Smith is reading an open book that was shut this morning. At least it certainly seems like the same book he placed closed on his nightstand and opened to read this evening. But, then again, nothing can be both shut and not shut, Smith's book being included among those things that cannot violate G.W. Leibniz's law. So, no matter that common sense dictates that Smith's shut book did not blink out of existence to be instantaneously replaced by an open book, perhaps it is a different book after all.
Very roughly, that is the start of the problem of persistence—an initial worry about how an object can persist through a change in its properties. It is a problem that may seem easily dismissed until we identify its source in some of our basic metaphysical commitments and recognize the costs that accompany any way of addressing it. The understanding of the problem of persistence expressed below was developed alongside and informed by Sally Haslanger's work (Haslanger 2003).
The Initial Worry
We can sharpen the initial worry about books and other ordinary objects that persist through change by noting that it emerges from the conjunction of three core metaphysical theses.
Three Core Metaphysical Theses
consistency : Nothing can have incompatible properties.
change : Change involves incompatible properties.
persistence : Objects persist through change.
The core theses express firmly held intuitions that most metaphysicians would agree are central to a coherent theory of how ordinary things—books, rocks, Smith, and even ourselves—exist and persist in the world. But, a commitment to any two of the theses seems to implicitly deny the remainder. Suppose persistence and change are true, that some objects persist through change that involves incompatible properties. For instance, consider the book that Smith removed from his nightstand to read that was shut, and though open now, remains the same book. If we also assume consistency is true, then nothing can have the incompatible properties of being shut and being open (given that a book is open if, and only if, it is not shut). Thus, it seems that the shut book from Smith's nightstand must be distinct from the open book in his hands. But that denies that the book persisted in the first place.
A careful reader will note that the contradiction was not precisely forced; nevertheless there is a significant tension that at least threatens contradiction. One strategy for responding to this worry is to bypass it by rejecting consistency, persistence , or change . A second strategy is to resolve the tension by first identifying its source and then clarifying or modifying our ideas to remove that source.
Dismissing the Initial Worry
There are three options in pursuing the straightforward strategy of dismissing the initial worry about persistence by denying one of the core theses, none of which is promising. First, we might contend that something can both have and not have a property (forfeiting consistency ). However, such a move entails rejecting the law of noncontradiction, Aristotle's "most certain of all principles" according to which "the same attribute cannot at the same time belong and not belong to the same subject in the same respect" (Barnes 1984. Aristotle's Metaphysics IV.3.1005b1.17). But, countenancing contradictions to find a noncontradictory account of persistence makes no sense (though someone like Donald Baxter, 2001, might disagree). Indeed, such a drastic step may allow for something to both have and not have the property of persisting.
Second, we might adopt the position that change either does not happen or does not involve incompatible properties (forfeiting change ). Here, we could deny change altogether, perhaps accepting Parmenides's picture of a static, monolithic reality in which "what is is ungenerable and imperishable, a whole of a single kind, and unshaking and complete" (Curd 1998, p. 68). Or, we could hold that change occurs without involving incompatible properties. But change just does involve either something being F and something becoming not-F, or something being not-F and something becoming F. Sacrificing our minimal metaphysical commitments about how change works amounts to change nihilism. This strategy avoids contradiction at a very high metaphysical cost.
Finally, we could argue that nothing persists (forfeiting persistence ). Heraclitus told us: "You could not step twice into the same rivers; for other waters are ever flowing on to you" (EpistemeLinks.com 2005, Heraclitus of Ephesus, On the Universe, fragment 41). We might go along with him, agreeing that: "Nothing endures but change," giving us a metaphysics that does not include persisting objects, but merely flowing processes (EpistemeLinks.com 2005, Diogenes Laertius, Lives of Eminent Philosophers, Bk. IX, sec. 8). Such persistence nihilism is again a move at odds with strong intuitions and a range of metaphysical theories.
Thus, the strategy of dismissing one of the core theses leaves us without an intuitively tenable account of how ordinary things—Smith, books, rocks—exist and persist in the world. This motivates the search for an account of persistence that genuinely addresses the worry by reconciling the core theses.
Finding the Source
The second way of dealing with the initial worry is to get much clearer about the source of the problem and then seek remedies by revising our ideas in a way that avoids the problem by attacking the source directly. Our understanding of consistency needs to remain intact unless we allow contradictions, which is off the table here. However, change and persistence leave room for interpretation. For instance, they leave open what counts as persistence, change, and incompatible properties being involved in change.
Modifying our understandings of these phenomena can ease the tension among the core theses. In our everyday understanding of the world, we assume that persisting objects survive the gain and loss of some simply instantiated properties. The following three aspects of this understanding are central to grasping why philosophical issues arise with persistence.
change as alteration
An object alters by gaining or losing properties. More precisely, an object alters if, and only if, it is numerically identical to objects that have different properties at different times. In our everyday understanding of the world, objects change by altering, and plenty of ordinary objects alter. Smith's book that was shut and Smith's book that is open is a single book that has the properties of being shut and open at different times. When Smith opened his book, the shut book did not wink out of existence exactly when an open book happened to blink into existence right into his hands. Rather, Smith's book was shut and then open—it altered as Smith turned to his bookmarked page.
persistence as survival
An object survives if it has more than a momentary existence. More precisely, an object survives if, and only if, it is numerically identical to something that exists at a different time. In our everyday understanding of the world, objects persist by surviving, and plenty of ordinary objects survive. Consider the book Smith placed on his nightstand last evening that went untouched until this evening, and the book he removed from his nightstand this evening. The book that Smith put down last evening is the very same book that he picked up this evening. Although a day older, it is numerically identical to the book Smith read the prior evening—it survived the day spent on his nightstand.
involving incompatible properties as just having incompatible properties
An object just has a property if, and only if, it simply instantiates (Fx ) that property. That is, an object just has a property if, and only if, no extrinsic facts are relevant to the truth of the proposition that the object has that property. In our everyday understanding, ordinary objects just have incompatible properties sometimes, regardless of how the rest of the world is. David Lewis brings out the intuitiveness of this when he writes: "When I sit I'm bent, when I stand I'm straight. When I change my shape, that isn't a matter of my changing relationships to other things, or my relationship to other changing things. I do the changing, all by myself. Or so it seems" (Lewis 1999, p. 187).
Like Lewis being straight, with respect to Smith's book, we tacitly hold that nothing beyond his book matters to its being shut—that there is a primitive, non-relational bond between the book and the property of being shut. If it is not open, Smith's book just has the property of being shut, regardless of its relation to the nightstand it rests upon at 7:00 a.m. We can capture these key aspects of our everyday understanding in terms of how objects persist through change with three additional theses.
Three Everyday Metaphysical Theses
alteration : If an object changes, then the object existing before the change and the numerically identical object existing after the change are the proper subjects of the incompatible properties involved in the change.
survival : If an object persists through change, then the object existing before the change is numerically identical to the one existing after the change.
atemporal instantiation : If an object is the proper subject of a property, then (i) the object has that property, and (ii) facts about time and tense are irrelevant to the truth of the proposition that the object has that property.
alteration constrains how things change. survival constrains how things persist. atemporal instantiation constrains how incompatible properties are involved in change. Making our everyday understanding explicit is useful because it allows us to see that: (1) This understanding conjoined with the three core theses forces a contradiction; and (2) reconciling the core theses requires denying or revising some part of our everyday understanding. The following argument demonstrates both points. In it, we suppose that Smith opens the book that had been resting shut on his nightstand.
An Argument Against our Everyday Understanding
What follows are three assumptions about the book that capture the three core metaphysical theses: (1) It is not the case that the book is shut and the book is open (captures consistency ); (2) the book persists through change (captures persistence ); (3) the book changes in a way that involves the incompatible properties of being shut and being open (captures change ).
The following steps draw on the three everyday metaphysical theses: (4) The book existing before the change is numerically identical to the book existing after the change (survival and step two); (5) the book is the proper subject of being shut and being open (alteration , steps three and four); (6) the book is shut and the book is open. (atemporal instantiation and step five). From these six steps, a contradiction arises as steps (1) and (6) cannot both be true. One can conclude, then, that given the truth of the core metaphysical theses, something within the everyday metaphysical theses is false.
This argument can be run for any ordinary object that persists through change. Thus, to address, rather than dismiss, the initial worry, one of the three everyday theses must be revised or forfeited. The problem is to do so while striking a balance between respecting our intuitions and achieving philosophical success. Such is the strategy of three broad approaches to persistence below. Each blocks step (6) in its own way and thereby achieves a consistent view. But, given the nature of the problem demonstrated above, each solution will obviously face trade-offs in terms of intuitive appeal.
Addressing the Worry
Perdurantism, exdurantism, and endurantism are each accounts of persistence that retain a commitment to the core metaphysical theses, but give up part of our everyday understanding of how things such as Smith, books, and rocks persist and change in our world. The first two accounts are built on a metaphysics of temporal parts, whereas the third depends on a metaphysics of enduring things.
metaphysics of temporal parts and persistence
Ordinary objects have spatial parts. Perhaps they also have modal parts, dependent parts, abstract parts, or logical parts, among others. The metaphysics of temporal parts (MTP) leaves that open. The particular claim MTP makes is that objects have temporal parts. These temporal parts, time slices, or stages exist only at a moment. So, on a view consistent with MTP, multiple momentary book stages could exist—a shut-book stage, a distinct open-book stage, and so on. Perdurantism and exdurantism rely on the temporal stages of MTP to explain the persistence of ordinary objects.
Perdurantists take change over time to be analogous to change over space. Just as color changes across the surface of a canvas when different spatial parts of the canvas have incompatible colors, so the color of a lemon changes across the time as it ripens when different temporal parts—a distinct green stage and a distinct yellow stage—have incompatible colors. In both cases, change consists in distinct parts of an object having incompatible properties.
On this view, ordinary objects are space-time worms composed of distinct momentary stages. So, just like a taut rope extends through space, it also extends through time. For, as a fusion of its temporal stages, it has parts in the past, present, and future. An object that is a space-time worm is only partially present at any one moment because its different stages exist at different times.
The perdurantist ontology makes the three core and two everyday metaphysical theses co-realizable. An object changes when distinct stages of a single space-time worm just have the incompatible properties involved in change (change and atemporal instantiation ). It survives a change in virtue of the space-time worm that exists at the times that its distinct stages exist (persistence and survival ). And, because distinct stages bear the incompatible properties rather than a single object, there is no one thing that has incompatible properties (consistency ).
For instance, Smith's book changes because its stages just have the incompatible properties of being shut and being open. The book survives this change because it is numerically identical to the space-time worm constituted by its stages. Finally, no contradiction arises because distinct stages of the book have the incompatible properties, rather than Smith's book as a whole.
However, perdurantism requires us to sacrifice change as alteration. alteration entails that change occurs only if one and the same thing has a property and then lacks the property. It entails that the book changes only if it and something numerically identical to it have the incompatible properties of being open and shut. But, perdurantists hold that distinct proper parts of a space-time worm book bear the incompatible properties—the shut-book stage and the open-book stage. So, there is no one thing that has incompatible properties—indeed that is how perdurantism avoids contradiction. By blocking step (5) in the argument above, perdurantists also block (6). Yet, in gaining a coherent account of persistence, perdurantists accept an account on which change is merely a succession of momentary stages that have incompatible properties.
Exdurantists or stage theorists take identity over time to be analogous to identity between possible worlds. To see this, assume that an actual sill-length window swag could be a floor-length swag in virtue of a floor-length counterpart in some possible world. Analogously, exdurantists assume that Smith's now open book was shut in virtue of a closed book counterpart resting on his nightstand in the past. In both cases, distinct objects (the sill-length swag and its floor-length counterpart, the present open book and its earlier shut counterpart) have incompatible properties.
On this view, an ordinary object is a single momentary stage that extends through space, but not through time, and that has temporal counterpart stages. Any object that is a single stage is wholly present at exactly and only the moment it exists.
The exdurantist ontology makes the three core and one everyday metaphysical theses co-realizable. An object changes when it and a counterpart stage just have the incompatible properties involved in change (change and atemporal instantiation ). It persists when it and its temporal counterpart exist at different times (persistence ). And, because distinct stages bear the incompatible properties rather than a single object, there is no one thing that has incompatible properties (consistency ).
For instance, the change in Smith's book involves incompatible properties because his book just has the property of being open and a counterpart stage just has the property of being shut. Smith's book persists through this change in virtue of standing in a counterpart relation to a stage from a different time in the actual world. Finally, because no single thing is open and is shut (rather, distinct stages are), no contradiction arises.
Notice that according to exdurantism, the object that changes and persists just has one of the incompatible properties—Smith's book, the entire book, just is open. In contrast, according to perdurantism the object that changes and persists never just has either of the incompatible properties—Smith's book is never just open or shut. Exdurantism thus fares a bit better intuitively on this point, for when we look at Smith and see him reading an open book, we think his book is open, not some other object that is merely part of his book.
However, exdurantism pays for this metaphysical perk elsewhere. Exdurance precludes the possibility of persistence as survival, for no ordinary objects survive. survival entails that a persisting object exist both before and after it changes. It entails that if Smith's book persists, then the shut book on the nightstand is numerically identical to the open book in Smith's hands. But, exdurantists maintain that no book is numerically identical to both the earlier open stage and the later shut stage. At best, a persisting object continues (in some sense) in virtue of a succession of distinct momentary stages bearing the relevant counterpart relations to each other. But, an earlier and a later stage in such a succession are no more one and the same object than the first and third links in a five-link chain are one and the same link. Thus, given the ontology in which ordinary objects are all momentary stages, nothing exists that could survive change.
Moreover, because it shares the strategy of using MTP to explain persistence with perdurantism, exdurantism also forfeits alteration . As above, there is no one object that loses one property and gains another. Instead, distinct objects bear the incompatible properties—Smith's open book and a shut stage to which it stands in a counterpart relation. But, the costs of exdurantism do return a benefit—giving up both survival and alteration blocks both (4) and (5) without which (6) does not follow. Of course, to recoup these costs, exdurantists may try to retain some form of alteration or survival by revising our notion of existence. They could hold momentary stages derivatively exist across time in virtue of counterpart relations to other stages that exist at different times. Clearly, the burden of proof would fall on an exdurantist to prove that derivative existence just is existence.
To sum up, both perdurantists and exdurantists endorse MTP. They maintain a commitment to the three core theses by using temporal parts to bypass the contradiction that arises by simply predicating incompatible properties to a single object. Both approaches conflict with change as alteration—so neither can hold simply that the book is open and the book is shut, rather distinct stages have these properties. Ultimately, though, the views differ in metaphysical costs. Perdurantists may maintain that persisting objects survive change because they attribute incompatible properties to different parts of a single space-time worm. Exdurantists must deny survival because they attribute incompatible properties to distinct ordinary objects.
metaphysics of enduring things and persistence
According to the metaphysics of enduring things (MET), some objects endure. To claim that some objects endure is to claim that in some cases a numerically identical object is wholly present at different times. This claim states the minimal metaphysical commitments that distinguish the ontologies of MET from MTP.
MET and MTP agree that ordinary objects have spatial parts, and that they may have modal parts, dependent parts, abstract parts, or logical parts, among others. MET also leaves open whether any objects have temporal parts.
However, although it permits stages, MET requires the existence of some objects that fall outside the ontologies of perdurantists or exdurantists. For, an enduring object is wholly present at different times and neither a space-time worm nor a single momentary stage can be wholly present at different times.
Endurantism relies on MET's enduring objects to explain how ordinary objects can be altered and survive change. These objects are the key resource that perdurantism and exdurantism lack by being grounded in MTP.
Endurantists hold that ordinary objects persist through change by enduring. In doing so, they take identity over time to be numerical identity between objects wholly present at different times. They take change over time to be the instantiation of incompatible properties by numerically identical objects at different times. So, arguably they hold the most intuitive understanding of change over time as a phenomenon that is nothing more than one and the same object gaining and losing properties across time.
On a basic endurantist view, ordinary objects are enduring things. For example, an endurantist would hold that as an ordinary object, a book is not constituted by stages because it is wholly present at different moments. Thus, an ordinary, enduring book would be distinct from any sort of space-time worm or single momentary stage or counterpart stage that may or may not also exist.
The endurantist ontology makes the three core and two everyday metaphysical theses co-realizable. An object changes by altering because, in some sense, it has the incompatible properties involved in change (change and alteration ). It survives a change in virtue of the single enduring object that has those properties in some sense at different times (persistence and survival ). Finally, although a wholly present ordinary object in some sense has incompatible properties, it does not just have those properties. Rather, facts external to an ordinary object concerning time or tense mediate the instantiation of incompatible properties. There are a variety of ways to mediate the instantiation. For instance, given a pair of incompatible properties and an object that has them in some sense, an endurantist could hold that the object has one property now and had the other property earlier. With various forms of mediated instantiation, the endurantist avoids contradiction (consistency ).
For instance, Smith's book changes because it has incompatible properties in some sense—his book is open but that very book was shut. Smith's book survives this change in virtue of being numerically identical to the book at the time it is open and the book at the time it was shut. Finally, because no single thing is open and is shut (rather, the book is open and was shut), the position remains consistent.
The important move of adopting temporally mediated property instantiation—instantiation mediated by time or tense—allows endurantists to hold that an ordinary object can be wholly present both before and after a change in spite of its having incompatible properties. This is why the view allows for the survival and alteration of objects so easily.
However, endurantism faces its own metaphysical cost—it requires us to give up the idea that an object just has the properties in virtue of which it changes. atemporal instantiation entails that there be a primitive bond unmediated by time or tense between the object and the relevant properties. Perdurantists and exdurantists preserve this bond because on their views distinct objects just have the incompatible properties. MTP allows them to say, without contradiction, that one book stage just is open and a distinct book stage just is shut (Fx and not-Fy ). In contrast, without stages as a resource, to preserve that bond the endurantist would have to say that the book just is open and that the book just is shut (Fx and not-Fx )—a flat contradiction. Instead, the view of change involving objects just having incompatible properties is replaced by one in which objects have incompatible properties in some sense mediated by time or tense (F is x and F was not-x ). This is how endurantism directly blocks step (6) in the argument above.
In contrast to the sacrifices of the MTP theorists that include losing robust notions of survival and alteration, giving up primitive instantiation in favor of mediated instantiation may be appealing. But there are repercussions.
First, temporal concerns intuitively seem irrelevant to whether an object has those intrinsic properties in virtue of which it can change. Smith's green eyes, the position of his nightstand, and, likewise, the time of day all seem to be matters outside of the metaphysical status of Smith's book in terms of whether it is open or shut.
Second, those concerned about Bradley's regress may worry about relying on mediated property instantiation to explain persistence. Some take the position that primitive bonds are required to block the regress. The endurantist strategy rules out the possibility of such bonds holding between persisting objects and the properties involved in change.
Third, it obscures how the properties involved in change are incompatible. An enduring object has the properties of being F and not being F involved in change in a way that does not generate contradiction because, in some sense, they can be co-instantiated. For instance, if Smith's book is shut-in-the-morning and open-in-the-evening, this looks no more problematic than Smith's book being rectangular and red. Thus, with any kind of mediated instantiation, the endurantist will need to explain the incompatibility of the relevant properties. For, without incompatibility between the properties, change itself becomes questionable.
Various strands of endurantism handle these worries more or less well, depending in large part on how they mediate property instantiation. Possible methods include: time indexed properties (x is F -at-t ), time relative predicate relations (x is-at-t F ), relations with times as arguments (x is F at t ), adverbial accounts (x is F t-ly ), temporal context sensitivity (obtains at t (x is F )), and tense (x was F ).
Perdurantism, exdurantism, and endurantism share the virtue of allowing us to maintain a commitment to the core theses of consistency , persistence , and change . Each does so by offering an account of persistence through change on which no single object just has the incompatible properties involved in change—whether it is because distinct objects just have those properties or a single object has them in a mediated way. Though they differ in particular metaphysical costs and benefits, this common feature is why they succeed in addressing rather than dismissing the initial worries with persistence.
At this point, the real problem with persistence is not deciding whether things persist—but rather explaining how they persist. The challenge today is to choose well among the metaphysical costs of reconciling the core theses so as to yield a coherent, useful theory that still respects our intuitions. The heart of the current persistence debate revolves around which view does the best job. Thus, it is worth remarking very briefly on three metaphysical concerns that provide, or seem to provide, reasons for favoring one approach to persistence over another.
First is the metaphysics of time. Eternalism, presentism, and the growing block view are among the main alternative accounts of the nature of time. Their different commitments regarding the reality of times make these views incompatible. The eternalist claims that all times exist, the presentist argues that only the present exists, and the growing block theorist holds that the past and the present exist, but not the future. The truth of eternalism or presentism or the growing block view would help choose between accounts of persistence if, as some have suggested, MTP entails either eternalism or the growing block view, or MET entails presentism. However, recent work on persistence suggests that MTP or MET can incorporate eternalism, presentism, or the growing block view, though perhaps not with equal ease.
Second is a concern with how propositions about the past, present, and future have truth values. At issue, is whether the is of predication is irreducibly tensed (serious tensing) or the is is timeless (surface tensing) in the logical structure of propositions. Some have thought this issue will help decide among approaches to persistence because they believe that endurantists must use serious tensing. However, though endurantists must use some form of mediated property instantiation, it need not be a form that depends on tensing.
Third is an issue about how temporary intrinsic properties must be instantiated. Intuitively, an intrinsic property of an object is one that the object has simply by virtue of being itself. Temporary intrinsics are intrinsic properties that an object has only temporarily. Above, being bent and being straight are temporary intrinsic properties of Lewis. Real change occurs when an object has, in some sense, incompatible temporary intrinsic properties at different times. Thus, any tenable account of persistence will need to explain how objects have temporary intrinsic properties.
Now, many hold the view that there must be a primitive bond between an object and its temporary intrinsic properties, that objects just have them. If so, then endurantism is not a viable account of persistence. For, endurantism achieves consistency only by insisting on some form of mediated property instantiation. However, among the many forms of mediated property instantiation, some mesh better than others with our intuitions and theoretical commitments regarding temporary intrinsics. So there is room for endurantists to come up with a reasonable account of temporary intrinsics when they devise an alternative to atemporal instantiation .
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Roxanne Marie Kurtz (2005)