˹Sam will not watch a movie at t˺ was settled before Sam refrained from going to the cinema.

Presumably, what is wrong with the belief that statements are not true until they are made true is that it rests on a confusion between two properties having to do with truth of statements: being true, and being made true. The former is a timeless property of statements (i.e. a property that is not relative to times), while the latter is a property that occurs at times, or through intervals. Although these two properties must be distinguished, this does not mean that they are not somehow related. Intuitively, if a statement is ever made true, it is true (where ‘is true’ is to be understood timelessly). However, the fact that a statement has not yet been made true by events, does not imply that it is not true. John Perry proposes the following analogy: “[t]he fact that [Kamala Harris] has not yet been chosen as our next President does not imply that [she] is not our next president” (2004: 235). If Harris ends up being nominated and elected in 2024, then she is the next president of the United States. If I call her ‘the next president of the US’ now, I am correct if the future goes one way, incorrect if it goes the other. After all, if Harris must not be the next President of the US (on the grounds that it has not been decided yet) then, by parity of reasoning, no one is the next president of the US, which will be a “constitutional crisis”! To avoid the crisis, Perry argues, one must acknowledge that being the next president of the US is a property Harris has if, at some point between now (June 2022) and November 2024, she is elected as the next president. Perry concludes: “[t]he fact that lots of propositions be true that have not yet been made true is sort of like that” (2004: 235). Assuming that Perry is right, it seems that a statement, such as ˹There will be a sea-battle tomorrow˺, can be true now, partly because of contingent events that have yet to occur.

Thus, when combined with Correia and Rosenkranz’s relaxed conception of the grounding requirement on tensed truths, the ‘no fact of the matter’ account seems to provide a powerful answer to the question of the open future, at least assuming that physical determinism is false. First, it enables us to preserve a classical logic, and in particular a bivalent semantics, even for future contingents. Second, it enables us to preserve the bivalence of future contingents without the future being bound to be a certain way. In that sense, although the statement ˹There will be a sea-battle tomorrow˺ is determinate in truth-value, because 1 day hence, there will be things whose existence will explain why this statement is true now (or false now), it is not determined to be true or to be false, because (i) there is no fact of the matter as to whether a sea-battle will take place tomorrow, and (ii) the current history of the world in conjunction with the laws of nature does not necessitate that a sea-battle will take place tomorrow. One therefore ends up with a substantial account of the open future, conceived as a kind of worldly unsettledness, which allows for unrestricted Bivalence, and hence resists the non-classical logic and semantic introduced in Sect. 2.2.

However, so far it has only been shown that the ‘no fact of the matter’ account of openness does as well as the ‘metaphysical indeterminacy’ account. No reason for privileging one account over the other has yet been provided. For instance, it is not clear that the latter account is more successful in delineating cases of open future indeterminacy from cases of other sorts of indeterminacy (e.g., cases of quantum metaphysical indeterminacy). After all, a statement like ˹Schrödinger’s cat will be alive˺ may also be said to be determinate in truth-value (since, when opening the box, there will be a cat whose life status will explain why this statement is true now (or false now)), while it is not determined to be true or to be false (since (i) there is no fact of the matter as to whether Schrödinger’s cat will be alive (or dead), and (ii) the current history of the world in conjunction with the laws of nature does not necessitate that Schrödinger’s cat will be alive (or dead)).⁵⁹ This invites us to answer the following question: is there any reason for preferring the ‘no fact of the matter’ account to the ‘metaphysical indeterminacy’ account?. The answer is ‘yes’; there are at least two reasons that put the former in a better position than the latter: (i) the ‘no fact of the matter’ account is more metaphysically illuminating; (ii) the ‘no fact of the matter’ account is more powerful in capturing a radical sense of openness. Let me develop these two reasons.

First, whereas the ‘metaphysical indeterminacy’ account accommodates the openness of the future by introducing an obscure indeterminate degree of obtaining (openness involves indeterminacy about which determinate state obtains, cf. Sect. 2.7), the ‘no fact of the matter’ account accommodates it by simply denying that any future state obtains. Not only does this second option appear to be decidedly clearer (how should indeterminacy in obtaining be interpreted?), it also seems to be closer to the commonsense view. Indeed, the commonsense view according to which the future is open seems to be naturally interpreted as expressing relevant states as determinately failing to obtain, not as being such that it is indeterminate which relevant determinate states obtain. In particular, if the future is genuinely open about tomorrow’s sea-battle, then intuitively, neither tomorrow’s sea-battle nor its peaceful alternative obtains – the future has not yet happened, after all. It therefore seems that the ‘no fact of the matter’ account is superior to its rival not only in intelligibility, but also in how it tallies with the way we commonly think of the future.

Second, as we have seen, there is a sense in which the future may be said to be open that the ‘metaphysical indeterminacy’ account fails to capture (since it presupposes that the future gets settled, one way or another): time could come to an end, with no ontological commitment to future things standing in the way (cf. Correia & Rosenkranz, 2018: 99). Yet, there are good reasons to think that the ‘no fact of the matter’ account is better positioned for capturing this radical sense of openness. Indeed, given that this account presupposes a gap in ontology (i.e. there is no future), it seems that, assuming physical indeterminism, it can allow for such a doomsday scenario. After all, the possibility that time could come to an end is no more than a possible interpretation of what a strong form of physical indeterminism can lead to. Considering the world history up to t (especially all the entities actually existing at t, or at any time earlier than t), it might be that any time later than t never exists. Supposing that the future may be said to be open in this radical sense, it clearly appears that only an account of openness that does not presuppose that there are times later than t can allow for it. There therefore is at least one sense in which the future may be said to be open which coheres with the ‘no fact of the matter’ account, but not with the ‘metaphysical indeterminacy’ account. It can therefore be concluded that the ‘no fact of the matter’ account of openness is more powerful than its main rivals, and hence that, assuming physical indeterminism, the intuitive asymmetry between the open future and the fixed past should be characterized in ontological terms: there being facts of the matter about what happened, but not about what will happen.

2.10 Conclusion

In this chapter, I showed that there are various ways in which the asymmetry reflected by our intuition of an open future and a fixed past can be characterized. I argued that the substantial characterizations of the asymmetry (the asymmetry reflects how the world truly is) are more promising than the perspectival characterizations (the asymmetry merely reflects how humans interact with world), as the latter fail to provide a fundamental explanation (i.e. not causal or thermodynamic) of the intuitive asymmetry. Considering physical indeterminism, I argued that, though necessary, this doctrine is insufficient for characterizing the openness of the future and must, therefore, be combined with a metaphysical account of unsettledness. In this last respect, I presented two very different accounts of how reality may fail to fully settle what will happen: (i) although there are facts about what will happen, it is indeterminate which of these facts will obtain (metaphysical indeterminacy), (ii) there is simply no fact of the matter about what will happen (no fact of the matter). Following Correia and Rosenkranz (2018), I argued that the latter account can be reconciled with the bivalence of future contingents (without settling how the future will be), provided there is an appropriately relaxed conception of the grounding requirement on tensed truths. Finally, I showed that the ‘no fact of the matter’ account of openness should be preferred, since (i) it is more metaphysically illuminating and (ii) it coheres with a radical sense in which the future may be said to be open that is unavailable to the ‘metaphysical indeterminacy’ account. The various accounts appear in Fig. 2.4.

Fig. 2.4

The main features of the perspectival and substantial approaches to the asymmetry