Understanding Perdurantism and Endurantism

1. Two Pictures of Persistence

Let's begin by defining the two central theories that attempt to explain how objects persist through time. At their core, they offer different answers to the question: What is the thing that exists at any given moment?

• Endurantism (or 3D-ism): This is the intuitive, common-sense view. It holds that objects are three-dimensional entities that are wholly present at every moment of their existence. The very same you that is reading this sentence existed five minutes ago and, hopefully, will exist five minutes from now. According to this view, you move through time, whole and entire at each point.

• Perdurantism (or 4D-ism): This view, which aligns naturally with the block universe, holds that objects are four-dimensional entities that persist by having different temporal parts (or "time-slices") at different moments in time. An object is a "spacetime worm" that is extended in time just as it is in space. The thing that exists right now is not the whole you, but merely your current temporal part.

The following short video provides a clear, animated introduction to these two concepts and the idea of temporal parts.

As a physicist, the perdurantist conception of a four-dimensional "spacetime worm" should resonate strongly with the world-lines of particles or objects in Minkowski spacetime diagrams. Endurantism, by contrast, tries to preserve the idea of a familiar, three-dimensional object navigating a separate temporal dimension. The tension between these two pictures becomes sharp when we consider the phenomenon of change.

2. The Paradox of Change: The Problem of Temporary Intrinsics

Change seems simple enough. A banana is green on Monday and yellow on Friday. A poker is straight before you put it in the fire, and bent after. But this apparent simplicity hides a deep paradox. Let's break it down into its constituent claims, all of which seem plausible on their own.

1. Change occurs: Objects have different, often incompatible, properties at different times. A banana is unripe at time $t_1$ and ripe at time $t_2$.
2. Persistence through change: The object that has these properties is the same object. It is the same banana that was unripe and is now ripe. If it were a different banana, we wouldn't call it change; we'd call it replacement.
3. Leibniz's Law (The Indiscernibility of Identicals): If $x$ is numerically identical to $y$, then $x$ and $y$ must share all of their properties.

Do you see the contradiction? If the banana at $t_1$ is the same object as the banana at $t_2$, Leibniz's Law demands they have identical properties. But they don't! The banana at $t_1$ has the property being unripe, which the banana at $t_2$ lacks. And the banana at $t_2$ has the property being ripe, which the banana at $t_1$ lacks. It seems the object is both the same and not the same, which is impossible.

This is the problem of temporary intrinsics. The "intrinsic" part is crucial: we are talking about properties an object has in and of itself (like its shape or chemical composition), not properties it has in relation to other things (like being to the left of an apple).

The following reading from the Stanford Encyclopedia of Philosophy (SEP) clearly articulates this problem and sets the stage for the two main solutions.

3. The Perdurantist Solution: Distributing Properties Over Parts

As the SEP article explains, perdurantism offers a clean and powerful solution. It resolves the paradox by rejecting the premise that a single thing has incompatible properties. Instead, the four-dimensional object—the spacetime worm—has different temporal parts, and these distinct parts have the different properties.

• The banana-worm is a single, four-dimensional object that persists through time.
• It has a temporal part on Monday, banana-Monday, which has the intrinsic property of being unripe.
• It has a different temporal part on Friday, banana-Friday, which has the intrinsic property of being ripe.

There is no contradiction. Banana-Monday and banana-Friday are not identical to each other, so Leibniz's Law doesn't apply to them. They are merely parts of a larger whole, the banana-worm. The analogy to spatial parts is exact: a road can be bumpy in one spatial part and smooth in another without contradiction. Perdurantism treats time as another dimension along which properties can vary.

An Objection to Perdurantism: Is This Really Change?

Critics of perdurantism, however, argue that this picture doesn't capture genuine change. They claim it replaces change with a static landscape of ordered events. McTaggart, whom we met in the last lesson, used the analogy of a poker that is hot at one end and cold at the other. We wouldn't say the poker is "changing" from hot to cold; it simply has different properties at different spatial locations. The perdurantist, so the objection goes, makes change nothing more than this kind of static variation along the temporal axis.

The perdurantist can reply that this is precisely what change is. As the philosopher Ted Sider puts it, change is qualitative difference between different temporal stages of a single persisting object.

4. Endurantist Solutions: Saving the Wholly Present Object

Endurantism, the view that the entire three-dimensional object is present at each moment, cannot use the perdurantist's strategy. If the whole banana is present on Monday and the same whole banana is present on Friday, the endurantist must find another way to avoid the contradiction. There are three main strategies.

Let's turn to a more detailed resource that lays out these endurantist responses.

As you've just read, the endurantist has a few difficult paths to choose from:

1. Presentism: This view, which we saw is an A-theory of time, claims that only the present exists. If the banana is now ripe, the unripe banana of the past simply does not exist. Therefore, there is no single object that possesses two incompatible properties, because one of them belongs to a non-existent past state. While this solves the problem, it requires accepting a very controversial ontology of time that many philosophers, especially those influenced by physics, find untenable.

2. Relationalism: This is perhaps the most common endurantist strategy. It proposes that properties like ripeness are not monadic (one-place) intrinsic properties, but are actually relational (multi-place) properties. The banana doesn't have the property of being ripe; it stands in the being-ripe-at relation to Friday. So, the banana has the relation being-unripe-at(t_1) and the relation being-ripe-at(t_2). These are two different, compatible relations, so there is no contradiction.

3. Adverbialism: A more exotic view, adverbialism suggests that the mode of having a property is what changes. The banana has the property being unripe Monday-ly and it has the property being ripe Friday-ly. Instead of changing the property or the object, this view changes the way the property is instantiated.

Evaluating the Endurantist Response: Lewis's Challenge

The relationalist strategy seems plausible, but it faces a powerful objection, most famously leveled by David Lewis. He argued that it fails to properly account for intrinsic properties. Intuitively, the shape of an object is something it has purely in virtue of itself, not in virtue of a relation it bears to a time. If all temporary properties are relations, it seems objects lose their intrinsic nature.

Perdurantism, Lewis argues, does a better job. The temporal part of the object—the time-slice—can have its shape intrinsically. The 4D worm has its shape derivatively, by having a part with that shape. But for the endurantist's 3D object, relationalism seems to force all properties to be extrinsic. This is often called "the problem of temporary intrinsics"—using the same name as the broader paradox, but here referring to this specific objection against the endurantist's relational solution.

To see this argument developed, let's watch one final clip.

This objection puts the endurantist in a difficult position. To save the idea of a "wholly present" object, they may have to sacrifice the idea that temporary properties like shape can be truly intrinsic.

Conclusion

We have dissected one of the central puzzles in the metaphysics of persistence. The simple fact of change forces us into a deep philosophical choice about the nature of objects and their relationship to time.

• Key Takeaways:
  • The Problem of Temporary Intrinsics is a paradox that arises from an object having incompatible properties at different times, seemingly violating Leibniz's Law.
  • Perdurantism (4D-ism) offers an elegant solution: the object is a 4D "spacetime worm," and its different temporal parts possess the incompatible properties. Change is variation across the temporal dimension.
  • Endurantism (3D-ism) maintains that an object is "wholly present" at each moment. To solve the paradox, it must adopt more complex strategies, such as appealing to Presentism (only the present exists) or Relationalism (properties are relations to times).
  • A major challenge for endurantist relationalism is that it seems to turn all temporary properties into extrinsic relations, failing to account for temporary intrinsic properties.

The debate between perdurantism and endurantism showcases how metaphysical theories are evaluated. Perdurantism aligns well with the "block universe" of physics and offers a clean solution to the paradox, but at the cost of our intuitive idea of an object. Endurantism preserves our intuition but requires more complex and controversial metaphysical machinery.

Preview of the Next Lesson:
Having explored how objects persist and change, we now turn to how they interact. The concept of one event causing another is fundamental to our understanding of the world, from physics to everyday life. But what is this "causal connection"? Is it a real force or glue that binds events together, or is it merely a regular pattern we observe? In our next lesson, we will investigate the problem of necessary connection in causation, beginning with David Hume's classic skeptical critique.