Section 0: Introduction

Change at least involves gain or loss of properties.[1] Gain or loss of properties requires difference in time.[2] Hence, change at least involves difference in time.[3] Intuitively, gain or loss of properties involves some property bearer,[4] i.e. an object.[5] A leaf, for example, might gain a color property – yellow – and lose another – green – in concert with the seasons. Moreover, it seems plausible objects involved in change remain the same through change, at least in some respects. A green leaf that becomes yellow likely retains other properties, e.g. shape, mass, etc. Hence, change appears to involve objects which gain or lose properties over time while often[6] retaining others.

A long-standing debate in contemporary analytic metaphysics is how to make sense of intuitions about the persistence of changing objects over time. Endurantism maintains – roughly – that objects are numerically identical across time and through property gain or loss.[7] The green leaf at t1 is numerically identical to the yellow leaf at t2. David Lewis[8] shaped contemporary discussion by posing the problem of temporary intrinsics for naïve versions of Endurantism. Lewis claimed objects bear intrinsic properties[9] – which do not depend on anything other than their bearer – such as shape and mass, and observed if Endurantism is true, it seems numerically identical objects may bear incompatible intrinsic properties at different times. But since it is plausible to maintain[10] that for any object(s) x and y, and any intrinsic property P, if x=y then x has P just in case y has P, it follows that incompatible properties at distinct times undermine numerical identity over time. This consequence of naïve Endurantism motivated Lewis’s alternative account of persistence – Perdurantism – which maintains an ontology of temporal parts each of which bear intrinsic properties. Characterizing a leaf changing shape over time, for example, involves a temporal part at t1 bearing a certain shape property and a temporal part at t2 bearing a distinct temporal property. Since these temporal parts are distinct objects bearing incompatible intrinsic properties, the problem of temporary intrinsics is no problem at all.

Advocates of Endurantism typically claim it is the commonsense view of persistence. This is both questionable and of unclear value in this metaphysics dispute. Fortunately, this is not the only motivation for accepting Endurantism. For this view of persistence has a native answer to what we might call the tracing problem, i.e. how objects are tracked over time.  According to Endurantism, tracking a given object from t1 to distinct time t2 is a matter of the numerical identity of the object at these distinct times. In contrast, while Perdurantism was designed to avoid the problem of temporary intrinsics, the mere existence of temporal parts bearing (in)compatible intrinsic properties at distinct times provides no answer to how to track a given object over time. For this reason, Perdurantism is often supplemented by claiming temporal parts are proper mereological parts of larger wholes, often characterized as worms stretching through space and time.[11] For Perdurantism thus supplemented, tracking an object over time amounts to tracking temporal parts through space and time. The leaf changing from green to yellow is, strictly speaking, a series of temporal parts – separated like a deck of playing cards viewed from the side – each bearing intrinsic properties. That is, the leaf is an entity extended in both space and time with proper parts appearing in series. Thus far, it seems then that Perdurantism[12] gains the upper hand in characterizing persistence, since it is designed to avoid the problem of temporary intrinsics, and can be straightforwardly supplemented to answer the tracing problem. But Endurantism can be supplemented just as easily to avoid the problem of temporary intrinsics, e.g. eschewing intrinsic properties and relativizing properties to times.[13] The leaf at t1 and t2 are numerically identical, though it bears, say, one shape-at-t1 property at t1 and another shape-at-t2 property at t2. Supplementing Endurantism in this manner results in a plausible contender in the dispute over the nature of persistence.[14]

We could say much more about which of these theories of persistence is preferable in this dispute, but our task here is not arbitration between these rival theories. Rather, we introduce a problem neither Endurantism nor Perdurantism is able to adequately address, even when supplemented as standardly done. In what follows, we examine to what extent Perdurantism and Endurantism can explain how objects generate other objects or sustain themselves over time through property gain and loss. Specifically in Section 1, we motivate the problem of generation, argue it is distinct from both the problem of temporary intrinsics and the tracing problem, and rebut reasons for thinking it is an insubstantial metaphysical problem. We examine prima facie answers to the problem of generation available to Perdurantism and Endurantism, noting the former can ultimately provide no answer to the problem while the latter provides at best inadequate answers. We then examine Endurantism supplemented with causally robust laws of nature in an attempt to address the problem of generation. Noting this version of Endurantism comes close to adequately addressing the problem of generation, we observe it still falls short. In Section 2, we provide a novel solution to the problem of generation based on dispositional properties, which explains how objects generate other objects and sustain themselves through property change over time. We examine how this solution differs from varieties of Endurantism, in particular the version supplemented with robust laws of nature, and argue dispositional properties succeed where robust laws of nature failed.

Section 1: The Problem of Generation

Change appears to involve objects which gain or lose properties over time while – in many cases - retaining other properties. Understood loosely, either Perdurantism or Endurantism might fit this gloss on change.[15] But change is not obviously exhausted by our initial observations. For example, persisting objects appear to generate later associated objects or sustain themselves over time.[16] An oak tree at t1 stands tall in a forest, but is reduced to ash by t2; a home constructed at t3 is given a new coat of paint at t4. A plausible explanation for the generation of ash from oak would seem to involve the existence of the oak being relevant to the existence of the ash; a plausible explanation for the home remaining the same through painting would seem to involve the existence of the home at the former time being relevant to the existence of the home at the latter time. Still, mere relevance is insufficient. That an arsonist remembered to set fire to the oak tree is relevant to the explanation of the existence of ash at t2; that an arsonist forgets to burn down the home at t3 is relevant to the explanation of why the home exists at t4. However, the arsonist’s memory does not seem to explain how the oak tree generates ash or how the home sustains its existence over time. Mere relevance is not enough. Intuitively, the existence of the oak at t1 is causally relevant to the generation of the existence of the ash at t2 and the existence of the home at t3 is causally relevant to sustaining the home at t4. Even so, mere causal relevance is insufficient to characterize generation. That there presumably was a Big Bang is causally relevant to the oak tree generating ash; the existence of construction workers who built the home is causally relevant to the home sustaining itself. But again, neither the Big Bang nor the existence of the construction workers explains respective generations.[17] An explanation of object generation seems to involve matters more local to the object than mere causal relevance captures, i.e. intrinsic properties. This suggests change involves in some cases objects generating other objects or sustaining themselves over time through causally relevant intrinsic properties. Call the task of adequately explaining this additional ‘generation’ aspect of change, the problem of generation.

Identifying a problem is one thing, but showing it is a problem worth pursuing another. To be worth pursuing an answer for, it must be shown the problem of generation is a distinct substantive metaphysical question and a distinct substantive metaphysical question. If the problem is not distinct from, say, the problem of temporary intrinsics or the tracing problem, then we should expect Perdurantism and Endurantism to provide an answer to the problem of generation since each provides respective answers to the other two. Supposing the problem is distinct, if the problem of generation is not a substantive metaphysical question, then it should not be viewed as a cost if a given theory of persistence does not provide an adequate answer. The appearance of object generation might be maintained as nothing more than an appearance. We will explore whether the problem of generation is distinct and substantive within the contexts of Perdurantism and Endurantism, arguing neither theory provides an adequate solution to the problem, and there seem few reasons to think the problem of generation is insubstantial.  

Perdurantism and Generation

Failure to adequately address the problem of generation is easiest to see with respect to Perdurantism. Strictly speaking, a temporal part at t1 is only related to another temporal part at t2 in virtue of being parts of the same whole. But proper parthood does not amount to generation. My index finger and thumb are also proper parts of the same whole, but either generates the other. This is mere difference, and mere difference is not change, any more than a fire poker being hot at one end and cold at another at the same time is. This is not a novel observation. Thomson, for example, famously criticized Perdurantism as “crazy metaphysics” on similar grounds, i.e. since it seems to involve the creation of objects ex nihilo.[18] Defenders of Perdurantism sometimes rebut such criticism by claiming temporal parts of the same mereological whole do generate other temporal parts.[19] For temporal parts bear causal relations to other temporal parts that are part of the same spacetime worm. However, this answer is misleading.[20] Causal links between temporal parts - as understood by defenders of Perdurantism – typically lack any sort of robust connection. Defenders of Perdurantism often understand this theory of persistence against a background commitment to Neo-Humeanism,[21] i.e. the thesis that there are no necessary connections joining events over time, rather, there is just “one thing after another.” As a consequence, there are only regularities through spacetime, though defenders of Neo-Humeanism claim some regularities are better than others, namely, those important to scientific investigation.[22] On this view, temporal parts over time are causally linked, and some of these regularities are more important than others, e.g. a series of temporal parts of a leaf is more important than a series of randomly selected temporal parts. But despite the legwork, it should be clear why this provides no answer to the problem of generation. Generation is more involved than merely identifying useful regularities. A temporal part p1 of a home at t1 generating a temporal part p2 of the same home at t2 is less a matter of whether we find this regularity important, and more a matter of the house. Perdurantism cannot accommodate the needed sort of robust causal connections to adequately answer the problem of generation. But if Perdurantism thus construed provides an answer to both the problem of temporary intrinsics and tracing, then since the theory does not provide an answer to the problem of generation, it seems the latter problem is distinct from the other two.

Defenders of Perdurantism might claim, however, not answering the problem of generation is not a cost, since generation is at best a confused concept. If what is meant by this response is that the pre-theoretic concept of generation is confused, I am willing to concede this may be true. But it seems no more or less confused than many other metaphysical pre-theoretic concepts were or are, e.g. modality, composition. Like these other concepts, intuitions about generation plausibly track something in reality. But this observation, combined with granting the pre-theoretic concept of generation is presently unclear, suggests we need further examination of generation, say, within the context of a systematic metaphysical theory, rather than that we should ignore generation and remain ignorant of it. On the other hand, if advocates of Perdurantism mean instead that generation seems confused within the context of Perdurantism, I concede the point. But Perdurantism is not the only lens through which we might view generation, so this response is hardly compelling.

More forcefully, proponents of Perdurantism may claim this theory of persistence is precisely the lens by which we should view generation, and any other persistence related topics. Such a response seems best understood as conceding that not answering the problem of generation is a cost, but simultaneously contending it is one worth paying. This, moreover, can be motivated by observing Perdurantism fits naturally within a broader systematic metaphysic that provides answers to various linguistic, ethical, and logical[23] problems, as well as answers the problem of temporary intrinsics and tracing. This broader systematic metaphysic is, additionally, parsimonious, well-confirmed, and perspicuous. Since this broader picture answers so many questions, and seems to accommodate many other intuitions, it seems worthwhile to reject other – perhaps less well understood – intuitions, such as that underwriting the problem of generation. This is common enough method in scientific investigations. Tables, apples, etc., are largely comprised of empty space, but our perceptions of these objects suggest otherwise. As we become more sophisticated investigators, we put aside some intuitions that conflict our otherwise well-confirmed, parsimonious, general, perspicuous theory of the world. So too for a broader systematic metaphysical picture that includes Perdurantism as a sub-theory.[24] Hence, advocates of Perdurantism might claim, giving up on the appearance of generation – whatever that appearance amounts to – is an acceptable cost. These are fair points in favor of pushing aside the problem of generation, but note while the Neo-Humean picture is impressive, it is not obviously the end of systematic metaphysical inquiry. Much recent work outside the Neo-Humean status quo has precisely sought to introduce robust causal connections between events, states of affairs, objects, etc., providing grounds on which an adequate answer to the problem of generation might be offered rather than ignored.[25] Insofar as one is moved by the intuition that generation is more robust than mere difference between temporal parts, one should at least be motivated to engage in construction of alternative systematic metaphysical theories amenable to theories of persistence other than Perdurantism. So while defenders of Perdurantism might admit the cost of not answering the problem of generation and claim Perdurantism is worth the price, negotiations are not yet over, and other theories of persistence will likely prove more amenable to generation.

Our tentative conclusions thus far then are that if it is granted that Perdurantism addresses the problem of temporary intrinsics and the tracing problem, it nevertheless does not address the problem of generation, which is plausibly worth addressing. The former conclusion strongly suggests the problem of generation is a distinct metaphysical problem from the other two; the latter conclusion suggests we have as of yet little reason to suspect the problem of generation is not a substantive metaphysical problem worth addressing. We turn next to Endurantism and explore whether this theory of persistence answers the problem of generation, or provides reasons to think this is not a substantive metaphysical problem worth our time.

Endurantism and Generation 

Supposing Endurantism provides an answer the problems of generation and tracing, one might think Endurantism provides an answer to the problem of generation. Not so. To see why, first note that Endurantism has a native explanation for how objects remain the same through the gain or loss of properties: numerical identity. Numerical identity is simple - an equivalence relation over its relata – and primitive – an indefinable commitment of the view. Note second, Endurantism is committed to whatever exists being a brute, unexplained, fact. This should be unsurprising; commitment to such a simple view of existence is something Endurantism shares with Perdurantism. Sure, once something is presumed to exist, both Endurantism and Perdurantism may provide explanations for why later objects exist. But neither theory of persistence is in the business of trying to explain existence proper, or explain – ultimately – why objects exist. Of course, when it comes to persistence, since Endurantism is committed to objects persisting as a matter of numerical identity, these theories sharply come apart. For since the existence of a given object is a brute fact for Endurantism, and objects persist according to a primitive notion of numerical identity, then persistence is ultimately explained by brute facts related by a primitive. This is – roughly – why Endurantism cannot adequately address the problem of generation. But this point is worth belaboring.

The issue the preceding observations raise for addressing the problem of generation in the context of Endurantism is easiest to illustrate by focusing on explaining how a given object sustains itself over time without property gain or loss. If Endurantism cannot adequately answer this aspect of the problem of generation, then it plausibly cannot adequately answer the more general problem of how a given object generates other objects or sustains itself through property loss or gain over time. Now, Endurantism claims numerical identity explains why object o at t1 sustains itself at t2. This is admittedly a more robust causal connection than anything Perdurantism allows. In this respect, Endurantism at least provides an answer to the problem of generation. But this answer is inadequate to explain the corollary problem of generation. For the explanation for why o1 at t1 generates o2 at t2 is because o1=o2, and since numerical identity is primitive and existence brute, this amounts to saying o1 generating o2 is a brute fact primitively related to itself. But asserting that objects sustain themselves is a brute fact bearing a primitive relation to itself seems more a description of the problem than an explanation. And if the Endurantism answer to the corollary problem to the problem of generation is inadequate then it seems transposing this answer to the general problem of generation will be equally unsatisfying. Since Endurantism provides answers to the problems of temporary intrinsics and tracing, but fails to provide a satisfying answer to the problem of tracing, it seems the problem of generation is distinct from the other two problems.  

Defenders of Endurantism might be unhappy with the sparse version of Endurantism employed in the preceding discussion. For Endurantism clearly needs to be supplemented to answer the broader problem of generation, even if we suppose numerical identity is an inadequate explanation of the generation of an object from itself over time. Objects gain and lose intrinsic properties over time, and presumably Endurantism must be supplemented with some machinery to explain how properties are gained and lost. Defenders of Endurantism might claim that whatever explains the gain and loss of intrinsic properties generally, will provide an answer to why objects generate later objects. Nevertheless, it is worth noting that standardly understood, Endurantism is also committed to whether an object having or not having a property at a given time being a matter of brute fact. Strictly speaking, according to Endurantism what explains why object o is a given shape at t1 and another shape at t2 is simply that o is the first shape at t1 and the second at t2. This explanation seems no better than appealing to numerical identity over time. More promising, however,[26] is supplementing Endurantism with commitment to laws of nature as governing the gain and loss of properties over time. For example, there may be a law of nature to the effect that necessarily, for any leaf at t1 with a certain shape in context C1, at t2 in context C2 that numerically identical leaf will have a distinct shape. Causal connections between property instantiation on such a view would be robust. And since these causal links are governed by necessary laws, this seems a better explanation of property gain and loss than simply assuming brute facts about property instantiation, existence, and numerical identity.[27] Moreover, this proposal appears to provide a straightforward answer to the corollary problem of generation: necessarily for any o1 at t1 in context C1, o2 at t2 in context C2 is such that o1=o2, where each context is spelled out appropriately. It seems then, we have discovered a supplement to Endurantism that provides an adequate answer to the problem of generation.

Putting aside worries one might have with laws of nature governing property gain and loss generally speaking,[28] there seems a significant worry worth raising to Endurantism thus supplemented. Simply put, on this proposal whatever was intrinsic about generation vanishes. An object numerically identical to itself over time is not due to the object sustaining itself over time, but rather an extrinsic law of nature generating numerical identity. Similarly, a leaf changing shape is understood, on this proposal, as extrinsic laws of nature governing transitions from one shape to the other. The intrinsic properties of the leaf at best play a role in generation insofar as they satisfy conditions for being governed by a particular law. But an object bearing intrinsic properties that satisfy being governed by an extrinsic law of nature through a process of generation to another set of intrinsic properties, is generation by an indirect route. The object itself plays an ancillary role in generation, and this seems to fall short of our motivating intuition that earlier objects generate later objects or sustain themselves over time.

If the preceding is correct, then it seems the answers provided by Endurantism to the problem of temporary intrinsics and the tracing problem do not adequately answer the problem of generation. Moreover, if the preceding is correct, then supplementing Endurantism with necessary causal laws of nature also falls short of answering the problem of generation, though it gets much closer than other varieties of Endurantism considered. However, at this stage advocates of Endurantism might simply reject anything more must be said to address the problem of generation. They might maintain the answers provided to the problem of generation – either generation being primitive or robust laws of nature - are adequate, since the problem itself deserves no better sort of answer. On the former view, an object o at t1 being numerically identical to t2 despite changing properties is an intrinsic matter to the object o, and numerical identity over time is at least a robust causal connection, even if property instantiation is brute. On the latter view, an object o at t1 being numerically identical at t2 despite changing properties is an extrinsic matter, due to governance by robust laws of nature, and property instantiation is explained by these laws. In either case, the respective advocate might claim, we have as adequate an answer to the problem of generation as we need. In response, I grant advocates of Endurantism of the second stripe make a good case for leaving the problem of generation without a full answer. In light of this second answer, however, I find answering the problem by appealing to primitive identity unsatisfying, so I am much less compelled to consider Endurantism of the first stripe as providing an adequate answer to the problem. Still, part of the difficulty in adjudicating any answer to the problem provided stems from not clearly seeing what an adequate answer to the problem of generation would be. It is thus worth examining what a full answer might be, in route to determining whether we should be satisfied with, say, this second form of Endurantism.   

Section 2: A Third Turn betwixt Them

Dispositional Generation

Neither Perdurantism nor Endurantism of any variety described above permits the existence of irreducible dispositional properties had by objects. Insofar as either countenances the existence of such properties, they are considered reducible, or supervenient, or grounded on other so-called categorical properties had by objects. It is not difficult to see why metaphysical theories have preferred reducing dispositional properties to others in most cases, since dispositional properties are not extensional. Adequately characterizing the shape, mass, electronegativity – that is, categorical properties – of a sample of table salt is something that can be done at a single time and place. In contrast, adequately characterizing the disposition table salt has to dissolving when placed in unsaturated water cannot obviously be done at a single time and place. Had no sample of table salt ever contacted water, it seems table salt would have still had the disposition to dissolve. Characterizing dispositional properties, it is commonly thought, requires extending beyond what happens at a time and place, into what could – but may never – happen. Suffice it to say, systematic metaphysics are much cleaner when dispositional properties can be entirely explained in terms of non-dispositional properties.[29] Otherwise, it seems one must introduce irreducible modal properties into one’s systematic metaphysic.

And yet many recent metaphysicians who advocate various powers-based theories of causation, laws of nature, and persistence, seem to prefer messiness to the neat standard options one finds in contemporary analytic metaphysics.[30] This recent movement suggests the last option we will consider for addressing the problem of generation: objects generate other objects or sustain themselves over time due to irreducible dispositional properties.[31] To illustrate, consider first an object o1 at t1 in context C1 generating the existence of a distinct object o2 at t2 in C2. The dispositional proposal on offer is committed to o1 having dispositional properties that act in concert with other dispositional properties in C1 and together bring about the existence of o2 in C2 at t2. Moreover, leaning further on the notion of dispositional properties acting in concert, we might say that the dispositional properties of o2 in C2 at t2 also act in concert with those properties of the preceding context, object, and time. More cleanly, the first object manifests a disposition to generate the second, and the second manifests a disposition to be generated by the first. On this proposal, moreover, the relevant dispositional properties are intrinsic to the respective objects. Object o1 generating o2 stems from an intrinsic dispositional property had by o1, and o2 permitting – as it were – generation by o1 stems from an intrinsic dispositional property had by o2. Moreover, on this proposal the relevant dispositional properties are causally robust. That is, we can say necessarily, if object o1 exists at t1 in C1, then o2 exists at t2 in C2.[32] We have then, an answer to the problem of generation that permits robust causal connections between generated objects and captures generation as an intrinsic affair. This proposal also answers the corollary problem of generation: necessarily, if object o1 exists at t1 in C1 then o2 exists at t2 in C2 and o1=o2, when the respective contexts are appropriately spelled out. Altogether then, this dispositional proposal provides robust causal connections and intrinsic properties in answering the problem of generation.

Dispositional answer to the problem of generation in hand, we can return to the answer offered by Endurantism supplemented with robust laws of nature. Recall, the latter answer solved the problem by introducing necessary laws of nature that governed objects generating other objects and sustaining themselves over time. While this variety of Endurantism allowed for robust causal connections in generation, we noted it seemed inadequate since the stated robust causal connections were extrinsic to object generation. The dispositional proposal, in contrast, ties robust causal connections to intrinsic properties of the relevant objects involved in generation. Glibly put, the dispositional proposal simply converts laws of nature into intrinsic properties, thereby satisfying the plausible constraint on an adequate answer to the problem of generation that generation be an intrinsic affair between the relevant objects. To that extent, the dispositional view provides a more satisfying answer to the problem than Endurantism supplemented with laws of nature.

That said, one may worry the dispositional proposal shares too much in common with the first Endurantism answer we considered to the problem of generation. There, existence and property instantiation was assumed a brute fact and numerical identity a primitive, which led to the explanation of persistence being brute and primitive. Similarly, one might argue that the dispositional view – thus far described – treats existence as brute, and both persistence and property instantiation as primitive. Hence, insofar as one found the former unsatisfying, one should also find the latter. In response, it is true that on this proposal existence is brute – just as it is on any of the other theories considered – and property instantiation is primitive just as on this rival version of Endurantism. Nevertheless, the properties instantiated on the dispositional proposal are not of the same kind as those one would have on the Endurantism proposal. That a given object instantiates a set of properties may be a primitive unexplainable fact, but if those properties are irreducibly dispositional, there are available explanations for why that object has or loses those properties later, namely, because dispositional properties are directed at other arrangements of properties in the world. Indeed, once the world is peppered with objects instantiating dispositional properties, which is admittedly a brute fact, gain and loss of properties over time is explained by these initial conditions. The same cannot be said for Endurantism of the first stripe, which lacks intrinsic irreducible dispositional properties. Given a world peppered with objects not instantiating irreducible dispositional properties, all properties on such a view will be reducible to some, say, categorical base. But then there is no obvious explanation for how the fact that an object has one set of categorical properties at one time is related to the fact that the same object has another – or the same set of – categorical properties later, other than numerical identity. In short, what distinguishes Endurantism of the first stripe from the dispositional proposal offered here is precisely that the latter provides an adequate answer to the problem of generation. So, even if these theories of persistence are similar, they can be distinguished based on how they address this problem.

Of course, much more must be developed for dispositional accounts of persistence to be considered legitimate contenders.[33] Still, some progress has been made on that front here. We have argued the little remarked on problem of generation finds no adequate answer among varieties of Perdurantism and Endurantism found in the extant literature on persistence. We have observed a novel dispositional solution seems to provide an adequate solution to the problem, while respecting intuitions about what features an answer to this problem should have. Generation, it seems, requires dispositional properties. And that is, perhaps, a surprising change to the standard picture of contemporary analytic metaphysics worth exploring in more detail.

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[1]There are nearby notions of change, e.g. mereological change. Gain or loss of parts may result in a gain or loss of some properties while retaining others, e.g. a red sphere is divided into two red hemispheres. I focus on property change as the more general notion.  
[2]We suppose time is a linear order of discrete temporal points (Benthem, 1983), though not much depends on this here.
[3]The converse does not seem to hold; time may proceed without change, e.g. two cards stacked against each other in equilibrium (Williams, 2019). (Shoemaker, 1969) argued for this claim, but the soundness of his argument is unclear. That does not mean the conclusion is false, however. See (Warmbrod, 2017).
[4]Trope theories of a certain stripe (van Cleve, 1985) might deny there are objects, but countenance change. We put such options aside for what follows.
[5]I intend to remain neutral over whether, say, objects are states of affairs, bare particulars, composites of tropes, etc.
[6]Change may involve complete loss of properties via destruction, e.g. a vase destroyed by a supernatural force.
[7]This is a standard gloss as found in (Sider, 2001), (Williams, 2019), among others.
[8](Lewis, 1986).
[9]The notion of intrinsic properties is notoriously difficult to characterize. The intuitive gloss suffices for our purposes, but see (Bird, 2007) and (Lewis, 1999), for discussion.
[10]This is, of course, a version of Leibniz’s Law restricted to intrinsic properties. (Ayer, 1954).
[11](Lewis, 1986). I put aside considering Stage Theory varieties of Perdurantism (Sider, 2001), in what follows.
[12]In the remainder, I will use “Perdurantism” to refer to the version of this theory of persistence supplemented with spacetime worms.
[13]E.g. (Haslanger, 2003).
[14]In the remainder, I will use “Endurantism” to refer to the version of this theory of persistence supplemented with relativized temporal properties. Admittedly, this restricts the scope of my conclusion, there is not enough space for a full treatment of varieties of Endurantism here.
[15]Perdurantism has the trickier time, since in most cases of change for this theory of persistence objects either always retain all their properties – if viewed as a spacetime worm – or never retain any – if viewed as temporal parts. 
[16](Armstrong, 1997, pg. 74) observes the “actual bringing into existence” of later temporal parts by earlier temporal parts is a necessary feature of persistence.
[17]Pace what (Lewis, 1986b) says about how we should understand causation. There, Lewis motivates thinking of explanation in purely causal – regularities we find important – terms. For x to explain y, all that is needed is that x exist in the causal history of y, e.g. the Big Bang is an explanation, in some sense, for me writing this paper. This would allow – at the risk of a verbal dispute - advocates of Perdurantism to say causal relations provide all the explanation one needs.
[18](Thomson, 1983).
[19](Sider, 2011).
[20]Some (Williams, 2019), say it is confused. I doubt Sider is confused about his commitments. I take him as providing damage control in the cited passage.
[21]See (Schrenk, 2010), (Jackson, 1998), (Lewis, 1986), and many others for evidence.
[22](Lewis, 1986), (Sider, 2011).
[23](Lewis, 1973; 1986; 1999), (Sider, 2001; 2011).
[24](Lewis, 1986).
[25]See (Martin, 1997; 2007), (Williams, 2019), (Mumford & Anjum, 1998), (Mumford, 2004), (Bird, 2007), (Armstrong, 1987; 1997), (Lowe, 1994), (Tugby, 2013; 2013b) among others.
[26]What follows is inspired by (Armstrong, 1983; 1997)’s characterization of nomic necessitation.
[27]One might worry there are nevertheless brute necessary laws of nature which need further explanation. This is outside the scope of our discussion. That said, even if this is a problematic feature of the variety of Endurantism under discussion here, it seems less problematic than simply brute facts and identity explaining generation.
[28]And there are many. See (Bird, 2007), (Bird, 2016), (Mumford, 2004), (Lewis, 1986) among others.
[29](Bird, 2003), (Jackson, 1998), (Sider, 2011).
[30](McKitrick, 2009; 2016), (Bird, 2003; 2007), (Williams, 2019), (Tugby, 2013, 2013b).
[31]Though I do not have the space to defend this here, I have a preference for fundamental irreducible intrinsic dispositional properties as constituents in states of affairs, i.e. particulars bearing properties. Higher level dispositional properties may be reducible to lower level dispositional properties, but ultimately everything is dispositional, and properties are dispositional all the way down. See (Williams, 2019), (Tubgy, 2013, 2013b), and (Bird, 2007) for similar versions of powers.
[32]One might wonder what it means for, say, o2 to have the dispositional property to be generated at t2 in C2 by o1 at t1 in C1, if at t1 in C1 o2 does not exist. I presume but do not have the space to defend, that the relevant dispositional properties are abstract objects realized in concrete objects when certain conditions obtain. The dispositional properties of o1 at t1 in C1 are realized, then generate C2 at t2 which realizes other dispositional properties, namely, those which act in concert to generate o2 at this time and context.
[33]For example, dispositional theories of persistence must also answer the problem of temporary intrinsics and the tracing problem. Concerning the latter, it seems plausible dispositional properties in concert with other dispositional properties constrain possible processes, e.g. lives, in which an object might participate, providing grounds on which to trace objects. Concerning the former, it seems open to advocates of dispositional theories of persistence to claim, say, an object of a certain shape at a given time may have the power to take on another shape at a later time. In the limiting case, this ‘other’ shape will in fact be the same shape. In more interesting cases, distinct shapes. John at t1 might manifest sitting while it being true of John at t1 that he has the power to stand though it is not manifesting, while John at t2 might manifest standing while it being true of John at t2 that he has the power to sit, though it is not manifesting.