p46

It’s easy to see how the story might go at specific possibilities. For instance, at all relationist worlds where enduring objects never overlap, perhaps we can uniquely pin down the future non-qualitative facts given qualitative lawfulness by requiring that enduring objects never pop out of existence and also never move discontinuously. However, we don’t think a single principle can do the requisite work in full generality; rather, worlds with different laws will call for different principles. To see this, consider worlds where enduring objects always move on continuous trajectories but can 41 This is an example of “b-” decay, as discussed in Basdevant et al. (2005). 42 If particle number is not conserved, then we don’t see any other strategy for the endurantist particle-based relationist to secure full lawfulness other than to accept anti-haecceitism, just like the perdurantist. 31 overlap. Nothing in this description tells us whether two enduring objects that briefly overlap on some occasion subsequently “passed through” each other or “bounced off” of each other. Yet the sought after principle dictating how objects endure across time must take a stand on this question. Notice, though, that both scenarios are perfectly conceivable: which occurred at some world will depend on the laws of nature of that world. The lesson here is that endurantist pluralists cannot aim to formulate a direct analogue of Ontological InertiaMonism that works in full generality, but should instead seek a more circumscribed principle that rescues full lawfulness on a case-by-case basis, in a manner that takes into account the details of the laws of nature at issue. Irrespective of how the relevant principle ultimately gets formulated given our laws or any others, the challenge facing pluralist endurantists will be the same as the one we discussed in section 4: independently motivate the truth of the pluralist version of ontological inertia, rather than simply stipulate it. The analogue of attempt 1, in terms of essential properties, we take to be unsuccessful for the reasons we’ve seen above. Attempt 2, by contrast, carries over unchanged: appealing to the weakened PSR in the form of Temporal Rationalism would also motivate the pluralist version of ontological inertia. Yet the problem of motivating even this weakened version of the PSR remains as glaring as it was before. Crucially, attempt 3 is a nonstarter in this pluralist setting. Yes, endurantism would enable non-Humeans to avoid violations of Hume’s Dictum concerning a single particle across time (because the particle at one time is not wholly distinct from the particle at some other time). However, most laws will also impose constraints relating wholly distinct particles. For example, Newton’s law of gravity in this non-Humean setting would describe a necessary connection between any particle there is and every other particle, and endurantism simply does nothing to address these other violations of Hume’s Dictum. Thus we see that attempt 3 to motivate ontological inertia—via preserving Hume’s Dictum for those who countenance necessary connections in accordance with the laws of nature—is applicable only in the monist setting we adopted in section 4. In a non-Humean pluralist setting, Hume’s Dictum is a non-starter from the get-go. What about attempt 4, in terms of strong laws of nature? This view gains plausibility in this pluralist setting, given that, as we just saw, the pluralist’s analogue of Ontological InertiaMonism at a possibility must be sensitive to that possibility’s laws. Nevertheless, all of our worries about developing strong laws, for each alternative conception of the metaphysics of laws, carry forward to the 32 pluralist setting unchanged. We see, then, that for endurantist pluralist relationists the only ways forward are attempts 2 or 4 (namely, appeal to Temporal Rationalism or strong laws of nature). Let us turn now from the relationist ontology to the two others, which countenance either only spacetime, or spacetime in addition to material objects. Both ontologies face the same problem given endurantism: commitment to enduring spatial points (irrespective of whether one countenances material objects as well) is widely held to be problematic because it seems to lead to physically redundant structure. The problem is that enduring spatial points immediately generate a standard of absolute rest: namely, being located at numerically one and the same region of space across time. As is familiar, such ideology of absolute rest seems to play no explanatory role in our best physical theories, and many for that reason will be reluctant to endorse enduring spatial points.43 Perhaps some endurantists will be content to just embrace this extra spatiotemporal structure, as independently motivated by their metaphysical theory despite playing no role in our best physics. To such endurantists we then pose the same dialectic as before. Avoiding counterexamples to full lawfulness akin to Future Tuesday Reset requires adopting a pluralistic analogue of Ontological InertiaMonism. The resulting principle will be more local, depending on the details of the laws of nature of whatever worlds are at issue. For example, because standard spacetime theories contain inertial structure, one such principle could require that necessarily all spatial points endure along inertial trajectories. In fact, the proponent of enduring spatial points could instead define inertial structure by reference to the structure of enduring spatial points: for example, a particle can be said to be on an inertial trajectory iff it is moving at a constant velocity with respect to enduring space itself. This reveals that it is far from clear whether the posit of enduring space is in fact physically redundant: those who do not countenance enduring space must regard any inertial structure in spacetime as fundamental, while those who do countenance enduring space can reduce inertial structure to facts about enduring spatial points and the spatial distances between such points.44 In any case, the key 43 For discussion of how exactly the inference here might proceed, see Dasgupta (2016b). 44 For a related point about the advantages of Newtonian spacetime, see Sider (2020: 108-109). 33 issue of motivating a pluralist principle of ontological inertia for spatial points will remain: in a pluralist setting the only means of independently motivating such a principle must stem from attempts 2 or 4 above, via Temporal Rationalism or strong laws of nature. As we have seen, attempt 1 via essential properties is problematic, and attempt 3 via preserving Hume’s Dictum for non-Humeans requires monism. Let us now turn, finally, to the “mixed” version of the second pluralistic ontology, which countenances both material objects and spacetime, and maintains that matter endures yet spacetime perdures. The issues raised by this view mirror some of the issues we’ve already seen in this section. We can generate threats to full lawfulness by considering permutations or replacements of particular spacetime points. We can also generate such threats by considering nomic possibilities where the enduring material objects are permuted or replaced by new enduring objects. Addressing the former perdurantist threats is arguably best done by adopting qualitativism. And in the present pluralist setting the latter endurantist threats call for Temporal Rationalism or strong laws of nature (which are the only means of independently motivating the pluralist’s analogue of Ontological InertiaMonism). And the challenges we have already seen for these strategies remain as glaring as ever. 7. Upshots We have covered a lot of ground, and the dialectical situation is somewhat messy. Let’s summarize the central conclusions we’ve reached. First, perdurantists should arguably also embrace qualitativism. Perdurantists had to embrace anti-haecceitism in order to vindicate full lawfulness, and qualitativism was the most promising means of independently motivating this modal principle. Of course they could embrace this principle as a brute modal constraint. But ideally they’d embrace a metaphysic that implies the principle if there is one to be found. We take the contrapositive here to be especially striking. If, like most philosophers, you embrace some individuals at the fundamental level, and hence reject qualitativism, then you should also embrace endurantism. In this way, our discussion offers a powerful argument for endurantism stemming from the constraint of full lawfulness. 34 If you’re an endurantist you have a few paths forward. If you embrace monism, you can attempt to independently motivate Ontological InertiaMonism via attempt 2 in terms of Temporal Rationalism or attempt 4 in terms of strong laws of nature. Nonetheless, we argued that the most promising strategy for monists goes via attempt 3, in terms of vindicating Hume’s Dictum given the presence of necessary connections in accordance with the laws of nature. If you embrace pluralism, on the other hand, your only options for independently motivating the pluralist’s analogue of Ontological InertiaMonism must go via attempts 2 or 4. Furthermore, endurantist pluralists faced some additional obstacles that endurantist monists did not (for instance, they seemed to require that particle number be conserved). We think this overall dialectical situation gives endurantists reason to embrace monism. Most notably, attempt 3 in terms of vindicating Hume’s Dictum fared significantly better than the rest as a means of motivating ontological inertia. Yet we also saw that this Hume’s Dictum motivation is available only in a monistic setting. So we see that full lawfulness also enables one to construct an argument for monism, stemming from endurantism and Hume’s Dictum. Lastly, we also take our previous discussion to have an important moral for the metaphysics of time, which we have so far not addressed. The moral concerns the A-theory of time, according to which the present is in some sense metaphysically privileged. Arguably the most serious challenge to the A-theory stems from relativistic physics: the A-theory requires there to be a privileged notion of simultaneity in order for there to be a privileged notion of the present, but relativistic spacetimes seem to lack a privileged notion of simultaneity. The standard A-theoretic response to this objection is to supplement orthodox relativistic spacetime with a privileged standard of simultaneity.45 However, many reject this extra posit on the grounds that it has no independent motivation. We believe our discussion provides the sought after independent motivation for a privileged notion of simultaneity, even setting aside the A-theory. Recall that we have argued that those who embrace the orthodoxy of nonqualitativism have reason to favor endurantism over perdurantism. Yet, crucially, any endurantist who embraces substantivalism is thereby committed to absolute simultaneity. As we saw in section 6, the endurantist substantivalist who embraces pluralism must countenance enduring spatial points. These points generate a standard of absolute rest, and in the context 45 See, for example, Markosian (2004) and Zimmerman (2011). 35 of Special Relativity, a standard of absolute rest also generates a standard of absolute simultaneity (being simultaneous with respect to the privileged inertial rest frame).46 On the other hand, if the endurantist substantivalist embraces monism—believing that the only fundamental individual is a three-dimensional space that endures though time—then this space itself serves as the privileged standard of simultaneity. So either way endurantist substantivalists are committed to a privileged notion of simultaneity. Moreover, substantivalism is widely taken to be more plausible than relationism in light of contemporary physical theories.47 Putting these points together, all who embrace the orthodoxy of nonqualitativism should arguably embrace a privileged notion of simultaneity, for reasons entirely independent of the A-theory of time. Let us, finally, reiterate the central general moral that we started with: the constraint of full lawfulness matters to debates about the metaphysics of persistence. We have seen that the constraint has independent motivation, and reveals some quite surprising commitments of the two central positions. There remains work to be done comparing and evaluating the resulting packages of views. Still, now we have before us the more fleshed out metaphysical visions of the world that we should arguably be adjudicating between. Whichever way the balance of considerations ultimately points, we’re confident that considerations of how best to preserve full lawfulness promise to breathe some new life into traditional debates concerning how things persist through time.