Persistence: Endurantism and Perdurantism

A poker is straight on Monday. On Tuesday someone hammers it into a hook, and it is bent. Earlier articles settled that this is one poker throughout: numerical identity is compatible with qualitative difference, and the poker has persisted through the change. What they left open is the more basic question of what it is for a thing to be there on Monday and there again on Tuesday. The two answers to that question disagree about what an ordinary object is, and the disagreement is not decided by any observation, since both describe the same poker doing the same things.

Two ways of being around for a while

The first answer is the one most people hold before they have considered the matter.

Endurantism treats time as unlike space in one respect. A poker is extended in space and has a handle end and a tip end, which are different parts of it. It is not extended in time in that way. Asked where the poker is, you point to one place and say that all of it is there, now.

The rival view takes the spatial comparison seriously and carries it across to time.

The two views agree on the history of the poker. They agree that it was straight and then bent, that it is the same poker, that it is now in the hearth. They disagree about what the poker is, and so about what the word "poker" refers to in the sentence "the poker was straight on Monday". The endurantist says it refers to an object that was entirely there on Monday. The perdurantist says it refers to something longer, whose Monday portion was straight.

Notice that neither view denies persistence. The perdurantist is not saying that things fail to last. The dispute is about the manner of lasting, which is why it cannot be settled by pointing at lasting things.

Temporal parts

Everything the perdurantist says depends on the notion of a temporal part, and the notion has to be stated with some care, because the casual gloss ("the poker as it was on Monday") invites the response that this is just a way of talking.

This is a version of the definition given by Theodore Sider in Four-Dimensionalism (2001), modelled on the way spatial parts work. The tip of the poker is a spatial part: it occupies just one region of the poker's extent, and it overlaps everything else that is part of the poker in that region. The temporal analogue is a part that occupies just one slice of the poker's history, and takes up all of what the poker is during that slice.

Two features matter. First, a temporal part is not a mere abstraction or a time-indexed description. It is supposed to be a genuine object, with a shape, a temperature and a location. The Monday part of the poker is straight and cold in just the way that the poker's tip is, in the spatial case, narrow and pointed. Second, the perdurantist does not say that the poker is a sequence of things that each exist for an instant and are somehow strung together. She says there is one poker, and that it has these parts, as a road has stretches. The poker is the whole, and the temporal parts are what it is made of, along the time axis.

Because parthood of this kind is not obviously available on the endurantist picture, endurantists are not attacking a straw target when they ask whether such parts exist at all. They commonly say they do not, or that if they do, a thing is not made of them. For the endurantist, "the poker on Monday" names the poker itself, considered at a time, not a part of it.

The problem of temporary intrinsics

The case that most people regard as the strongest argument for perdurantism comes from David Lewis, in On the Plurality of Worlds (1986), where he called it the problem of temporary intrinsics.

The point of insisting on intrinsic properties is to block a cheap answer. Relational change is harmless. Someone who is taller than her sister on Monday and shorter on Tuesday, because the sister grew, has not gained and lost the same property in any troubling sense: she has stood in a relation to one thing and then to another. But shape is not like that. Being bent is not a relation to anything. It is how the poker is, itself.

Seen as a puzzle about Leibniz's law, the difficulty is plain. If the Monday poker is identical to the Tuesday poker, whatever is true of one is true of the other, and the Monday poker is straight while the Tuesday poker is bent. The ordinary reply is "straight on Monday, bent on Tuesday", which does not contradict. The question is what the qualifications "on Monday" and "on Tuesday" contribute, and Lewis's claim is that every answer open to the endurantist costs something.

The perdurantist solution

The perdurantist denies the third premise. The poker is not wholly present on Monday. What is present on Monday is a temporal part, and that part is straight. A different temporal part, present on Tuesday, is bent. They are two different things, so there is no single object with two incompatible shapes. The poker, the whole worm, has each shape only derivatively: it is straight on Monday in the sense that it has a part on Monday that is straight, just as a road is wide here and narrow there in virtue of having a wide stretch and a narrow stretch.

The road comparison is the whole of the explanation, and its force is that nobody finds a contradiction in a road that is wide at one place and narrow at another. Nothing has the incompatible shapes without qualification. Each shape belongs to a part, and the parts are distinct. Time on this picture is simply another dimension along which a thing can vary, and variation along a dimension is not inconsistency.

Endurantist replies

The endurantist cannot ignore the argument, since the conclusion is a contradiction. Lewis himself listed the options, and the main ones are worth setting out with their costs.

The first is to deny that shapes are intrinsic, and to say that being bent is really a relation to a time. The poker bears the straight-at relation to Monday and the bent-at relation to Tuesday, and nothing is incompatible about bearing different relations to different things. The cost is that shape then ceases to be a way the poker is in itself. Lewis thought this a heavy price: it is hard to believe that the poker's bentness has anything to do with a calendar.

The second is to deny that the past and future poker are real, so that only the present shape is had by anything. This is presentism about time, and it removes the incompatibility by removing one of the two shapes. It is a position held on grounds quite apart from persistence, and it leaves the endurantist with the burden of defending it, along with an account of how past truths about the poker are true.

The third, and the one most endurantists prefer, keeps shape intrinsic and puts the time in the having. Mark Johnston, Sally Haslanger and E. J. Lowe each developed versions of what is often called the adverbial view in the late 1980s. The poker is not straight-at-Monday. It has straightness in a Monday-ish way, and it has bentness in a Tuesday-ish way. The time qualifies the instantiation, the way in which the thing has the property, and not the property itself, so the property stays intrinsic and the poker stays whole.

What else is at stake

Temporary intrinsics is the central argument, but it is not the only consideration, and the other considerations cut in different directions.

Perdurantism handles puzzle cases with a uniform tool. In the ship of Theseus, the perdurantist says there are two four-dimensional ships that share all their temporal parts up to the point of the reassembly and diverge afterwards, so that the question of which is the original has no unique answer to be found. The endurantist has to choose among the options the earlier article set out, because a wholly present thing cannot be shared in that way. Whether this counts for or against perdurantism depends on whether you find overlap a neat resolution or a cheat.

Perdurantism also gives a simple account of coincidence. A statue and the lump of clay that makes it seem to be in the same place, and to differ in what they could survive. If the two come into being and cease to exist together, the perdurantist can say that they have all their temporal parts in common and so are identical. An endurantist who thinks them distinct has to explain how two things can be wholly in the same place at once. That problem has an article of its own in the advanced tier.

On the other side, perdurantism seems to many to misdescribe the ordinary use of parthood. When we say that the engine was part of the car, we usually mean at a time, since the engine may be replaced. The endurantist takes parthood to be a relation among an object, a part and a time. The perdurantist reads the same sentences as being about temporal parts that were parts of the car-worm, which is a systematic reinterpretation of what we say.

Some arguments for perdurantism go through the theory of composition instead. Sider has argued that if composition is unrestricted, so that any things whatever have a sum, then for any temporal parts there is a worm composed of them, and that arguments from vagueness favour unrestricted composition. If that is correct, the existence of temporal parts comes cheaply. This argument is contested at every step, and it is best read as showing how persistence is entangled with what there is to be composed.

None of these considerations is clean. What the debate shows is that a seemingly trivial fact, that things last, is explained by one of two quite different pictures of what a thing is, and that an observer who accepted all the facts could still be endurantist or perdurantist. That is why the choice tends to be made on the grounds of theoretical economy and fit with the rest of one's metaphysics.

The next article takes the question to the case where we care about it most, and asks what has to be preserved for a person to persist, which is a problem the debate between worms and wholly present objects makes sharper, not easier.