Two Accounts of a Change in Properties: Perdurantism and Endurantism

Jenna Wichterman

Two theories that attempt to explain how things persist over time in spite of change are endurantism and perdurantism, and I will be making the case that a certain version of endurantism (with time-modified properties) does not account for real change, while perdurantism does – though in a surprising way. First, I will explain the puzzle.

The Puzzle

The puzzle is this: when Brian was a one-year-old, he was one foot tall. Years later, Brian is 20 years old, and is now six feet tall. However, Brian’s one-year-old self and his 20-year-old self are numerically[1]identical to one another. So Brian has both the property of “being one foot tall” (or “being not six feet tall”) and “being six feet tall.” So Brian has both the property of “being not six feet tall” and the property of “being six feet tall,” which are contradictory properties. However, one would generally posit that objects (including Brian) cannot have two contradictory properties. Wrapped up in this example are three claims that seem to be contradictory:

The Persistence condition: Objects (in this example, Brian) can persist through change
The Incompatibility condition: Objects that persist through change (like Brian) have incompatible properties
Law of non-contradiction: No object (like Brian) can have incompatible properties, like “being X and not-X”[2]

These three sentences together generate a contradiction. Therefore, one (or more) of these statements must be false, or there must be another way to interpret each sentence in order for it to be compatible with the other two statements.[3]Any theory that attempts to explain how things persist despite change must either make claims about one statement’s falsity, or re-interpret what one of these statements means. Endurantism and perdurantism are attempts to do just that.

Endurantism and How it Fails

Endurantism is the theory that objects are three-dimensional, and objects persist by being “wholly present” at every point in the time of their existence.[4]Objects are not “spread out” in time (as we will see later that perdurantism claims), but rather are only “spread out” over space. A three-dimensional object has properties (unlike a version of perdurantism, which claims that only an object’s temporal parts have properties). There is one version of endurantism that tries to get out of the puzzle using time-modified properties. ^[[5]^{] [}[6]^]This version of endurantism denies statement (2) of the puzzle, by claiming that objects undergoing change do not really have contradictory properties, because properties are always modified by time. So properties are not simply “p” or “not p.” An object has the property “being p at time t₁” and also the property “being not-p at time t₂.” Since these are not opposite properties, no contradiction is generated. But David Lewis presents an argument for how endurantism does not account for real change in his famous argument from “Temporary Intrinsics.”[7]He argues “reduction ad absurdum” that the idea of properties being held by objects only with respect to a certain time leads one to false conclusions. Consider the argument:

When objects undergo real change, a change in intrinsic properties is required, and not just a change in relational properties
Endurantism claims that objects always hold their properties in relation to a certain thing – time
So endurantism does not account for real change.

First, allow me to motivate premise (1). Ephemera are defined as “those properties and relations involved in ordinary matters of change.”[8]Lewis argues that ephemera are intrinsic properties, or “properties that an object has in virtue of itself alone,”[9]and not relational properties. Relational properties are properties that have to do with a relation to something else, like another object, space, or time. Some examples of an intrinsic properties would be “being six feet tall,” “having brown hair,” “being purple,” “being spherical,” etc. Some examples of relational properties would be like “being tall,” “being short,” “being five feet away from a blue wall,” “being six feet tall at time t₂,” etc. What motivates this claim that properties involved in ordinary matters of change (also known as “ephemera”) are intrinsic, and not relational? Take, for example, someone who is seven feet tall. If she walks into a room full of people who are five feet tall, she has the relational property of “being tall.” But suppose these five-feet-tall people leave, and the person is left standing there alone, in the same spot. Within a few minutes, a group of people who are all ten feet tall people enters the room. This seven-foot-tall person now has the relational property of “being short.” The seven-foot-tall person experienced a change in relational properties, and not a change in intrinsic properties. One would not say that the seven-foot-tall person changed properties in a real way by standing in a room in which people with different heights walked in and out.[10]

Another example of a relational change that does not constitute real change would be in spatial relation to other objects. For example, suppose I am standing five feet away from a chair. I have the relational property “being five feet away from a chair.” Now suppose my friend comes over, picks up this chair, and moves it ten feet away from me. Now I have the relational property “being 15 feet away from a chair.” One can see that I did not change in this example. I did not even move. So relational properties (with regard to space) do not constitute real change. By analogy, think of an example in which I have the property of “standing at t₁” (a relational property). Now suppose I am “picked up” and transported to time t₂, and that during the “move,” time is frozen and nothing else moves. I am put down at time t₂, and thus have the property of “standing at t₂.” Though one of my properties changed from being “standing at t₁” to “standing at t₂,” I did not change in any way. So this is an example of relational change (with time-modified properties) not constituting real change. [11]

Therefore, when an object undergoes real change, this does not include “changes” like going from “being five feet away from the chair” to “being 15 feet away from the chair.” Rather, real changes include things like going from “having brown hair” to “not having brown hair.” Therefore, endurantism does not provide an accurate understanding of real change. The way endurantism is able to get out of the contradiction of having two opposing properties (by claiming properties exist with respect to a certain time) is also the means by which endurantism fails to account for real change. This contradiction shows that endurantism cannot account for real (intrinsic) change when sorting properties by time periods, but rather can only account for relational change, which is really not change at all.[12]Thus endurantism does not really get us out of the puzzle since it tried to deny statement (2) that “objects that persist through change have incompatible properties.” But Lewis’ Argument from Temporary Intrinsics shows us that this is not real change at all, and thus endurantism does not get us out of the contradiction generated by real objects persisting through real change over time. We will see later that perdurantism provides a better way to get out of the puzzle than endurantism.

Response to the Passage of Time Objection

One might object: things cannot change without the passage of time. In fact, inherent in the definition of change is that it occurs over time. So it is incoherent to require the endurantist to give objects their properties unmodified by time in order to account for “real change.” This objection holds a misunderstanding of the previous claim. Saying that “real change requires that properties be intrinsic and not relational” does not mean that no time passes during the change. On the contrary – at t₁,O has the property “p,” and at t₂O has the property “not p.” Thus time has moved from t₁to t_2.But the argument instead is claiming that properties are not modifiedby time. Rather, these properties must be held by the objects simpliciter – not modified in some way by time.[13]There is a difference between saying “at t₁, O has property ‘p’” and saying, “O has property ‘p at t₁.’” In the first statement, O could have this property “p” at any point in time (t₁, t_2,t_3,etc) without it being a contradictory statement. In the second statement, O could only have this property “p at t₁” at a single time: t₁. If O had the property “p at t₁” at t₃, this would generate a contradiction.[14]

Perdurantism and How it Gets out of the Puzzle

So if endurantism fails to account for real change, how about perdurantism? First, I will explain what perdurantism is. Perdurance is commonly referred to as four-dimensionalism. Perdurance states this: everyday objects are four-dimensional space-time worms (“spread out in time”), and an object persists through time by having temporal parts at each time segment of its existence. ^[[15]^][[16]^]In other words, time should be thought of very similarly to the way that space is thought about. For example, with regard to space: my hand is not me. My foot is notme. They are both spatial parts of me. Perdurantism claims that time works similarly to space in this way. I am spread out in parts over time in what are called “temporal parts.” My temporal part (at time t₁) is not me, nor is my temporal part (at time t₂). Finally, these two temporal parts are not identical to each other (because they are two numerically distinct temporal parts).

Perdurance claims to solve the aforesaid puzzle (of persistence over time) by also denying statement (2), that “objects that persist through change have incompatible properties.” The contradiction is avoided by claiming that objects (four-dimensional worms) do not gain or lose familiar properties. Rather, the temporal parts are the things that have these familiar properties, and not the object (four-dimensional worm).[17] So one cannot say that an object has contradictory properties. An object does not have familiar properties – properties like “being 6 feet tall” and “not being 6 feet tall.”[18]This, like endurantism, denies statement (2) of the puzzle, that “objects that persist through change have contradictory properties,” but for a different reason: because objects themselves do not have familiar properties. This argument will be further developed later in response to a parallel objection raised to perdurance.

Perdurance provides a way to explain real persistence. Since within perdurance an object is a worm (the sum of its temporal parts), there is no way that this worm cannot persist throughout the whole time it is in existence. This is the case because an object is defined as the sum of its temporal parts, and though the temporal parts are not identical to one another, the object is identical to itself. So persistence is accounted for in the very definition of an object: a four-dimensional space-time worm that is “spread out” for as “long” as the time period that it exists.

The Parallel Objection to Perdurance

One could object to perdurantism the same way that Lewis objected to endurantism. Since an object is a four-dimensional worm composed of its temporal parts, then are not properties modified by an object’s temporal parts for perdurantism in the same way that properties are modified by time for endurantism?[19]One could object that having the properties “p at t₁” and “not p at t₂” are the same as having the properties “p at temporal part A” and “not p at temporal part B.” Let’s go back to the example of Brian, who is one foot tall at one-years-old, and six feet tall at 20 years old. Let us also call the one-foot-tall/one-year old temporal part of Brian Temporal Part A. Let us call the six-foot-tall/20-year-old temporal part of Brian Temporal Part B. Since Brian is a four-dimensional worm that is composed of Temporal Parts A, B, C, etc, Brian stands in the has-a-part relation to Temporal Part A, and also stands in the has-a-part-relation to Temporal Part B. So to say that Brian is not six feet tall at one years old and six feet at 20 years old is also to say that Brian has the property “not being six feet at Temporal Part A” and “being six feet at Temporal Part B.” Thus, for perdurantism, properties are modified by temporal parts in the same way that endurantism modified properties by time. Perdurantism thus attempts to account for change using relational properties and not intrinsic properties. An argument was given before that real change occurs not when an object changes relational properties, but only when an object changes intrinsic properties. So perdurantism similarly does not give an accurate account of real change.

Perdurantist Response to the Objection

The perdurantist could respond to this objection by denying that four-dimensional worm objects have properties themselves – at least familiar properties.[20]Their temporal parts have properties, but these objects themselves do not have familiar properties. Though this response may seem initially unattractive to hold, think back to the analogy of temporal parts being like spatial parts. Suppose we say, “Shelby is holding a cup,” or “Shelby has the property ‘holding a cup.’” What we mean by saying that “Shelby has the property ‘holding a cup,’” is that Shelby’s hand (one spatial part of her) is holding the cup. In other words, Shelby’s hand(and not Shelby) has the property of “holding a cup.” So we are actually speaking loosely when we say, “Shelby is holding the cup.” Shelby (as the collection of all her spatial parts) cannot hold a cup. Once we realize that we are speaking loosely when we say that Shelby (and not Shelby’s hand) is holding a cup, it becomes less alarming to say that, metaphysically speaking, Shelby herself cannot hold a cup – and only her hand can.

Temporal parts work the same way. A four-dimensional object Brian cannot have the property “being six feet tall.” However, a temporal part of Briancanhave the property “being six feet tall.” Thus one way to account for change in properties for four-dimensional objects is to claim that objects do not have familiar properties – only their temporal parts do. Familiar properties are ordinary, day-to-day properties that we normally ascribe to objects – properties like “being six feet tall” or “being blue.”[21]Four-dimensional objects do, on the other hand, have metaphysical properties like “being four-dimensional” and “being composed of x number of temporal parts.” But four-dimensional objects do not have familiar properties. Thus, when we ask, “Is Brian six feet tall?” we are speaking loosely. Metaphysically, we mean to ask, “Is Temporal Part B of Brian six feet tall?” to which the answer is “yes.” So, objects do not have properties modified by temporal parts. Nor do objects have familiar properties at all. Temporal parts have familiar properties.

Perdurantist Response to Another Objection

Another objection one might raise to the perdurantist account of change is the following: if four-dimensional objects do not themselves have familiar properties, and it was stated before (in Lewis’ argument for Temporary Intrinsics) that real change required a change in intrinsic properties, then how do objects really change under perdurantism? The answer the perdurantist could provide is this: for a four-dimensional object,[22]change requires a change in temporal parts, and this is simply a version of a change in intrinsic properties. So a four-dimensional object changes in virtue of having different temporal parts across time. What distinguishes different temporal parts from one another is a change in intrinsic properties between temporal parts, and not a change in relational properties between temporal parts. In other words, an object’s temporal parts are distinct from one another in virtue of having different intrinsic properties. Thus real change still occurs. Again, let us return to the analogy of temporal parts as being like spatial parts. Suppose there is a 6-inch tall block on the floor. I would not distinguish your hand (one spatial part) from your foot (another spatial part of you) by saying, “one is three feet away from the block on the floor, and the other is a few inches away from the block on the floor.” For, if you do a handstand, this becomes untrue. So these properties are not intrinsic to your spatial parts. Instead, I should distinguish your hand from your foot by describing each of their intrinsic features. Some examples of intrinsic features of your spatial parts would be: your hand has the property of “having 3 inch phalanges,” while your foot has the property of “having 1 inch phalanges.” These are properties that the hand and the foot have in virtue of themselves, and not in relation to any other object or time. So relational properties do not account for distinctions between spatial parts. In the same way, relational properties should not account for distinctions between temporal parts. So distinctions between temporal parts are based on intrinsic properties, and thus an object’s having different temporal parts does account for real change.

Conclusion

Perdurantism provides a more compelling account for real change than does endurantism – at least the version of endurantism with time-modified properties and the version of perdurantism that claims that temporal parts have familiar properties and not four-dimensional objects themselves.

Works Cited

Dyke, Heather. “Katherine Hawley: How Things Persist.” University of Notre Dame.9 November, 2016. http://ndpr.nd.edu/news/23240-how-things-persist/
Eddon, Maya. “Three Arguments From Temporary Intrinsics.” Philosophy & Phenomenological Research. 9 Nov, 2016. http://people.umass.edu/mayae/TI.pdf
Haslanger, Sally. The Oxford Handbook of Metaphysics.New York, NY: Oxford University Press, 2003.
Merricks, Trenton. Persistence, Parts, and Presentism. Nous, 1999.
Sider, Theodore. All the World’s a Stage. Australian Journal of Philosophy, 1996.
“Time.” Stanford Encyclopedia of Philosophy. 25 Nov, 2002. 9 Nov, 2010. Plato.stanford.edu/entries/time/#PreEteGroUnlThe

¹Numerical identity has to do with the number of things in a story. So, for example, if I tell a story about “Mr. Smith” and “Richard,” but am referencing a certain “Richard Smith” both times, then

Richard is numerically identical with Mr. Smith.

[2]Sally Haslanger. The Oxford Handbook of Metaphysics.New York, NY: Oxford University Press, 2003.

[3]Sallly Haslanger. The Oxford Handbook of Metaphysics.New York, NY: Oxford University Press, 2003.

[4]Heather Dyke. “Katherine Hawley: How Things Persist.”University of Notre Dame.9 November, 2016. http://ndpr.nd.edu/news/23240-how-things-persist/

[5]From now on in this paper, whenever I refer to endurantism, I am speaking about the version that accounts for change with time-modified properties.

[6]It should be noted that there are other ways that the endurantist can attempt to get out of the puzzle. This is merely one of the major ways, and it will be compared with the way that perdurantism attempts to get out of the puzzle. One of the other notable ways that the endurantist tries to get out of the puzzle is by a belief in presentism (a theory about time), which states that only the present exists. Since only the present exists, then for any object O, all of O’s parts at time t (the present) are the only parts of O. So O is wholly present, since all of O’s parts (namely, the parts it holds at the present time) are there. So endurantism with presentism also denies statement (2) of the puzzle, by showing how objects do not have contradictory properties because only the present and presently-existing properties exist.

[7]Maya Eddon. “Three Arguments From Temporary Intrinsics.” Philosophy & Phenomenological Research. 2010. 9 Nov, 2016. http://people.umass.edu/mayae/TI.pdf

[8]Eddon, Maya. “Three Arguments From Temporary Intrinsics.” Philosophy & Phenomenological Research. 2010. 9 Nov, 2016. http://people.umass.edu/mayae/TI.pdf

[9]Maya Eddon. “Three Arguments From Temporary Intrinsics.” Philosophy & Phenomenological Research. 2010. 9 Nov, 2016. http://people.umass.edu/mayae/TI.pdf

[10]Many thanks to Anthony Getter for helping to fully develop this example.

[11]Thanks to AJ Getter, who helped originate these examples.

[12]This gets to the question about whether or not time is really analogous to space. Is “being 5 feet away from blue wall” a relational property in exactly the same way that “having x property at time t₁” is a relational property?

[13]Trenton Merricks. Persistence, Parts, and Presentism. Nous, 1999.

[14]This objection was raised by Yifan Wang. Many thanks to her for anticipating this objection.

[15]Theodore Sider. All the World’s a Stage. Australian Journal of Philosophy, 1996.

[16]Trenton Merricks. Persistence, Parts, and Presentism. Nous, 1999.

[17]Sally Haslanger. The Oxford Handbook of Metaphysics.New York, NY: Oxford University Press, 2003

[18]Of course, the object will have some properties, like “being four-dimensional” and “having temporal parts,” but not the familiar properties that we normally ascribe to ordinary objects. Special thanks to Professor Trenton Merricks for formulating this nuance to my response to the objection.

[19]Special thanks to Professor Trenton Merricks for raising this objection.

[20]Familiar properties are properties that we ordinarily ascribe to ordinary objects. For example, “being blue,” “being cubed-shaped,” “existing,” etc. Metaphysical properties, on the other hand, are things like “being four-dimensional,” “having temporal parts,” etc.

[21]Special thanks to Professor Trenton Merricks for formulating this nuance of “familiar” properties for my response to the objection

[22]This is unlike a three-dimensional object, for which a change in intrinsic properties is required. So Lewis’ Argument from Temporary Intrinsics should only apply to three-dimensional objects, since four-dimensional objects do not have parts.