A Model for the Asymmetry

Abstract

As has been argued, there are good reasons to think that, assuming physical indeterminism, the asymmetry between the ‘open future’ and the ‘fixed past’ is to be characterized as a kind of worldly unsettledness: there being facts of the matter about what happened, but not about what will happen. However, the main models of the temporal structure of the world – eternalism and presentism – do not reflect any ontological asymmetry between the future and the past. According to these models, either both the future and the past exist, or neither the future nor the past exists. So, in this chapter, I argue that we should opt for an alternative model of the temporal structure of the world – the growing block theory (GBT) – that seems better designed to accommodate the asymmetry in openness between the future and the past.

This chapter (especially Sects. 3.6, 3.7, 3.8, 3.9 and 3.10) is based on Grandjean (2021b, c) and Grandjean (2022) but contains new material.

3.1 Introduction

In the previous chapter, it was argued that there are good reasons to think that, assuming physical indeterminism, the asymmetry between the open future and the fixed past is to be characterized as a kind of worldly unsettledness: there being facts of the matter about what happened, but not about what will happen. This characterization seems indeed to be required to fully account for the various ways in which our intuition that the future is open and the past fixed may be expressed. In particular, the radical sense of openness in which time could come to an end (with no ontological commitment to future things standing in the way) can only be captured by an account that presupposes a real gap in ontology (there is no future). However, the main models of the temporal structure of the world do not reflect any asymmetry between the future and the past. According to eternalism and presentism, the future and the past are ontologically on a par. Eternalists hold that both the future and the past exist, while presentists hold that neither the future nor the past exists. In other words, the two main competing models of the temporal structure of the world do not ontologically distinguish the future from the past (either both of them exist or none of them exists). Therefore, neither eternalism nor presentism seems able to accommodate the asymmetry reflected by our basic intuition regarding the nature of time.

This conclusion leads us to think that we should opt for another model of the temporal structure of the world that provides an ontological ground for the asymmetry in openness between the future and the past. In that respect, the growing block theory (GBT), most famously put forward by C. D. Broad (1923), seems to be a natural candidate. This theory is indeed committed to the existence of the past (and the present), but not to the existence of the future. It depicts the block universe as increasing, with new moments of times coming into existence to join the moments that already exist. However, since GBT is commonly defined as a hybrid between eternalism and presentism (the growing blocker agrees with the eternalist that the past exists and agrees with the presentist that the future does not exist), it is often criticized for accumulating the flaws that are identified in the two traditional models. For example, just like eternalism (at least in its tense-realistic version), GBT seems to face with the so-called ‘epistemic objection’ (according to which there is no way of knowing that our time is the objective present) and, just like presentism, GBT seems to conflict with the theories of relativity (e.g., by requiring an absolute notion of objective simultaneity).

Therefore, in order to provide a defense of GBT, I argue that the traditional way of defining the A-theories of time – in terms of whether the future and the past exist – should be abandoned. To make that case, I argue that whereas nothing in actual intuition answers to the question ‘Do the future and the past exist?’, we clearly intuit that the future differs from the past (e.g., causes occur prior to their effects, the arrow of time points from past to future, the future is open while the past is fixed, etc.). My proposal in this chapter is therefore to make a fresh start in the debate by distinguishing two groups of A-theories of time: the asymmetric theories that have intrinsic resources to explain why (at least some) differences between the future and the past are intuited, and the symmetric theories that need extrinsic resources (e.g., entropy, irreversibility). I then distinguish the various forms asymmetric and symmetric theories may adopt by introducing two dynamic principles: Temporal Becoming and Annihilation. One immediate consequence of this proposal is that, contrary to what traditional definitions suggest, it is not essential to GBT to be an ontological hybrid between the polar opposites of eternalism and presentism. Rather, what is essential to this theory (at least in its full form) is to be asymmetric, while accepting Temporal Becoming and rejecting Annihilation. In this revisited picture, GBT does not represent an intermediate view, but a real alternative: assuming that some intuitive past-future time differences reflect the deep structure of reality, GBT is better positioned than its rivals to accommodate them.

The chapter is structured as follows. In the second section, I present the traditional way of introducing the various A-theories of time; I start from the McTaggartian distinction between the A- and the B-series, two ways of ordering positions in time, and explain why they both lead McTaggart to think that time is unreal. Then, using Kit Fine’s reconstruction of the argument, I show that various ways of rejecting the principle of Neutrality allow one to derive various A-theories of time. In the third section, I express my dissatisfaction regarding the traditional way of defining the A-theories of time, since it neglects the role our intuitions are meant to play in the debate. In the fourth section, I make a fresh start in the debate by introducing two questions the specific answers to which will allow us (i) to get a comprehensive categorization of the A-theories of time and (ii) to reveal the metaphysical singularity and potential of GBT. In the fifth section, I focus on GBT and argue that, combined with physical indeterminism, it provides a solid basis to accommodate the intuitive asymmetry between the open future and the fixed past. In the sixth section, I present what is generally taken to be one of the most prominent objections against GBT, commonly referred to as the ‘epistemic objection’. In the seventh section, I review various unsatisfactory attempts to address the epistemic objection, in particular Merricks (2006), Forrest (2004), and Correia and Rosenkranz (2018). In the eighth section, I show why the epistemic objection naturally leads to an anti-essentialist picture of kinds. In the ninth section, I show how an intuitive appeal to the continued existence of bare particulars may help solve the epistemic objection and, more generally, may account for how things located in the past exist. Finally, in the tenth section, I justify the claim that there are such bare particulars.

3.2 The McTaggartian Picture

In his best-known paper published in 1908, J. M. E. McTaggart argues that time is unreal, because our descriptions of time are either insufficient, contradictory or generate a vicious circle or an infinite regress. McTaggart begins his argument by distinguishing two ways of ordering positions in time. First, positions can be ordered according to their possession of properties like being two days past, being present, being one day future, etc. – these properties are often referred to now as ‘A-properties’. McTaggart calls the series of positions ordered by these properties the ‘A-series’. Second, positions in time can be ordered by two-place relations like two days earlier than, simultaneous with, one day later than, etc. – these relations are often referred to now as ‘B-relations’. McTaggart calls the series of positions ordered by these relations the ‘B-series’.¹ This distinction between the A-series and the B-series has served as a natural starting point for most of subsequent work on the metaphysics of time. In particular, it has offered a framework within which the main models of the temporal structure of the world have since been developed.

Nowadays, philosophers of time are said to hold an ‘A-theory of time’ or a ‘B-theory of time’, depending upon their attitudes to the A-properties and B-relations. These labels, first coined by Richard M. Gale (1966), can be understood as follows: the ‘A-theorists’ (or ‘tense realists’)² claim that there is an objective distinction between what is past, present or future, while their opponents, the ‘B-theorists’ (or ‘tense anti-realists’)³ deny the objectivity of any such distinction. To put it another way, A-theorists and B-theorists agree that every thing in time is ‘past relative to’ some things, ‘future relative to’ others, and ‘present relative to’ itself – just as every place on earth is south relative to some places, north relative to others, and at the same latitude as itself. But, whereas B-theorists regard this spatial analogy as deeply revelatory of the purely relative nature of the division of time, A-theorists claim that it is misleading. According to A-theorists, every thing in time that is past, present, or future in a merely relative sense is, in addition, past, present or future in a non-relative sense (i.e. past, present, or future simpliciter) (cf. Zimmerman, 2011: 163–164).

Although there is an ongoing debate about whether there is a genuine metaphysical conflict between the A- and the B-theory of time,⁴ it is generally accepted that these two theories draw their legitimacy from different sources of evidence: whereas the A-theory seems backed by our intuitions, the B-theory is favored by the scientific community.⁵ More specifically, the A-theorist generally emphasizes that her theory can account for how we ordinary think of time: (i) time has a direction,⁶ (ii) ‘our present’ extends throughout the universe, (iii) the future is open whereas the past is fixed, etc. By contrast, the B-theorist generally emphasizes that her theory can account for what science, especially contemporary physics, says about time: (i) time has no direction (since there is no objective sense in which time is flowing one way rather than the other), (ii) there is no unique present (since there is no absolute relation of objective simultaneity), (iii) there is no asymmetry in openness between the future and the past (since the ‘block universe’ view of time is isotropic and the fundamental laws of physics are time-reversal invariant), etc.⁷

Of course, A-theorists disagree on many points (e.g., on whether all of reality is confined to the present), but they usually share the same high concern for accounting for our commonsense view of time, especially for our genuine conception of change. In that sense, the A-theorist’s picture of the world is essentially dynamic: events are constantly changing with respect to their A-properties by first becoming less and less future, then becoming present, and subsequently becoming more and more past. The passage of time is thus depicted as a real and inexorable feature of the world. By contrast, B-theorists regard time as being closely akin to space, i.e. as a static dimension in which everything is permanent. After all, events do not change with respect to their B-relations: if the Battle of Waterloo is earlier than the conquest of Mars, then the Battle of Waterloo is always earlier than the conquest of Mars. The concern of A-theorists for change as we experience it plays a crucial role in McTaggart’s argument for the unreality of time. This argument can be reconstructed in various ways (Kit Fine’s version of McTaggart’s argument will be examined below) but, as a first approach, it will suffice to consider the four following claims:

• 1. Genuine change is essential for the reality of time.

• 2. Only the A-series involves genuine change.

• 3. The A-series is either contradictory, or generates a vicious circle or an infinite regress.

• 4. Therefore, there is no genuine change, and so time is unreal.

First, McTaggart argues that genuine change is essential for the reality of time. He does not say much in support of this claim.⁸ The reason is presumably that, since Aristotle (Physics, IV, 219a 4–6), time is most often defined as the measurement of change. In that sense, things change continually and we call ‘time’ the measurement, i.e. the counting of this change. This idea runs deep: time is what we refer when we ask ‘When?’. ‘After how much time will you return?’ means ‘When will you return?’. The answer to the question ‘When?’ refers to something that happens. For example, ‘I will return in 2 days’ means that between departure and return the sun will have completed 2 circuits in the sky (cf. Rovelli, 2018: 49).⁹ So if nothing changes, time does not pass, because time is our way of situating ourselves in relation to what changes. If nothing changes, there is therefore no time. According to Aristotle, even when “[…] it is dark and our body experience is nil, but some change is happening within the mind, we immediately suppose that some time has passed as well” (1999: 105). In other words, even the time that we perceive flowing within us is the measure of a change.

We had to wait until the end of seventeenth century to get a completely different picture. In his Principia, Newton recognizes that there is a kind of ‘Aristotelian’ time that measures days and movements. But he also contends that, in addition to this, another time must exist: an ‘absolute, true and mathematical’ time that flows by itself, independently of things and of their changes. As Carlo Rovelli puts it: “[i]f all things remained motionless and even the movements of our souls were to be frozen, this time would continue to pass, according to Newton, unaffected and equal to itself” (2018: 76). ‘Absolute, true and mathematical’ time, Newton says, is not directly accessible, only indirectly, through calculation. It is not the same as that given by days, because “[…] the natural days are truly unequal, though they are commonly consider’d as equal, and used for a measure of time: Astronomers correct this inequality for their more accurate deducing of the celestial motions” (Newton, 1729: 12). However, even if the Newtonian picture theoretically allows for ‘temporal vacua’ (i.e. periods of time during which nothing changes), it still seems true that time is the dimension in which changes do and can occur. So, McTaggart is certainly right in saying that a world without change is a world without time, i.e. a world in which change cannot possibly occur.

This latter claim has nonetheless been challenged by Sidney Shoemaker (1969) who has famously argued that time can pass without change. In particular, Shoemaker invites us to imagine a world divided into three regions: A, B, and C. From time to time, one or more of these regions get ‘frozen’ in the sense that change of all kinds comes to a complete halt within the region. When this occurs, the inhabitants of the frozen region observe nothing amiss: “[…] the period passes without their noticing it or measuring it in any way, so they rely on the testimony of the inhabitants of other regions in forming beliefs about their own frozen periods” (Le Poidevin, 2010: 172). Comparing their notes, the inhabitants of all three regions have found (by the use of clocks located in unfrozen regions) that: (i) each local freeze lasts for exactly 1 year and (ii) A is frozen every 3 years, B every four, and C every five. Since the three regions constitute the whole of this world, a simple calculation shows that, every 60 years, there is a total freeze lasting 1 year. Taking this scenario seriously,¹⁰ the inhabitants of this world seem to have reasons “[…] for believing that there are intervals during which no changes occur anywhere” (Shoemaker, 1969: 371). However, although Shoemaker’s argument is both imaginative and subtle, it misses its target. Many objections can be found in the literature (cf. Scott 1995; Warmbrod, 2017); the most striking one shows that Shoemaker begs the question: he assumes the possibility of changeless time instead of proving it. After all, as Denis Corish has pointed out, Shoemaker’s scenario allows for another interpretation: “[…] instead of a year of changeless time passing, in say region A, there is no time there […]” (2009: 222). The only reason why Shoemaker does not retain this interpretation is that he assumes that “[…] if there is time in one place, there is the same time in another, distant, place, whether anything happening in that other place or not” (2009: 221). For instance, he assumes that the same year as passing in B occurs in A, though everything in A is frozen – this is the assumption of changeless time. But since this possibility is precisely what Shoemaker is arguing for, it cannot be assumed in the argument without begging the question. Also, there is change in McTaggart’s A-series sense even during the frozen periods.

Second, McTaggart argues that only the A-series involves genuine change. This claim is more contentious than the first one. It rests on the idea that the only way in which events can genuinely change is by first being future, then present and finally past, i.e. by changing positions in the A-series. McTaggart thus denies that an event having different properties over time – such as a discussion that begins politely and becomes rude – is a paradigmatic example of change, since it is always the case that the earlier part of this event is politer than its later part. After all, supposing that the B-theorist is right and that time could exist without the A-series, everything is permanent: events possess different properties at different locations in a static dimension. So, just as variations in properties across space at a given moment of time do not amount to change (because all locations in question coexist), variations in properties over time do not amount to change either.¹¹ For this reason, McTaggart rejects Bertrand Russell’s account of change, according to which something changes just in case a proposition is true at one time but not true when evaluated at a later time. As McTaggart insists, if a proposition p has some truth-value when evaluated at a time, it is always the case that p has that truth-value when evaluated at that time.¹²

The situation is quite different when introducing the A-series into the equation: we still have the permanent B-facts – the discussion is polite at t₁ and rude at t₂ – but in addition we have ever-changing A-facts. The discussion’s being polite at t₁ is first in the distant future, then the near future, then the present and thereafter the ever more distant past. McTaggart hence concludes that genuine change requires ever-changing A-facts and, therefore, that an eternal B-world (i.e. a world without such facts) is a world where genuine change cannot occur and, in virtue of (1), is a world without time. To be sure, McTaggart does not disagree with the commonsensical view according to which a discussion that is polite at one time and rude at a later time has changed; his claim is rather that in the absence of ever-changing A-facts, there are no times at all, since change cannot occur.

Third, McTaggart argues that the A-series, which has been shown to be essential for the reality of time, entails a contradiction: every event in the A-series (assuming that there is no first or last event) has the mutually incompatible properties of being past, being present and being future. In that sense, since everything starts off as being future, then becomes present before sinking into the past, it follows that every event has all three A-properties, while no event can possess any two of them without generating a contradiction. If an event is present, for example, it cannot also be either past or future. The obvious reply to this apparent contradiction is to say that no event has two or more of these incompatible properties at the same time, but rather has them successively at different moments of time. McTaggart is not blind to this obvious reply; as he puts it: “[i]t is never true, the answer will run, that M is present, past and future. It is present, will be past, and has been future. […] The characteristics are only incompatible when they are simultaneous, and there is no contradiction to this in the fact that each term has all of them successively” (1908: 468).

However, McTaggart maintains that this obvious reply fails, because it involves either a vicious circle or an infinite regress. First, this reply is clearly circular: confronted with an apparent contradiction involving the A-series (every event possesses mutually incompatible A-properties), the A-theorist is employing the A-series itself to get around the problem. In particular, the A-theorist is claiming that every event in the A-series being past, present, and future, has these properties successively at moments of time, while the successive order of those moments of time needs to be described by invoking the A-properties themselves. This is not satisfactory: one cannot presuppose the A-series when trying to rid it of contradiction. Of course, as McTaggart concedes, a reply could be the following: “[o]ur ground for rejecting time […] is that time cannot be explained without assuming time. But may this not prove – not that time is invalid, but rather that time is ultimate?” (1908: 470). For example, it may well be impossible to explain notions such as ‘goodness’ or ‘truth’ in completely different terms, but this does not lead us to reject the notions in question. So, perhaps time is also a primitive concept, one that cannot be explained in other terms. However, this reply does not seem to apply here: notions such as ‘goodness’ or ‘truth’, though they may not be explained in a non-circular way, do not involve any contradiction. The notion of time must therefore be rejected as paradoxical, unless the contradiction it involves can be removed.

In that respect, claiming that the contradiction inherent in the A-series can be removed by introducing a second-level A-series (M is present in the present, past in the future, and future in the past) does not help solve the problem, since this clearly involves an infinite regress. What then about the contradiction inherent in the second-level and following A-series? At any point in this regress at which we stop we are left with an A-series that suffers from the same difficulty as the previous one. For example, take an event such as the death of Kennedy and consider second-level properties such as being present in the present, being past in the future, being future in the past, etc. It clearly appears that some of these properties are incompatible: if the death of Kennedy is past in the present, it cannot also be either present in the present or future in the present. Of course, the A-theorist might again insist that this event does not have two or more of these second-level incompatible properties at the same time, but rather has them successively at different moments of time. But once again, the succession of those moments of time needs to be described by invoking third-level properties that will in turn be incompatible, so that the contradiction will never be removed by ascending in the hierarchy (no matter how many levels we add). This leads McTaggart to conclude that introducing higher-level properties fails to eradicate the initial paradox, since precisely the same paradox exists at each level of temporal predication. The A-series is therefore inherently paradoxical, and so it cannot correspond with anything in reality. Given this, McTaggart maintains that there is no change (in virtue of (2)) and, therefore, that time does not exist (in virtue of (1)). What does exist, according to McTaggart, is an atemporal ‘C-series’: “[…] an eternal four-dimensional block of events, whose contents are ordered but not in a temporal way” (Dainton, 2010: 17).

One may agree with Peter Geach that sometimes “[t]ime is so perplexing that we can understand philosophers’ wishing to cut the knot by denying the reality of time […]” (1973: 213). In this perspective, McTaggart’s argument is surely powerful, but suffers from at least two weaknesses: (i) it presupposes an ontology of events, and (ii) it neglects the variety of forms the A-theory may adopt in order to avoid the contradiction. That is partly why Kit Fine (2005: 272–273) proposes a revised version of this argument.¹³ Specifically, Fine formulates four general metaphysical assumptions, the conflicts between which threaten the reality of time (cf. also Correia & Rosenkranz, 2012, Lipman, 2015: 3120–3121, Deng, 2017: 1116):

• 1. Realism: Reality is constituted (at least, in part) by tensed facts.¹⁴

• 2. Neutrality: No time is privileged, the tensed facts that constitute reality are not oriented towards one time as opposed to another.

• 3. Absolutism: The constitution of reality is an absolute matter, i.e. is not relative to a time or other form of temporal standpoint.

• 4. Coherence: Reality is not contradictory, it is not constituted by facts with incompatible content.

Fine’s version of McTaggart’s argument (at least in its simple form)¹⁵ can be expressed as follows. Realism states that reality is constituted by some tensed facts. There is therefore some time t at which this fact obtains. Now, it follows from Neutrality that reality is not oriented towards one time as opposed to another. In particular, the totality of tensed facts constituting reality are not merely ones that presently obtain (the present is no privileged time). So, reality is presumably constituted by similar sorts of tensed facts that obtain at other times (the present is only one time among others, after all). Since any reasonable view of reality should allow for its being variegated over time, it must be assumed that the facts constituting reality that obtain at t are incompatible with the facts constituting reality that obtain at other times. For instance, if such a view allows for the present fact that ‘Kit Fine is sitting’, then it should also allow for the subsequent fact that ‘Kit Fine is standing’. Finally, given Absolutism, reality is absolutely constituted by these facts, while this contradicts Coherence (cf. Fine, 2005: 272).¹⁶

The standard realist response to Fine’s McTaggartian argument is to retain Realism but to reject Neutrality and, therefore, to claim that reality is somehow oriented. Fine calls those realists who reject Neutrality ‘presentists’. Roughly, if there is no more than one time at which reality is constituted by tensed facts, which is intended to be the present time, then reality is not contradictory, since no two facts with incompatible content can simultaneously obtain. For example, reality is constituted by the present fact ‘KF is sitting’, but not by the subsequent fact ‘KF is standing’. However, contrary to what Fine suggests, there are (at least) two other ways to reject Neutrality, i.e. to deny that the totality of facts constituting reality are those obtain at past, present and future times. Specifically, one can argue that (i) the totality of facts constituting reality are merely those obtained at past and present times (GBT), or (ii) the totality of facts constituting reality are merely those obtained at present and future times (Shrinking Block Theory – SBT).¹⁷ It is worth noting that the moving spotlight (MSL) is not an option here, since it entails that the facts constituting reality are not oriented towards one time as opposed to another (no time is ontologically privileged) and, therefore, that Neutrality is retained. Although Fine only considers presentism, there are also various ways for the other two options (GBT and SBT) of avoiding the contradiction (cf. Correia & Rosenkranz, 2012, Broad, 1923: 79–84). This will later be a matter of great concern (cf. Sects. 3.9 and 3.10), but I can already give an insight into my own GBT solution to Fine’s McTaggartian argument.

In order to derive a contradiction (e.g., reality is constituted by the facts ‘KF is sitting’ and ‘KF is standing’), Fine presupposes that the tensed facts which constitute reality at more than one time do not undergo any intrinsic change as time goes by. For example, if the fact ‘KF is sitting’ constitutes reality at the present time, then the very same fact ‘KF is sitting’ constitutes reality at every future time (especially at every future time at which the fact ‘KF is standing’ also constitutes reality, which generates a contradiction). Yet, there might be a plausible alternative to this presupposition: whatever constitutes reality at the present time (I will speak of events rather than tensed facts) undergoes intrinsic changes by becoming past, to such an extent that it does no longer belong to its natural kind. This change will be introduced as an alteration of certain intrinsic properties, namely the properties that make, for instance, an event belong to the natural kind to which it belongs when present (rejection of natural kind essentialism). Just as a bronze statue exists in a changed form after having been melted, an event exists in a changed form after having become past. For example, the battle of Waterloo is an event when occurring at the present time, but is no longer an event when past (without it ceasing to exist). Once this alternative is accepted, Fine’s argument for the joint inconsistency of non-presentist rejections of Neutrality, Realism, Absolutism, and Coherence is blocked, since reality is not constituted by the very same entities (tensed facts, events, etc.) at present and past times. For instance, the fact ‘KF is sitting’ constituted reality one minute ago, when he was sitting, while it is no longer a fact now, when he is standing. Provided that the fact (the event) ‘KF is sitting’ still exists in a changed form, this solution seems compatible with the claim that nothing ever ceases to exist. There therefore are no times at which two same entities, with incompatible content, are both constituting reality.

The non-standard realist response to Fine’s McTaggartian argument is to retain Realism but to reject either Absolutism (relativism – reality is constituted by all the tensed facts that obtain at some time or other, but it is constituted by them at different times)¹⁸ or Coherence (fragmentalism – reality is constituted by all the tensed facts that obtain at some time or other, even though some of these are incompatible). These two non-standard responses, Fine claims, are the best options for tense realists to account (i) for the passage of time, (ii) for the connection between language and reality, and (iii) for the compatibility between tense realism and special relativity (cf. 2005: §§7–9). However, since the non-standard options are not fully intelligible, they will not be considered in the remainder of this chapter. Specifically, one reason why relativism is not fully intelligible is that, contrary to what this theory implies, temporal reality is naturally thought as being ‘one’ (rather than ‘many’): “[j]ust as there is not one reality where you are and another where we are, there does not seem to be a succession of distinct realities corresponding to different times […]” (Correia & Rosenkranz, 2012: 311). Admittedly, from an historical point of view, it sometimes makes sense to speak of different epochs (e.g., the Enlightenment, the Victorian era, etc.) as corresponding to a succession of realities. This allows one to insist on the political, economic, and sociocultural differences between epochs. But, “[…] when it comes to metaphysics, one tends to see these different epochs as parts of a single reality” (Correia & Rosenkranz id.). Thus, since relativism – that views temporal reality as a mere collection of different successive realities – goes against this unified picture, it is hard to give it metaphysical relevance.

Then, one reason why fragmentalism is not fully intelligible has to do with the very notion of ‘coherence’ at work in the definition of a fragment – a fragment is a maximal collection of mutually coherent facts. According to fragmentalism, temporal reality is ‘one’ (i.e. there is no diachronic shifts in what facts constitute it), but is somehow ‘fragmented’, insofar as it is constituted by facts with incompatible content across the fragments. Now, the notion of ‘coherence’ at work in the definition of a fragment – call it ‘coherence*’ – cannot be the ordinary notion of coherence that holds amongst propositions. Otherwise, “[…] the reduction of times to fragments would be inadequate due to an over-generation of fragments. We would find more times than there actually are” (Lipman, 2015: 3124). For example, perhaps there is no time at which two facts – e.g., ‘Socrates is furious’ and ‘Plato is anxious’ – obtain, so that a fragmentalist should say that there is no fragment that comprises both of these facts. Yet, these two facts clearly cohere: “[…] it could have been the case that, at some time, Socrates is furious and Plato is anxious” (Correia & Rosenkranz, 2012: 312). Although Fine suggests that the notion of coherence* should be taken as primitive (2005: 281), this notion is too mysterious for this being an option. Thus, since it is far from clear how the crucial notion of ‘coherence*’ should be understood, it is hard to make sense of fragmentalism. Both standard and non-standard positions are summarized in Fig. 3.1.

Fig. 3.1

Standard and non-standard realist theories of time

Thus, although McTaggart’s argument takes the moving-spotlight theory (which results from the acceptance of the four Finean assumptions and, therefore, leads to contradiction) as its primary target, Fine’s revisited version of the argument shows that other sorts of tense realism (both standard and non-standard) can be identified. In general, since tense realists disagree about how Neutrality should be rejected (e.g., is all of reality confined to the present?), it is common to define the different versions of the standard A-theory by how they answer to the question ‘Do the future and the past exist?’.¹⁹ According to the traditional definitions, eternalism and presentism are the two extreme answers that can be provided to that question: the former says that both the future and the past exist, whereas the latter says that neither the future nor the past exists. Intermediate between these two extreme answers are the growing block theory (GBT), which says that the past exists but the future does not exist (cf. Sider, 2001: 12, Callender, 2011: 3), and the shrinking block theory (SBT), which says that the future exists but the past does not exist. For example, as Caspar Hare puts it: “[s]ome imagine that the past exists but the future does not […]. Some imagine that the future exists but the past does not […]. Presentists, meanwhile, hold that only present objects, events, moments exist (and perhaps things that exist timelessly, like gods and numbers). There are no past or future things” (2009: 17).

However, there are some reasons to complain about this traditional way of defining the A-theories (cf. Williamson, 2013: 24, Deasy, 2017: 381–389). In particular, it leads to think of GBT as a hybrid between eternalism and presentism, with the consequence that this theory is often criticized for accumulating the flaws that are identified in the two extreme forms of the A-theory. For example, just like eternalism (at least in its A-theoretic version), GBT seems to face with the so-called ‘epistemic objection’ (according to which there is no way of knowing that our time is the objective present) and, just like presentism, GBT seems to conflict with the theories of relativity (e.g., by requiring an absolute notion of objective simultaneity). These two issues will be a matter of great concern in the remainder of the book. Specifically, in the fifth section of this chapter, I will argue that the ‘epistemic objection’ relies on a mistaken assumption, namely that past beings (e.g., Cesar, Napoleon) are still believing to be in the objective present, and therefore that it does not apply to GBT. Further, in the next chapter, I will argue that GBT, far from being disqualified by contemporary physics, might be underpinned by some recent approaches to quantum gravity. As a preliminary step, however, it will be useful to change the way GBT is generally perceived among the A-theories of time in order to reveal the whole potential of this theory (especially when it comes to accommodate the asymmetry between the open future and the fixed past). In the following sections, I will therefore first express my dissatisfaction regarding the traditional way of defining the A-theories of time, and then make a fresh start in the debate by introducing two questions whose specific answers will allow (i) to get a comprehensive categorization of the A-theories of time and (ii) to reveal the metaphysical singularity and potential of GBT.

3.3 Complaining About the McTaggartian Picture

One may agree with Timothy Williamson (2013: 22) that there is a “feeling of dissatisfaction” with the eternalism-presentism distinction. The reason, he says, is that there is no satisfactory way to spell out what is meant by ‘is present’ in the traditional definition of presentism, according to which ‘everything is present’.²⁰ There are indeed good reasons to reject all the most plausible candidate interpretations. For example, consider the natural idea that “[…] to be present is just to be real or to exist” (Zimmerman, 1996: 117). The problem with this interpretation is that it makes presentism trivially true: if presentism is to be interpreted as the thesis that ‘everything exists’, then everyone is a presentist! Another natural idea is to claim that to be present is to instantiate the primitive property of presentness. However, as Zimmerman himself claims, “[…] no real presentist has any reason to believe in a special quality of ‘being present’” (1996: 125). Moreover, as Daniel Deasy argues, this interpretation reduces the debate between A-theorists to the debate about whether everything or only something instantiates this property, which sounds like “[…] a parody of the philosophy of time” (2017: 383). Finally, Williamson mentions a third interpretation: “[…] something is present when and only when it is spatially located” (2013: 24). However, it is not clear that this interpretation would be false in a non-presentist setting (as it is meant to be) – there would, for instance, be nothing prima facie problematic in an eternalist’s asserting that everything has a spatial location. Furthermore, this latter interpretation makes presentism incompatible with theories that have no ramification with the philosophy of time, such as the platonist theory that there are spatially unlocated abstract objects (e.g., numbers). Since the predicates ‘is past’ and ‘is future’ – as they appear in the other A-theories of time (MSL, GBT and SBT) – are respectively defined in terms of ‘to be earlier than the present things’ and ‘to be later than the present things’, the mystery surrounding the term ‘is present’ seems to infect all the traditional definitions.²¹

Another issue raised by the traditional definitions of the A-theories of time has to do with the interpretation of the universal quantifier ‘everything’ (cf. Crisp, 2004; Ludlow, 2004; Meyer, 2005, 2011; Miller, 2013; Sider, 2006a). The question is whether, when presentists claim that ‘everything is present’, the quantifier is to be interpreted as tensed or tenseless. Both options seem problematic. If it is tensed, then presentism is the trivially true thesis that ‘everything present is present’ (which hence makes eternalism trivially false). If it is tenseless, then presentism is the trivially false thesis that ‘everything past, present or future is present’ (which hence makes eternalism trivially true). It therefore seems that presentism is either trivially true (and eternalism trivially false), or trivially false (and eternalism trivially true). In other words, it appears that the traditional way of defining the A-theories of time turns what is meant to be a metaphysical debate between two venerable positions – presentism and eternalism – into a purely semantic debate about how the universal quantifier in the definitions should be interpreted. This is what leads Ulrich Meyer, for instance, to conclude that “[…] there is no reading on which [presentism] expresses a substantial metaphysical truth” (2005: 213–214).

However, although it should be acknowledged that traditional definitions of the A-theories of time (i) make unclear what it is for something to be present, and (ii) threat the metaphysical nature of the eternalism-presentism debate, this is not what should concern us most. After all, following Williamson (2013), Correia and Rosenkranz (2018) have shown that presentism (and other A-theories) can be defined without using the mysterious notion of ‘presentness’. In particular, they argue that presentism is the only theory that accepts both of the following principles: (P2) ‘every time is new at itself’ (Tx → At x, H¬E!x), where ‘T’ is a predicate for times and ‘H’ stands for ‘Always in the past’, and (P3) ‘every time is last at itself’ (Tx → At x, G¬E!x), where ‘G’ stands for ‘Always in the future’.²² Furthermore, it is not clear that in using ‘everything’ in the tenseless way, presentists are saying something trivially false. As Correia and Rosenkranz (2015, 2018) have argued: just as saying that ‘every black or non-black raven is black’ is “[…] a perfectly sound way of saying that the only ravens that exist are black”, saying that ‘everything past, present or future is present’ is “[…] a perfectly sound way of saying that the only things in time that exist are present – and this will remain to be so even if it is assumed that what is present may also be past or future” (2018: 62). For his part, Deasy (2017: 381) argues that there is a natural reading of the traditional definition of presentism on which it expresses a thesis which is neither trivially true nor trivially false: ‘A ∀x Present(x)’, where ‘A’ stays for ‘always’ and ‘∀x’ is the universal quantifier of classical first-order logic and is, following Marcus (1962), neither tenseless nor tensed.

Rather, the main problem with the traditional way of defining the A-theories of time is that it rests on an ontological question – ‘Do the future and the past exist?’ – while we have no strong intuitions thereon. A-theories of time are indeed meant to match the ordinary intuitions we have regarding the nature of time (e.g., time flows uniformly and universally, our ‘present’ extends throughout the universe, the future is open while the past is fixed, etc.), and if we define these theories in terms of whether the future and the past exist, then we risk simply missing the point. For instance, a statement such as ˹The conquest of Mars exists˺ can neither be confirmed nor refuted by any intuition or experience whatsoever. As Clifford Williams puts it: “[…] there is no experiential way to differentiate between [events] being equally real and not being equally real” (1998b: 386); the only events we experience are the ones occurring at the time of our experience, whether this be in eternalist or in presentist settings. For his part, Craig Callender compares the eternalism-presentism debate to two people arguing about whether the refrigerator lightbulb goes out when the door is shut: “‘[R]efrigerator presentists’ believe the light is off when the door is shut; ‘refrigerator eternalists’ believe the light remains on” (2000: 588). This debate is pointless since, barring drilling a hole into the side of the refrigerator, we can only check the light by opening the door (while this will not test either hypothesis).²³

A reply might be that empirical science, especially observational astronomy, is precisely what allows us to drill a hole into the side of the refrigerator and, therefore, to determine who of the eternalists or the presentists are right. For example, it might seem that the recent observation of gravitational waves speaks in favor of eternalists, since this observation informs us about the very early universe. But, as it should be clear, all that the observation of gravitational waves allows us to conclude is that the past existed (not that the past is still existing), while this is compatible with both eternalist and presentist theories. When we observe gravitational waves, we do not observe the past (or do so only in a metaphorical sense); we observe disturbances in the curvature of spacetime that, although they emerge from the very early universe (and might therefore offer a unique probe to explore it), are simultaneous with our observation. So, even empirical science – with its powerful instruments and super sensitive detectors – only allows us to observe events that occur at the time of our observation. It therefore seems hopeless to appeal to empirical data in order to settle the debate between eternalists and presentists.

To the question ‘Do the future and the past exist?’, we thus have no pre-theoretic answer. The dispute between eternalists and presentists cannot be solved by means of intuition – that is probably why this dispute may appear so stipulative (cf. Williams 1998a, 1998b; Callender, 2000; Dorato, 2006a; Savitt, 2006). Of course, this does not mean that it is false to say that the various A-theories of time differ with respect to how they answer to the question ‘Do the future and the past exist?’. For instance, it is usually right to say that eternalists hold that both the future and the past exist, while presentists hold that neither the future nor the past exist. What I ultimately want to argue is that, since these definitions can neither be confirmed nor refuted pre-theoretically, they cannot be essential to the A-theories, i.e. they cannot be true in virtue of the nature of the A-theories, which are primarily meant to match our ordinary intuitions on time. Of course, one could object that matching (at least some of) our intuitions should not be A-theorists’ primary concern; but, if so, then it is not clear why one should not adopt a B-theory of time which, as has been said, has the advantage of being favored by the scientific community. As a reminder, the theories of relativity seem to imply a static view of time, in which past, present and future are equally real (the ‘block universe’ view of time) (cf. Sect. 3.2).

This approach could be criticized for ascribing more weight to intuitions than they can actually bear. After all, the controversy between A-theorists of time is primarily a metaphysical one, not an experiential one. The answer, it seems to me, is that there are several kinds of metaphysical controversies. Admittedly, many metaphysical controversies cannot be solved solely by appeal to experience. For example, if one wants to challenge Williamson’s claim that vagueness is a form of ignorance (cf. Williamson, 1994), one will not deny that we experience some borderline cases; it is something that both Williamson and his critic agree upon.²⁴ What one will criticize is rather Williamson’s inference from this experience, namely that there are sharp boundaries but we are unable to figure out their exact location. However, there are also metaphysical controversies that are more closely connected to experience. For example, Whitehead ([1934] 2011) argues that if we look carefully at our experience, we will find that fundamental concepts are not Aristotelian substances but activity and process: temporal entities are what we experience as basic, not concrete objects (which are regarded to be composites of many occasions of experience). If Whitehead is right, then the conflict between these two ontologies is “[…] decidable more by probing our experience than by making inferences from them” (Williams, 1998b: 391).

The debate on the nature of time seems more like the second of these disputes than the first. In the first, we all agree that we experience borderline cases, but we do not appeal to any experience to state whether these cases are ontic, semantic, or epistemic phenomena. It is the reverse with respect to the debate on the nature of time. Eternalism and presentism are not to be conceived as rival metaphysical explanations of one commonly agreed upon set of experiences. They are indeed not inferred from a prior knowledge of the temporal structure of the world. Rather, the debate on the nature of time is (partially) about which theory experience confirms. For instance, it is common for A-theorists of time to argue that a particular version of the A-theory is true partly because it matches with how time is ordinary experienced (see, for example, Zimmerman 2008: §7). Experience is thus evidence for theories of time, not the other way around. Therefore, one can reject the traditional way of defining the A-theories of time on the ground that the definitions can neither be confirmed nor refuted by experience, without jeopardizing the metaphysical nature of the debate. Some metaphysical debates are much more closely connected to experience than others, and the debate on the nature of time is presumably one of them.

A second, though less important, reason why traditional definitions should not be taken as essential to the A-theories is that there are some specific times at which they fail to distinguish between the theories in question. For example, at the start of the Big Bang (where there is no past), eternalism and SBT, on the one hand, and presentism and GBT, on the other hand, are ontologically indiscernible: eternalists and shrinking blockers are both merely committed to the existence of the present and the future (‘everything is either present or future’), whereas presentists and growing blockers are both merely committed to the existence of the present (‘everything is present’). Likewise, at the last moment of time (where there is no future), eternalism and GBT, on the one hand, and presentism and SBT, on the other hand, are ontologically indiscernible: eternalists and growing blockers are both merely committed to the existence of the past (‘everything is past’), whereas presentist and shrinking blockers are both merely committed to the existence of the present (‘everything is present’) (cf. Fig. 3.2).²⁵ Therefore, since the traditional definitions of the A-theories do not allow us to distinguish between them at all times, it seems that they cannot be considered as essential to them. After all, the following principle looks plausible: if there is at least one time t at which the definition D fails to singularize x, then D is not true in virtue of x’s nature, i.e. D is not essential to x.

Fig. 3.2

A-theoretic structures at first and last moments of time

Thus, the fact that the traditional way of defining the A-theories of time (i) neglects the role that intuitions are meant to play in the debate on the nature of time, and (ii) fails to distinguish between the A-theories at all times, suggests that the A-theories should be introduced differently. In the next section, I therefore propose a fresh way of singularizing the A-theories of time, by introducing two questions – ‘Is there a geometric asymmetry between the future and the past?’ and ‘Is temporal becoming (i.e. the creation of new things in the present) real?’ – the respective answers of which can be pre-theoretically evaluated. When these answers are super-imposed, they allow one to get a comprehensive categorization of the A-theories of time. One immediate consequence of this proposal is that GBT will no longer represent a hybrid between eternalism and presentism, but a theory in its own right, which seems better designed than its rivals to accommodate the intuitive asymmetry between the open future and the fixed past.

Two concessions must nevertheless be made here before we can proceed. First, although GBT and SBT are marginalized by the traditional way of framing the A-theories of time, they have been defended in important and recent publications. Concerning GBT, one can mention Briggs and Forbes (2012, 2017, 2019), Deng (2017), and Correia and Rosenkranz (2013, 2018). Concerning SBT, publications are rarer, but one can still mention Casati and Torrengo (2011) and Norton (2015). Second, the ontological way of framing the A-theories of time, in terms of whether the future and the past exist, does not fully reflect the richness of the current debate. Many sophisticated views, such as McCall’s (1994) shrinking tree, have been widely recognized as important features of temporal ontology. In that sense, although the eternalism-presentism distinction might appear dominant, it should not overshadow the fact that many philosophers have already proposed to reformulate the debate in order to capture the nuances it contains – some of these proposals will be discussed in the next section. The goal of reframing the debate is therefore not original in itself, but the reasons for which this reframing is undertaken in this book and the reframing itself are.

3.4 The McTaggartian Picture Revisited

As has been said, we have no intuition as to whether the past and the future exist. But an intuition that we surely have regarding the nature of time is that the future differs from the past. For example, causes occur prior to their effects, the arrow of time points from past to future, the future is open while the past is fixed, etc. In the previous chapter, I provided various reasons to think that this latter manifestation of how the future differs from the past should be explained by how reality truly is. It might therefore be tempting to extend this result to a large range of intuitive past-future time differences. John Earman (1974), for example, seems to yield to the temptation, when he argues for The Time Direction Heresy, i.e. the thesis according to which ‘temporal orientation’ (understood as a thicket of differences between the future and the past) cannot be reduced to non-temporal features.²⁶ Likewise, Tim Maudlin (2002, 2007) argues that a wide variety of time-asymmetries (including the passage of time and the direction of time) are ultimately grounded in the intrinsic time-asymmetry of the universe.²⁷ A third example is George Ellis (2006, 2013), who argues that the various arrows of time (e.g., the passage of time, the openness of the future) derive from an evolving block universe. All these approaches take our intuition that the future differs from the past seriously, i.e. as reflecting the deep structure of reality. To put it another way, all these approaches bridge the gap between phenomenal and physical time, by taking some of our intuitions as reliable indicators of how reality truly is.

Of course, one might object that, without further arguments (of the sort provided in the previous chapter), it is not clear that a large range of intuitive past-future time differences need to be grounded in the structure of reality. For example, it might be argued that causal direction is due to a projection of our experience as agents (Price, 1996, 2007), or to The Past Hypothesis (Albert, 2000, 2015).²⁸ Each of these claims provides an explanation as to why causes occur prior to their effects, without appealing to the deep structure of reality. The answer, it seems to me, is that as soon as one accepts that an intuition (e.g., the intuition that the future is open while the past is fixed) should be explained by the intrinsic structure of reality, all the alternative accounts for similar intuitive past-future time differences become redundant. This is not to say that all alternative accounts for temporal differences are false, but rather that they are non-fundamental, in the sense that they can ultimately be explained by the asymmetric nature of time itself. In other words, local phenomena (e.g., entropy, irreversibility) may not be as important as some philosophers would have us believe for past-future time differences. A proposal would therefore be to abandon the traditional debate (since there are no pre-theoretic reasons to adopt either eternalism or presentism), and to make a fresh start with a clearer distinction between two groups of A-theories of time: those that have intrinsic resources to explain why (at least some) differences between the future and the past are intuited, and those that need extrinsic resources.

This proposition immediately raises a question: ‘What does ‘intrinsic’ mean here?’ Roughly, an A-theory has intrinsic resources to explain why (at least some) differences between the future and the past are intuited iff the spatiotemporal structure it describes encodes a relevant past-future time asymmetry in its geometric features. To understand this, it is crucial to reconceptualize the A-theories as primarily describing contentless geometric constructions, whose features do not refer to objects antecedently given (by some sort of experience or prior knowledge) but only have a purely ‘formal-logical’ meaning stipulated by some primitive axioms (which therefore serve as implicit definitions).²⁹ In that sense, A-theories of time are not empirical constructions, but result from irreducibly theoretical choices: they primarily outline geometric structures in which individuals (e.g., spacetime points, events, and objects) participate. Of course, this does not prevent A-theories from being subsequently confirmed (or refuted) by experience; it is even a crucial step! But, as has been said, experience is to be understood as evidence for the A-theories of time, not the other way around (cf. Sect. 3.3).

There are reasons to believe that the geometric structures described by the A-theories are fundamental, in the sense of not being dependent on sets of spacetime points, events or objects. Against a powerful tradition, which takes spacetime geometry to be a system of external relations that are instantiated by spacetime points, the idea is that spatiotemporal structures are ontologically primary, while individuals (such as spacetime points, events, and objects) have a mere derivative status. This ‘structuralist’ view is directly inspired from an influent current in the philosophy of science, sometimes called Ontic Structural Realism (OSR), which inflates the ontological priority of structure and relations.³⁰ However, whereas OSR is generally motivated by the interpretation of quantum physics (cf. Ladyman & Ross, 2007), the present structuralist view is motivated by the nature of the A-theories itself. Once again, A-theories are not set up from objects antecedently given; they primarily outline geometric background structures, the properties of which are stipulated by some primitive axioms. Therefore, taking A-theories seriously (i.e. as saying something about how time truly is), it is natural to regard the background structures they outline as fundamental and, thus, as ontologically prior to the individuals that participate within them. As a result, although some important geometric features of the spatiotemporal structures can hardly be expressed with no reference to individuals (such as spacetime points, events, and objects), one has to keep in mind that these individuals only play a heuristic role: they allow for the description of geometric structures which then carry the ontological weight.

Given this ‘geometric’ reconceptualization of the A-theories of time, ‘the present’ can be regarded as an axis around which some transformations can be operated. In particular, in the Euclidean plane, reflection symmetry is known as a transformation that preserves all geometric features. Such a transformation can, for instance, be operated on spatiotemporal structures, understood as primitive systems of fundamental spatiotemporal relations and derivative spacetime points. Interestingly, when reflection symmetry is operated around ‘the present’ axis of a spatiotemporal structure, the outcome is either an unchanged (or invariant) structure (when it is described by eternalism or presentism), or a transformed structure (when it is described by GBT or SBT). The reason is roughly that, unlike eternalism and presentism, GBT and SBT do not take what lies below (or above, respectively) ‘the present’ axis (viz. spatiotemporally related points) to be a structural reflection of what lies above (or below) it (cf. Figure 3.3). Therefore, whereas the structures described by eternalism and presentism do not change upon undergoing a reflection symmetry around ‘the present’ axis, those described by GBT and SBT do change: by ‘symmetrizing’ the growing block structure one obtains the shrinking block structure, and by ‘symmetrizing’ the shrinking block structure, one obtains the growing block structure. It thus seems that a simple operation, such as reflection symmetry, when applied around ‘the present’ axis on spatiotemporal structures, allows one to distinguish between two groups of A-theories of time: the symmetric theories (e.g., eternalism, presentism) and the asymmetric theories (e.g., GBT, SBT). As a first approach, an A-theory is called ‘symmetric’ if, when reflection symmetry is applied through ‘the present’ axis on the spatiotemporal structure it describes, we are left with an unchanged (or invariant) structure. Conversely, a theory is called ‘asymmetric’ if, when reflection symmetry is applied through ‘the present’ axis on the spatiotemporal structure it describes, we are left with a transformed structure.

Fig. 3.3

Reflection symmetry on A-theoretic structures

However, it might be objected that there are versions of eternalism for which reflection symmetry around ‘the present’ axis fails to deliver an invariant structure: (a) if time has a beginning but no end (or vice versa), and (b) if time has both a beginning and an end, but the present is not equidistant from them. For instance, take any time t in version (a), reflection symmetry around t does change the structure; it delivers a structure where time has no beginning but an end (or vice versa). Of course, it could be replied that this is no big deal, since the opposition between symmetric and asymmetric theories is only meant to carry out a first sorting: symmetric theories include classical forms of presentism and eternalism, whereas asymmetric theories include classical forms of GBT and SBT. In that sense, this opposition does not rule out the possibility of developing non-classical forms of eternalism, which do not satisfy the geometric criterion, provided that they can subsequently be distinguished from both GBT and SBT. That is fair enough, but a better reply would be to define symmetric and asymmetric theories admitting no exceptions. In this regard, appealing to a modal characterization of these theories³¹ could be salutary: a symmetric theory is a theory such that possibly always the structures it describes is reflection invariant; conversely, an asymmetric theory is a theory such that necessarily sometimes the structure it describes is not reflection invariant. The qualification ‘sometimes’ is there because (i) in a given world at the first moment of time (if there is one) the structure described by GBT is reflection invariant, and (ii) in a given world at the last moment of time (if there is one) the structure described by SBT is reflection invariant. Given this modal characterization, non-classical forms of eternalism (a) and (b) also fall under the scope of ‘symmetric theories’. By convention, ‘eternalism’ will refer to eternalism tout court (i.e. classical or not) in the remainder of the text.

Since spatiotemporal structures have no more fundamental features than geometric ones (these features are theoretically posited, after all), asymmetric theories (e.g., GBT, SBT) are naturally seen as better suited than symmetric ones (e.g., eternalism, presentism) to account for (at least) some intuitive differences between the future and the past. Whereas asymmetric theories provide, through the geometric features of the structures they outline, an immediate, fundamental, and relevant reason as to why the future intuitively differs from the past, proponents of the symmetric theories must provide further explanations, presumably involving local phenomena (e.g., entropy, irreversibility), to account for the same intuition. In particular, the asymmetry is called ‘relevant’ because, as will be made clear in Sect. 3.5, it seems required to accommodate, for example, the ‘no fact of the matter’ account of openness introduced in the previous chapter (Sect. 2.9). Of course, this does not mean that if one accepts an asymmetric theory of time, one has to invoke geometric features to explain one or another intuitive past-future time difference. As Ross Cameron (2015: 194) makes clear, a growing blocker can perfectly claim that the geometric structure she describes plays no role in the way time is commonly intuited. But, it seems that the most natural move for her is to take widespread intuitions of how the future may differ from the past as manifestations of the intrinsic time-asymmetry of her model.

However, it might be objected that this use of geometry is analyzable in ontological terms and, therefore, that the revisited picture does not genuinely differ from the traditional one. For instance, it might be claimed that to say that the past geometrically differs from the future is only a sophisticated way to say that the past exists, while the future does not. This would clearly be problematic, since the main reason why the traditional picture was abandoned is that one has no strong intuitions on whether the future or the past exists. As a reminder, there is no experiential way to differentiate between the past and the future being equally real and not being equally real. However, there are (at least) 3 reasons to think that this objection does not apply here. First, one can agree on the asymmetric nature of time, while disagreeing on what exists. For example, growing and shrinking blockers agree that necessarily sometimes the future geometrically differs from the past, while they always disagree about what exists (either both the present and the past, or both the present and the future). Second, it clearly appears that a theory such as ‘forward-branching time’ makes a geometric distinction between the future and the past (the future is branching, the past is singular), while this theory rests on an eternalist ontology (where both the future and the past exist) (cf. Sect. 2.8). Finally, although it should be acknowledged that reflection symmetry on spatiotemporal structures can hardly be operated without involving individuals (e.g., spacetime points, events, and objects), this does not imply that these individuals should be taken as ontologically primitive. As explained above, individuals play a heuristic role allowing for the description of geometric structures, which is not indicative of any ontological priority. It therefore seems that the main difference between the symmetric and asymmetric A-theories of time is not ontological, but structural (or geometric).

One immediate consequence of the revisited picture is that GBT is no longer to be seen as an ill-conceived hybrid. As a reminder, GBT is traditionally depicted as an intermediate between the polar opposites of eternalism and presentism, with the consequence that this theory accumulates the flaws that are identified in the two traditional models (cf. Sider, 2001: 12, Miller, 2013: 347). But, since eternalism and presentism are no longer to be defined in terms of whether the future and the past exist (because nothing in actual intuition answers to this question), GBT is not a mere mixture of eternalism and presentism (which by itself does not guarantee that GBT escapes the objections that are usually formulated against eternalism and presentism). In the revisited picture, what is essential to GBT is to be asymmetric, i.e. to say that necessarily sometimes the structure it describes is not reflection invariant. GBT is thus distinct by nature from eternalism and presentism. Another consequence is that eternalism and presentism are no longer to be seen as polar opposites, but rather as similar theories: to the question ‘Is there a geometric asymmetry between the future and the past?’, they both possibly never answer ‘yes’. Surprisingly, this leads to a conclusion close to that of the skeptics, who deny that there is a genuine dispute between eternalists and presentists (cf. Crisp, 2004; Ludlow, 2004; Meyer, 2005, 2011; Miller, 2013; Sider, 2006a). But, whereas the skeptics generally justify their claim by invoking the two interpretations of the universal quantifier ‘everything’ (tenseless or tensed), the suggestion here is to say that eternalism and presentism are similar with respect to some relevant geometric features.

In the McTaggartian picture revisited, the answer (‘possibly never’, or ‘necessarily sometimes’) provided to the question ‘Is there a geometric asymmetry between the future and the past?’ should therefore be considered an essential component of the classical A-theories of time. However, this is obviously not sufficient. First, as Maudlin (2007: 109–110) makes clear, space could contain some sort of asymmetry, but that alone would not justify, for instance, the claim that ‘Space is open’. The openness of the future underwrites claims such as ‘Anything can happen’ or ‘History is not written beforehand’, while a generic spatial asymmetry would not underwrite such locutions. Second, although the geometric component provides a clear distinction between symmetric and asymmetric theories, it does not allow us to distinguish between the various forms these theories may adopt. For example, it does not allow distinguishing between eternalism and presentism (which are both symmetric theories), nor between GBT and SBT (which are both asymmetric theories). Therefore, in order to get a complete categorization of the various A-theoretic views, another component, which does not concern the geometry but the evolution of the model, should be considered essential: the answer (‘yes’ or ‘no’) that A-theories provide to the question ‘Is temporal becoming (i.e. the creation of new things in the present) real?’.³² This second component allows one to distinguish between two new groups of A-theories of time: the pure becoming-views (e.g., presentism, GBT)³³ and the non-generative-views (e.g., SBT and eternalism).

Although the question ‘Is temporal becoming real?’ is of an ontological nature, it can be pre-theoretically evaluated, because, unlike the question ‘Do the future and the past exist?’, it concerns existence in the present that we therefore experience – by contrast, existence in the future and the past cannot be experienced. Thus, not only do we experience a difference between the future and the past, but we also experience that what is occurring (e.g., moments of times, events, etc.) has just been created – this is the idea that Temporal Becoming is intended to unpack. According to Henri Bergson, for example, when we are intuiting time we are primarily intuiting novelty and creation: “[…] we understand, we feel, that reality is a perpetual growth, a creation without end. […] Every human work in which there is invention, every voluntary act in which there is freedom, every movement of an organism that manifests spontaneity, brings something new into the world” (1944: 261). Formally, Temporal Becoming can be expressed as follows: S(∃x H¬∃y y = x), where H is the operator ‘always in the past’; this formula literally means: ‘sometimes, some things have never existed in the past’. This seems justified by the fact that we do experience things as moving from non-existence to existence and, although this is compatible with the exotic phenomenon of intermittent existence, the most plausible assumption is that those things have never existed in the past. It is worth noting that ‘to create’ is a non-transitive verb (as opposed to other verbs, such as ‘to avoid’ or ‘to prevent’, which are properly transitive in the sense that they link two noun-phrases to signify some relation between real objects). In that sense, a creation is not an action upon what is created, since what is created (e.g., an event) is not there until the productive process is finished (cf. Geach, 1973: 209). That explains why Temporal Becoming, which implies creation, is not available to eternalism and SBT: if always, everything has always existed (A(¬∃x P¬∃y y = x)), where P is the ‘past-tense operator’ (read as ‘it was the case that’), then nothing can be created. I thus suggest that the following A-theories should be identified with the conjunction of the two logically independent³⁴ answers they provide to both of these new questions – one concerning the geometry, the other the evolution of the temporal structure – as follows:

• Eternalism: possibly always the temporal structure of the world is reflection invariant (symmetric theory) & there is nothing such as temporal becoming (non-generative-view)

• Presentism: possibly always the temporal structure of the world is reflection invariant (symmetric theory) & new things are created in the present (pure becoming-view)

• SBT: necessarily sometimes the temporal structure of the world is not reflection invariant (asymmetric theory) & there is nothing such as temporal becoming (non-generative-view)

• GBT: necessarily sometimes the temporal structure of the world is not reflection invariant (asymmetric theory) & new things are created in the present (pure becoming-view).

Classifying the above theories this way offers a number of advantages. First, it provides an illuminating and comprehensive categorization of the A-theories of time. Second, whereas it makes presentism, SBT and GBT inconsistent with the classical B-theory by definition (geometric asymmetries and temporal becoming are both incompatible with the B-theory), it allows for two kinds of eternalism: A-theoretic (the moving spotlight) and B-theoretic (B-eternalism). Third, it draws on our intuitions by putting the focus on two questions whose specific answers can be confirmed (or refuted) through non-stipulative methods. Finally, and perhaps most importantly, it reveals the metaphysical singularity of GBT: this theory is not essentially a hybrid between two polar opposite views (eternalism and presentism),³⁵ but is an alternative to two symmetric models that mainly differ with respect to whether they accept (or not) Temporal Becoming. Thus, there are good reasons to abandon the traditional way of introducing the A-theories of time in favor of the new claims formulated above. Specifically, whereas the traditional definitions rely on a question – ‘Do the future and the past exist? – that calls for speculative answers, the new claims rely on two questions that can straightforwardly be evaluated by means of intuitions: ‘Is there a geometric asymmetry between the future and the past?’ and ‘Is temporal becoming real?’. A-theories should therefore be seen as the combinations of two components: one geometric, the other dynamic (cf. Fig. 3.4).

Fig. 3.4

Two definitional components for the A-theories

The situation may nonetheless turn out to be more complex than this for at least two reasons. First, one might argue that the two features above – relevant geometric time-asymmetry and Temporal Becoming – do not single out GBT. For example, these two features are compatible with the view that ‘sometimes, some things go out of existence’, which betrays C. D. Broad’s original claim that “[t]here is no such thing as ceasing to exist; what has become exists henceforth for ever” (1923: 69). A suggestion would therefore be to regard a further component as essential to GBT: the rejection of Annihilation. Formally, this can be expressed as follows: A(¬∃x F¬∃y y = x), where F is the operator ‘sometimes in the future’. This formula literally means that always, everything will always exist in the future and, therefore, prevents the block’s erosion. This suggestion is appealing, provided that one wants to strictly respect Broad’s intentions. But, one might want to adopt a more liberal stance and allow for other sorts of theories, e.g., ‘Partial-GBT’ (as opposed to Full-GBT), according to which Temporal Becoming holds whereas sometimes, some things will never exist in the future: S(∃x H¬∃y y = x) & S(∃x G¬∃y y = x), where G is the operator ‘always in the future’. It indeed seems that such a theory may, under certain conditions (which are not guaranteed by the two principles above), deserve the label ‘GBT’, since it may also depict a growth in ontology. Intuitively, for all times t, if there are more things created than things annihilated up to t, then we get a growing block model at t. Formally, considering the finite set C(t) of created things up to t, and the finite set A(t) of annihilated things up to t, it seems that the partial theory deserves the label ‘GBT’ iff, for all t, the cardinality of C(t) is greater than the cardinality of A(t). Conversely, if (and only if) the cardinality of C(t) is less than the cardinality of A(t), then the partial theory seems to deserve the label ‘SBT’ (cf. Figure 3.5).

Fig. 3.5

Full and Partial asymmetric structures

Admittedly, some philosophers might regard Partial-GBT and Partial-SBT with suspicion, insofar as (i) nothing guarantees that the set C(t) is finite, and (ii) the expressions ‘growing’ and ‘shrinking’ have a quite different meaning in full and partial theories, so that the labels ‘GBT’ and ‘SBT’ assigned to the latter might seem usurped. After all, if C(t) is finite, then given that time is dense, the times are not among the things that are created as time goes by. For comparison, suppose one focuses on the spatial size of things and claims that the view that the size of things constantly grows as time goes by is a version of GBT, it clearly seems that one’s claim would be wrong. In reply, although one should acknowledge that Partial-GBT goes against many versions of GBT, such as Correia and Rosenkranz’s version (cf. Sect. 4.4), it does not go against all versions of GBT. For instance, a growing blocker who says that growth concerns only the occupants of time (e.g., events, people, objects, etc.) would have no a priori reason to dismiss Partial-GBT. Of course, one could then question the motivation behind Partial-GBT, since GBT originally rests on the inexorable increase in the ontology of times to explain, for example, the passage of time. However, our question is not whether this view is motivated, but whether it is consistent.³⁶

Concerning the symmetric theories, some of them also seem to allow for at least two interpretations, one full and the other partial. In this respect, ‘Partial-eternalism’ corresponds to the rejection of both Temporal Becoming and Annihilation: A(¬∃x H¬∃y y = x) & A(¬∃x G¬∃y y = x). This form of eternalism is called ‘partial’, because it is compatible with intermittent existence: e.g., a thing exists for 1 s, then ceases to exist for 1 s, then comes back into existence for another second, and so on from all eternity. The full form of eternalism corresponds to the conjunction of the two following principles: A(¬∃x P¬∃y y = x) & A(¬∃x F¬∃y y = x). It is worth noting that Full-eternalism entails permanentism, i.e. the view that ‘always, everything always exists’: A ∀ x A∃y y = x (cf. Williamson, 2013: 4). By contrast, presentism intuitively comes in only one flavor: S(∃x H¬∃y y = x) & S(∃x G¬∃y y = x). For example, a presentist will typically claim that every living human being never existed before his birth and will never exist after his death. To sum up, if one thinks of C. D. Broad’s version of GBT, Full-GBT, as the only palatable version of the theory, then one has to count the rejection of Annihilation among the essential components of GBT (with the difficulty of making it pre-theoretically evaluable). But, if one wants to be more liberal and allow for partial theories, especially Partial-GBT, then the rejection of Annihilation must not be regarded as essential component (cf. Fig. 3.6).

Fig. 3.6

Full and Partial symmetric structures

A second reason why the situation may turn out to be more complex than what the revisited McTaggartian picture suggests is that it seems possible to reconcile an eternalist view with a time-asymmetry. For instance, Maudlin’s view of time is explicitly eternalist – “I believe that the past is real […]. I similarly believe that there is (i.e. will be) a single future” (2007: 108–109) – while it admits an irreducible intrinsic time-asymmetry – “I believe that it is a fundamental, irreducible fact about the spatiotemporal structure of the world that time passes” (2007: 107). This suggests that there is room for a midway position between the reductionist accounts of the asymmetry (e.g., those of Boltzmann, 2003, and Reichenbach [1956] 1971, which involve the increase of entropy) and the above ‘geometric’ account. Huw Price also points in this direction when he confesses that: “[l]ike Maudlin, I am a fan of Earman’s Heresy […]. I think that Earman is right to reject reductionism […]; but wrong to the extent that he believes that the answer might lie somewhere else” (2011: 286). To that claim, the most plausible reply is that, although Maudlin argues for an intrinsic and irreducible orientation of the universe, his view should not count among the asymmetric theories, at least as defined above. After all, Maudlin (2007: 108) explicitly denies that the time-orientation, as he conceives it, has anything to do with the geometric structure of spacetime (though it is not clear, at least to me, what intrinsic structures of spacetime, according to his account, actually yield such orientation).³⁷

In a nutshell, this section proposed to reconceptualize the classical A-theories of time in terms that make ineliminable reference to the geometric structures in which individuals (e.g., spacetime points, events, and objects) participate, by using theoretical claims that can subsequently be confirmed (or refuted) by experience. These claims allowed one to distinguish between the symmetric and the asymmetric A-theories of time. Then, the various forms these theories may adopt were identified thanks to two principles – Temporal Becoming and Annihilation – in charge of the evolution of the models. The revisited McTaggartian picture showed many advantages, including the power of generating ‘partial’ versions of eternalism, GBT, and SBT. Another advantage is that the revisited picture changed our perception of GBT, which is no longer seen as a hybrid between eternalism and presentism, but as a theory in its own right. Keeping this in mind, we can now focus on GBT and show that this theory seems suited to successfully accommodate the intuitive asymmetry between the open future and the fixed past (at least as characterized in the previous chapter).

3.5 The Growing Block Theory (GBT)

GBT was first set out in C. D. Broad’s Scientific Thought (1923). Originally, this theory was characterized as the combination of at least two thoughts: one concerns the geometry and the other the dynamics of the temporal structure of the world. Let’s introduce these two thoughts with Broad’s own words. First, “[i]t will be observed that such a theory [GBT] as this accepts the reality of the present and the past, but holds that the future is simply nothing at all. […] 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” (1923: 66). Second, […] when an event becomes, it comes into existence; and it was not anything at all until it had become. […] The relation between existence and becoming […] is very intimate. Whatever is has become,³⁸ and the sum total of existence is augmented by becoming” (1923: 68–69). Although these two thoughts are expressed in ontological terms, they can naturally be read as answers to the 2 definitional questions introduced in the previous section: ‘Is there a geometric asymmetry between the future and the past?’ and ‘Is temporal becoming real?’

To the first question ‘Is there a geometric asymmetry between the future and the past?’, the growing blocker necessarily sometimes answers ‘yes’. She clearly thinks of the time-asymmetry, not as a natural process (to be explained in psychological or thermodynamic terms), but as reflecting the geometry of spacetime itself. In that sense, the growing blocker takes the difference between the future and the past to be embedded in the structure of spacetime: just as in the ‘forward-branching time’ theory (cf. Sect. 2.8), the present is a point-like boundary, around which no reflection symmetry can be operated on fundamental spatiotemporal relations (and derivative spacetime points) without transforming the background structure. But whereas by ‘symmetrizing’ the forward-branching structure one obtains the backward-branching structure, by ‘symmetrizing’ the growing block structure one obtains the shrinking block structure. However, since there could have been a first moment of time, a more cautious characterization of GBT is to say that necessarily sometimes the structure it describes is not reflection invariant (asymmetric theory). Thus, according to GBT, what lies below ‘the present’ axis (viz. spatiotemporally related points) necessarily sometimes fails to be a structural reflection of what is (or precisely is not) beyond this axis. This geometric characterization of GBT does not collapse into an ontological characterization, because of the structuralist approach to the A-theories of time: ‘fundamentality’ ought to be construed in terms of geometric structures (especially spatiotemporal relations), not in terms of spacetime points (which only play a heuristic role in the description of the spatiotemporal structures). Therefore, assuming that A-theories primarily describe geometric constructions, the essential properties of which are theoretically posited (cf. Sect. 3.4), GBT appears different by nature from the traditional models, eternalism and presentism, which both describe structures that are possibly always invariant after a reflection symmetry is operated around ‘the present’ axis.

To the second question ‘Is temporal becoming real?’, the growing blocker also answers ‘yes’. She clearly thinks of some things (e.g., moments of times, events) as being created in the present. Just as presentism, GBT is therefore depicted as a pure-becoming view, which admits that sometimes, some things have never existed in the past: S(∃x H¬∃y y = x). As a result, GBT takes the present to be both changing and distinctive; it is defined as reality’s most recent accretion.³⁹ By being present, we (as living beings) are therefore located at the leading edge of the block, i.e. at the point of flux itself, where we undergo experiences of the creation of new moments of time.⁴⁰ But this is not the end of the story. According to Broad’s original version of GBT (Full-GBT), when new things come into existence they always remain in existence: “[t]here is no such a thing as ceasing to exist; what has become exists henceforth for ever” (Broad, 1923: 69). Full-GBT therefore requires an additional component to prevent the block’s erosion, the rejection of Annihilation: A(¬∃x F¬∃y y = x). Intuitively, if one removes this latter condition, there might still be a sense in which the theory deserves the label ‘GBT’, or more accurately ‘Partial-GBT’, provided that the sum of what has been created up to a time t is greater than the sum of what has been annihilated up to t. This can be expressed by the following formula: ∀ t, Card (C(t)) < Card (A(t)).

Taking C. D. Broad’s two thoughts seriously brings many benefits. For example, as Broad (1923: 65–66) himself makes clear, they jointly allow for two different senses in which an entity can be said to change its relational properties. Consider the two following cases: (i) Ted, the son of Marie, becomes taller than his mother, (ii) Ted ceases to be the youngest son of Marie. Intuitively, these two cases are very different by nature. In the first case, there are two (partially overlapping) life histories (T and M, say); the earlier sections of T have the relation of ‘shorter than’ to the contemporary sections of M, while the later sections of T have the relation of ‘taller than’ to the contemporary sections of M. So, this first case merely reflects a difference of relation between corresponding sections of two existing and temporally-extended entities. In the second case, the change is more substantial. When we state that ‘Ted is the youngest son of Marie’, we mean that ‘There is no entity in the universe such that it is both a son of Marie and it is younger than Ted’. So, when we state that ‘Ted has ceased to be the youngest son of Mary’, we mean that the universe now contains an entity, which did not formerly exist (and therefore could stand in no relation whatsoever to Ted), that satisfies both of these conditions. This second case does not merely reflect an evolution in a particular relation between two existing entities, but the coming-into-existence of an entity, a baby, which consequently starts to stand in certain relations to Ted. Whereas GBT has no difficulty in accounting for these two kinds of change, the same cannot be said for symmetric theories (e.g., eternalism, presentism), which possibly always treats the future and the past on a geometric par, and for non-generative-views (e.g., eternalism, SBT), which admits no ‘coming-into-existence’.

Moreover, Broad’s two thoughts jointly provide an intuitively appealing explanation for (at least some) local asymmetries, such as the increase in entropy.⁴¹ As has been argued, the many attempts to explain (at least some) intuitive past-future time differences thanks to the Second Law of thermodynamics are doomed to fail, because no asymmetry is to be found in the time-reversal invariant fundamental laws of physics (Sect. 2.6). An idea might therefore be to claim that the grounds for the increase in entropy are not to be found in the laws of physics, but rather in the temporal structure of the world as depicted by GBT. Accordingly, the role of the explanandum and the explanans are reversed: the thermodynamics asymmetry, instead of explaining the asymmetric nature of time, is explained by it.⁴² This explanation turns out to be indispensable if one wants to be able to distinguish between the initial and the final state of the universe. As Tim Maudlin makes clear: “[t]he atypical final state is accounted for as the product of an evolution from a generically characterized initial state […]” (2007: 133). In other words, the increase of entropy away from a low-entropy initial state is the product of a one-way evolution; absent such an evolution, there is no way of determining which state is which. This one-way evolution requires that there be a principle, such as Temporal Becoming, that provides a direction of time, and can therefore underwrite locutions such as ‘The universe evolves towards ever higher entropy’. To put it another way, the evolution of the universe (as we experience it) needs more than phenomenal laws to be explained; it needs principles by which these laws can be interpreted, and Temporal Becoming seems well suited to play this role. This explanatory reversal, if successful, blocks the physical possibility of a GBT world in which, although the block grows and the current slice causally brings into existence the new slice, entropy is decreasing, and we therefore have no record of past times but apparent records of future times (which turn out to be records, when the future time comes).⁴³ This is good news, since such a weird world could have served as a counterexample to the claim that the spatiotemporal structure, as described by GBT, is the ultimate explanans for our time-asymmetric intuitions. After all, some might have argued that, in such a world, it is the past that would have seemed open and the future fixed.

Finally, and more importantly for our purposes, Broad’s two thoughts jointly provide a solid basis to accommodate the asymmetry between the ‘open future’ and the ‘fixed past’, at least understood as a type of worldly (un)settledness to be expressed in terms of there being facts of the matter about what happened but not about what will happen (cf. Sect. 2.9). Indeed, in addition to the failure of physical determinism (cf. Sect. 2.5), the openness of the future requires a structural difference between the future and the past: necessarily, the future should sometimes not be a geometric reflection of the past. The reason is roughly that if the future was always a geometric reflection of the past and, therefore, was also composed of spatiotemporally related points, then no gap in the ontology would be found: facts about what will happen would supervene on the spatiotemporal structure, just as facts about what happened supervene on it. After all, assuming that nothing is more basic than structure (structuralism), then everything else (including facts about what did and will happen) has a derivative status, so that a structure and its geometric reflection – which share all their geometric properties – cannot allow for different types of facts to supervene.⁴⁴ To put it another way, if what lies above ‘the present’ axis (viz. spatiotemporally related points) always is the geometric reflection of what lies below it, then either both facts about what will happen and facts about what happened supervene, or none of these facts supervene – other possibilities are ruled out by the covariant nature of the supervenience relation. As a result, if one wants to exclude facts about what will happen from our ontology – as is required by the ‘no fact of the matter’ account of openness – then one has to adopt an asymmetric A-theory of time.

An immediate reply might be that the former condition is too strong, since nothing a priori prevents presentism – which has been introduced as a symmetric A-theory of time – from accommodating the ‘no fact of the matter’ account of the openness of the future. After all, just as GBT, presentism implies that there are no facts of the matter about what will happen. Therefore, assuming that physical determinism is false, presentism can also allow for a great variety of senses in which the future can be called ‘open’, including the radical sense according to which time could come to an end (with no ontological commitment to future things standing in the way). In this regard, GBT therefore appears to be in no better position than presentism. This is a fair point. However, only GBT can avail itself of the ‘no fact of the matter’ account of openness, while keeping the past fixed: for presentism, if the future is open (partly) because there are no facts of the matter about what will happen, so must be the past. In other words, although the ‘no fact of the matter’ account of the openness of the future is available to presentists, they cannot endorse it without acknowledging that the past is open in the very same sense, in which case they can no longer account for the asymmetry between the ‘open future’ and the ‘fixed past’ (cf. Correia & Rosenkranz, 2018: 116). Therefore, insofar as the asymmetry has to be preserved, GBT is much better positioned than presentism to accommodate the open future.

Is it sufficient to adopt an asymmetric A-theory of time to accommodate the asymmetry between the ‘open future’ and the ‘fixed past’ (as characterized above)? The answer is obviously negative (and so even in an indeterministic context). For example, SBT is an asymmetric theory, but since it takes all of what exists to have always existed (A(¬∃x P¬∃y y = x)), it cannot be reconciled with an open future (cf. Sect. 2.9). As a reminder, if my grandson (who is neither located in the present nor in the past) exists, then his existence 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 (cf. Sect. 2.5). Likewise, forward-branching time is an asymmetric theory, while this theory was shown incapable of capturing a genuine notion of openness that does not arise from our non-neutral perspective on time (cf. Sect. 2.8). Thus, claiming that necessarily the future is sometimes not a geometric reflection of the past is not sufficient to accommodate the intuitive asymmetry in openness between the future and the past; what is further required is a principle that involves the creation of new things in the present and, thereby, excludes that all of what exists has always existed, namely Temporal Becoming: S(∃x H¬∃y y = x). Specifically, Temporal Becoming, when combined with physical indeterminism, allows that some new things are created in the present, while (at least) some of them are not made inevitable by how things located in the present or the past of now are or were (and therefore excludes that all of what exists was predetermined). In a nutshell, assuming physical indeterminism, the combination of some specific geometric properties plus Temporal Becoming makes GBT better positioned than its rivals to accommodate the asymmetry between the ‘open future’ and the ‘fixed past’.

From a wider perspective, it thus seems that GBT does a good job of vindicating the way the temporal structure of the world is pre-theoretically apprehended. Specifically, it satisfies our implicit representation of the future’s being open. First, GBT depicts temporal reality as asymmetric, which provides a ground for our intuition that the future differs from the past in various respects, including openness and fixity. Second, GBT is the only theory that can avail itself of the ‘no fact of the matter’ account of openness, while keeping the past fixed. For, if presentists say that the reason why the future is open is that there is no fact of the matter about what will happen, they must acknowledge (on pain of arbitrariness) that the past is open in the very same sense; after all, they think that there is no fact of the matter about what happened either. So, assuming that the openness of the future is a case of worldly unsettledness that must be expressed in the terms of the ‘no fact of the matter’ account (cf. Sect. 2.9), it appears that GBT has a decisive advantage over presentism: it preserves the asymmetry that grounds our intuition. Of course, this is not enough to explain the emergence of certain of our practices, emotions, attitudes, and observations that are time asymmetric. This would require further psychological investigations. But this is enough to give a metaphysical basis to the intuition (understood as a pre-theoretic representation of the temporal structure of the world) that is manifested by these practices, emotions, attitudes, and observations.

An observation could be that our phenomenology and practices can be explained by the fact that we do not know what the future will be like. For instance, the reason why it makes good sense to deliberate about what to do in the future but not in the past, or to think that we can causally influence future events (insofar as they counterfactually depend on us) in a way that we cannot influence past events, is that we have past records and no future records. This observation is reinforced by the fact that ontology does not seem to be relevant in that matter: we have no evidence that the future does not exist; so, this ontological feature can hardly be involved in the explanation of our phenomenology and practices. A difficulty might then be the following: since this kind of epistemic explanation is just as available to eternalists and presentists as it is to growing blockers, it may seem that GBT has no advantage over the main competing theories (viz. eternalism and presentism), at least in this respect. As a reply, I do not deny that knowledge asymmetry may play an important role in explaining our phenomenology and practices, but I insist that this kind of explanation is at best intermediate. It has then to be explained where the knowledge asymmetry comes from. In this last respect, GBT has an immediate explanation that is neither available to eternalists nor to presentists: the knowledge asymmetry is grounded in the geometric features of the spatiotemporal structure. One might reply that there may be other explanations. But, since the laws of nature are time-reversal invariant, and there is nothing fundamentally time-asymmetric in these laws, it is hard to see what explanation eternalists and presentists could resort to. Perhaps they could invoke the increase of entropy, but, once again, this at best postpones the problem: given that there is no directedness in fundamental physics, where does the thermodynamic asymmetry in time come from? (cf. Sects. 2.3, 2.6).

However, despite these attractive features, GBT (at least as defined above) is subject to (at least) four sorts of objections, which one may group as logical, theological, epistemic, and scientific. First, logical objections purport to show that there is something incoherent about GBT per se; for example, for the block to literally ‘grow’, some say, there must be a sensible answer to the question ‘At what speed does the block grow?’, while such an answer can hardly be found. Second, theological objections highlight the apparent tension between GBT (at least when combined with indeterminism) and God’s foreknowledge. Third, epistemic objections contend that GBT leads to radical skepticism; in particular, GBT would provide no basis for knowing that we are living in the present, i.e. on the leading edge of the block. Fourth, scientific objections claim that both the asymmetric nature of GBT and the principle of Temporal Becoming are incompatible with our best science, and so would demand a radical revision of the account of temporal structure provided by physics. In order to provide a defense of GBT, these four sorts of objections will be addressed. In particular, logical, theological and ‘soft’ scientific objections will find concise answers within the remainder of this section; epistemic objections will be the subject of further investigations in Sects. 3.6, 3.7, 3.8, 3.9, and 3.10; finally, the fourth chapter will be entirely devoted to the study of the tension between GBT and Relativity. Let’s focus on logical objections.

First of all, the so-called ‘rate objection’ was first imagined by C. D. Broad (1923) himself, and further developed by some B-theorists of time, such as Smart (1949: 484), Williams (1951a: 463–464) and Price (1996: 13). The rate objection can be formulated as follows: taking seriously the idea that the block grows, it must make sense to ask how fast it grows, which does not seem to be a sensible question.⁴⁵ As an analogy, when we ask how fast a car is driving, we ask for a rate of change specified in terms of units of length (for some interval of length taken as a unit) and units of time (for some interval of time taken as a unit). For example, if the car drives at 30 mph to the south (and maintains a constant rate), then after one hour the car will be 30 miles further south. To ask how fast a car is driving is therefore to ask how far the car will have gone when a certain period of time has passed. Of course, if GBT is true, the change that takes place as the block grows is not a spatial movement, and so when we ask how fast the block is growing we are not asking for a rate of change in terms of units of length and units of time. But then what are we asking for? As Huw Price says: “[s]ome people reply that [the block grows] at one second per second, but even if we could live with the lack of other possibilities, this answer misses the more basic aspect of the objection. A rate of seconds per second is not a rate at all in physical terms. It is a dimensionless quantity, rather than a rate of any sort” (1996: 13).

In reply, although one should acknowledge that there is no better answer than saying that the block grows at one second per second, one can argue that this answer is perfectly meaningful and, therefore, that it does not require any objectionable concession. When we ask how fast the block grows, we must mean to ask how the temporal state of things will have changed after a certain period of time has passed. In one hour’s time, for example, how will Barack Obama’s temporal position have changed? Clearly, Barack Obama will be one hour further into the future, one hour further from his birth, and one hour closer to his death. Admittedly, this answer is not interesting (or informative), but that is only because the question itself is not interesting (cf. Broad, 1959: 766). So, the block does indeed grow at the rate of one hour per hour, one second per second, or 3600 seconds per hour, etc. What is supposed to be objectionable about this answer? Price claims that a rate of change in terms of units of time and units of time is not really a rate, but rather a “dimensionless quantity”. But why should one believe this? As an analogy, consider the notion of a fair rate of exchange between currencies, which is usually defined by equality purchasing power: “[…] a fair exchange of euros for dollars is how many euros will purchase exactly what the given amount of dollars will purchase, and similarly for yen and yuan and so on” (Maudlin, 2007: 112). If one asks ‘What is a fair rate of exchange of dollars for dollars?’, the only sensible answer that can be provided is: one dollar per dollar. This answer is perfectly meaningful – if you think it is not, “[…] imagine your reaction to an offer of exchange at any other rate!” (Maudlin id). Thus, just as an exchange rate of one dollar per dollar is not free of any specified currency, a rate of one second per second is not a dimensionless quantity.⁴⁶ In a similar vein, Bradford Skow (2012: 388–389) argues that the rate at which the period of a pendulum changes can be expressed in seconds per seconds.

Another logical objection has to do with the point-like boundary conception of the present, which seems to leave no room for non-instantaneous events entirely located in the present.⁴⁷ After all, supposing that a non-instantaneous event e occurs at t, when t is present, e can only bear one of the 3 following relations to t: “[…] either (1) t is the last moment of e’s existence (i.e. e has just finished occurring at t), or (2) t is the first moment of e’s existence (i.e. e has begun to occur at t), or (3) e is presently occurring at t by straddling t (i.e. e has some temporal parts that are earlier than t, and some that are later than t)” (Diekemper, 2013: 1097). According to Joseph Diekemper, (2) and (3) are no options for GBT, since no event exists (or has temporal parts) later than the present moment. This leads to the counterintuitive conclusion that, given GBT, all non-instantaneous events are past. However, contrary to what Diekemper claims, it is not clear that GBT fails to allow for (2) and (3) – although these two options do indeed require that future (and therefore non-existent) temporal parts compose e. At least, provided a distinction (that will be detailed in Sect. 4.7) between two senses of ‘exist’ – the ‘straightforward sense’ in which instantaneous temporal parts exist at a time, and the ‘derivative sense’ in which non-instantaneous entities exist at a time – it seems that, even in a non-eternalist context, events can exist at the present time t without having all their parts at t. What is merely required is that one of their temporal parts exists at t (cf. Lombard, 1999). It therefore seems that speaking of ‘present non-instantaneous events’ could make sense, even for growing blockers.

Let us now turn to the theological objections. The most famous of them, which has been left pending in the previous chapter (cf. Sect. 2.4), is freely inspired from theological fatalism (i.e. the thesis that God’s foreknowledge and human freedom are incompatible): GBT combined with indeterminism is meant to imply an open future, while this seems incompatible with God’s foreknowledge. As a reminder, if there is a God who knows the entire future infallibly, then the future is fixed, because nothing can happen that can make God mistaken in his beliefs that the future will unfold in such or such a way. However, just as there are compatibilist strategies to reconcile God’s foreknowledge and human freedom, there must be strategies to reconcile God’s foreknowledge and the ‘open future’ view. In this regard, it might be argued that this theological objection rests on a confusion between two different notions: to be true, and to be inevitably true.⁴⁸ In brief, if the statement ˹There will be a sea-battle tomorrow˺ is true, God knows it; if it is false, God knows it. But knowing that the statement ˹There will be a sea-battle tomorrow˺ is true, say, does not make the statement inevitably true and, therefore, does not undermine the ‘open future’ view. Before detailing this strategy, it is worth saying a bit more about the relation between God and GBT.

First, let us agree that if God exists, he probably exists outside of time, since Christian tradition has always held that time had a beginning (Augustine, 2006: book 11, chap. 13). It therefore seems more appropriate to speak of God’s omniscience rather than of God’s foreknowledge. Second, one may wonder whether God’s timeless (or atemporal) existence is compatible with GBT. The answer seems to be ‘yes’. As Peter Geach, for instance, puts it: “[i]f God sees the world as it is, and the world is temporal and changing, then God must see the world as temporal and changing” (1973: 213). It can therefore be argued that God witnesses the growth of the four-dimensional block, and hence that the future does not exist, even from God’s perspective. Third, to the question ‘How God’s omniscience is to be understood in this context?’, a natural answer is the following: God knows the truth-value of all statements that have a truth-value, including the truth-value of all future contingents that have a truth-value. As a reminder, it was argued that future contingents should not be regarded as exceptions to Bivalence (they now have a classical truth-value), while this represents no threat to the ‘open future’ view (cf. Sect. 2.9). Accordingly, God knows whether the statement ˹The number of stars is even˺ is true (or false) and, more interestingly, he also knows whether the future-tensed statement ˹There will be a sea-battle tomorrow˺ (the truth-value of which is not predetermined by the present or the past) is true (or false).

Yet, the latter claim might seem at odds with the ‘open future’ view: suppose that God knows that the statement ˹There will be a sea-battle tomorrow˺ is true, since knowledge is factive, it seems that no peaceful alternative can take place tomorrow and, therefore, that the future is fixed (at least with respect to sea-battles). But is it really the case? Arguably, a clarification of what the factivity of knowledge amounts to allows one to answer ‘no’ to the latter question. Let me explain. Whereas the present truth-value of future contingents is not epistemically accessible to us, the same cannot be said for God. Assuming that future contingents are bivalent, the attribute of omniscience allows him to know which of them are true and which are false. So, admittedly God knows that the statement ˹There will be a sea-battle tomorrow˺ is true (supposing that it is). However, the factivity of knowledge states that ‘X knows that p’ entails ‘p’, not that ‘X knows that p’ entails ‘inevitably, p’. Therefore, although God knows that the statement ˹There will be a sea-battle tomorrow˺ is true, his knowing does not make this statement inevitably true and, therefore, does not undermine the ‘open future’ view. Otherwise, the openness of the future would rest on the mere epistemic fact that we (as human beings) ignore the truth-value of future contingents, which was shown unacceptable (cf. Sect. 2.3). This seems corroborated by the obvious fact that many contingent truths can be the subject of knowledge. For instance, I know that the statement ˹There are two beers in the fridge˺ is true; but my knowing that this statement is true does not make this statement inevitably true. There could have been 3 beers in the fridge, after all. Thus, once one has stated that the factivity of knowledge entails true and not inevitable true, it seems that the ‘open future’ view, which is implied by GBT plus indeterminism, and God’s omniscience can be retained altogether.

Let’s now focus on the scientific objections against GBT. The most striking ones concern the unreality of the future, which seems to require an objective notion of absolute simultaneity forbidden by the theories of Relativity (cf. Putnam, 1967; Rietdijk, 1966). However, the tension between GBT and Relativity deserves special attention and some additional material to be properly understood. It will therefore be treated at length in the last chapter of this book. Other scientific objections concern the principles at work in the definition of GBT, especially Temporal Becoming. It might, for instance, be argued that Temporal Becoming cannot serve as a definitional principle of a metaphysical theory that aims to describe the temporal structure of the world, since this principle was shown to be mind-dependent. According to Adolf Grünbaum (1967), for example, Temporal Becoming requires a notion of presentness that is not some physical attribute of events, but depends on mind-possessing organisms experiencing events at a time t such that at t, these organisms are conceptually aware of experiencing these events at t. Yet, as Grünbaum claims, this notion of presentness is ‘scientifically untutored’; one proof is that two events – such as a stellar explosion that occurred several million years before t, and a lightning flash originating only a fraction of a second before t – may both be qualified as occurring ‘now’ by an observer. Therefore, contrary to what the definition of GBT requires, Temporal Becoming cannot be thought as reflecting a process that occurs objectively, i.e. irrespectively of its relation to conscious organisms, since no event can be called ‘present’ without being experienced.

However, one may doubt that these scientific facts support Grünbaum’s analysis of presentness in terms of a conceptualized awareness of one’s own experiences. It indeed seems that these facts can be interpreted in a way that is perfectly consistent with the view that presentness is a mind-independent feature of events. As, for instance, Quentin Smith puts it: “[t]hese facts can be taken as suggesting that commonsense ascriptions of presentness to physical events are often in error about when these events are present” (1985: 111). In that sense, perhaps the conscious organisms in question are just mistakenly ascribing the time at which the visual effects of the stellar explosion are present to the explosion itself. If so, then the only revision that such scientific facts require is that “[…] the presentness ascribed by commonsense to the stellar events should be taken as a presentness of their visual effects” (Smith id).⁴⁹ In other words, if conscious organisms are mistaken about associating ‘absolute simultaneity’ with presentness, then the relevant revision need not be that presentness be regarded as mind-dependent, but that the ascriptions of presentness to a physical event e be construed relativistically, so that ‘e is now’ means ‘e is now in this reference frame’. After all, “[i]f the simultaneity of two events is relative to a reference frame and yet mind-independent [as Grünbaum believes], then there is no reason to doubt that the now cannot be also” (Smith id).

A related, though more general, scientific objection is to claim that, since sciences (and especially contemporary physics) do not take into account Temporal Becoming in their explanations, the explanatory success of GBT – which takes Temporal Becoming to be a definitional principle – is threatened. After all, as Hans Reichenbach puts it: “[i]f there is Becoming, the physicist must know it” ([1956] 1971: 16). This objection looks like the one raised against the fundamentality of the asymmetry between the ‘open future’ and the ‘fixed past’ (cf. Sect. 2.3). As a reminder, the latter objection was framed as follows: since neither the spatiotemporal model favored by physicists (the ‘block universe’ view), nor the fundamental laws of physics seem to reflect any asymmetry in time, it must be concluded that the asymmetry is at best a non-fundamental phenomenon, at worst an illusion. In the next chapter, I will provide some reasons to believe that Temporal Becoming could be restored in the physical context by a dynamics (the so-called ‘classical sequential growth’ dynamics), which usually enriches the causal set approach to quantum gravity (CST). But, for the moment, I can only repeat what has been said in the previous chapter: there is no reason (neither analytic nor empirical) to think that all fundamental phenomena are taken cognizance of by physics. Philosophers like Yuval Dolev (2006) and Mauro Dorato (2008), for instance, have warned against the so-called ‘exclusivity dogma’, namely the view that “[…] if something is not part of the ontology of physics, then it is not part of the world” (Dolev, 2006: 189).

At this point of the discussion, GBT seems to provide a friendly environment to accommodate various intuitive past-future time asymmetries, including the asymmetry between the ‘open future’ and the ‘fixed past’. The reason is roughly that GBT (i) has itself an asymmetric structure, in the sense that necessarily sometimes it does not treat the future as a geometric counterpart of the past (asymmetric theory), and (ii) allows for the contingent creation of new events in the present (pure becoming-view). Moreover, GBT appears to have the resources to overcome some immediate objections stemming from logic, theology, and contemporary sciences. However, the hardest part remains to be done. First, some philosophers have notoriously argued that GBT leads to an absolute form of skepticism, according to which we (as thinking subjects) have no way of knowing where we are temporally located. Second, GBT has often been accused of contradicting relativistic physics, by requiring, for example, an objective notion of absolute simultaneity. These two objections will be examined in that order. Specifically, in the following sections, I will argue that the former objection rests on an uncharitable rendition of GBT. This will give me the opportunity to explain how the existence in the past should be conceived, and why it sharply differs from the existence in the present. Then, in the next chapter, I will show that, even if GBT turns out to be inexpressible in a relativistic framework (which is doubtful), one can question the credentials of the theories of relativity and argue that our most fundamental physics is rather to be found in the nascent theories of quantum gravity, while some of them seem compatible with GBT.

3.6 A Skeptical Challenge for GBT

GBT is often criticized for not being a viable alternative to presentism because of the so-called ‘epistemic objection’. This objection was first pressed by Craig Bourne (2002) and further developed by David Braddon-Mitchell (2004) and Trenton Merricks (2006). In its original form, this objection purports to show that GBT leads to absolute skepticism about where we are temporally located. In particular, GBT would provide no basis for saying that our time is the objective present. But it is also possible to sharpen the epistemic objection in order to obtain an even more problematic conclusion: GBT would imply that we are, almost certainly, located in the objective past. In other words, the growing block’s edge is most likely located in the future of now. Although there are distinctive ways in which the epistemic objection can be formulated, we will focus on the following one.

GBT (at least in its full form) implies, through the rejection of Annihilation, that everything that is either past or present exists. For example, Napoleon exists (although he is not located at the present time), as well as everything that concerns Napoleon, such as his beliefs. Among Napoleon’s beliefs is presumably the belief that he is located in the present when, for example, he is crowning the Emperor⁵⁰. It indeed seems that, just as we believe that we are located in the present at the current moment, Napoleon believes that he is located in the present when he becomes the first Emperor of the French. In other words, GBT seems to imply not only that thinking subjects located in the objective past exist, but also that they believe that the time they exist at is the objective present. Yet, we obviously know that these thinking subjects are wrong in holding this belief, since we succeed them. In particular, we have no doubt that Napoleon is located in the past (he died two hundred years ago, after all). Of course, that does not mean that Napoleon has never been right to believe that he was located in the present: his belief was true in 1804, but is clearly false in 2022.

Given this, the question that Craig Bourne (2002), David Braddon-Mitchell (2004) and Trenton Merricks (2006) have asked to growing blockers is: ‘Assuming that GBT is true, what guarantees that we, as thinking subjects, are located in the present?’. Perhaps, in the year 2120, some people look at us just as we look at Napoleon, and think: ‘these naive people believe that they are located in the present, while they are embedded in the past!’. In other words, we are in no better epistemic position than thinking subjects located in the objective past who are wrongly believing that they are located in the objective present, since “[…] we would have all the same beliefs […] even if we were past” (Bourne, 2002: 362). GBT seems therefore to lead to skepticism about our temporal localization. Specifically, this theory seems to provide no reason to believe that we are located in the present time.

Worse, the probability that our time is the objective present (and therefore that we are right to believe that it is) is vanishingly small. After all, the objective present might well be located tomorrow, next year, or five billion years beyond the current moment, so that we are actually located in the objective past. Since all these alternatives should be regarded as equally likely (our beliefs would in each case be the same, after all), the hypothesis that our time is the objective present is almost certainly false (cf. Braddon-Mitchell, 2004: 200). In other words, the only possibility that we are located in the present does not carry any weight (in terms of probability) in the face of the multitude of possibilities that we are actually located in the past, so that we can assert without a doubt that we are living in the past. These two implications – skepticism about our temporal localization, and the quasi-certainty of being localized in the past – look absurd and must, according to some, lead us to reject GBT.

There are several ways to deal with this objection. First, it may be noted that there is something paradoxical in arguing that GBT leads to absolute skepticism about where we are temporally located and, at the same time, that GBT implies that we are (almost certainly) located in the objective past. It seems that these two implications cannot both be true: either a theory is guilty of generating doubts, or it is guilty of generating counterintuitive certitudes. But, clearly, if GBT implies that we are (almost certainly) located in the objective past, then it is simply wrong to claim that this theory provides no basis for knowing where we are temporally located: we are in the past, there is (almost) no doubt about this! Of course, one could reply that, although GBT implies that we are (almost certainly) located in the objective past, this does not rule out any form of skepticism; proponents of the epistemic objection seem mainly concerned with our exact location. For example, it might be argued that GBT provides no basis for saying whether we are located in the recent or the distant past. But, even if one concedes this, it is still wrong to claim that we have no way of knowing that our time is (or, in this case, is not) the objective present. Obviously, this preliminary remark does not put an end to the debate since, even taken on an individual basis, these two implications remain problematic for GBT. But it indicates that the epistemic objection might rest on some sophistic premises that may (and will) be challenged.

Second, it may be noted that the epistemic objection does not merely concern GBT, but is equally applicable to every A-theory of time that distinguishes between the notions of existing at the present time and just existing.⁵¹ For example, the epistemic objection is equally applicable to the moving spotlight theorists. In a certain sense, the problem is even more serious for them, since not only could their theory imply an infinite number of possibilities that we are located in the objective past, but also an infinite number of possibilities that we are located in the objective future. In an A-eternalist context, the probability of being localized in the objective present is therefore even lower than in GBT. By contrast, presentism seems to be immune to the epistemic objection: if no other times exist, then there is no puzzle in knowing that we are currently in the objective present (cf. Bourne, 2006: 24, Braddon-Mitchell, 2004: 199, Heathwood, 2005: 50, Zimmerman, 2008: 216).⁵² Of course, pointing out the flaws of other theories does not put GBT in a better position; but it shows at least that if we take the epistemic objection seriously, then we are compelled either to accept presentism or to abandon the idea of an objective present, which sounds suspicious. It would indeed be quite surprising that such a skeptical challenge, though embarrassing, could undermine any attempt to defend a non-presentist A-theory of time, even though sometimes some facts are indeed surprising.

Third, one could regard the epistemic objection as completely harmless. After all, as its name suggests, this objection is of an epistemic nature and, therefore, cannot pose a threat to GBT, which is a metaphysical theory. In that sense, GBT may perhaps lead to absolute skepticism about where we are temporally located (or even to the quasi-certainty that we all are temporally located in the past), but this does not imply that GBT is false. What we can (or cannot) know about our temporal location has no impact on the temporal structure of the world. Assuming that the world is such as growing blockers claim, we might have no choice but to accept skepticism as an unfortunate consequence. This reply sounds acceptable, but since my defense of GBT rests on a concern for accommodating a basic intuition we have regarding the nature of time (the future is open while the past is fixed), it would surely be problematic to end up with a theory that implies the truth of positions as counterintuitive as skepticism. Worse than this: if the skeptical conclusion is accepted, the openness intuition for accepting GBT in the first place is undermined, because the future is open only when one is at the present – if I am deep into the past of the block, the future (or at least my immediate future for as long as the present is in my future) is closed.

Finally, and perhaps more interestingly, one may want to properly address the skeptical challenge raised by the epistemic objection. To this end, many options have been considered. I will develop and discuss three of the most interesting ones: Merricks (2006), Forrest (2004), and Correia and Rosenkranz (2018). Then, I will submit my own solution based on the continued existence of bare particulars. From a more general perspective, the presentation of my own solution to the skeptical challenge raised by the epistemic objection will give me the opportunity to explain (i) how existence in the past should be conceived, and (ii) why existing in the past differs sharply from existing in the present.

3.7 Three Unsatisfactory Attempts to Meet the Skeptical Challenge

A first solution to the skeptical challenge is due to Trenton Merricks (2006), who argues that the epistemic objection relies on an uncharitable interpretation of what beliefs, such as ˹I am sitting here at the present time˺, are about. After all, assuming that a belief about the present cannot occur instantaneously, the growing blocker might have no choice but to concede that such beliefs are never (not even for an instant) true, which sounds implausible.⁵³ Merricks therefore proposes to distinguish the ‘objective present’ (i.e. the growing edge of reality) from the ‘subjective present’ (i.e. an indexical, like ‘here’ or ‘this place’). According to him, growing blockers should say that Napoleon’s beliefs like ˹I am crowning the Emperor at the present time˺ are always about the subjective present, so that such beliefs can be true even though Napoleon is not on the edge of reality. Similarly, growing blockers should say that everyone else’s beliefs about ‘the present’ are in fact beliefs about the subjective present, which prevents GBT from implying that every belief about the present is almost certainly false. In brief, Merricks argues that GBT should be regarded as a hybrid between the A- and the B-theory of time: growing blockers should agree with B-theorists that ‘the present’ is typically an indexical (i.e. the present is typically a matter of perspective), and they should agree with A-theorists that, in addition, there is an objective present (the growing edge of reality) used when GBT itself is being discussed.

However, as Merricks himself points out, the distinction between the ‘objective present’ and the ‘subjective present’ detracts GBT from its original purpose: to provide a natural view of time. The distinction between the ‘objective present’ and the ‘subjective present’ calls for other distinctions, especially between the ‘objective future’ (i.e. the time which is not yet part of being) and the ‘subjective future’ (i.e. the future that follows the subjective present).⁵⁴ In particular, growing blockers must acknowledge that, just as our typical beliefs about the present are in fact beliefs about the subjective present, our typical beliefs about the future are in fact beliefs about the subjective future. For example, we are certainly right to believe that ˹The discovery of a cure for cancer is in the future˺, provided that by ‘the future’ we mean ‘the subjective future’. After all, for all we know, this discovery is in the objective past! As a result, it is only philosophers of time, while they are discussing GBT, who use ‘the future’ to mean ‘the time beyond which nothing exists’. But this is clearly problematic, since it is our ordinary beliefs about the future (not philosophers’ ones) that GBT is meant to guarantee by stating that nothing exists beyond the present! It therefore seems that as soon as GBT distinguishes between two notions of the present – objective and subjective – it betrays the ordinary intuitions that initially made this theory attractive.⁵⁵

Another reason why Merrick’s suggestion is not appealing is that it makes every typical belief about the present trivially true, while – assuming that non-present people may also have such beliefs – we clearly think that they are wrong in holding them. Specifically, if all our typical beliefs about the present are in fact about the subjective present (which is to be understood as an indexical that merely refers to ‘the moment at which these beliefs are held or uttered’), then we cannot be wrong in holding these beliefs. People at any location in spacetime are trivially right to believe (supposing that they do) that they are located in the present, since all that this belief requires to be true is to be held or uttered. Yet, supposing that Napoleon has the belief that the time he exists at is the present, it seems that he is wrong. Napoleon is obviously not located in the present and, therefore, he is wrong to believe (supposing that he does) that he is. In other words, not only do we think that we are right when we believe we are located at the present time, but we also think that people existing at other times (e.g., Napoleon) are wrong in holding this belief. It therefore seems that as soon as one admits that we can have the belief that we are located at the present time without being actually located at that time, one should allow for the possibility of being wrong in holding this belief. In brief, it seems that either only people being actually present can have the belief that they are located in the present, or every person can have this belief (including non-present ones) but with the risk of being wrong in holding it.

A second solution to the skeptical challenge is due to Peter Forrest (2004), who claims that the epistemic objection relies on a mistaken assumption, namely that both past and present beings are conscious and, therefore, presumably think that the time they exist at is the objective present. According to his highly controversial ‘dead past hypothesis’, consciousness is a phenomenon which emerges only at the edge of the growing block; it is a by-product of what Forrest calls the “causal-frisson” (2004: 359). If we believe that we are located in the present then we are necessarily right to believe it, since, if we were located in the past, we would not believe anything – we would be zombies (devoid of consciousness). As Forrest puts it: “[l]ife and sentience are, I submit, activities not states. Activities only occur on the boundary of reality, while states can be in the past. […] The past is […] dead” (2004: 359). Thus, according to Forrest, Napoleon exists and he is like us in some respects (e.g., he is a physical entity just as we are), but he is not like us in all respects, as, in particular, he is not conscious. Of course, this is not to say that Napoleon has never been conscious; he was conscious when the time he exists at was the boundary of reality, since it is precisely the fact of being on the boundary of reality that gave him consciousness. However, in 2022 Napoleon is a zombie, while we are not. We can therefore be sure (by introspection) that we are located in the present (cf. also Curtis & Robson, 2016: 77–78).

Nonetheless, although Forrest’s response certainly overcomes the epistemic objection, the ‘dead past hypothesis’ brings its own range of problems. First, this hypothesis seems incompatible with GBT’s claim that there always was an edge of reality, including at times when there was no consciousness at all (e.g., 4 billion years ago): if consciousness were a by-product of the ‘causal frisson’, then consciousness should be observed at all times, which is obviously not the case. Of course, Forrest might reply that the ‘causal frisson’ is merely one of the many necessary conditions for consciousness to emerge. But then, it is not clear what further conditions must be met. Second, the ‘dead past hypothesis’ entails that presentness generates consciousness in a non-trivial sense. There are indeed many philosophers who argue that “[…] there is no interesting connection between consciousness and presentness” (Meyer, 2016: 151). Worse, there are even philosophers who defend the exact opposite view, i.e. that if there were no judgmental awareness, then there would be no presentness: “[a]n event’s occurring now depends on someone’s being judgmentally aware of it now” (Baker, 2010: 32, see also Grünbaum, 1967: 17).⁵⁶ This is certainly not the place to settle this debate, and we do not want GBT to commit us to any controversial theory of the emergence of consciousness; so it seems preferable to reject the ‘dead past hypothesis’.

A further objection against the ‘dead past hypothesis’ is most famously put forward by Christopher Heathwood (2005): if the ‘dead past hypothesis’ is true, it makes it difficult for growing blockers to explain how statements attributing consciousness to past beings can be true now. In particular, given the classical conception of the grounding requirement on tensed truths (the truth-value of tensed truths must be grounded in how things located in the present are), it seems that nothing can make true a statement such as ˹Napoleon was conscious when he crowned the Emperor˺ (which is surely a present truth, though it is expressed in the past tense). After all, according to the ‘dead past hypothesis’, things are such that Napoleon exists but is not conscious of crowning the Emperor.

However, it seems that Correia and Rosenkranz’s relaxed conception of the ‘grounding requirement on tensed truths’ (introduced in Sect. 2.9) allows one to solve this issue: 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. In particular, it seems that the truth of the statement ˹Napoleon was conscious when he was crowning the Emperor˺ merely requires that things have once been that way, i.e. that Napoleon has once been conscious of crowning the Emperor, which is something Forrest explicitly endorses. As has already been said, Forrest argues that past beings were conscious when the time they are at was the ‘boundary of reality’. It therefore seems that Correia and Rosenkranz’s relaxed conception of the grounding requirement on tensed truths provides the resources needed to protect the ‘dead past hypothesis’ from Heathwood’s objection.⁵⁷

Finally, a third solution to the skeptical challenge is due to Correia and Rosenkranz (2018), who argue that the epistemic objection rests on an uncharitable rendition of the growing block view: “[…] to say, on the one hand, that the past is real (exists), and hence that so are (do) the events that once occurred, is not to say, on the other, that past events are still occurring” (2018: 89). There indeed seems that behind each formulation of the epistemic objection lies the presumption that, according to GBT, past beings (e.g., Cesar, Napoleon) still believe that they are in the objective present⁵⁸ – which sounds absurd, since these people are long dead! This presumption clearly distorts the tensed metaphysics underpinned by GBT: the block is not like a “[…] multi-storey building, with lower floors corresponding to the more distant past, where what happens on each floor is still happening, even if it is not happening on the last floor” (2018: 89). The solution proposed by Correia and Rosenkranz is to regard ‘occurring’ as a temporary property that an event, such as ‘Napoleon is having conscious thoughts’, once had at some time earlier than now, but no longer has now (without this event having ceased to exist). It indeed seems that C. D. Broad’s original view can allow for this solution, since it is anyway committed to temporary properties (that an event once had, but no longer has), such as being new. Therefore, contrary to what is presumed in the epistemic objection, it does not follow from GBT that if once Napoleon believed himself to be in the objective present, he is still believing so.⁵⁹ Assuming that there are temporary properties, it can be argued that, whereas we believe that our time is the objective present, Napoleon (who still exists in the past) once had this belief but no longer has it. In short: events can cease to occur without ceasing to exist.

However, although one may agree with Correia and Rosenkranz (and with Forrest) that past beings no longer have belief about the present (or about anything else), it is far from clear that one can always distinguish between the existence of an event and its occurrence. As Peter Geach puts it: “[o]bviously we cannot take this seriously: an actor can be distinguished from his appearance on the stage but we cannot distinguish an event on the one hand and the occurrence or emergence or appearance or taking place of the event on the other hand” (1973: 210). Of course, Correia and Rosenkranz might reply that their theory does not involve non-occurring events, but only events that do not occur at all times at which they exist. However, this reply is not satisfying. This becomes evident when considering a particular event, such as a pain (e.g., a headache): how could a pain exist at a time without being painful at that time? This sounds like a category mistake. A pain, at least as defined by the International Association for the Study of Pain, is “[…] an unpleasant sensory and emotional experience associated with actual or potential tissue damage, or described in terms of such damage” (IASP, 1994: 209).⁶⁰ In other words, pains are subjective; their existence depends on feeling them. There is no time at which pains exist without being felt. Yet, Correia and Rosenkranz explicitly integrate into their ontology pains that are no longer painful. As they put it: “[one might want to] reject the idea that insofar as the past pain still exists, it still is painful, just as we reject the idea that insofar as WWI still exists, people are still dying in the trenches” (2018: 90). Thus, although Correia and Rosenkranz’s solution to the skeptical challenge rests on a fair point (GBT does not imply that events that once occurred are still occurring), it must be rejected on pain of generating paradoxical entities (such as pains that are not painful at all times they exist).

3.8 An Anti-Essentialist Picture of Kinds

Generally speaking, it seems absurd to claim that when objects and events pass from being present to being past, they merely change with respect to their A-properties (i.e. they do not undergo any other alteration whatsoever). As Dean Zimmerman puts it: “[e]verybody knows that when events and things ‘recede into the past’ they are very different from the way they are when present” (2008: 221). It is therefore uncharitable to presuppose – as Zimmerman (2011), Sider (2011), Merricks (2006) and others do – that GBT implies that dead people are currently believing things. If it was really a consequence of GBT, there would not be a single philosopher to defend this theory! Hopefully, GBT offers room for arguing that objects and events, when they are present (i.e. on the edge of the block), are somehow different from the way they are when past. Of course, this difference could be thought as being merely extrinsic. For example, it might be argued that present and past things merely differ with respect to their temporal location: for objects and events, to become past is just to cease to be located at the last time. However, although this is a straightforward option for growing blockers, it leads to the same category mistake that was found in Correia and Rosenkranz (2018). For, to say that the difference between present and past things (e.g., present and past pains) is merely extrinsic is to say that things do not intrinsically evolve by becoming past, and therefore that they belong to the same natural kind (e.g., pains) when present and past, while past pains are not painful anymore. Indeed, since membership in a natural kind is (partly) grounded in sharing natural properties, which are usually taken to be intrinsic properties (cf. Bird & Tobin, 2017: §1.1), it seems that no two entities sharing all their intrinsic properties can belong to different natural kinds. This is not acceptable: either a pain is painful at each time it exists, or it is not a pain. That is why it seems preferable to maintain that becoming past involves alterations in a thing’s intrinsic properties, to such an extent that it ceases to belong to its natural kind: a former pain is neither a pain that no longer exists (presentism), nor a pain that still exists but is not painful anymore (Correia and Rosenkranz), it is no longer a pain.

This option was considered by McTaggart himself when he wondered whether “[…] the change consisted in the fact that an event ceased to be an event […]” (1908: 459). Although McTaggart promptly rejected this option, on the ground that “[a]n event can never cease to be an event” (natural kind essentialism), it is worth reconsidering it. Natural kind essentialism is the view that membership of a natural kind is essential to its members: if a belongs to kind K, then it is an essential property of a that it belongs to K (cf. Fine, 1994; Kripke, 1980). According to this view, a pain is essentially a pain, and gold is essentially gold. Hence, a pain is always if anything a pain, and gold is always if anything gold.⁶¹ However, natural kind essentialism (at least as stated above) is presumably too strong. For example, in chemistry, it is readily acknowledged that “[…] a nucleus of neptunium-239 may undergo beta decay, in which one of its neutrons emits an electron leaving a proton” (Bird & Tobin, 2017: §1.3). As a result, the nucleus in question has one more proton and, therefore, is no longer a nucleus of neptunium-239 but a nucleus of plutonium. Yet, it is intuitively the same nucleus (in the numerical sense of the term) that persisted through this transformation. The nucleus has thus retained its identity while undergoing a change of natural kind.⁶²

Another example concerns biology, and especially Ernst Mayr’s influential biological species concept. According to this concept, species are “[…] groups of actually or potentially interbreeding natural populations, which are reproductively isolated from other such groups” (1942: 120). As Mohan Matthen (2009) points out, this definition allows for the creation of new species by the advent of reproductive isolation, which will typically split existing populations.⁶³ Consequently, the existing organisms in at least one (but presumably both) of the newly isolated (sub-)populations will belong to a new species. As Matthen puts it: “[…] species membership is relational, and consequently, an organism can change its species during its lifetime […]” (2009: 95). Assuming that species are natural kinds, this case offers a second example of particulars changing their kinds.⁶⁴ Taking the two above counterexamples seriously, it seems that nothing a priori precludes that events may continue to exist, when no longer present, as a different kind of entity. For instance, ‘Napoleon is having conscious thoughts’ can be an event when it occurs in the present and be identical to something else when it is located in the past, without anything having ceased to exist. This option has two immediate advantages: (i) it seems compatible with GBT (since it involves no annihilation) and (ii) it does not generate paradoxical entities (such as events that do not occur at certain times they exist).

Moreover, our own experience seems to match with this anti-essentialist picture. We perfectly know what some intrinsic properties are like when they are present, especially the properties we grasp through our own conscious experience. For example, we all know what a pain, a sound, or a color feels like. By contrast, a past pain, a past sound or a past color are not being felt, and so they lack this phenomenal quality. Of course, as Dainton puts it, “[…] we do not know what the intrinsic character of a past experience is like, simply because as soon as an experience ceases to be present it is no longer experienced. But [he continues] we can be confident that, whatever this intrinsic character is like, it is different from that of present experiences” (2010: 20). Intuitively, the same reasoning can be applied to material things: “[…] although we know quite a lot about their causal and structural properties (e.g., the shape, size and mass of an electron […]), we have no knowledge of their non-structural intrinsic properties (e.g., what the intrinsic nature of a proton is like in itself). Given this ignorance, we certainly cannot rule out the possibility that the non-structural intrinsic properties of material things undergo changes when they become [past]” (Dainton id).

Taking seriously the idea that a thing undergoes an intrinsic alteration when it becomes past, the question that immediately arises is: ‘Which intrinsic property is altered?’. Timothy Williamson (2013) suggests that a thing that becomes past loses its concreteness.⁶⁵ In brief, he conceives reality’s dynamic nature as grounded in temporal shifts from non-concreteness to concreteness and from concreteness to non-concreteness. According to him, a pain is thus something before and after it occurs (namely a non-concrete pain), and it is concrete only while it is occurring. Of course, this does not imply that a non-concrete pain is an abstract entity (pace Sider, 2001: 127). As Williamson makes clear, ‘non-concrete’ and ‘abstract’ are not to be treated as synonyms. ‘Abstract’ has its own positive paradigms, such as numbers and directions. So, when a pain disappears (and therefore becomes past), it is not trans-formed into an abstract object; it merely ceases to be concrete. However, although this solution may look attractive, it has (at least) two drawbacks that I mention now.

First, since Williamson provides no perspicuous account of his notion of concreteness, his proposal is not fully intelligible. As he himself concedes: “[t]he term ‘concrete’ is used informally throughout this book. For present purposes, we need not decide between various ways of making it precise (being material, being in space, being in time, having causes, having effects, …)” (2013: 6). Without any further specification, it is therefore hard to make sense of Williamson’s proposal. Second, assuming that non-concrete things do not occupy any spacetime region (which sounds both conventional and respectful of Williamson’s intention), it is not clear that this proposal is available to GBT. Of course, one can conceive a Williamsonian version of GBT, according to which future things do not exist, present things exist concretely, and past things exist non-concretely. However, unless the past is to be thought as an empty place, this version of GBT renders superfluous the existence of the past, at least understood as a physical location (i.e. a place where concrete things can be located). If the present is taken to be the unique temporal location for concrete things, then there is no reason to assume that other temporal locations (such as the past) exist – these temporal locations would always remain empty, after all. It therefore seems that if one adopts the Williamsonian version of GBT, one must reject the view that some things can be temporally located elsewhere than in the present. This makes this version of GBT (i) very similar to certain versions of presentism, such as ‘thisness presentism’ (according to which past things survived by abstract entities: their thisnesses),⁶⁶ and (ii) difficult to reconcile with contemporary physics (according to which concrete things can be located elsewhere than now, just as they can be located elsewhere than here).

A Williamsonian reply could be that, although Socrates is not in space now, i.e. Socrates is not located at the present three-dimensional slice of the four-dimensional manifold (this is presumably the sense in which Socrates is non-concrete now), he does occupy a spacetime region now, in the sense that he was in space some years ago. In this regard, the spacetime region that Socrates occupies now is, for instance, wholly before the spacetime region that Napoleon occupies now. However, although one must acknowledge that ‘being in space’ (unlike ‘being in spacetime’) can be introduced as a relative notion and, therefore, that a thing can be located in spacetime now without being located in space now, this reply misses its target. The reason is that this should not be the sense in which growing blockers say that, for instance, Socrates is in spacetime. I mention two arguments in favor of this claim. First, even presentists (who deny the existence Socrates) would agree that Socrates was in space some years ago and, therefore, that he is located in spacetime now (in the above sense). Yet, since GBT and presentism might disagree on what is located in spacetime now (e.g., either both Socrates and Obama, or only Obama), it seems that ‘being in spacetime’ should have a more specific meaning within GBT, which entails that everything that is in spacetime now is also in space now. Second, supposing that a thing can be in spacetime now without being in space now (as permitted by the above sense of ‘being in spacetime’), it follows that the hundredth President of the United States (who does not exist according to GBT) does occupy a spacetime region now, simply because he will be in space in a few years. This is not acceptable. Growing blockers should therefore argue that everything that is located in spacetime now is located is space now, and hence that Socrates is still (and will always be) a concrete entity (pace Williamson).

So, if ‘concreteness’ is not the right answer to provide to the question ‘Which intrinsic property is altered when a thing becomes past?’, what could it be? As a first approach, the most plausible answer is ‘it depends’: although a thing that becomes past undergoes an alteration in some of its intrinsic properties, the intrinsic properties concerned by this alteration depend upon what kind of entity is becoming past.⁶⁷ There are indeed good reasons to believe that a person, a pain, and a stone do not change in the same way by becoming past, since they did not share the same bedrock of intrinsic properties in the first place. For example, while a person who dies (and therefore becomes past) presumably loses the property of being conscious, it would be absurd to extend this to all entities, since most of them have never been endowed with consciousness. Likewise, events seem to no longer occur when past, while this cannot be said about people or stones.

For now, all that can be said in order not to fall back into the pitfalls of Correia and Rosenkranz’s theory is that whatever the sort of alteration a thing that becomes past undergoes, this implies that this thing no longer belongs to its natural kind (rejection of natural kind essentialism). A person that is no longer conscious is no longer a person; an event that no longer occurs is no longer an event; and a pain that is no longer painful is no longer a pain.⁶⁸ Yet, just as it is the same nucleus that persists through the addition of a proton to become a nucleus of plutonium, these are the same things that persist through the passage of time to become past. There is therefore nothing such as ceasing to exist; when past, the same things continue to exist, falling under a different natural kind. Given this, the interesting question to ask is not ‘Which property is altered when a thing becomes past?’ (since the answer varies depending on what kind of thing is considered),⁶⁹ but rather ‘What remains of a thing that became past?’. For example, ‘What remains in 2022 of Napoleon’s belief that he is located in the present?’. In order to answer this question, I will introduce, in the next section, the notion of ‘bare particular’. This notion will be conceived, in a deliberately open-ended manner, as what is responsible for the continuity of existence of both continuants (people, tables, planets, etc.) and occurrents (events, processes, etc.), through both superficial change (e.g., becoming warm) and radical change (e.g., becoming past). It is worth insisting that bare particulars are merely intended to explain how existence in the past should be conceived, not to provide grounds for present truths about the past, since these grounds are already guaranteed by the relaxed conception of the ‘grounding requirement on tensed truths’ introduced in Sect. 2.9.

Before proceeding any further, it could be objected that involving bare particulars in the debate is not an alternative to Williamson’s view, but rather a way of making his proposal definite or precise: the shift from concrete to non-concrete can be understood as the shift from non-bare to bare. Supposing that one can accurately determine what the intrinsic properties are, the loss of which makes a thing turn from non-bare to bare, it seems that nothing prevents Williamson (who is not known as a friend of bare particulars) from claiming that the loss of these properties is precisely what makes a thing become non-concrete. In reply, two things can be said. First, it is not clear that this is an objection to bare particularism. As has been said, one of the major drawbacks of Williamson’s view is that it is not fully intelligible – it lacks a perspicuous account of the notion of concreteness. So, if bare particularism, while not being an alternative, helps lift the veil of mystery surrounding the term ‘concrete’, then it is surely worth considering it. Of course, the risk is to end up with two views, only one requiring the pseudo-exotic notion of a bare particular, which seems to be a decisive advantage for Williamson’s view. But, as will be shown, the notion of a bare particular is less exotic than it might seem: it merely refers to what resides over and above the properties of any continuant and occurrent whatsoever and, therefore, is an ontological free lunch for those who accept the classical theory of individuation (the substratum theory). Moreover, even if the notions of bareness and non-concreteness turn out to be co-extensive, one might prefer to work with the former, since it echoes a long-standing conception of change, according to which change is possible only if something always persists through any change that occurs.

Second, it is not clear that bare particularism can be understood as a way of making Williamson’s view definite or precise. Although it might seem difficult to answer the question ‘What are exactly the properties the loss of which makes a thing turn from non-bare to bare?’, one thing is certain: it cannot be the properties that make things concrete (at least assuming that only concrete entities occupy spacetime regions). As has been said, GBT requires that (at least) some past things are concrete, otherwise the past would be a superfluous empty place. So, if bare particulars are what remains of things that became past, then they must be concrete and, therefore, they cannot be confused with Williamson’s past things. Perhaps Williamson could reply that some non-concrete things do occupy spacetime regions. For example, consider the two following things: Wittgenstein’s possible daughter and Descartes. According to Williamson, whereas the former occupies no spatiotemporal region whatsoever, there are certain times (e.g., January 1, 1650) at which the latter is spatially located. There therefore is a sense in which Descartes, despite not being concrete, occupies spacetime regions. However, although it must be acknowledged that Williamson’s view allows one to distinguish between non-concrete things that have been spatially located (e.g., Descartes) from those that have never been (e.g., Wittgenstein’s possible daughter), this example misses its target. The times at which Descartes was spatially located (e.g., January 1, 1650) are the times at which Descartes was concrete. So, this example provides no reason to believe that, in Williamson’s view, some things are spatially located at the times at which they are non-concrete. In a nutshell, whereas Williamson thinks that Descartes was concrete but is not anymore (Descartes is not concrete now), the ‘bare particular’ theorist thinks that Descartes is concrete now and has always been so. There therefore seems to be no extensional overlap between the notions of bareness and non-concreteness.

3.9 Bare Particulars to the Rescue of GBT

If one wants to account for how things located in the past exist, it is worth considering the primitive notion of a ‘bare particular’. This notion comes from the substratum theory, according to which “[…] particulars are, in a certain sense, separate from their universals” (Sider 2006b: 387). More specifically, the substratum theory says that particulars and universals are only connected to each other by a relation of instantiation. That means that particulars do not have properties as parts; they instantiate them. As Ted Sider puts it: “[t]hey are nothing but a pincushion into which universals may be poked” (id.). John Locke speaks of them as the “I know not what” substrata ([1689] 1975, II, xxiii, §2), while Plato (2000) uses the term “receptacles” (Timaeus 48c-53c).⁷⁰ I personally prefer the expressions ‘bare particular’, ‘substratum’, or ‘thin particular’ (as opposed to ‘thick particular’ which refers to the fusion of a thin particular and its universals).⁷¹ In other words, a ‘bare (or thin) particular’ is the mereological difference between a thick particular and its universals. Whereas bare particulars play a predominant role in the individuation debate – they are usually posited to account for the identity and distinctness of particulars (cf. Bergmann 1967, Moreland 1998, Sider 2006b) – they might also, as we will see, be helpful in the philosophy of time.

Importing a notion issued from the individuation debate into the philosophy of time is less crazy than it might seem. After all, in the Physics (Book I, chap. 6), Aristotle (1999) himself connects the notion of a ‘material substratum’ (in which the properties exemplified by a particular inhere) to the question of change. He argues that any change must be analyzed in reference to an invariant substratum. However, it would be a mistake to claim that the notion of a ‘bare particular’ has an antecedent in Aristotle; for, he explicitly says that everything that exists (with the notable exception of the eternal substance of the unmoved mover) is a compound of matter and form (hylomorphism). Specifically, Aristotle distinguishes two types of change: sometimes a change is just a change in a characteristic or two, as when the cold bronze sphere becomes a warm bronze cube, and sometimes the matter itself changes and we are no longer dealing with bronze at all (cf. Cohen, 1996: 67–68). The first type of change is called ‘reciprocal’, since there can be a transformation back into the original stuff, whereas the second change is called ‘nonreciprocal’, since it is definitive. However, both types of change require something that survives the transformation (otherwise, the process would not be called ‘a change’), namely a substratum which is responsible for the continuity of existence – this substratum is matter (hyle), which is not to be understood as a bare particular, but as a pure potentiality. As Christopher Byrne explains: “[t]hese requirements apply to essential change just as much as to accidental change, for Aristotle insists that there is a persisting substratum in generation and destruction as well” (2018: 47). Of course, it is the second type of change (i.e. ‘nonreciprocal change’) that will be matter of great concern in the remainder of this chapter, since becoming past is, in every sense of the expression, a definitive process.

Against the substratum theory there is the bundle theory, according to which “[…] particulars are just bundles of universals” (Sider 2006b: 387).⁷² Although substratum and bundle theorists agree on much – e.g., they agree that both particulars and universals exist, and that a particular somehow has universals – they do not share the same conception of what a particular is. Whereas a bundle theorist affirms that a particular is nothing but all the universals it has (i.e. it is the mereological fusion of all its universals), a substratum theorist denies this. According to the latter, when you take a particular, and you mereologically subtract away all its universals, there is something left: a bare particular. So, assuming the principle of uniqueness of mereological fusion (no universals can have two fusions), the bundle theory and the substratum theory differ sharply over the possibility of exactly similar particulars: whereas a bundle theorist affirms that no two particulars can have exactly the same universals (since a particular is just the sum of its universals),⁷³ a substratum theorist affirms that distinct particulars can have exactly the same universals (since they will have distinct bare particulars, i.e. distinct non-universal ‘cores’). The benefits of adopting a substratum theory rather than a bundle theory will be detailed in the next section.

Now, assuming that bare particulars constitute a fundamental ontological category, it might be argued that, although becoming past involves alterations in a thing’s intrinsic properties (to such an extent that it ceases to belong to its natural kind), the bare particular of that thing will continue to exist. For example, if the Battle of Waterloo is conceived as a temporally-extended particular instantiating some properties⁷⁴ (e.g., having opposed France to the Seventh Coalition, having been won by the Duke of Wellington), then this battle will always be something when no longer occurring: a bare particular. This bare particular is what persisted through the intrinsic alteration that affected the battle of Waterloo when it became past. As an analogy, consider the case of a statue made of bronze, and suppose, for the sake of argument, that bronze is the substratum. The statue is, in that sense, bronze instantiating some properties (e.g., having the shape of a woman, being cast by Rodin). Now, suppose that this statue is melted so that all that remains is a warm bronze cube. Clearly, after such a process, bronze has lost some properties (e.g., it no longer has the property of having the shape of a woman, nor the property of being cast by Rodin). As a result, it can no longer be called ‘a statue’ (or perhaps only in a non-trivial sense by a bunch of contemporary artists). Nonetheless, bronze survived the transformation. Of course, this analogy has limits: whereas melting is a superficial (or reciprocal) change which does not affect bronze in its proper kind (bronze remains bronze), becoming past is a radical (or non-reciprocal) change which definitely turns every thick particular into a bare particular.

To the question ‘What remains of a thing that became past?’ a plausible answer might therefore be: a bare particular. An immediate objection is that, according to this answer, the proper name ‘Socrates’ seems to refer to two distinct entities: a thick particular ‘T’, which has gone out of existence, and a bare particular ‘B’, which is still with us. This poses at least two issues: (i) it is not clear whether Socrates should be identified with B, T or both B and T, and (ii) it seems that T’s going out of existence is incompatible with GBT, the full form of which rejects the principle of Annihilation. Let us start with the first issue. At first sight, it seems perfectly acceptable and convenient to say that Socrates is T, and that Socrates is B. The most natural view is indeed that Socrates came into existence in 469 BC, then lived as a thick particular until he drank the hemlock in 399 BC, and continues to exist as a bare particular since then. To put it another way, just as it seems that it is the same bronze that is a statue at t₁ and a warm cube at t₂, it seems that it is the same particular (Socrates) that is thick in 350 BC, and bare in 2022 AD. This natural view escapes, by the way, the second issue, since it does not imply any form of annihilation: there is simply a single entity (Socrates) which, although it has existed in two different forms (a thick particular and a bare particular), has never (and will never) cease to exist.

Unfortunately, things are not so simple, especially because if Socrates is both B and T, then it follows that B is T, which seems to betray Leibniz’s law. To illustrate, suppose that t is a moment at which Socrates was alive: at t, T has the property of being alive as a part, but at t, B does not have the property of being alive as a part. By the Principle of the Indiscernibility of Identicals (necessarily, if two particulars are identical, then they have all the same qualitative properties), it follows that B is not identical to T. This is analogous to a well-known situation in the metaphysics of constitution, which is usually introduced as ‘the puzzle of Tibbles the cat’ (cf. Burke, 1996; Geach, 1980; Wiggins, 1968). In brief, suppose that before us stands a cat named ‘Tibbles’. Before us is also that part of Tibbles which consists of all of Tibbles except his tail. Let us call that part of Tibbles ‘Tib’. Since Tibbles has a tail, but Tib does not, it follows, by the Leibniz Law, that Tib is not identical to Tibbles. Suppose now that Tibbles loses his tail. At this moment, we are inclined to say that Tib is identical to Tibbles. After all, Tib and Tibbles now occupy the same volume at the same time and, as David Wiggins puts it, “[i]t is a truism frequently called in evidence and confidently relied upon in philosophy that two things cannot be in the same place at the same time” (1968: 90). Hence, assuming that identity is not contingent, we are faced with a contradiction: Tib is and is not identical to Tibbles. Of course, claiming that either Tib or Tibbles has ceased to exist is not an option for growing blockers (at least given the full form of GBT) and, in any case, would be arbitrary. As Michael Burke makes clear: “[t]he identity of a cat surely is not tied to its tail. So Tibbles still exists. But surely Tib has not ceased to exist: Tib lost none of its parts” (1996: 63). So, what should we do?

First, it must be noted that the puzzle of Tibbles the cat does not only concern bare particularism, but any view that analyzes change in reference to an invariant substratum and, thereby, allows things to retain their identity while losing parts. Therefore, if one wants to reject bare particularism on this basis, one should be ready to endorse a view such as mereological essentialism, i.e. “[…] the doctrine that every part of an object, no matter how small, is essential to its identity” (Burke id), which brings its own range of problems. For example, how can mereological essentialism account for the fact that common-sense objects persist through change? Considering that bananas ripen and houses deteriorate, how can this view say that they are the same things, if they are not quite the same? Second, there is a battery of well-known solutions to the puzzle of Tibbles the cat, which strongly suggests that the above objection against bare particularism is not definitive. For example, some philosophers opt for four-dimensional entities whose parts may extend in time as well as in space (cf. Heller, 1990; Lewis, 1986; Sider, 2001), some others argue that identity is a contingent relation that may hold at some times but not at others (Gallois, 1990; Gibbard, 1975; Myro, 1985), Peter van Inwagen (1981) claims that there are no such things as arbitrary undetached parts, David Wiggins (1968) distinguishes between the ‘is’ of constitution and the ‘is’ of identity, etc. The question is then, ‘Which of these solutions are available to bare particularism within GBT?’ It would be difficult to provide an exhaustive answer to this question, but it a priori seems that at least two solutions could be retained: (a) relativizing numerical identity, and (b) distinguishing between two senses of ‘is’ (constitution and identity).⁷⁵

However, option (a), which amounts to saying that B was identical to T when Socrates was alive and that B is now distinct from T since Socrates died, has two major drawbacks: (i) it looks ad hoc (at least in the present context), and (ii) it forces one to reject the ‘constituent thesis’, according to which every thick particular has a bare particular (and some properties) as constituents, which is at the core of bare particularism (cf. Bailey, 2012). Of course, this is not to say that these drawbacks cannot be overcome. Niall Connolly (2015), for example, happily rejects the ‘constituent thesis’. He argues that the best version of bare particularism takes the relation between a substance (e.g., a tree) and its substratum to be identity, and not the relation of constitution. Nonetheless, a better option (which requires fewer concessions) is to preserve the ‘constituent thesis’, by arguing that when one says that Socrates is T and that Socrates is B (which again is perfectly acceptable and convenient), one actually means that Socrates constitutes T and that Socrates is identical to B. The distinction between these two senses of ‘is’ was first highlighted by David Wiggins (1968) and Peter Geach (1980). As, for instance, Wiggins puts it: “[t]he ‘is’ of material constitution is not the ‘is’ of identity. The tree is made of (or constituted of or consists of) W, but it is not identical with W. And ‘A is something over and above B’ denies ‘A is (wholly composed of) B’ or ‘A is merely (or merely consists of) B.’ If A is something over and above B, then of course A ≠ B, but the proper point of saying ‘over and above’ is to make the further denial that B fully exhausts the matter of A” (1968: 91–92). It is however worth noting that, according to Wiggins’ constitution view, the substratum W which constitutes the substance T is not to be under-stood as a bare particular, i.e. as something ‘over and above’ T, but as a ‘superinternal relation’⁷⁶ that organizes the parts of T. So conceived, the relation of constitution is distinguished from identity insofar as it is asymmetric: W constitutes T, but not vice versa.

Now that we have distinguished between the two senses of the word ‘is’ (constitution and identity), we can return to the case of Socrates and see how this applies to it. As a reminder, GBT (at least in its full form) commits us to the claim that T still exists now, just like B (rejection of Annihilation). A question then arises: ‘What are the properties that T now has?’. Certainly not those that were specific to Socrates when he was alive (e.g., being conscious, breathing, etc.). The most plausible answer is that T and B now have exactly the same properties. Taking this seriously, the situation is as follows: B has always been a bare particular (at least since it began to exist); on the other hand, T is bare now but has not always been so: when Socrates was alive, T was a whole constituted by (i) a bare particular (namely B) and (ii) properties such as breathing and being conscious. The situation is depicted in Fig. 3.7. An immediate objection is that this version of bare particularism is ontologically costly: it generates a colossal number of bare particulars. A reply could be that, from a qualitative point of view, the doctrine remains parsimonious, by keeping down the number of sorts of entities (it only involves thick and thin particulars). And, according to Lewis (1973a: 87), it is the only parsimony criterion one should consider.

Fig. 3.7

Bare and thick particulars at various times

Another objection is formulated by Andrew Bailey (2012). Roughly, this objection says that if one accepts ‘the constituent thesis’ (i.e. the thesis that every thick particular has two kinds of constituents: its properties and its bare particular), then one should abandon ‘the having thesis’ (i.e. the thesis that every thick particular has its properties by having as constituents properties that are instantiated by another of its constituents: its bare particular). Proof is that, taken together, these two theses imply that two co-located entities (the bare particular and its host thick particular) have the same properties, which sounds false. However, although persuasive, this objection exerts no pressure on the above view, since ‘the having thesis’ is not taken to be true. In general, a bare particular does not instantiate the properties had by its host thick particular (rejection of ‘the having thesis’); it merely has these properties in a derivative way. For example, Socrates only had in a derivative way the properties that one usually attributed to him (e.g., being conscious, breathing, etc.). Does this undermine the view as a version of bare particularism? It does not seem so, since other self-appointed ‘bare particular theorists’ reject ‘the having thesis’ (cf. Wildman, 2015).

The claim that what remains of a thick particular that became past is a bare particular looks attractive for the following four reasons. First, the notion of a bare particular is (at least in itself) economical: it is an ontological free lunch for those who accept the classical substratum theory of individuation, according to which particulars are not exhausted by the properties they exemplify, but are associated with a substratum. Second, the notion of a bare particular is familiar: it echoes a long-standing conception of change, according to which change is possible only if something always persists through any change that occurs. In this perspective, ‘becoming past’ should just be conceived as a radical (or nonreciprocal) type of change. Third, this view is compatible with GBT’s main imperatives: the possibility that thick particulars may continue to exist as a different kind of entity (a bare particular) is not excluded by the rejection of Annihilation (i.e. the ontological preservation of what is no longer present), which was characterized as an essential feature of GBT (at least in its full form). Fourth, bare particulars have a great explanatory power: they allow for a conception of the past – ‘the bare past’ – in which nothing occurs (e.g., there are no events, no movements, so that no property can be gained or lost) and, therefore, offer an appealing account for the fixity of the past. For all these reasons, it seems that bare particulars should be conceived as what is left of a thick particular when certain of its intrinsic properties were subtracted by the passage of time. Quentin Smith endorses a similar view when he claims that “[past particulars] are ‘bare particulars’ in the sense that they lack nonrelational, monadic properties” (2002: 132). But while Smith’s view (so-called ‘degree presentism’) attributes this ‘bareness’ to the fact that past particulars are only partly real,⁷⁷ GBT should not allow for degrees of existence: past and present particulars are just as real.

Unfortunately, as previously said, it seems difficult to identify one unique intrinsic property whose loss would make particulars turn from thick to bare, since thick particulars of various kinds (e.g., events, people, stones) do not share the same bedrock of intrinsic properties in the first place. Nonetheless, it seems possible to provide an informative criterion: the properties that a particular loses when it turns from thick to bare are (at least) the ones that make it belong to the natural kind to which it belongs when present. These are the properties in terms of which natural kinds are traditionally defined. For example, in June 1815, if it is the property of occurring that makes a thick particular, constituted by the battle of Waterloo, belong to the kind ‘events’ (Simons, 2003: 357), then it is at least this property that the particular in question loses when it becomes past. Likewise, in the fifth century BC, if it this the property of being a featherless biped (Categories, 3a 23–5), or the property of being a rational animal (Politics, 1253a 10), that make a thick particular, constituted by Socrates, belong to the kind ‘man’, then these are at least these properties that the particular in question loses when it becomes past. In other words, ex-thick particulars are free from all the properties that jointly define the natural kind to which they belonged when present. This is what turns them to bare. This criterion does justice to the idea that both continuants and occurrents continue to concretely exist when no longer present (rejection of Annihilation), but as a different kind of entity (rejection of natural kind essentialism) – a bare particular – which results from the alteration of some specific intrinsic properties they possess.

Taking this criterion seriously, an immediate question is: ‘Do things that cease to belong to their initial kind necessarily belong to a new kind?’. Or, to put it another way: ‘Are there particulars free from any natural kind?’. For cases of reciprocal change, the answer is quite obvious. For example, it is clear that a nucleus of neptunium-239 that undergoes beta decay (in which one of its neutrons emits an electron leaving a proton) does belong to a new natural kind after the transformation, namely plutonium. Likewise, given Ernst Mayr’s biological species concept, it is clear that reproductive isolation splits existing organisms of the new (sub-)populations into new species, which correspond to new natural kinds. But, the question arises in a more interesting way when asked about things that became past: ‘Do bare particulars, such as Socrates or the thick particular he constituted, still belong to a natural kind after Socrates’ death? The most plausible answer is ‘yes’. Aristotle, for instance, leaves no room for entities that do no not belong to any natural kind. But then, the question is: ‘To which natural kind do these particulars belong after Socrates’ death?’. The most straightforward answer is ‘the kind of bare particulars’ (which does not imply that bare particulars are, in themselves, natural kinds). This answer seems partly justified by the fact that Socrates, Napoleon, and WWI have some relevant properties in common, such as being a particular, being concrete, having belonged to another natural kind, etc.⁷⁸ Is it the end of the story? Perhaps Socrates and Napoleon should have more in common than Socrates and WWI (though they are all bare particulars). Perhaps there should be a kind to which both Socrates and Napoleon belong, but not WWI. Yet, I strongly reject this suggestion: there is no qualitative distinction among bare particulars. The reason is that all the properties that would be required to constitute kinds were lost through temporal change. Of course, this is not to say that one cannot distinguish between Socrates, Napoleon, and WWI. According to the substratum theory, the individuation is ensured by the bare particulars themselves.

Despite their attractive features, Ted Sider observes that there is a complaint against bare particulars: “[they] are widely regarded as the grossest of metaphysical errors” (2006b: 392). For example, it might seem that if a thing has no properties, then there is at least one property that this thing has, namely the property of having no properties, which renders the notion of ‘bare particular’ incoherent. An immediate reply is that if the objection is that bare particulars have no properties at all, then the objection is just wrong. Once again, the bare particulars involved in the above view of ‘how things become past’ do not need to be free from all properties, but merely from those that together make these things belong to the natural kind to which they belong when present. In that sense, bare particulars do have some properties, such as being a particular, being bare or being concrete – the nature of a bare particular is, by the way, given by the properties it instantiates.⁷⁹ In that respect, the expression ‘bare particulars’ is misleading; it does not mean that some particulars are entirely free from properties, but rather that properties are not constitutive parts of a substratum. As Bradley Rettler and Andrew Bailey make it clear: “[b]are particulars are ‘bare’ in at least this sense: unlike objects, they have no properties as parts” (2017: §3.2). In other words, the expression ‘bare particulars’ conveys the idea that the link between a substratum and the properties it bears cannot be a relation of constitution, but must be a relation of instantiation; otherwise the substratum (assuming it has no further constituents) would be just a bundle of properties.

A more charitable interpretation of the objection, then, is that if particulars were wholly distinct from their universals, it would be possible for there to exist truly bare particulars (i.e. particulars that instantiate no properties at all), while this proposal is incoherent. Again, truly bare particulars would have at least one property, viz. the property of having no properties. In reply, three things can be said. First, one can prevent the possibility of truly bare particulars through an appropriate conception of modality (though this does not seem desirable).⁸⁰ David Armstrong (1989), for instance, builds the impossibility of truly bare particulars into his theory of possibility. Second, a similar objection can be addressed to bundle theorists, since nothing a priori excludes the possibility “[…] where no universal is compresent with any universal, not even itself” (Sider 2006b: 392). Third, and perhaps most importantly, this objection rests on a confusion between sparse and abundant properties.⁸¹ In the abundant sense of ‘property’, each meaningful predicate corresponds to a property; so “[…] if we could predicate ‘has no properties’ of a thing, then that thing would indeed have a property corresponding to the predicate” (Sider 2006b: 392). But this is clearly not the relevant sense here; rather ‘property’ is to be understood in the sparse sense: just as being red or being red or round, has no property does not correspond to a property. As Sider puts it: “[j]ust as a thing can be red or round without having a sparse property of being red or round […], a thing can have no sparse properties without having a property of having no sparse properties. And of course, the substratum theorist’s universals are sparse” (id).

A further complaint might be that substratum theorists are unable to give a coherent account of the instantiation of universals, which is a major reason for rejecting their theory. As David Lewis puts it: “[c]onsider the predicate ‘instantiates’ (or ‘has’), as in ‘particular a instantiates universal F’ or ‘this electron has a unit charge’. No one-off analysis applies to this specific predicate” (1983: 353–354). However, although one must acknowledge that most substratum theorists remain silent on the predicate ‘instantiates’,⁸² it is not clear that such an analysis has to be provided. In particular, it seems that substratum theorists can argue that ‘instantiates’ is part of their ideology – this might even seem required, since postulating a dyadic universal of instantiation (to bind particulars to their universals) would at best postpone the need for primitive predication and, therefore, generate an uneconomical regress. Moreover, it is not clear that bundle theorists are in a better position: they need to take the predicate of ‘compresence’, i.e. the predicate that relates the universals had by a given particular to one another, as primitive. This indeed seems required in order (i) to say which fusions of universals count as particulars (e.g., there are fusions containing the universals of goldenness and mountainhood as parts, whereas there is no particular such as a golden mountain),⁸³ and (ii) to prevent that any universal had by a part of a particular is had by that particular (e.g., Geneva is a town, while Switzerland is not a town, though Switzerland has Geneva as a part).⁸⁴

A last complain concerns proper names. Against the descriptivist tradition (cf. Frege 1982), names are typically seen as having no linguistic meaning beyond their reference. Ruth Barcan Marcus (1961), for instance, argues that proper names should be regarded as ‘tags’, since they refer directly to their bearers, i.e. not by way of descriptions. Taking that for granted, the question that arises is: “[…] what it is, if not an associated description, that fixes what a name refers to [?]” (Reimer, 2019: §2.2). The most popular answer to this question is the so-called ‘causal theory of reference’, according to which (i) a name’s referent is fixed by an original act of naming, and (ii) subsequent uses of that name succeed in referring to that referent by being linked to the original act of naming via a causal chain (cf. Kripke, 1980). As Marga Reimer puts it: “[…] speakers thus effectively ‘borrow’ their reference from speakers earlier in the chain, though borrowers needn’t be able to identify any of the lenders they are in fact relying on” (2019: §2.2). This popular answer, however, might seem at odds with bare particularism. Suppose that the proper name ‘Socrates’ refers to a bare particular. Since bare particulars are typically taken to be causally powerless (causal powers are necessarily connected with natural properties, after all),⁸⁵ it might seem that the link between ‘Socrates’ and its referent is broken. As Keith Campbell puts it: “[a]ll causal action is exerted by way of the properties of things and all effects are effects on the properties of things. The substratum, precisely because it is without properties, including passive powers, ought to be totally immune to all causal activity” (1990: 9). In reply, one should insist on the fact that bare particulars being powerless does not imply that the reference-link is broken.⁸⁶ For instance, although Socrates is a bare particular, and therefore is powerless (after having been causally active, through a thick particular he constituted, for more than 70 years), we can still successfully refer to him. The reason is that our act of referring is causally linked to the original naming of Socrates (by which ‘Socrates’ became a rigid designator of that particular). Specifically, Socrates (via his initial baptism) is at the origin of a causal chain (which ensures that later uses of the name ‘Socrates’ succeed in referring to him), although he is devoid of all the properties in virtue of which he was (in a derivative way) causally active.

At the end of the day, the continued existence of bare particulars seems to offer an elegant story (i.e. a story that does not generate any paradoxical entity) about the kind of change continuants (people, tables, planets, etc.) and occurrents (events, processes, etc.) undergo when they become past. In particular, once an event ceases to be present, it is no longer in any sense occurring and, therefore, it is no longer in any sense an event (rejection of natural kind-essentialism). Of course, this is not to say that something ceases to exist (rejection of Annihilation); what remains (and will always remain) from that event is a bare particular, i.e. a substratum that is at least freed from the property of occurring (supposing that this property is what makes a particular belong to the kind ‘events’). Events are thus to be thought as a natural kind to which some particulars do belong when present; by becoming past, the same particulars continue to exist but, since they have undergone an intrinsic alteration (which involves the loss of the property of occurring), they are now bare. Is this story sufficient to solve the epistemic objection? The answer is ‘not quite’. It cannot be simply because my believing is occurring that I know that this belief is located at the present time; I might well ignore that it is occurring, in which case I would not know that it is located at the present time. What is further required to solve the epistemic objection is the claim that, as a matter of general fact, if one’s belief is occurring, then one knows it by introspection. Thus, the reason why we know that our time is the objective present is that (i) such an event (i.e. ‘someone’s believing to be present’) could not occur in the past (which is to be conceived as a spatiotemporal region exclusively populated by bare particulars), and (ii) we introspectively know that our belief that we are located in the present is occurring.

To be sure, the above conception of the past – ‘the bare past’ – allows growing blockers to deny that GBT entails that events are still occurring in the past (pace Bourne, 2002, Braddon-Mitchell, 2004, Merricks, 2006). Indeed, assuming that bare particulars are what will forever be left of events, GBT coheres with the intuitive idea that an event, such as ‘someone’s believing to be present’, can only occur at the present time. The past is therefore fixed. Accordingly, ‘Napoleon’s thinking about crowning the Emperor in the present’ is not occurring in the past; rather, ‘Napoleon’s thinking’ occurred, and what remains of that former event is a bare particular. Then, given that if one’s belief is occurring, one introspectively knows it, we can be confident that we are located in the present, i.e. at the leading edge of the growing block, when we think we are (rejection of skepticism). Thus, contrary to what the epistemic objection states, we (as constituents of conscious events) do find ourselves in a far better epistemic position than Napoleon, who is no longer the constituent of any event whatsoever. The situation is summarized in Fig. 3.8.

Fig. 3.8

Continuants and occurrents at present and past times

A quick look at my conception of the past – ‘the bare past’ – might lead one to believe that my theory is more akin to a version of presentism than to a version of GBT. For example, it is correct to say that my theory (like Correia and Rosenkranz’s one, by the way) leaves no room for events (e.g., the Battle of Waterloo) that are still occurring in the past. It is also correct to say that past beings (e.g., Cesar) are no longer having beliefs. Both of these features would be enthusiastically accepted by a presentist. But one crucial difference between my position and presentism is that I do think the Battle of Waterloo and Cesar still exist concretely in the past. Admittedly, these things exist in a different form than when they were present (since they lost many temporary properties in the process of becoming past), but they remain concrete things (viz. bare particulars), which a presentist would never admit! This offers, by the way, some advantage to my position on presentism, since the conception of the ‘bare past’, according to which the past exists although nothing happens in it, provides an appealing account for the fixity of the past. As a result, the ontology is clearly increasing according to my theory, as new things (e.g., times, events) come into existence to join the things that already exist, which again seems incompatible with presentism. This conception of the past fits perfectly with the spirit of GBT, which does not imply that events that once occurred are still occurring. Recall Correia and Rosenkranz’s metaphor: the growing block is not like a multi-storey building (cf. Sect. 3.7) – to say otherwise would be to misrepresent the tensed metaphysics underpinned by GBT. For these different reasons (and some others mentioned earlier, cf. Sect. 3.5), there seems to be no risk of confusing my version of GBT with presentism.

Finally, one could object that my ‘bare particular’ view betrays our intuitions, although I suspect that this has more to do with the term ‘bare particular’ than with the concept itself. After all, this notion comes from the substratum theory, which is arguably the most intuitive theory of individuation (cf. Sect. 3.9); at least, the idea that particulars are, in a certain sense, separate from their universals, seems to be widely shared. Likewise, with respect to the question of change, the idea that for something to change, something (that is responsible for the continuity of existence), thus potentially a bare particular, must survive that change, also seems intuitive (cf. Sect. 3.9). But, let us leave that aside. The important point is that, even if bare particulars should definitely be regarded as exotic entities, this would not detract from the intuitive character of my theory. To be clear, my theory is not intuitive in the sense that it resorts only to intuitive entities – this would be an unreasonable requirement for a metaphysical theory that aims at ruling on the structure of reality. Rather, my theory is intuitive in the sense that it accounts for some basic intuitions we have regarding the nature of time. Specifically, it posits bare particulars for accounting for two intuitive aspects of reality: (i) the fact that existing in the present differs from existing in the past, and (ii) the fact that the past is fixed. In that respect, the label ‘intuitive theory’ does not seem to be usurped as far as my theory is concerned.

3.10 The Virtues of Bareness

When considering the previous story about how things located in the past exist, based on the continued existence of bare particulars, the most important worry to deal with is to justify the claim that there are such entities. After all, many philosophers think that the concept of ‘what it is for a particular to be the particular that it is’ can be captured by an exhaustive list of all that particular’s qualitative properties and, therefore, that ontological parsimony dictates against the postulation of bare particulars. In this section, I will argue that, notwithstanding their bad reputation, bare particulars exist and are required in order to account for how things located in the past exist. As has been said, bare particulars are to be thought as what is responsible for the continuity of existence, through both superficial change (e.g., becoming warm) and radical change (e.g., becoming past). In particular, they are what is left of events (and other kinds of thick particulars, such as people or stones) when certain of their intrinsic properties (viz. the properties that make these particulars belong to the kinds of entities to which they belong) were subtracted by the passage of time. In that purpose, I will first provide an accurate characterization of what bare particulars are, so they cannot be confused with other entities that can be found in the philosophical literature. Then, I will mention various independent contexts in which bare particulars may be useful. Finally, I will provide some reasons to think that the ‘bundle’ alternative is false.

The first thing to say is that bare particulars are individuals, not properties, and are concrete (i.e. they occupy spacetime regions), not abstract entities. Consequently, they cannot be confused with thisnesses, where the thisness of a thing x is the abstract non-qualitative property of being x (or the abstract non-qualitative property of being identical to x).⁸⁷ In this sense, the thisness of a thing x is not merely a conjunction of all of x’s qualitative properties, but it is x’s property of being just that thing. For example, the thisness of an event, such as the Battle of Waterloo, is the property of that particular event, and of nothing else. The reason why it is worth distinguishing bare particulars from non-qualitative thisnesses is that both of these notions stem from the individuation debate: they are posited as competitive alternatives to the view according to which particulars are just bundles of universals. More specifically, substratum and thisness theorists agree that there may be distinct particulars that do not differ in respect of the universals they possess. But, whereas the former thinks that a particular is individuated by its substratum, the latter thinks that it is individuated by its thisness.

Of course, the nature of thisness is controversial, but one view is that thisnesses are primitive, i.e. they are elements of reality that cannot be reduced to anything more fundamental. Those who believe in primitive thisnesses typically believe that a thisness comes into existence with its thing, and continues to exist as long as it is exemplified by that thing. But some philosophers, e.g., Robert Adams (1986), Simon Keller (2004), and David Ingram (2016, 2018), go a step further by arguing that the property of thisness continues to exist, even though it is no longer exemplified. As Ingram puts it: “[o]n my view, for any entity x, x’s thisness T comes into being with x, T is uniquely instantiated by x throughout x’s existence, and T continues to exist uninstantiated when x ceased to exist” (2018: 61). Following these people, it might therefore be argued that non-instantiated thisnesses – rather than bare particulars – are what is left of things (e.g., events) when they become past.

As a result, the ‘thisness view’ might also seem to provide a solution to the epistemic objection: there are no events, such as ‘someone’s believing to be present’, occurring in the past, since all that remains of past events is their non-qualitative property of thisness. Given that if one’s belief is occurring, one introspectively knows it, we (as constituents of conscious events) can be confident that we are at the present time when we think we are. However, this solution does not seem available to GBT (at least in its full form). The most obvious reason is that friends of the thisness view hold that past entities cease to exist while being survived by their thisnesses, which is incompatible with GBT’s rejection of Annihilation. Moreover, just as with Williamson’s proposal, the ‘thisness view’ renders the existence of the past superfluous. As has been said, thisnesses (and therefore non-instantiated thisnesses) are abstract entities, while abstract entities are generally taken to occupy no spatiotemporal regions. Thus, unless the past is to be thought as an empty place (i.e. a place where no concrete entities are located), the ‘thisness view’ can only be accommodated by presentism, which takes the present to be the unique temporal location for concrete entities.⁸⁸ It is no coincidence that most philosophers accepting thisness ontology – Adams (1986), Keller (2004), Ingram (2016, 2018) – are presentists.

It should now be clear how bare particulars can be helpful in telling how things located in the past exist. However, since bare particulars are often perceived as exotic entities, it might be objected that any story involving them is, without any further justification, inevitably ad hoc. In the previous section, one provided some reasons to think that bare particulars are less exotic than it might seem; a further reply might be to show that the ‘epistemic objection’ is not the only problem bare particulars may help solve. For example, it seems that bare particulars might help growing blockers reply to Kit Fine’s McTaggartian argument for the unreality of time (since the rejection of Neutrality does not necessarily dispel the contradiction). As a reminder, this argument rests on the claim that, in every A-theoretic ontology (with the exception of presentism), reality is constituted by events with incompatible content (at least assuming that reality should allow for its being variegated over time).⁸⁹ Specifically, either the totality of events constituting reality are those that obtain at past, present, and future times (MSL), or the totality of events constituting reality are merely those that obtain at past and present times (GBT), or the totality of events constituting reality are merely those that obtain at present and future times (SBT) (cf. Sect. 3.2). Now, assuming that what remains from past events are merely bare particulars, the argument for the unreality of time is no longer a threat to GBT. The growing blocker can indeed argue that events come into existence in virtue of their substratum being present, but then that it is merely bare particulars (understood as the forever-existing traces of what is no longer present) that exist in the past. Growing blockers are therefore no longer committed to a reality being constituted by events with incompatible content: there merely are events that presently occur and bare particulars that forever belong to the past. There therefore is no time at which two events with incompatible content are both constitutive of reality.

Moreover, bare particulars (especially truly bare particulars, i.e. particulars that instantiate no properties whatsoever) seem to be useful in various independent contexts, such as the metaphysics of spacetime. For example, considering the Ontic Structural Realism (OSR) of Ladyman and Ross (2007), i.e. the view that the world has an objective modal structure that is ontologically fundamental, it appears that physical relations do not relate particulars with intrinsic qualities, but merely undifferentiated spacetime points. As Ladyman and Ross put it: “[t]here are objects in our metaphysics but they have been purged of their intrinsic natures, identity, and individuality, and they are not metaphysically fundamental” (2007: 130). Although OSR is often regarded as the most plausible alternative to supersubstantivalism (i.e. the view that material objects are identical to spacetime regions),⁹⁰ it faces difficulties in distinguishing the relations that hold (i.e. that are instantiated) from those that do not. A solution might therefore be to take the physical relations that are instantiated by truly bare particulars. In that sense, spacetime points might be considered as truly bare particulars that stand in a fundamental structure of physical relations (cf. Sider 2006b; Schmidt, 2008; Connolly, 2015). This solution provides a reasonable alternative to both antirealism about science (i.e. the view according to which scientific terms are not to be interpreted as referring to anything) and eliminative structuralism (i.e. the view that there are no objects, but merely relations), without threatening the ontological priority of the structure.⁹¹ It will in particular be useful in Sect. 4.6, when we will interpret the causal sets theory (CST) in structuralist terms.

Finally, assuming that sui generis mathematical entities exist, such as natural numbers ordered in an arithmetical ω-sequence, a question might be: “[w]hat distinguishes these objects from others, in virtue of which they are numbers?” (Sider 2006b: 393). Of course, many answers can be provided to that question. For example, one might argue that there is a distinctive property – Sider speaks of a “numerical glow” (cf. 2006b: 393) – that is shared by these entities and only by them. However, since it is not clear what such a property would be like (mathematical knowledge fails to describe any intrinsic properties of mathematical objects), a better answer might be that it is the relation ordering the ω-sequence that is distinctive (cf. Shapiro, 1997, Sider 2006b, Ladyman, 2005, Leitgeb & Ladyman, 2008). This answer (so-called ‘mathematical structuralism’), which can be understood as OSR’s counterpart in the metaphysics of mathematical entities, leads us to think of the members of any arithmetical sequence as truly bare particulars. Here again, this solution preserves structuralism from both antirealist and eliminativist views, by providing minimal relata to fundamental relations.

Now, if the successful uses of bare particulars in various independent contexts is not convincing enough to accept them into the ontology, one last thing that can be done is to show why the ‘bundle’ alternative – x’s identity is merely a conjunction of all of x’s properties – is not satisfying. According to the ‘bundle’ view (a particular is nothing but a bundle of qualitative properties), individuation is ensured by the fact that no two particulars can be absolutely indistinguishable in the sense of possessing exactly the same set of qualitative properties. This claim has traditionally been expressed as the ‘Principle of Identity of Indiscernibles’ (PII): necessarily, any two particulars that have all the same qualitative properties are the same particular.⁹² Of course, the plausibility of PII depends on what properties are to be included within its scope. That is why at least two forms of the Principle are commonly distinguished: PII(1) that excludes spatiotemporal properties from the domain of quantification (strong version), and (PII)(2) that quantifies over all properties without exception (weak version). Although many philosophers take PII(2) to be trivially true and, therefore, incapable of yielding interesting metaphysical theses (cf. Diekemper, 2009: 258, Russell & Whitehead, 1957: 57), it seems that counterexamples to both forms of PII can be provided. In the following lines, I will therefore introduce some classes of suitably arranged particulars for which either PII(1) or both PII(1) and PII(2) possibly fail to apply. This will serve to show that, since two particulars can share all their properties without being identical, there might be no better alternative than distinguishing them by accepting bare particulars in our ontology.

First, the most famous counterexample to PII(1) is arguably from spatial dispersion. Max Black’s version of this counterexample, involving two iron globes, is the most commonly cited in the recent literature (cf. Black, 1952: 153–164).⁹³ We are to imagine a world consisting solely of two exactly resembling, large, solid globes of iron. These two globes always have been, are, and always will be exactly similar in shape (perfectly spherical), size, chemical composition, color, etc. And, importantly, it is not only their non-relational qualitative properties that these globes share, but also their relational properties. For instance, “[…] each of them has the property of being two diameters from another iron globe similar to itself” (Adams, 1979: 13).⁹⁴ In short, all the relations that one globe bears to the other are born by the latter to the former: it is a perfectly symmetrical world. In this example, the only reason why we know that these two globes are not identical is that they are spatially distant from one another, while the same particular cannot be in two places at once (i.e. a particular cannot be spatially distant from itself).⁹⁵ Since such a world seems to be logically possible, it must be concluded that there could be qualitatively indiscernible, yet numerically distinct, things, and therefore that PII(1) is false.

Second, taking the previous counterexample for granted, it is easy to set up a similar counterexample to PII(1) from temporal dispersion: we only have to substitute events for globes, and time for space. Assuming that events are non-repeatable, concrete particulars,⁹⁶ we can imagine a world consisting solely of temporally dispersed events, some of which being qualitatively indistinguishable. This world might consist of “[…] an infinite series of sounds … A B C D A B C D A …, succeeding one another at equal intervals, with no first or last term” (Hacking, 1975: 254). In this example, each term ‘A’, ‘B’, ‘C’, and ‘D’ refers to an event with a particular set of qualitative properties. For instance, perhaps every occurrence of A has the property ‘having pitch A’.⁹⁷ It is worth elucidating this example with the type/token distinction: there are four types of events in this world, which are individuated by the set of qualitative properties (both relational and non-relational) that are instantiated by every token of that type. Thus, “[…] every occurrence of, for example, A, is a token of the event type ‘A’; that is, an occurrence of an event with the properties ‘having pitch A’, ‘being earlier than a token of event type ‘B”, ‘being later than a token of event type ‘F”, etc.” (Diekemper, 2009: 264). It therefore seems that each of the token events in this world shares all of its qualitative properties with all of the other tokens of its type. Yet, it clearly appears that tokens of event type ‘A’, for example, are all distinct events, given that they are temporally dispersed (a particular cannot be temporally distant from itself). Once again, since such a world is logically possible, it must be concluded that PII(1) is false.

Third, Steven French (2015) provides good reasons to believe that PII(1) fails in the quantum domain. As in the previous counterexamples, there indeed is a sense in which quantum objects of the same kind (such as electrons) – since they share all their state-independent properties (charge, spin, rest, mass, etc.) – are indistinguishable. According to the ‘Indistinguishability Postulate’: “[i]f a particle permutation P is applied to any state function⁹⁸ for an assembly of particles, then there is no way of distinguishing the resulting permuted state function from the original unpermuted one by means of any observation at any time” (French, 2015: §2). So, if one wants to regard such particles as individuals (as Boltzmann (1887) urges to do), then we have to argue that their individuality resides in something over and above their state-independent properties (rejection of PII(1)).⁹⁹

But it seems that quantum objects are indistinguishable in a much stronger sense: according to the most plausible understanding, “[…] no measurement whatsoever could in principle determine which one is which” (French, 2015: §4). Specifically, since some particles are taken to possess not only their state-independent properties in common, but also their state-dependent properties (i.e. “the properties expressed by expectation values of all quantum-mechanical physical magnitudes” (French & Redhead, 1988: 240)), then it can be shown that these particles violate PII(2) (which includes spatiotemporal properties). Indeed, whereas, in classical physics, the state-dependent properties of a particle are completely specified by the maximally specific state description, in quantum mechanics, there might be no pure states (i.e. no maximally specific assignment of expectation values) that can be ascribed to separate particles. Therefore, whereas, in classical mechanics, two particulars can always be distinguished via their spatiotemporal trajectories (since they cannot overlap – impenetrability assumption), the situation appears to be very different in quantum mechanics. Consider, for example, two fermions in a spherically-symmetric singlet state: they are not only indiscernible in the weak sense, but they also “[…] possess exactly the same set of spatiotemporal properties and relations” (French, 2015: §4, cf. also Ladyman & Ross, 2007: 135). It thus seems that if one wishes to maintain that quantum particles are individuals, then their individuality cannot be grounded without appealing to something like bare particulars, which implies that PII is false, even in its weakest form – PII(2).¹⁰⁰

A last issue encountered by the ‘bundle’ view has to do with change. In brief, whereas the substratum theory makes it clear how a particular (e.g., Napoleon) undergoes a change (e.g., becoming the Emperor), the ‘bundle’ alternative has a hard time to account for the same phenomenon. Roughly, the substratum theorist argues that when Napoleon becomes the Emperor, a thick particular (whose identity is independent of the properties it has) acquires the property of being the Emperor. Such a straightforward option is however not available to bundle theorists, since they take the particular ‘Napoleon’ to be nothing but the bundle (or the mereological fusion) of all his properties. As such, any property change (e.g., becoming the Emperor) seems to amount to a change in a bundle of properties and, therefore, to the creation of a new particular, rather than to a change in the same particular. In other words, the ‘bundle’ view seems to have the unwelcome consequence of construing change as “[…] a replacement of one individual by another, not change in the properties of one and the same individual” (Van Cleve, 1985: 98). Given the natural assumption that particulars remain identical (or survive) through changes, one should conclude that something is wrong with the ‘bundle’ view. For all these reasons, the substratum theory appears to be a much more plausible option than the ‘bundle’ view.

3.11 Conclusion

In the McTaggartian picture, GBT is introduced as an intermediary between two extreme answers – eternalism and presentism – that can be provided to the question ‘Do the future and the past exist?’. However, this traditional way of introducing the A-theories of time is unsatisfying, since, from an ontological point of view, there is no pre-theoretic reason to adopt one theory rather than another. After all, the only events we experience are the ones occurring at the time of our experience, whether this be in eternalist or in presentist settings. Therefore, a proposal in this chapter was to make a fresh start in the debate by introducing the A-theories in terms of a new question: ‘Is there a geometric asymmetry between the future and the past?’. The notion of ‘geometry’ refers here to basic, intrinsic properties of the spatiotemporal structures described by the A-theories. These structures are to be thought as ontologically prior to the individuals (e.g., spacetime points, events and objects) that participate within them (structuralism). In short, A-theories that possibly always answer ‘no’ to the above question are called ‘symmetric’ (e.g., eternalism, presentism), whereas A-theories that necessarily sometimes answer ‘yes’ are called ‘asymmetric’ (e.g., GBT, SBT). One consequence of this proposal is that GBT is no longer to be seen as an ill-conceived hybrid between two polar opposites (eternalism and presentism), but as a real alternative to two symmetric theories.

However, the question ‘Is there a geometric asymmetry between the future and the past?’ was shown insufficient to distinguish between the various forms the symmetric and asymmetric theories may adopt. Therefore, in order to get a complete categorization of the various A-theories of time, a second question was introduced: ‘Is temporal becoming (i.e. the creation of new things in the present) real?’. This second question allows one to distinguish between pure becoming-views (e.g., presentism, GBT) and non-generative-views (e.g., SBT, eternalism). In the McTaggartian picture revisited, GBT is thus singled out as the only asymmetric A-theory of time that accepts Temporal Becoming: S(∃x H¬∃y y = x). These new characterizations reveal GBT as being better positioned than its rivals to accommodate various past-future time asymmetries, including the asymmetry between the ‘open future’ and the ‘fixed past’. First, since GBT is an asymmetric A-theory, it can avail itself of the ‘no fact of the matter’ account of the openness of the future, while keeping the past fixed: unlike presentism, GBT allows one to say that facts about what happened supervene on the spatiotemporal structure, while facts about what will happen do not. Second, assuming that physical determinism is false, GBT implies, through Temporal Becoming, that new things are created in the present, while (at least) some of them are not made inevitable by how things located in the present or the past of now are or were. GBT thus satisfies the two necessary conditions (introduced in the second chapter) to capture a great variety of senses in which the future can be called ‘open’, including the most radical ones.

Despite some attractive features, GBT is often criticized for not being a viable alternative to presentism because of the ‘epistemic objection’. According to this objection, GBT would provide no basis for saying that our time is the objective present. Worse, this theory would commit to conclude that we are, almost certainly, located in the objective past. However, as has been argued, this objection relies on a mistaken assumption, namely that the reality of the past entails that events are occurring in the past. Indeed, it is one thing to say that the past is real, it another to say that past events are still occurring. In particular, assuming that bare particulars of past events will always exist, GBT can be reconciled with the intuitive idea that events can only occur at the present time. In this perspective, becoming past involves alterations in a thing’s intrinsic properties to such an extent that it ceases to belong to its natural kind, while the bare particular of that thing will continue to exist. The intrinsic properties that are lost in the process are (at least) those that define the natural kind to which the thing in question belonged when present. As a result, since (i) there are no events – such as ‘Napoleon’s thinking about crowning the Emperor in the present’ – occurring in the past, and (ii) if one’s belief is occurring, then one introspectively knows it, we (as constituents of conscious events) can be confident we are located in the present, i.e. at the leading edge of the growing block. The above story about how things located in the past exist, involving bare particulars, is not ad hoc, since (i) bare particulars are useful in various independent contexts (e.g., temporal ontology, metaphysics of spacetime and metaphysics of mathematical entities), and (ii) the ‘bundle’ alternative is not satisfying (e.g., there are classes of individuals for which both weak and strong versions of the Principle of the Identity of Indiscernibles fails to apply.