p43

For a sampling of arguments against qualitativism, see Kment (2012), Cowling (2017), and Turner (2017). 9 only constrain the qualitative facts that obtain at particular times (an assumption that we will revisit later on), Newton’s Laws do not distinguish these two worlds, because they are qualitative time-slice duplicates. However, while these two worlds are qualitative time-slice duplicates, they are not qualitative duplicates simpliciter. In one of the worlds, there are 2N particles throughout the history of the universe, and in the other there are only N particles throughout the history of the universe. This is a purely qualitative difference between these two worlds. This kind of case serves as a counterexample to the claim that qualitativism on its own entails that if our world is qualitatively lawful then our world is fully lawful. Even under qualitativism, the laws of nature may still be silent on qualitative cross-time identity facts, such as the cross-time identity facts that differ between Future Tuesday Reset and No Reset. In order to secure full lawfulness given qualitative lawfulness, qualitativists must supplement their view with some principle that fixes the qualitative cross-time identity facts across all nomic possibilities. It’s easy to see how this might work for perdurantists: simply supplement qualitativism with the claim that it’s impossible for fundamental physical objects wholly located at one time to be numerically identical to fundamental physical objects wholly located at another time. The laws of nature can be used to determine the (chances of) qualitative timeslice propositions at future times, and the additional qualitative cross-time identity facts can be determined by the thesis that any two things wholly located at distinct times must also be distinct. In other words, qualitativists can bridge the gap between qualitative laws and full laws by endorsing the following thesis: Strong Perdurantism: Necessarily, for all x and y, if x is wholly located at time t and y is wholly located at time t’, where t and t’ are distinct, then x and y are distinct.13 How might the story go for qualitativists who also endorse endurantism? There are several options here. For example, at all worlds where the laws imply that particle number is conserved, the endurantist might propose that particles endure throughout all of time, thereby 13 The technical notion “wholly located” (and related notions like “exact location”) has been defined by different philosophers in different ways, but none of our arguments will turn on the details of the definition. For an influential way of understanding the term, see Sider (2001). 10 precluding any enduring objects from popping into or out of existence. However, there remains the further issue of stating precisely how particles endure through time, in order to rule out strange possibilities where (for example) particles discontinuously “swap places” with one another. We will discuss principles in this spirit in detail below, under the heading of ‘Ontological Inertia’. We shall see that the principle is easy to formulate in a monistic setting, where there is only one fundamental object at any time, but trickier to write down in an orthodox pluralist setting. The second way in which one might try to collapse the distinction between qualitative laws and full laws is by endorsing a version of monism, which might seem to trivialize the further constraint stemming from non-qualitative regularities. According to monism, the universe as a whole is a fundamental individual, and there are no fundamental parts of this universal whole. If the only fundamental individual is the entire universe, then there doesn’t seem to be any room for non-qualitative irregularities of the kind present in Future Tuesday Reset. Such irregularities require that there be more than one fundamental individual, which we can then change across nomic possibilities. Yet this is precisely what monism denies, and so it seems like the doctrine entails that our world is fully lawful if it’s qualitatively lawful. Again, however, this tempting thought goes by too quick. One can distinguish two versions of monism. On a three-dimensional version of monism, the entire universe at a time corresponds to a fundamental individual, and on a four-dimensional version of monism, the entire “block universe” corresponds to a single fundamental individual. At least in principle, a three-dimensional version of monism is consistent with the claim that there is only ever one fundamental individual. For example, on an endurantist version of threedimensional monism, one might hold that there is a single fundamental three-dimensional object that eternally endures through time.14 Still, three-dimensional versions of monism, even 14 It is worth noting that some of the standard arguments for Monism are more naturally construed as arguments for a three-dimensional version of monism. For example, Schaffer’s (2013) argument that the cosmos is fundamental because it is the one and only thing that evolves by the fundamental laws is primarily carried out in a three-dimensional, endurantist setting. Moreover, the kind of holism implied by quantum entanglement (e.g. see Ismael and Schaffer 2020), at least in a non-relativistic setting, supports only a three-dimensional version of 11 espoused as necessary truths, do not on their own bridge the gap between qualitative laws and full laws, since they are vulnerable to the same problems as non-monistic theories. For example, in an endurantist setting, one could consider the monistic analog of Future Tuesday Reset, where the world endures through time until next Tuesday, and then instantly gets replaced by a numerically distinct enduring universal object. In a perdurantist setting, where there are infinitely many fundamental individuals that correspond to different time-slices of the universe, one can generate distinct nomic possibilities simply by permuting any two individuals at different times without making any qualitative changes to the universe. By contrast, four-dimensional versions of monism, if regarded as at least nomically necessary, do successfully bridge the gap between qualitative laws and full laws, provided these theses are formulated using notions that are acceptable to the four-dimensional monist.15 Since it is nomically necessary that there is only ever one object, there cannot be any non-qualitative irregularities as the world ‘evolves’ in time. For the four-dimensional monist, the evolution of the world merely corresponds to qualitative variation within the single world-object. Still, we want to stress that four-dimensional monism falls outside of the standard dichotomy between endurantist and perdurantist theories of persistence. No fundamental objects are wholly present at different times, so the view does not vindicate endurantism. Yet neither does the fundamental ontology consist of instantaneous temporal stages, so the view also doesn’t vindicate perdurantism. For this reason, we doubt that those invested in the traditional debate will see four-dimensional monism as an attractive supplement to their position; rather, the position seems to embody a revision of the very notion of persistence through time that sparks the traditional debate. Monism, since quantum entanglement relations do not relate things across time. Of course, there are independent relativistic reasons for why one might favor a four-dimensional ontology rather than a three-dimensional ontology, and there is an ongoing debate about how endurantists (as well as A-theorists of time) should respond to this challenge from relativity. For a sampling of different responses, see Gibson and Pooley (2006), Gilmore (2008), Balashov (2010), and Zimmerman (2011). 15 As currently formulated, both full determinism and full stochasiticty appeal to things that the four-dimensional monist would reject (e.g. the existence of distinct times and appeals to “the history of w up to t”). The fourdimensional monist must paraphrase full determinism and full stochasiticty using their own preferred ideology. See Cornell (2016) and Sider (2008) for how the monist might try to do this. 12 In sum, there are certain versions of qualitativism, and perhaps monism, that ensure that our world is fully lawful, given that it is qualitatively lawful. In particular, qualitativist views that endorse some modal principle akin to Strong Perdurantism, and four-dimensional versions of monism both bridge the gap to full lawfulness. In the rest of the paper, we’ll examine whether more standard endurantist and perdurantist views can bridge the gap between qualitative laws and full laws. We’ll start by dropping qualitativism and considering these views in the simplest possible setting, where there is only ever a single fundamental individual at any given time (corresponding to a three-dimensional version of monism). Doing so simplifies the exposition, allowing us to outline our central claims without introducing other complications. We’ll then consider various more popular pluralist ontologies, according to which multiple individuals like particles, or spacetime points, or both, are fundamental. 4. Endurantism and Full Lawfulness Suppose it’s nomically necessary that, for any time t, there is a single fundamental individual ψt (the ‘world-at-a-time’), and that the world is qualitatively lawful. In an endurantist setting, the primary obstacle to the world being fully lawful comes by way of the kind of counterexample present in Future Tuesday Reset. What if the world has always endured through time until now, but then is suddenly replaced by a numerically distinct enduring world-individual next Tuesday? We think there are two natural strategies for the endurantist to pursue. First, the endurantist might embrace some principle about how things endure that holds with metaphysical necessity; in particular: Ontological InertiaMonism: Necessarily, if three-dimensional Monism is true, then, for all times t and t’, ψt = ψt’ Ontological InertiaMonism rules out any case analogous to Future Tuesday Reset where the universe simply pops out of existence, and it also bridges the gap between qualitative 13 lawfulness and full lawfulness. By Ontological InertiaMonism, any initial segment of a nomically possible world will involve only a single enduring object. So, for any two worlds w and w’, if they agree on all of their intrinsic properties up to a time, they must include the same enduring object up to that time. The qualitative laws together with Ontological InertiaMonism will then secure the same truth values (or chances) for all future propositions in w and w’, since the only haecceitistic propositions in w and w’ must concern the same enduring object that existed in the past. A second strategy that the endurantist might pursue is to claim that some feature of our laws of nature ensures that the world eternally endures through time, in effect transforming a principle like Ontological InertiaMonism into a distinctively nomic necessity rather than a metaphysical necessity. We will begin by discussing the prospects of the first strategy. The main problem for this strategy is to independently motivate the truth of Ontological InertiaMonism. Why can’t the world simply pop out of existence and be replaced by an enduring duplicate? This rhetorical question can be supplemented with a conceivability argument. It seems perfectly conceivable for there to be a world that violates Ontological InertiaMonism. On the assumption that conceivability is at least a prima facie guide to possibility, we have a prima facie counterexample to Ontological InertiaMonism. We see three ways in which the endurantist might defend Ontological InertiaMonism. We’ll consider each in turn. We’ll then turn to the prospects of the alternative, distinctively nomic, strategy. 4.1. Attempt 1: Essences Some philosophers appeal to essences to block conceivability arguments.16 For example, it might be conceivable that water is XYZ, but it is still impossible that water is XYZ because it is essential to water that it is H2O, and hence necessarily water is H2O.17 In the case we are 16 See Goff (2019) for a recent example. 17 Here we’re assuming that if some proposition is essential to some object, then that proposition is necessary. One way to secure this implication is by reducing necessity to essence, following Fine (1994). However, we take the instances of the implication we’ll rely on in the main text to be plausible irrespective of whether the general Finean reduction itself succeeds. 14 considering, the endurantist could say that, for any time t, it is essential to ψt that, for any time t’ after t, ψt = ψt’. In other words, the endurantist could say that it is an essential property of the world that it continues to exist so long as time continues to exist.18 Notice that it is not enough for the endurantist to say that this essential property holds for actual ψt’s. Ontological InertiaMonism is a modal claim that would be false so long as it’s even possible for there to be a world that lacks these essential properties. The essentialist must therefore endorse the following claim: Essential Ontological InertiaMonism: Necessarily, if three-dimensional Monism is true, then, for all times t, it is essential to ψt that, for all times t’ after t, ψt = ψt’ Although Essential Ontological InertiaMonism does imply Ontological InertiaMonism, we don’t think it’s a very attractive strategy for the endurantist to pursue. Our main worry is that positing these sorts of metaphysically necessary essential properties simply doesn’t get us very far in independently motivating Ontological InertiaMonism. Insofar as we find ourselves puzzled about why Ontological InertiaMonism should be true, we also find ourselves puzzled as to why Essential Ontological InertiaMonism should be true. One could always come up with some hypothesis about the essences of things in order to reach one’s desired modal conclusions, but we don’t find this kind of procedure very illuminating.19 Our second worry is that this kind of strategy is entirely disanalogous to the standard essentialist replies to conceivability arguments. In the case of water, when we conceive of a world where water is XYZ, our conceiving does correspond to a possible world that could have turned out to be the actual world. It is just that, given that water is actually H2O, the world we are conceiving of is misdescribed. While we do successfully conceive of a possible world where the watery-stuff around us is XYZ, the corresponding substance doesn’t get to 18 This essential property need not conflict with cosmological models where the universe comes to an end in a “big crunch,” provided that there is no time “after” the big crunch. 19 For discussion and defense of the worry about essentialist theses in this paragraph, see Teitel (2019, 383-386), who argues for it as concerns attempts to explain modal principles about spacetime in terms of essentialist theses. 15 count as water.20 In the case of Essential Ontological InertiaMonism, when we are conceiving of a three-dimensional monistic world where the universe endures for some time but then gets instantly replaced by a numerically distinct enduring object, there is no possible world that corresponds to our conceiving. Although it seems perfectly conceivable for there to be a threedimensional monistic world that simply lacks the essential properties described in Essential Ontological InertiaMonism, anyone who endorses this kind of essentialist strategy must think that this conceiving doesn’t correspond to any metaphysical possibility.