p42

Lawful Persistence* David Builes and Trevor Teitel Penultimate Draft of Feb 15, 2022 Forthcoming in Philosophical Perspectives Abstract The central aim of this paper is to use a particular view about how the laws of nature govern the evolution of our universe in order to develop and evaluate the two main competing options in the metaphysics of persistence, namely endurantism and perdurantism. We begin by motivating the view that our laws of nature dictate not only qualitative facts about the future, but also which objects will instantiate which qualitative properties. We then show that both traditional doctrines in the metaphysics of persistence must take on surprising further commitments in order to vindicate our universe being law-governed in this strong sense. For example, we argue that endurantists should adopt a particular version of monism, and that perdurantists should adopt a qualitativist doctrine that dispenses with all individuals at the fundamental level. 1. Introduction All of our best physical theories, from Newtonian Mechanics to Quantum Field Theory, seem to imply that our world evolves in a regular, law-governed way. Either the future is fully determined by the past, or else the chances of future events are fully determined by the past. However, on closer inspection, it turns out that none of our best physical theories, at least on its own, constrains the future in such a strong way. Our physical theories only secure the truth values (or chances) of certain qualitative propositions (those not about any particular objects) concerning the future on the basis of the past. Because the laws of these theories are purely qualitative, for all these physical theories say there might be all sorts of hidden irregularities concerning the evolution of non-qualitative features of the universe. The evolution of the universe might be much more chaotic and irregular than we thought. *The authors are listed alphabetically: we contributed equally to the paper. For very helpful comments and discussion, we’d like to thank Mark Balaguer, Michael Caie, Ezra Rubenstein, Ted Sider, as well as audiences at MIT and Princeton. 1 We’ll begin by making the distinction between qualitative and non-qualitative regularities more precise. We’ll then motivate the view that our universe is law-governed in both of these respects. Our central aim in what follows is to use this strong notion of being law-governed in order to develop and evaluate the two main options in the debate over the metaphysics of persistence, namely endurantism and perdurantism. We’ll see that each of these views must take on surprising further commitments in order to vindicate the non-qualitative regularity of the universe. For example, we’ll see that arguably perdurantists must also adopt a qualitativist doctrine that eschews individuals at the fundamental level, and that endurantists have reason to adopt a particular version of monism. Our central goal in what follows is to develop and assess the best endurantist and perdurantist packages of views that secure the non-qualitative regularity of the universe. Our hope is that developing and assessing these competing views will serve to advance what currently feels like a dead-locked debate between endurantists and perdurantists. What are these two positions? Numerous definitions are out there, and the details can get quite delicate. Perdurantists hold that the fundamental individuals are instantaneous temporal stages, each of which exists at only a single time. Facts about how objects persist across time hold in virtue of facts concerning certain sequences of such instantaneous stages.1 Endurantism, by contrast, countenances fundamental individuals that exist at multiple times, and are wholly present whenever they exist. For our purposes, just these minimal characterizations of the views will suffice. How to state a precise positive vision behind endurantism is hotly contested: some appeal to a primitive notion of exact location, and others cash out the theory by appealing to presentism, among other options.2 Fortunately, we need 1There is a third position in the metaphysics of persistence, sometimes called “exdurantism” or “stage theory,” which agrees with perdurantism on these two points. The main disagreement between stage theory and perdurantism concerns whether ordinary English words like ‘table’ and ‘banana’ refer to three-dimensional objects or four-dimensional objects. However, their fundamental ontology is the same. Because their fundamental ontology is the same, all of our arguments concerning perdurantism apply equally well to the stage theory. 2See Sider (2001) for a canonical definition of the two views. See Merricks (1995) for an alternative, which ties endurantism to presentism. See Magidor (2016) for a critical overview of the traditional arguments in the debate, and an argument that they often fail to distinguish the two views. We take our arguments to avoid this worry. 2 not take a stand on this issue here: our arguments will not turn on the details of how precisely these two competing views get characterized. One last preliminary before we get going. Throughout, we’ll be restricting our attention to the fundamental facts that are described by our best physical theories (e.g. those about particles, spacetime points, or perhaps the universe as a whole). We won’t be considering facts about ordinary macroscopic objects like tables or chairs, whatever these facts turn out to amount to. Given the standard view that non-fundamental facts supervene on fundamental facts, this restriction won’t affect any of our arguments. If the laws of physics, together with the past, determine the truth value (or chance) of every fundamental qualitative fact, they will also determine the truth value (or chance) of every non-fundamental qualitative fact. After all, qualitative non-fundamental facts supervene on qualitative fundamental facts. Moreover, if the laws of physics, together with the past, determine the truth value (or chance) of every fundamental fact, they will also determine the truth value (or chance) of every nonfundamental fact. Every non-fundamental fact, whether it’s qualitative or not, supervenes on the totality of fundamental facts.3 2. How Might Laws Govern? Let us start by defining the various respects in which our universe might be law-governed.4 Distinguish qualitative propositions, which aren’t about any particular objects, from all of the rest (which we’ll interchangeably call haecceitistic or non-qualitative propositions). For example, the proposition that someone is standing is qualitative, but the proposition that Larry is standing is haecceitistic. Call a property F qualitative just in case the proposition that something has F is qualitative; call all other properties non-qualitative or haecceitistic (e.g. the property of being Alice is non-qualitative, but the property of being red is qualitative). 3Hawthorne (2006) argues against full determinism (determinism with respect to both qualitative and nonqualitative facts) by reference to ordinary macroscopic objects. Since we are inclined to accept full determinism for fundamental facts, as well as the claim that non-fundamental facts supervene on fundamental facts, we are inclined to modus tollens these arguments, by construing them as arguments against the existence of ordinary macroscopic objects. 4The definitions in this section closely mirror and build on those in Teitel (2019). 3 We will also need the notion of two worlds being qualitative time-slice duplicates. For any world w, let a temporal foliation of w be a function tw defined on a subset of ℝ, such that, (i) for every real number r in its domain, tw(r) is some time-slice of w, (ii) for any real numbers r and r’ in tw’s domain, where r > r’, tw(r) is r-r’ units of time after tw(r’), and (iii) for every time-slice of w, there exists some r such that tw(r) is identical to that time-slice. Utilizing this definition, we may say that w and w’ are qualitative time-slice duplicates just in case there exist temporal foliations tw and tw’ of w and w’ that are defined on the same subset of ℝ, such that for every real number r in the domains of tw and tw’, tw(r) and tw'(r’) have all of the same qualitative intrinsic properties.5 With these definitions in hand, we can formulate two notions of determinism: Full Determinism: For all metaphysical possibilities w and w’ where L is true, if there is a time t at both w and w’ such that the history of w up to t has the same intrinsic properties as the history of w’ up to t, then w and w’ agree on the truth value of every proposition. Qualitative Determinism: For all metaphysical possibilities w and w’ where L is true, if there is a time t at w and a time t’ at w’ such that the history of w up to t has the same qualitative intrinsic properties as the history of w’ up to t’, then w and w’ are qualitative time-slice duplicates.6 5 In this paragraph and in the definitions to follow we are taking for granted that the worlds at issue can be foliated into times. In doing so we are ignoring certain general relativistic worlds that don’t admit of anything like a Cauchy surface (the natural analogue of a time in a relativistic setting), as is common in discussions of the hole argument. Relativistic worlds that can be foliated into times of course admit of infinitely many such foliations. The definitions that follow still work as intended at such worlds. 6 Determinism, in either its full or qualitative guise, is often formulated so as to be time-symmetric rather than future directed (see, for example, Teitel 2019, 353). We formulate determinism in a time-asymmetric way in order to have analogous definitions concerning stochastic laws, which are not time-symmetric. Still, none of our arguments below will crucially turn on this choice-point when defining determinism. For further discussion of distinctions analogous to qualitative vs. full determinism, see Belot (1995), Brighouse (1997), and Melia (1999). 4 One might be wondering why we didn’t end our definition of qualitative determinism by requiring that w and w’ be qualitative duplicates simpliciter. We intentionally avoided this stronger formulation because empirical evidence for our best physical theories on its own does not support it. We will discuss this point in detail in section 3. An analogous distinction can be drawn in the case of stochastic laws. Following Lewis (1980), we will take fundamental chances to be relative to a time. For example, the chance in 2020 that a particular tritium atom will decay by 2030 is some non-trivial value between 0 and 1, but the chance in 2040 that that particular tritium atom decayed by 2030 is either 0 or 1. The t-chance of some proposition P is simply the chance at t that P is true. We also need some new definitions. Let a qualitative time-slice profile be a maximal qualitative intrinsic property that could be instantiated by a time-slice of some world.7 Now, for any qualitative time-slice profile P, time t, and real number r, let Pt,r be the proposition that the time-slice r units of time after t instantiates P. We can now draw the following distinction: Full Stochasticity: For all metaphysical possibilities w and w’ where L is true, and for all times t, if (i) t exists at both w and w’ and (ii) the history of w up to t has the same intrinsic properties as the history of w’ up to t, then w and w’ agree on the t-chance of every proposition. Qualitative Stochasticity: For all metaphysical possibilities w and w’ where L is true, and for all times t and t’, if (i) t exists at w and (ii) t’ exists at w’ and (iii) the history of w up to t has the same qualitative intrinsic properties as the history of w’ up to t’, then, for all qualitative time-slice profiles P, and all real numbers r, the t-chance at w of Pt,r is equal to the t’-chance at w’ of Pt’,r. 7P is a maximal qualitative intrinsic property of x if and only if P is a qualitative intrinsic property of x, and, for every qualitative intrinsic property Q, that x is P metaphysically necessitates that x is Q, or that x is P metaphysically necessitates that it’s not the case that x is Q. 5 For convenience, we will say that a world is fully lawful iff its laws satisfy either full determinism or full stochasticity, and we will say that a world is qualitatively lawful iff its laws satisfy either qualitative determinism or qualitative stochasticity. As alluded to above, we have strong empirical reasons for believing that our world is qualitatively lawful. However, there is reason to think that it might not be fully lawful, because all candidate laws of nature are qualitative propositions. This possibility has been extensively discussed in the literature on the hole argument, which purports to show that General Relativity (GR) fails to be fully deterministic, because GR’s laws fail to fix haecceitistic propositions about which particular spacetime points have which field values. Responses to the argument generally seek a doctrine in the metaphysics of spacetime or modality that restores GR’s full determinism (see Norton 2019 for an overview). Yet this all raises the question: why care about full determinism in the first place (see Teitel, 2019, 356-57)? Why not simply call the argument sound and move on? Indeed, some (e.g. Brighouse 1997) claim that any reasons to expect our physical theories to be deterministic support only qualitative determinism. Given that the vast literature on the hole argument is premised on there being reason to rescue GR’s full determinism, the absence of a compelling argument in support of our laws obeying this strong sense of determinism is a striking omission.8 Fortunately, we think that this omission can be remedied. One way to motivate the thought that our world is fully lawful is by pointing out that, if the laws are silent on future non-qualitative facts, then the evolution of the universe might be much more irregular, complicated, and chaotic than we thought. For example, consider a classical Newtonian theory of N particles evolving through spacetime. Suppose the laws of physics constrain only the qualitative facts that will obtain at future times. Moreover, for now suppose that the laws of nature are neutral between competing theories of persistence (we will consider the option of dropping this assumption later on). Then the following scenario is nomically possible: 8The closest one finds to an argument is Earman and Norton’s oft-quoted claim that “a metaphysics which automatically decides in favour of indeterminism is […] unacceptable. Determinism may fail, but if it fails it should fail for a reason of physics” (1987, 524), where both uses of ‘determinism’ here refer to full determinism. We don’t find this claim compelling, for the reasons given in Teitel (2019, 356). 6 Future Tuesday Reset: Up until now, there have always been the same N particles, which have been enduring through time as they evolve by Newton’s laws. However, next Tuesday, at exactly midnight, each of these particles will spontaneously pop out of existence and be replaced by numerically distinct particles, in such a way that preserves the (qualitative) truth of Newton’s laws at all times. The new N particles continue to endure forever. Analogous haecceitistically different nomic possibilities can also easily be generated on a perdurantist view. For example, consider any perdurantist world that obeys Newton’s laws, which consists of N particle trajectories through space-time, each of which is composed of infinitely many numerically distinct particle time-slices. For any such possibility, one can consider a distinct nomic possibility that arbitrarily interchanges two particle-time slices, while keeping the qualitative history of the universe unchanged. In general, if the world is merely qualitatively lawful, and the laws do not explicitly take a stand on the metaphysics of persistence, then the world leaves open all sorts of complex non-qualitative nomic contingencies. To the extent that we don’t think our world is subject to such irregular evolution, we should regard our world as fully lawful. The second, and in our mind most important, motivation stems from the metaphysics of laws. We think that the best explanation for why our world is qualitatively lawful also supports the claim that our world is fully lawful. This explanation takes qualitative laws to be evidence for some non-Humean conception of laws. When we look at the guiding slogans behind the nonHumean conception of laws, they support the view that our world is fully lawful rather than merely qualitatively lawful. One of us (Teitel (2019, 356-357)) has pressed this point before, arguing that proponents of non-Humean views “should be reluctant to concede that our laws of nature are simply silent on a huge range of non-qualitative facts” (356), as they must be if our world is merely qualitatively lawful. The idea here is that if our world fails to be fully lawful then future states are massively underdetermined by past states and the laws, because the laws don’t fix which objects follow which. Intuitively, the laws of physics are supposed to make the world evolve in the way that it does, but the world wouldn’t “know” how to evolve if it didn’t know which future objects to generate. The non-Humean view seeks to explain the future in terms of the past and the laws of nature. This explanatory ambition is a failure if 7 non-qualitative features of the future are entirely brute and inexplicable. This kind of nonHumean conception of laws is controversial. Still, those convinced that the qualitative regularity of our universe supports such a conception also thereby have reason to regard our world as fully lawful.9 A final motivation for thinking that our world is fully lawful stems from certain views in the metaphysics of time, namely presentism and the growing block theory.10 According to presentism, only present things exist, and according to the growing block theory, only past and present things exist. Because both of these views deny the existence of future objects, they face the challenge of accounting for non-trivial truths about the future. It certainly seems that there are some non-trivial truths about the future, such as the claim that a particular banana will not be ripe in one week, or the claim that our laws of physics will still hold true tomorrow. However, given the view that truth depends on being, these non-trivial truths about the future must somehow be made true by the present (and/or the past). A natural way to account for these truths is by appealing to the laws of physics. In the case of presentism, Markosian (2013) has defended the view that all propositions about the future (or the past) are true if and only if (and because) they are nomically necessary given the present time.11 In the case of the growing block view, Briggs and Forbes (2012) have defended the related view that all propositions about the future are true if and only if (and because) they are nomically necessary given the past and present. However, if our world is merely qualitatively lawful, there is a danger that this kind of strategy won’t be able to secure any non-trivial haecceitistic claims about 9See Bhogal (2020b), Builes (2021b), and Segal (forthcoming) for reasons to think that Humeanism leads to inductive skepticism. There’s an important question of which non-Humean views are rendered more likely by regularities like qualitative determinism. We won’t take a stand on this issue here, but for discussion see Hildebrand (2013, 2014, 2018), Tugby (2017), and Hildebrand and Metcalf (forthcoming). 10 For defenses of Presentism, see Markosian (2004) and Zimmerman (2011). For defenses of the growing block view, see Tooley (1997) and Forbes (2016). 11 Similar proposals (at least for future truths) have been defended by Peirce (1934), Lukasiewicz (1967), and Thomason (1970). As Sider (2001: 39) points out, because the presentist can only appeal to the laws and a single instant of time, they need to believe that certain physical quantities concerning rates of change (such as velocity or momentum) are intrinsic to a time in order for a corresponding time-slice version of full determinism to have a chance of being true. For more on the question of whether rates of change are intrinsic, see Lange (2005), Easwaran (2014), Builes (2020), and Builes and Teitel (2020). 8 the future, such as the claim that a particular particle, or a particular person like you or I, will continue to exist in one second. This is perhaps particularly pressing for the presentist who wishes to account for past truths in a similar way. There are all sorts of non-qualitative truths about the past, such as the fact that Aristotle was a philosopher. In order for this kind of strategy to be a fully general strategy regarding past and future truths, our world must be fully rather than merely qualitatively lawful. 3. Two Radical Options: Qualitativism and Monism We’ve argued that a wide range of different metaphysical commitments should incline one to regard our world as fully lawful. As mentioned at the outset, our plan is to use this constraint to develop the best versions of the two main competing views in the metaphysics of persistence, endurantism and perdurantism. We now turn to this task. There are two radical ways that endurantists or perdurantists might try to secure a fully lawful world: either by rejecting fundamental non-qualitative facts altogether or by rendering them trivial. The first option involves a commitment to Qualitativism, according to which necessarily there are no fundamental non-qualitative facts. Many different versions of qualitativism have been developed, however it is fair to say that they all remain controversial.12 Still, qualitativism seems to provide one promising way to bridge the gap from qualitative laws to full laws. At least at first glance, it seems that the entire distinction between qualitative laws and full laws is collapsed given qualitativism. However, this tempting thought is too quick. By itself, qualitativism does not automatically bridge the gap from qualitative laws to full laws. Consider the case of Future Tuesday Reset and a corresponding world, call it No Reset, that is a qualitative time-slice duplicate of Future Tuesday Reset, except that no reset ever occurs. On the assumption that the laws of nature 12 For a sampling of Qualitativist views, see Van Cleve (1985), Hawthorne and Cortens (1995), Dasgupta (2009, 2017), Builes (2021a), and Turner (2011, forthcoming).