p45

For Humean responses to this worry, see Dorst (2019), Bhogal (2020c), and Hicks (2021). 23 counterexamples like Future Tuesday Reset drive home that nothing in endurantism itself secures full lawfulness, if in fact things never pop out of existence we’d like some independent motivation for this additional feature of our world. Why is it that things never pop out of existence? This independent motivation is what the strong laws strategy is meant to provide. Yet given the Humean theory, its being a law of nature that, say, things never pop out of existence, just consists in things in fact never popping out of existence, and moreover this claim being very simple and informative. In this way, given the Humean theory, the strong law strategy merely presupposes that things don’t pop out of existence, rather than providing any independent motivation for this claim. What about the broad family of views that explain lawhood in terms of the intrinsic causal powers of fundamental properties? The general view here is that something having certain fundamental properties might necessitate certain dynamical effects, simply in virtue of the thing having the fundamental property. Laws of nature are then the necessary truths stating that everything that has the fundamental property has such-and-such dynamical behaviour.32 As a toy example, it might be that necessarily anything with mass thereby attracts other objects with mass, simply in virtue of what it is to have mass. We think that such views hold some promise of securing endurantist strong laws, but they still face significant challenges. A first worry is that prominent versions of this view, often called ‘dispositional essentialism’, would need to appeal to the essences of fundamental properties in order to secure a distinctively nomically necessary version of Ontological InertiaMonism, and this appeal to essences raises some of the same concerns as our first attempt of explaining Ontological InertiaMonism by appeal to essences.33 Moreover, alternative ways of developing the view that do not employ the notion of essence arguably nevertheless also fall prey to one of the worries we raised for the essentialist strategy, stemming from lack of informativeness. For instance, suppose that instead of employing the notion of essence, the view stated that what it is to be a 32 For some views in the relevant family, see Shoemaker (1980, 1998), Bird (2007), Jacobs (2011), Demarest (2017), Tugby (2021), Builes (2021b), and Kimpton-Nye (2021). 33 As mentioned above, views in the family at issue often explicitly aim to vindicate the result that the laws of nature turn out metaphysically rather than merely nomically necessary. On such versions, we could speak of Ontological InertiaMonism itself, rather than its distinctively nomic analogue. 24 certain fundamental property (say being a material object) necessitates that anything that instantiates it never pops out of existence. Yet this would still not get us very far in independently motivating why necessarily nothing pops out of existence. Insofar as we were unsure about this latter claim, we will be just as unsure about this claim detailing what it is to be a certain fundamental property (or analogous claims about what certain causal powers necessitate, and so on). A second worry has to do with the kinds of dispositions or causal powers that are needed to secure endurantist strong laws. One natural way to think of dispositions is that they necessitate that an object will behave in certain ways in certain conditions if that object continues to exist. For example, perhaps the property being negatively charged necessitates that (say) an electron will take a certain trajectory in the presence of certain electromagnetic fields if the electron continues to exist. Alternatively, perhaps the property being negatively charged necessitates the unconditional claim that an electron will take a certain trajectory in the presence of certain electromagnetic fields (and hence that an electron will continue to exist in the presence of certain electromagnetic fields). Let us say that a weak disposition of an object is a disposition whose manifestation conditions are always conditional on the future existence of that object, and let us say that a strong disposition of an object is a disposition whose manifestation conditions are not conditional on the future existence of that object. In order to secure endurantist strong laws, the causal powers theorist must hold that the causal powers of fundamental properties involve strong dispositions. This claim merits further discussion than we can give it here. But let us register a couple of difficult questions proponents of the claim must answer. Is it metaphysically necessary that fundamental causal powers involve strong dispositions? If it is, then why are weak dispositions impossible? If it isn’t, then presumably there are possible casual powers, which we can label mass, charge, spin, etc., that are just like the fundamental causal powers in the actual world except that they involve only weak dispositions. Why is it that our world has the properties of mass, charge, and spin, rather than the properties of mass, charge, and spin? Furthermore, on the assumption that fundamental dispositions must have a categorical basis, what is the difference between the categorical bases of (say) mass, charge, and spin, and the categorical bases of 25 mass, charge, and spin?34 These are some of the questions that this strategy would have to answer in order to give a compelling account of endurantist strong laws. We don’t want to claim that principled answers to these questions cannot be found, but the proponent of the present strategy has their work cut out for them. The final main theory of lawhood is primitivism, according to which the notion of lawhood is fundamental.35 Like Humeanism, primitivism imposes no in-principle constraints on the form of the laws, so there’s no barrier to the endurantist’s strong laws counting as primitive laws of nature. Does countenancing the nomic analogue of Ontological InertiaMonism as a primitive law of nature independently motivate the principle? The answer will depend on one’s background views regarding the viability of primitive laws. Some have worried that primitive laws do no better than Humean laws at accounting for natural regularities (e.g. see Hildebrand 2013), and many have worried that it is unclear how primitive laws are supposed to “govern” the evolution of the universe.36 However, insofar as one is willing to appeal to primitive laws to account for other qualitative natural regularities, it seems that one should be equally willing to appeal to primitive laws to account for the distinctively nomic analogue of Ontological InertiaMonism. That being said, primitivism about laws of nature is a controversial theory, and one that we suspect many endurantists won’t want to endorse. To sum up, we think that the strong laws strategy faces different objections depending on one’s background metaphysics of laws. On some views, appealing to strong laws is perhaps more successful than attempts 1 and 2 above, in terms of essence or Temporal Rationalism. Nevertheless, we still maintain that the most promising and illuminating strategy for endurantists to pursue goes via attempt 3 above, which appeals to Hume’s Dictum. 34 Alternatively, a defender of endurantist strong laws can say that the kinds of physical properties investigated by physics (e.g. mass, charge, and spin) only involve weak dispositions, but every physical object in the universe possesses an additional “metaphysical” strong disposition to keep on existing. Many of the same questions would arise on this proposal. Is it metaphysically necessary that everything possesses the strong disposition to keep on existing? If not, why do things in the actual world possess that disposition? Lastly, what is the categorical basis of this strong disposition? 35 For proponents, see Carroll (1994, 2018), Maudlin (2007), and Kment (2014). 36 See Emery (forthcoming) for some different accounts of the notion of governance. 26 5. Perdurantism and Full Lawfulness This time, suppose again for illustration that it is nomically necessary that, for any time t, there is a single fundamental individual ψt (we’ll turn to more orthodox pluralist views in the next section). Further, suppose that Strong Perdurantism is true. As a result, for any distinct times t and t’, ψt ≠ ψt’. Given these assumptions, how might one bridge the gap between qualitative laws and full laws? The trouble for such a view comes via examples we’ve already seen, of mere haecceitistic differences between nomic possibilities. For example, given any four-dimensional nomic possibility w, we can simply generate new nomic possibilities as follows: pick two times t and t’ and swap the individuals ψt and ψt’ without changing any qualitative facts about w. Alternatively, consider some nomic possibility w containing some individual ψt, and consider the nomic possibility w, that’s qualitatively identical to w, except it contains some new individual ψ*t, that doesn’t exist at w, in place of ψt . Like the case of endurantism, the perdurantist might pursue two different strategies. First, they may supplement the laws of nature with a principle that holds with metaphysical necessity, which renders impossible the problematic putative possibilities. Second, they may try to modify the laws of nature so that the problematic possibilities are rendered nomically impossible, albeit still metaphysically possible. We think that this second strategy is untenable for the perdurantist. It is an important feature of endurantist strong laws that they can pin down which fundamental objects exist at future times in a purely qualitative manner: future fundamental objects are just whatever objects have already existed in the past. This is the crucial feature that allowed these qualitative laws to avoid threats to full lawfulness like Future Tuesday Reset. However, for perdurantists fundamental objects wholly located at one time never exist at any other times. So their strong laws must instead be non-qualitative, stating precisely which distinct things exist at future times. Otherwise, the laws will be vulnerable to haecceitistic threats to full lawfulness. There would presumably then need to be infinitely many such strong perdurantist non-qualitative laws, stating which particular things there will be for any way things could be non-qualitatively at any time at any nomic possibility. We don’t see how such laws could be stated in anything 27 approaching a non-arbitrary fashion, not to mention their infinite complexity. Indeed, none of the central positions in the metaphysics of laws would render an infinite list of nonqualitative propositions plausible candidates to be laws of nature. Consequently, we think that the perdurantist must maintain that the problematic putative possibilities are in fact metaphysically impossible. In particular, to block the relevant counterexamples, perdurantists should appeal to the modal doctrine of anti-haecceitism:37 Anti-Haecceitism: No metaphysical possibilities differ without differing qualitatively. Anti-haecceitism precludes mere haecceitistic differences between metaphysical possibilities, and clearly bridges the gap between qualitative and full lawfulness. The challenge for perdurantists is to independently motivate the modal doctrine of antihaecceitism: why is modal space restricted in this manner? After all, anti-haecceitism implies that every qualitative structure can be realized in only one possible way by any individuals. What explains this strong restriction on modal space? Indeed, it seems perfectly conceivable for a qualitative structure to be filled in by different individuals.38 It seems to us that the only way to adequately motivate anti-haecceitism is to endorse a qualitativist view, which recall says that necessarily there are no fundamental non-qualitative facts. Recall also from the outset that we’re taking for granted that every non-fundamental fact supervenes on some fundamental facts. As a result, qualitativism renders anti-haecceitism unmysterious: if necessarily all fundamental facts are qualitative, then no metaphysical possibilities differ only over non-qualitative facts, otherwise we’d have a case where the non37 Some more exotic weaker modal doctrines would also do the job here (e.g. those that allow for mere haecceitistic differences, provided some such difference must occur at all times or none, thereby preserving full lawfulness). However, we doubt anyone tempted by some such modal doctrine would settle for anything weaker than the principled stopping point of anti-haecceitism itself. 38 For further discussion and development of this worry for anti-haecceitism, see section 4 of Teitel (2021). 28 fundamental fails to supervene on the fundamental.39 We don’t think there could be a satisfying explanation of anti-haecceitism that doesn’t go via such a qualitativist doctrine. 40 The alternative would be to reject the demand to independently motivate anti-haecceitism, and instead to adopt it as a brute constraint on the space of metaphysical possibilities. We want to just make a comparative response to such a view: notice how sharply it contrasts with the sorts of proposals that we considered in the previous section on behalf of endurantists. For example, the endurantist proposal of appealing to Temporal Rationalism, or appealing to Hume’s Dictum while also espousing non-Humean necessary connections in nature, each offer some independent motivation for full lawfulness given endurantism. The present proposal to accept anti-haecceitism as a brute modal constraint fails to offer any similar insight. We therefore conclude that those who reject qualitativism should take endurantism to have a distinctive advantage over perdurantism. 6. Full Lawfulness and Pluralistic Ontologies We have so far been discussing how the constraint of full lawfulness promises to transform the traditional debate between endurantists and perdurantists given the assumption of threedimensional monism as a simplifying expository device. Does the dialectical situation change dramatically under more orthodox pluralistic conceptions of what fundamental individuals there are? We’ll see in this section that many, but not all, of the conclusions we reached in the sanitized monistic setting carry forward unchanged. There are three standard pluralistic ontologies. The first is a relationist ontology with only material objects like particles. The second is a “supersubstantivalist” vision that eschews material objects and countenances only spacetime, often motivated by contemporary field 39 On an eliminativist version of qualitativism, which says that necessarily there are no non-qualitative facts fullstop (whether fundamental or non-fundamental), we can simplify the reasoning in this paragraph (in particular, we’d no longer need the supervenience claim). 40 Those who reject qualitativism might try to explain anti-haecceitism by appealing to certain kinds of very strong qualitative and non-qualitative essential properties, of the sort investigated by Teitel (2019). But as discussed earlier in the main text, we agree with his claim there that such essentialist approaches are not actually explanatory. 29 theories combined with the doctrine that fields (including matter fields) are just properties and relations distributed over spacetime. The third is the standard “dualist” picture which countenances spacetime as well as some material objects, such as particles, located in spacetime. We’ll consider each of these visions in what follows, starting with perdurantism, then turning to endurantism, and then finally discussing “mixed” option according to which matter endures but spacetime perdures. a common Starting with perdurantism, here the dialectic rehearsed in section 5 is unchanged on any of the standard pluralistic ontologies. Given a perdurantist relationism, for example, we can generate threats to full lawfulness by considering nomic possibilities that permute particular temporal stages of whatever material objects there are, or by replacing some such stage with some new instantaneous stage, leaving everything qualitatively unchanged. Supersubstantivalism, as standardly understood, is a perdurantist view where the only objects are spacetime points and regions (which perdure), with various fields distributed over spacetime. Threats to full lawfulness in this setting are just those extensively discussed in the literature on the hole argument (recall section 2). The new nomic possibilities at issue agree on all qualitative propositions, but differ over which particular spacetime points have which field values within some subregion of spacetime. Finally, a pure perdurantist version of the dualist view would countenance perduring material objects located in a perduring spacetime. And here we are saddled with both the threats to full lawfulness faced by the perdurantist relationist as well as those faced by the perdurantist supersubstantivalist. The way forward for perdurantists who countenance any of the standard pluralistic ontologies is just the one we outlined in section 5. We think blocking the threats to full lawfulness requires adopting the modal doctrine of anti-haecceitism. Yet this modal doctrine demands some independent motivation. And the best means of doing so goes via the qualitativist doctrine that necessarily there are no fundamental non-qualitative facts. We don’t take appealing to essentialist facts to offer a promising alternative. Indeed, the only alternative option for perdurantists would seem to be to embrace anti-haecceitism as a brute modal principle. Let’s turn now to how the three pluralistic ontologies look under endurantism. Here the dialectic is more complex. Let’s start with an endurantist version of a relationist view, and for 30 simplicity let’s assume that the relevant fundamental material objects are just particles. Notice that Future Tuesday Reset poses a counterexample to full lawfulness for endurantists in a pluralist setting: just imagine whatever enduring particles there are popping out of existence and being replaced by distinct enduring particles, all the while preserving all qualitative facts. So it seems that pluralist endurantists must embrace some analogue of Ontological InertiaMonism to rule out such possibilities. In the monist setting, just requiring that the one thing there is continues to endure forever was sufficient to pin down all future non-qualitative facts given some initial state and qualitative lawfulness. However, there are two new worries that arise in a pluralist relationist setting. First, there is a worry that particle number might not be conserved through time. For example, consider an example of radioactive decay where a neutron (made up of one up quark and two down quarks) transforms into a proton (made up of two up quarks and one down quark), an electron, and an electron antineutrino.41 In this example no pluralist principle akin to Ontological InertiaMonism can fix the identity of the post-decay particles since there are strictly more particles after the radioactive decay than before the radioactive decay. This shows that any endurantist particle-based ontology has a hope of securing full determinism via a principle of ontological inertia only if particle number is conserved.42 Second, even if we restrict ourselves to a particle-based ontology where particle number is conserved, we need a principle that not only rules out enduring objects popping out of existence, but also dictates how they endure across time.