Perdurantism is traditionally construed as the view that persisting objects are four-dimensional (4D) entities with temporal parts. 1 Endurantism, the chief rival, is associated with the denial of every aspect of the perdurantist picture—that is, endurantism is typically understood as the view that persisting objects are temporally unextended three-dimensional (3D) entities without temporal parts, which exist entirety at every instantaneous region through which they persist. However, the endurantism/perdurantism distinction is not exhaustive. There are two principal questions at stake here: (i) do persisting objects have temporal parts? And, (ii) are persisting objects temporally extended? Perdurantism is associated with affirmative answers both, whereas endurantism is associated with negative answers to both. But in the following discussions it will become clear that these questions are separable—one need not give the same answer to both. To this end, I argue here that there’s room left in the persistence landscape for a theory of persistence that’s too often overlooked; a theory of persistence according to which persisting objects are 4D objects without temporal parts. This view is sometimes conflated with endurantism, other times it’s conflated with perdurantism. But I argue that it should be considered separate from both, and each of these three views bear different burdens.
To this end, I first distinguishing perdurantism and endurantism with an eye towards emphasizing the room left for the non-standard theory of persistence I ultimately want to focus on here. I then present this account—which I call transdurantism—and disambiguate it from perdurantism and endurantism. In doing so, I initially set the three views apart in the simplest terms, but in the interest of precision I capitalize on a few related metaphysical discussions to develop a more precise account of the key differences: location relations and the distinction between different kinds of simples (multi-locators and spanners). As we’ll see, the proponent of transdurantism will answer (i) in the negative, and (ii) in the affirmative. 2 As my primary aim here is to highlight this under-discussed theory of persistence and emphasize why it must not be conflated with endurantism or perdurantism, my goal isn’t really to convince the reader that transdurantism should be the favoured theory of persistence tout court. Rather, the purpose of this paper is to establish that transdurantism is distinct from endurantism and perdurantism, and that it is not untenable—I want to get transdurantist to the table as a separate theory of persistence as it has unique metaphysical commitment compared to endurantism and perdurantism; we do a disservice when we fail to disambiguate transdurantism from the other prominent theories of persistence. And once we properly pull these three views apart, we can more accurately assess the challenges they each face. I end by taking steps in this direction by briefly looking at a few classic and contemporary problems from the persistence literature to show some of the ways in which transdurantism might handle such worries. I’ll show that transdurantism should be a participant in the persistence debate in its own right, even if some have reservations about it.
The Persistence Landscape
Let’s start by articulating perdurantism and endurantism. 3 Then, we’ll turn to transdurantism.
Perdurantism and Endurantism
As noted at the outset, perdurantism is the view that objects persist through time by having temporal parts in an analogous way to how we ordinarily think objects are extended across space: Something perdures iff it persists by having different temporal parts, or stages, at different times, though no one part of it is wholly present at more than one time. (Lewis 1986: 202) So, according to the perdurantist, a persisting object is one which exists at a 4D region with (proper or improper) parts at every sub-region thereof—here a persisting object is a “space-time worm”, divisible every which way into parts. 4
While this is the standard way of articulating perdurantism, endurantism is often parsed in a variety of different ways. For instance, endurantism is sometimes parsed merely as the denial of temporal parthood (Parsons 2007; Dorato 2012). However this is not the only way endurantism is presented. Other times, endurantism is presented as a thesis about multi-location (Barker and Dowe 2003; Sattig 2006). Or in terms of the denial of temporal extension (Hale and Johnson 2003; Hawley 2004: 203; McGrath 2007). This survey of the different ways in which endurantism is traditionally characterized is by no means exhaustive, but it highlights the different notions used to capture the endurantist picture. While it’s not obvious that any one of the above characterizations entails the others, because they’re often treated interchangeably we can say that endurantism is typically characterized by all these claims. So understood, endurantism is the view that persisting objects exist at more than one instantaneous space-time region, yet do not have any proper temporal parts and are not 4D objects; they are, instead, at most 3D objects. However, before proceeding any further, it’s important that we pre-empt a source of potential confusion. Confusion might arise here depending on what we take the denial of temporal extension to entail. If to have temporal extent just means to exist at more than one instantaneous space-time region, then an object which lacks temporal extent is one which does not exist at more than one instantaneous space-time region. But this would mean no object would ever endure if enduring objects lack temporal extension—there could be no persisting 3D objects! Since I don’t want to prejudice this discussion against the endurantist, more needs to be said about how an enduring object can be a 3D object. The endurantist does so by conceptualizing them as recurring entities. I take it that when someone talks about endurantism as the view that 3D objects persist from one time to the next in virtue of the selfsame 3D object existing at those different times, this notion of recurrence is what they have in mind—it’s in this way that the endurantist gets persistence without temporal extension.
We can better understand the difference between endurantism and perdurantism, and the theoretical space left for other positions, if we unpack a few key concepts. In particular, we can specify what we mean when we say that some object bears some particular location relation with some particular space-time region. Location relations pick out the relationship between an object and the space-time regions at which it exists: for some object, O, which exists at some space-time region, R, we can say that there exists some kind of relationship between O and R—this will be a location relation. As we’ll see, an object can have different location relations with different regions, which each carry different implications. For our purposes here we need to draw apart only a few location relations: weak location, exact location, and whole location. Let’s start with weak location and say that: O is Weakly Located at R, iff R is not completely free of O. Notice that weak location only requires that there be some portion of O in R. To illustrate with an example, say I’m sitting in my car. I’m weakly located in the region defined by the car interior as it’s not completely free of me. This is the case even though I don’t entirely fill up that region. Also notice that I would still be weakly located there whether all of me were in the car or if I had an arm out the window. We can use weak location neutrally between our theories of persistence to define persistence: to say an object persists is to say that it’s temporally weakly located at many, temporally disjoint, space-time regions. This will be satisfactory for the perdurantist since, according to her, persisting objects will only ever be partially at those instantaneous space-time regions through which it persists (and thus weakly located at them). This will also be satisfactory for the endurantist since, according to her, an object persist by recurring at many temporally disjoint space-time regions (and thus will be weakly located at all those regions).
In other cases, though, we might mean something more precise when we talk of an objects’ location. Sometimes we might want to pick out a region which an object perfectly fits into. That is, it’s exact location. More precisely, let’s say that: O is Exactly Located at R iff O has the exact same size, shape, and dimensionality as R and that O exists at R. 5 Regions I’m exactly located at will be those regions I exactly fit into. Were I to exist only for an instant, my exact location would be the region defined by the 3D outline of my body. Notice that when it comes to persisting objects, perdurantists and endurantists will disagree about an objects’ exact location. The perdurantist will say it can only be the 4D region through which it persists (since a perduring object is a 4D object, the 4D region at which it exists will be the only region which has the same size, shape, and dimensionality as that object), meanwhile the endurantist will say that a persisting object can only be exactly located at instantaneous 3D regions (since enduring objects are merely 3D objects, a 4D region cannot be an eligible candidate for the exact location relation of an enduring object). 6
There’s a third location relation we might sometimes need to use. Sometimes, we might want to say that: O is Wholly Located at R iff O is exactly located at R, or exactly located at a super-region of R, and no proper part of O is missing from R. One might be tempted to think O will be exactly located anywhere it’s wholly located. This is certainly what a perdurantist thinks. The perdurantist, would say your exact location and your whole location are the same—that 4D region through which you persist. This is the case because a perduring object is a 4D entity, and that the 4D region is the smallest region at which you aren’t missing any of your proper parts. So, leaning on these location relations, O perdures iff O is temporally weakly located at more than one instantaneous space-time region, is only exactly and wholly located at the fusion of those regions (i. e. the 4D region), and no temporal proper part of it is exactly or wholly located at more than one of the instantaneous 3D subregions of that 4D region. In contrast, the endurantist will say that, O endures iff it’s temporally weakly located at more than one instantaneous space-time region, is both wholly and exactly located at all and only those regions, but is neither exactly nor wholly located at the fusion of those regions (i. e. the 4D region). In this way the endurantist maintains that persisting objects are merely instantaneous, recurring, 3D objects—because they are 3D objects, they cannot be located at the 4D region through which they persist. As Kurtz (2006: 9) puts it, ‘an enduring object cannot be a space-time worm.’
However, it’s at least conceivable that an object could lack temporal parts yet be exactly located at a 4D region. And so, we can distinguish between perdurantism, endurantism, and a theory of persistence which denies that persisting objects have temporal parts, yet maintains that they are temporally extended. Moreover, according to this view regions you’re wholly located at won’t always also be regions you’re exactly located at—here you’ll have no parts missing from each of the instantaneous regions though which you persist. For lack of a better moniker, call this view transdurantism. Let me first explicate transdurantism and disambiguate it from endurantism and perdurantism, and then I’ll explain the work it can do to motivate it (in § 3).
According to the transdurantist, O transdures iff it’s temporally weakly located at more than one instantaneous space-time region, is exactly located only at the fusion of all those regions (i. e. the 4D region), and is wholly located at all the instantaneous subregions of that fusion as well as the 4D fusion of those regions. As noted above, endurantism is sometimes parsed as a multi-location thesis such that enduring objects are multi-located at each of the instantaneous space-time region through which they persist. But we can see that as long as multi-location is left ill-defined, we tempt confusion between transdurantism and endurantism. After all, both enduring and transduring object will bear the whole location relation to many regions—but while enduring objects will also be multi-exactly located, transduring objects will not. Transduring objects have only one exact location because transduring objects are 4D entities, but they’re nevertheless multi-wholly located because lack temporal parts. The fact that both endurantism and transdurantism are multi-location theses might partially explain why they’re sometimes conflated, but we can now see that enduring and transduring objects are multi-located in different senses. 7
Parsons (2007: 219; c.f. 2000) argues that the way to divide believers is between those who endorse temporal parthood and those who don’t: ‘what unifies endurantists, on any interpretation, is their opposition to temporal parts.’ However in doing so we run the risk of confusing transdurantism and endurantism. Similarly, if we divide believers between those who endorse temporal extension and those who don’t, we run the risk of confusing transdurantism and perdurantism. But these three views are distinct and they each bear distinct metaphysical burdens. Crucially, the disagreement between endurantism and transdurantism is a disagreement about exact location, while the disagreement between transdurantism and perdurantism is a disagreement about temporal parthood. 8 If we further develop transdurantism we can better understand why it should not be conflated with either endurantism or perdurantism.
First, the transdurantist believes persisting objects are temporally extended simples. This is ultimately what the transdurantist asserts when she says transduring objects are temporally extended without parts. And so it’s important to ensure the transdurantist is well understood on this point. When the transdurantist talks of temporally extended simples, she simply means the same sort of thing someone means when they talk of spatially extended simples, but having temporal extension without parts instead of spatial extension without parts. The plausibility of extended simples has been defended at length, for instance, by Braddon-Mitchell and Miller (2006), Parsons (2000), Simons (2004), Markosian (2004), and McDaniel (2007a; c.f. 2009). Those who believe in the possibility of spatially extended simples and think space and time are very much alike (e. g. eternalists), should find the idea of temporally extended simples palatable.
In the simplest terms, an object is mereologically simple iff it has no proper parts (McDaniel 2007b: 233). But one might want to say an object is spatially simple and temporally complex, or temporally simple and spatially complex. So a proper simple is one with no temporal proper parts and no spatial proper parts. With that in mind, we can draw out some further useful distinctions. We can say that: an object is a spatial simple iff it has no proper spatial parts. 9 Such an object will be spatially point-size but exist for some duration with temporal proper parts. And we can similarly say that: an object is a temporal simple iff it has no proper temporal parts. 10 A temporal simple will be a spatially complex instantaneous entity. If such a thing could exist at more than one time, it would be a recurring entity—this is what the endurantist typically has in mind when she talks about a persisting object. And finally: an object is an extended simple iff it has no proper parts and it exists at a greater than point-size region. Drawing upon the notion of classical atoms, extended simples will have a non-arbitrary shape which corresponds to the shape of the greater than point-size space-time region at which it’s exactly located. Since such an object will not have any proper parts, it will be wholly located at every subregion of the region at which it’s exactly located. Again, we can further distinguish between mere spatial extension and mere temporal extension. When we limit our attention to the former, we have spatially extended simples. When we concern ourselves with the latter, we have temporally extended simples. And so, when we consider persisting objects, they could be recurring temporal simples (endurantism), temporally extended simples (transdurantism), or temporally complex objects (perdurantism). Put another way, with these distinctions we can clearly disambiguate our three theories of persistence as we can say that: according to the perdurantist, there can be no temporally extended simple objects, but there will be temporally simple objects (e. g. the smallest proper temporal part of a persisting object); according to the endurantist, all persisting objects will be recurring temporally unextended simples; and, according to the transdurantist, persisting objects will be temporally extended simples.
The way in which both endurantists and transdurantists believe persisting objects are temporally simple might partially explain why the views are easily conflated. But we can lean on a further distinction to avoid confusing them. There’s two ways in which a simple might exist at many unextended space-time regions: it could be a multi-locator or spanner. 11 Whether a simple is a multi-locator or a spanner is determined in virtue of how it fills a region: multi-locators are unextended simples which are exactly located at many unextended regions (i. e. they are multi-located in this particular way), whereas spanners are extended simples in virtue of being exactly located at an extended space-time region without being exactly located at any of its subregions (i. e. they span a region in this particular way). Equipped with this vocabulary, we can see that temporal multi-locators are what the endurantist has in mind when she thinks of enduring objects: whether spatially simple or complex, they are merely instantaneous 3D objects which exist at more than one time; a multi-locator is the selfsame object at every region at which it is exactly located. 12 In contrast, we can see that according to the transdurantist, persisting objects will be temporal spanners as they have temporal extension and yet are temporally simple; as a result, such persisting objects will be space-time worms. The fact that perdurantists and transdurantists both believe persisting objects are space-time worms might partially explain why these views are sometime conflated. But we can now see where they come apart: only according to the endurantist are persisting objects are temporal multi-locators; only according to the transdurantist are persisting objects are temporal spanners; and, only according to the perdurantist is it the case that no persisting object is either a temporal multi- locator or spanner, as persisting objects are not temporally simple. 13
Second, consider what they’ll each say about the mereological fusion of an object over time. For instance, imagine an ordinary persisting pearl. Call this object, Pearl. Further suppose that Pearl exists from t1 until t4. Say we point to it at t1; call that which we point to at t1, P1. Further say that we do the same at t2, t3, and t4, such that we get P2, P3, and P4 as well.
According to the perdurantist, Pearl is a 4D object which exists at the 4D region through which it persists, but it has parts at each subregion thereof, irrespective of how we might want to slice up space-time. If she could look at it along its temporal axis, she might say it looks similar to a “string of pearls”: the object has 3D spherical temporal parts at each instantaneous sub-region of the region through which it persists, but the object is actually the totality of these—the “string of pearls” made up of all of them. The perdurantist denies any identity relation between the “individual pearls” (its temporal parts) and the “string of pearls” (Pearl itself). That is, according to the perdurantist, Pearl is merely the “string of pearls” (i. e. the fusion of P1, P2, P3, P4), and Pearl is not equal to each individual pearl (i. e. Pearl is not P1, P2, P3, or P4). In contrast, according to the endurantist, Pearl is exactly (and wholly) located at each of the instantaneous 3D regions; all the “individual pearls” (i. e. that which the perdurantist would call temporal parts of Pearl) are identical in the relevant sense: according to the endurantist, Pearl is identical to each individual pearl, and nothing else (i. e. Pearl just is P1, P2, P3, and P4). This is what it is to be enduring object. Some might have reservations about this and wonder what the endurantist can say about mereological fusions of all instances of an object with itself over the course of its persistence. While the endurantist is under pressure to say that such a fusion is the object (Pearl, in this case), the endurantist doesn’t mean this in the same way as the perdurantist (or, as we’ll see, as the transdurantist). That is, crucially, according to the endurantist there is no 4D object here. (See Barker and Dowe (2003), Effingham and Robson (2007), and Daniels (2014) for a discussion on this sort of mereological worry.) And finally, according to the transdurantist, the “string” and the “individual pearls” are all identical, and there is no temporal parthood relation at work here—there is only one object. That is, there is merely an object which exists, wholly, at the 4D region and at every instantaneous 3D subregion. The “individual pearls” are all identical and they are identical with the “string of pearls” and as such, Pearl is a space-time worm without parts (i. e. Pearl just is P1, P2, P3, P4, as well as the fusion of P1, P1, P2, P3, and P4). 14 Ultimately, though, the transdurantist will resist talk of P1, P2, P3, and P4; according to her, talk of the “individual pearls” is misleading. In a way, this is the reverse of what the endurantist maintains. The endurantist will argue that talk of the fusion of P1, P2, P3, P4 is misleading as such a fusion is not part of her ontology. This is worth drawing out as it reveals how potentially confusing our ordinary ways of thinking about persistence and identity can be. After all, according to both the endurantist and transdurantist, there’s at least a loose sense in which that which exists R1 is not a different thing than that which exists R2—at least insofar as they agree that which exists R1 is the very same thing as that which exists R2, not just some part of it (i. e. no parts of it are missing from either region). But, crucially, if we ask: is that which is exactly located at some particular region identical with that which is exactly located at this other particular region? For any two regions where the endurantist would answer in the affirmative, the transudrantist will not. That is, if we consider R1 and R2, the endurantist will say yes, while the transdurantist will not as she maintains there’s nothing which bears the exact location relation to R1 or R2. Likewise, any region where the transdurantist finds a transduring object exactly located, the endurantist will not.
Transdurantism and Some of the Problems of Persistence
We can further cement our justification for setting transdurantism apart, and motivate the view, if we look at a few of the prominent problems which feature in the persistence debate. While we will only sample a few of these worries here, after doing so we will be able to see that the transdurantist handles some of these in a similar way as the endurantist, but others in a similar way as the perdurantist—this might also partially explain why transdurantism is sometimes confused with its rivals.
First consider the problem of temporary intrinsics. Roughly, the problem of temporary intrinsics charges that according to non-perdurantists, persisting objects can have incompatible properties. Imagine a poker that is hot at t1 and then cold at t2. Being hot and cold are incompatible properties. So if it’s the very same poker at t1 and at t2, as the endurantist (and transdurantist) maintains, it follows that the poker must have incompatible properties. The perdurantist avoids this by pointing out that the poker has distinct temporal parts at t1 and at t2 and it’s these mere parts which have these different heat properties, not the object in toto; one temporal part of it is hot, a different temporal part of it is cold. The endurantist (and transdurantist) cannot say the same as only perduring objects have temporal parts—according to the endurantist (and transdurantist) the very same object, not just a part of it, is wholly located at t1 and at t2 (Haslanger 1989: 119; c.f. Lewis 1986).
The endurantist has several replies at the ready. Here’s a popular one: according to the indexicalist reply, it’s not the case that objects, like the poker, have incompatible properties because objects only have time-indexed properties—e. g. it isn’t the case that the poker is hot and cold simpliciter, but rather the poker has the hot-at-t1 property and cold-at-t2 property—and these are not incompatible properties (Van Inwagen 1990). A related problem from time travel sometimes arises as a follow up: say I travel back in time and stand next to my younger self sitting on the couch. At that time I have both the property of being straight-shaped (standing me) and the property of being bent-shaped (sitting me)—these are incompatible properties and indexing to a time won’t save the endurantist. This is merely a variation on the same problem, but here the object has incompatible properties at different spatial locations at a particular time. However instead of presenting a genuine further worry, the endurantist is merely pushed to say properties are spatio-temporally-indexed—e. g. I’m standing at R1 and sitting at R2—in this case, R1 and R2 are different spatial regions at a particular time, while in the original case (the poker) we were concerned with different temporal regions at a particular place. Thus, having different properties at the same time but at different places (or the same place but at different times) is not contradictory because properties are only ever spatio-temporally-indexed to regions and never had by an object simpliciter.
The transdurantist is at least as well off as the endurantist here, as the transdurantist can make a similar sort of move as the endurantist. But the transdurantist will do so by a different route. Because transduring objects are temporally extended simples, this is a problem of qualitative heterogeneity—of explaining how an extended simple can have different qualitative properties at the different subregions at which it exists, without appealing to properties had by parts. What’s the transdurantist to say? Transduring objects undergo change merely by having non-uniform distributional properties. And they have these in a way that’s not reducible having properties at parts. We’re following Parsons here:
If an object has extension, then it must be capable of having a shape; and since it would be arbitrary to insist that a simple object must have any particular shape, it must be capable of having any of the shapes that a similar complex object might have. Thus, it must be possible for it to have a non-uniform cross-section over time. For example, a conical object, with the axis of the cone oriented along the time dimension could be small in the spatial dimensions at one time, then larger at a later time. It would be growing, in other words—it would have a non-uniform spatial size distribution (2000: 412; c.f. 2004)
Or consider the spatial analogue to make the explanation plain. Imagine the poker again, but now imagine that, at a time, it’s hot at one end and cold at the other; its heat property is non-uniformly distributed across it. In the case of an ordinary poker, we might ordinarily say its spatial parts have slightly different heat properties. But we couldn’t say this if the poker were a spatially extended simple. The transdurantist just says the same thing about properties over time as we say about such a spatially extended simple poker and the non-uniform distributional properties it has at-a-time. We might think these distributional properties can be metaphysically basic—the object doesn’t have the distributional properties it does in virtue of having parts with particular properties, or in virtue of anything else. Notice that the transdurantist, like the endurantist, could also say that properties are spatio-temporally-indexed. But here they are had derivatively—i. e. having a certain non-uniform distributional property may entail having some particular uniform property at a subregion where it exists. But the endurantist will say the reverse: if objects have certain non-uniform distributional properties over time, it’s only because objects have certain properties in a spatio-temporally indexed way.
Let’s turn to another problem. Many worry about implications from relativistic physics. For instance, consider this “Pole and Barn” case:
Consider a 10-meter pole moving at the speed v=2.6×108 m/sec through the open doors of a 10-meter barn. Will the pole fit completely inside the barn? First, consider the situation from the point of view of the barn. In the barn rest frame, the pole is Lorentz-contracted to 5 meters and thus perfectly fits in. In the pole rest frame, on the other hand, it is the barn that is Lorentz-contracted (and becomes only 5 meters wide). (Balashov 2010: 203-204)
In short, observers in different frames of reference will judge the length of an object to be different—as neither perspective is privileged, neither observer is wrong. There’s a genuine sense in which, in a relativistic world, the pole both fits entirely within the barn and protrudes out both ends of the barn. This is merely a consequence of the phenomenon of length contraction. What makes a difference, and allows us to avoid a contraction, is that the pole will fit entirely within the barn only according to the barn-frame and the pole will protrude out of the barn only according to the pole-frame. That is, there’s just is no objective fact of the matter about what 3D shape an object has. We can grasp this more easily if we consider a more everyday case. Setting aside relativistic physics for the moment, consider the different 2D shapes a 3D object might appear to have from different perspectives. For instance, consider an octahedron. Its 2D shape will appear to differ from one perspective than another—e. g. if you look at it from the top down, it will appear to have a square shape, whereas if you looked at it straight on from the side, it will appear to be diamond shaped. But these are mere perspectival representations of the one octahedron shaped object—the actual object has one an invariant 3D shape.
The perdurantist can handle this sort of “Pole and Barn” case as she believes persisting objects are 4D objects which have an invariant 4D shape and, in a relativistic world, the apparent 3D shape of any such object will merely be a perspectival phenomenon:
the temporal part of the pole at a certain moment of time in the barn frame is shorter than the corresponding temporal part of the barn, whereas the temporal part of the pole at a particular moment of time in its rest frame is longer than the corresponding temporal part of the barn. (Balashov 2010: 206)
That is, just as we can make sense of the 2D perspectivalism cases because we believe there is an invariant 3D object, the perdurantist can make sense of the 3D perspectivalism cases because she believes there is an invariant 4D object. The endurantist cannot say the same thing since, according to her, there are no 4D objects and she seem ill-equipped to handle cases like this one. For brevity, we won’t review possible responses the endurantist try to offer—Balashov surveys the prominent attempts that have been made and voices concerns with them (2010: 209–216, c.f. Eagle 2011). I raise this objection here merely to highlight that the transdurantist fares at least as well as the perdurantist here since the transdurantist, like the perdurantist, believes in 4D objects. This is the case since, as Balashov (2010: 206 n.13) notes, ‘the argument directly supports the thesis that objects have temporal extent’, not temporal parts. So it’s because transduring objects are temporally extended simples—they are 4D objects—the transdurantist can also appeal to an object’s invariant 4D shape to handle these sorts of cases. Interestingly, if transdurantist didn’t have equally good options as the endurantist for the problem of temporary intrinsics, that would be a unique problem for the view. But it does have equally good options. And, similarly, if transdurantist didn’t have equally good options as the perdurantist for the problem of relativistic perspectivalism, that would be a unique problem for the view. But it fares at least as well as its rivals on both.
An advantage for transdurantism, though, may be that it avoids an objection from quantum mechanics. Pashby (2013) argues that the spatial analogy—which perdurantists rely upon—breaks down under quantum mechanics. The technical reasons are not essential for this paper, but the thrust of the issue is this: while we can provide an account of spatial parthood for quantum objects if spatial parthood is unpacked in terms of spatial regions, quantum mechanics does not allow an analogous notion of temporal parthood. In short, Pashby (2013: 1145) argues, ‘no quantum object has temporal parts.’ So, if Sider’s (1997: 204) assessment that ‘the heart of [perdurantism] is the claim that the part-whole relation behaves with respect to time analogously to how it behaves with respect to space’ is correct, then perdurantism is ruled out by certain interpretations of quantum mechanics. Because this is a problem with temporal parthood, the transdurantist avoids this worry as she simply denies that persisting objects have temporal parts. While the endurantist avoids this worry as well, as she also rejects temporal parts, Pashby (2013: 1145) points out that the endurantist faces other challenges if we consider relativistic quantum mechanics which transdurantism doesn’t face.
Transdurantism, though, does face its own problems. Miller (2009), for instance, worries about transduring objects which appear to gain or lose parts over time. Intuitively, ordinary objects gain and lose parts over time. For instance, someone might be fat at one time, and thin at another; a car might have four wheels one moment, and only three at the next. What can the transdurantist say here? There are a number of different options available; I will highlight a few here, but I won’t commit to the trandurantist to any one in particular. First option: the trandurantist can say, leaning on the literature in personal identity, that no macroscopic objects persist through the loss (or gain) of parts—an object can survive such a change, but that which exists before and that which exists after the loss (or gain) of a part are not identical. Second option: the transdurantist can say that our account of distributional properties explains why even macroscopic transduring objects never lose proper parts—if I were to lose my leg, I wouldn’t have lost any proper parts; I just have different properties now (e. g. shape, mass). This may seem odd to some, but when we’re talking about objects as extended simples, change in mass is no different than, say, change in colour. Macroscopic transduring objects, like you and I, merely have certain non-uniform colour, mass, shape, etc. properties. Third option: the trandurantist can say that macroscopic objects are transduring non-fusions. That is, they are composite persisting entities which are not merely fusions of persisting transduring simples but rather entities which spatio-temporally coincide with fusions of transduring simples and whose existence is entailed by those fusions. 15 This survey is merely meant to demonstrate some of the escape route available here. While I’ve gestured at some available options, much more would need to be said if we wanted to evaluate which response is actually best. And while each of these option here bears burdens some might consider unattractive, these burdens aren’t enough to condemn transdurantism. As the persistence literature demonstrates, endurantists and perdurantists are also burdened with defending the counter-intuitive consequences of their views.
Here’s another problem for transdurantism: can transduring objects be spatially complex, yet temporally simple? If the transdurantist wants to say that some are, she may face a unique worry from relativistic physics. Consider a relativistic world with a spatially complex object that transdures (perhaps a chair or person). From one frame of reference, it will have only spatial parts. But from another frame, what were its spatial parts in the first frame will be temporal parts in this other frame. That is, because we lose the spatial/temporal division in such a world, any mixing—simple along one dimension, complex another—will prove problematic. What might the transdurantist say here? Again, she has more than one possible option available. First option: while I want to stay neutral between theories of time here, some transdurantists may be happy to favour one where there is a privileged frame of reference; e. g. a presentist transdurantist who follows, say, Monton (2006). Transduring objects need only be simple from the privileged frame. Here’s a second option which doesn’t commit the transdurantist to any particular theory of time: the transdurantist may just embrace extended simples tout court. That is, the transdurantist could endorse the view that persisting objects are both spatially and temporally extended simples. The distributional properties framework is quite powerful as it allows the transdurantist to do a lot of the work we want parthood to do, so if she’s prepared to lean on it for the temporal case, perhaps she may as well in the spatial case too. A third option: the transdurantist may concede that macroscopic objects do not transdure and merely maintain that simples transdure. A locative framework, like the sort I utilize here, permits the possibility that some entities transdure, while others perdure or endure. Following Gilmore (2006: 207), I take it that were I able to point to a spatial simple now and tomorrow, it’s at least possible that I’m pointing to the same object—i. e. that such simples do persist through time. But the perdurantist cannot say this. According to the perdurantist, simples can only be instantaneous entities as an allegedly persisting simple will have some proper parts—its instantaneous temporal parts. So anyone who believes that simples can persist cannot believe that all persisting objects perdure; such simples must either endure (as temporal multi-locators) or transdure (as temporal spanners). Transdurantism may then be the best account of persistence for fundamental particles, at least if we take fundamental particles to be mereological simples. McDaniel (2007b), for instance, interprets string theorists as defending the thesis that fundamental particles are mereologically simple. 16 If fundamental particles are spatially simple, we’re well incline to consider them temporally simples as well. Perhaps even more strongly, following Dorr (2002), the trandurantist could be eliminativists about macroscopic objects (like people and chairs). That is, while talking about them might be useful, only the fundamental particles that populate our world genuinely feature in our ontology, and the fundamental particles transdure. (This strategy could also handle Miller’s worry above.) Again, this survey of possible responses isn’t exhaust, and I haven’t fully unpacked these possible options. I merely want to show the sorts of unique problems the transdurantist might face, and demonstrate show she might be incline to response. This isn’t done to defend the view, but rather to merely demonstrate the flavour of it.
So while the transdurantist must accept a cost to bear in response to each of the problems raised above, she does have escape routes. Some of these options make greater concessions than others, but any one would be enough to entitle transdurantism to its own seat at the table for our discussion on the metaphysics of persistence.
Transdurantism, Going Forward
The theory of persistence advanced here has been discussed at elsewhere in the literature (e. g. Parsons 2000, 2007; Eagle 2010: 58; Gilmore 2006, 2008; Balashov 2010: 36–39). Miller (2009) gives it the (unfortunate) name terdurantism, Pashby (2013) calls it temporal holism, while Giordani and Costa (2013) refers to it as temporal bare uni-locationism. Whatever technical term we use it pick it out is ultimately immaterial. What’s important is that we do not conflate it with other theories of persistence—it needs its own seat at the table.
There is a variety of reasons why transdurantism has often been confused with its rivals. As discussed, the trandusrantist adopts perdurantist strategies to handle some of the problems of persistence, while other times the trandusrantist adopts endurantist strategies. The way in which both endurantists and transdurantists believe persisting objects are temporally simple might partially explain why the views are easily conflated, but only enduring objects are multi-locators while only transduring objects are spanners. And if multi-location is left ill-defined, we run the risk of confusing transdurantism and endurantism as both enduring and transduring object will bear the whole location relation to many regions. But only enduring objects are multi-exactly located. When we divide believers between those who think persisting objects are space-time worms and those who don’t, we fail to distinguish between perdurantism and transdurantism. And when we instead divide believers between those who think persisting objects have temporal parts and those who don’t, we fail to distinguish between endurantism and transdurantism. For all these reasons, transdurantism should stand apart from both endurantism and perdurantism. Parsons (2007), though, defends transdurantism as the proper characterization of endurantism. And Hawley (2010) characterizes it as a form of perdurantism. But for the reasons emphasized above, neither of these characterizations is apropos—both ways of carving up the terrain are ultimately too crude. So, I take transdurantism to capture a theory of persistence that’s different than the way endurantism and perdurantism are traditionally characterized. As such, we mischaracterize the persistence landscape when we use perdurantism and endurantism exhaustively. 17
But which should we favour? We might hope that our intuitions could provide some guidance here. However, it’s not readily apparent that they’ll point us towards one particular theory. Do your intuitions lie with temporal parthood? Only here would you be committed to perdurantism. But temporal parthood is not widely considered to be part of the common sense repertoire, so we should turn to the other considerations if we want assess which theory of persistence best captures our intuitions about persistence. Do your intuitions lie with persistence as temporal extension? If so, then you may be a perdurantist or a transdurantist. Do your intuitions instead lie with whole location? Then you may be an endurantist or a transdurantist. Intuition, it would seem, cannot play a significant role here.
At a minimum, transdurantism represents a unique way of understanding the nature of persistence, as unique burdens to bear, and it has an important role in the persistence debate. Here I’ve sought to give greater credit to it by rigorously developing and highlighting how it differs from both perdurantism and endurantism. It should stand apart from them and not be confused with either of them. To be sure, transudrantism will face some unique challenges. While I’ve gestured at how the transdurantist may be incline to respond to some such worries, in the fullness of time it would be interesting to consider them in greater detail. But that’s best left for another occasion. 18
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I don’t use temporal part atypically here; I take it that all parties in the persistence debate can at least make sense of temporal parthood, whether or not they believe that persisting objects have temporal parts. Whatever we take spatial parts to be, temporal parts will be the temporal analogue of spatial parts. So, if we would say of spatial parts that spatially extended objects (which aren’t mereologically simple) have spatial parts in all the spatial subregions of the spatial region it occupies at a time, then we should say of temporal parts that persisting objects which have temporal parts will have temporal parts in all the temporal subregions of the interval through which such an object persists. And, building on this, we should say that x will be an instantaneous temporal part for an object at some time iff x is a part of that object at that time, x exists at and only at that time, and x overlaps at that time all parts of that object at that time (Sider 2001: 59). Strictly speaking, perduring objects have distinct instantaneous temporal parts at every instantaneous region through which they persist. Relative to the other views considered here, the perdurantist uniquely endorses temporal parthood.
Those familiar with the literature may already recognize that this discussion will utilize finer distinctions than some will allow for, as we’ll see, Parson’s (2007) view will fall within the trandurantist camp here—yet he resists key distinctions the transdurantists and endurantists rely upon to distinguish themselves from one another (see Parson 2008).
Where x is a proper part of y just in case x is a part of y but x is not identical to y. I take it that every object—i. e. according to everyone, regardless of their preferred theory of persistence—has at least one improper part (spatial, temporal, or spatio-temporal); that is, the part which is identical to it.
Parsons argues that enduring objects can only have one exact location. Parsons, though, has a different conceptual understanding of exact location than, for instance, Hudson (2008) and Balashov (2010: 16)—I merely follow the latter here. (For Parsons, an object cannot be found outside its exact location, but this is not the case according to my usage.)
I utilize whole location here because it has played a somewhat pervasive, and sometimes problematic, role in the persistence literature. But, the transdurantist can avoid it by focusing on exact location: a transduring object is (i) exactly located at a 4D region, R, (ii) is not exactly located at any time within R, (iii) and every part of the object is weakly located at every time within R. (I thank [blinded] here.)
See, for instance, Gilmore (2006) for more on this point.
For such an object, x is a proper temporal part of y just in case x is a temporal part of y but x is not identical to y. That is, for any object that exists at a 4D space-time region, x will be a proper temporal part of y iff x is a part of y but x does not have the same temporal extent as y. (I take it this is what is usually meant when we discuss temporal parthood and persistence—i. e. endurantism and transdurantism both deny that persisting objects have proper temporal parts of this sort.)
See McDaniel (2007a; c.f. 2009) and Hudson (2005) for discussions of multi-locators and spanners. I’ve tried to bring my usage here in line with these existing notions, but what I say may not completely align with theirs. For instance they take multi-locators to be extended simples, whereas I deny that that follows merely from the fact that they exist at an extended space-time region. And according to Hudson, spanners are not multi-located in any way—not even multi-wholly located; I cannot see how this could be the case given that they exist at an extended space-time region and lack proper parts. It seems to me that they must be multi-wholly located at all the subregions of an extended region, at least given how I use the terms here.
The fact that mutli-locators are exactly located at a set of instantaneous 3D regions does not entail that it’s exactly located at the fusion of them. Multi-locators are unextended objects because they don’t bear such a location relation to a 4D region. (I say more about such fusions below.)
Following this discussion, some want to raise a particular worry about time travel here. Imagine a time traveller with a discontinuous worldine—an instantaneous time traveller—who “jumps” from her departure time to her arrival time. Must the transdurantist concede that such an object would be a multi-locator? No: whether or not an object is a spanner or a multi-locator hinges on where it’s exactly located. The transdurantist would merely say that such an object is exactly located at the fusion of all those scattered regions through which it persists. The endurantist, on the other hand, denies that the time traveller is ever exactly located at those scattered regions, since the endurantist maintains that it is a multi-locator. (That an object can be exactly located at a scattered region may seem odd, but this is an exotic worry. After all, time travel has numerous counter-intuitive consequences and we ought not put too much stock in the idea that we find another one here.)
If we imagine that this pearl is a spatial simple in a world where no other objects exist, we can additionally see that the transdurantist and endurantist will agree that only one object ever exists here (whereas the perdurantist will maintain that there are five objects). But how many instances of the exact location relation do we find here? It depends on who you ask: According to the perdurantist, there are five instances of the exact location relation—P1, P2, P3, and P4 are all temporal parts which are each exactly located at subregions R1, R2, R3, and R4 respectively, as well as the fusion of P1, P2, P3, and P4 which is exactly located at the spatio-temporally extended 4D region, R. And even though the endurantist takes P1, P2, P3, and P4 to all be identical, she will say that there are four instances of the exact location relation—i. e. at R1, R2, R3, and R4—however the endurantist will deny that anything bears the exact location relation to R. The transdurantist will unique say that there is just one instance of the exact location relation here: Pearl at R.
Miller (2009: 632–646) considers this the strongest and she explores it in detail. She argues that such a transdurantist faces burdens about the oddity of non-fusion entities, property instantiation, and incompatibility with super-substantivalism. That said, Miller concedes that taking this path isn’t untenable—merely that it brings certain baggage.
Although Callender (2011) raises concerns about this sort of claim.
Alternatively, we could treat endurantism and perdurantism as umbrella concepts. Here, then, one could characterize the view I call endurantism as classic endurantism and the view I call transdurantism as neo-endurantism or neo-perdurantism. Again, these are merely technical terms and we may use them however we like. But this characterization impedes clarity and is strategically a poor move for the transdurantist since, for instance, the transdurantist isn’t motivated to claim ownership of the endurantist namesake as the transdurantist should want to distance herself from the burdens traditionally associated with endurantism.