By James Pyle
The way in which we think about change is inherently intertwined with time. Without time all our notions of change start to unfurl. It is ironic then that explanations of the relationship between time and change remain polarising. Despite this, it is generally agreed that things persist over time and maintain their identity through this process – that is, the James of now is the same James as five minutes ago. One of the main accounts of this process is perdurantism. Under a perdurantist account, identity persists through change due to particulars possessing not only physical parts, but temporal ones as well.[i] In this essay, I will establish the four-dimensionalist view of the perdurantist account of change, explain why I believe it is the best explanation of change through the work of David Lewis, and respond to the allegation that perdurantist change does not qualify as real change.
The relationship between time and change is underpinned by our experience of diachronic sameness, or the idea that our identity persists through time. While certain philosophers, such as J. M. E. McTaggart, deny this type of change entirely, almost all theorists agree that (generally speaking) temporal change is real and the particulars that experience it maintain a single identity throughout the process. This assumption “underlies some of our most fundamental beliefs about ourselves and the world around us… and unless we believe… that we are beings who persist through time, we [can] make little sense of the notion of experience”.[ii] Explanations of persistence can be divided into two primary schools of thought: endurantism and perdurantism (also somtimes called three-dimensionalism and four-dimensionalism). The difference between the two is a disagreement concerning the relationship between parts and time. Katherine Hawley neatly explains this disagreement as the way in which “Endurantists think about what parts you have at different times, past, present or future [while] perdurantists prefer to think atemporally about what parts you have, full stop”.[iii] This debate on how identity persists through time sets the stage for contrasting perspectives about the nature of temporal existence and highlights the foundational divide between endurantism and perdurantism. These two competing frameworks offer fundamentally different accounts of how objects maintain their identity through time, with endurantism providing what many consider the more intuitive explanation
For endurantists “a concrete particular persists through time by existing wholly and completely at each of several different times… Persistence through time, then, is construed as the numerical identity of a thing existing at one time with a thing existing at another time”.[iv] This account of persistence aligns with our intuitions that concrete particulars are composed of physical parts which endure through time. Put simply, it is a formalisation of our natural experience of the passage of time.
Perdurantists, however, see “assertions of diachronic sameness are not assertions of literal identity at all… expressions [such as the “James of yesterday”] refer to numerically different parts of a concrete particular”.[v] They understand time as functioning the same as space in terms of its relations and properties, meaning that the “James of yesterday” is a spatiotemporal part of the object which is James (James being the sum of my past, present, and, depending on the perdurantist, future). Perdurantists refer to these as temporal parts, time-slices, phases, or stages. Important to note is that perdurantists do not believe that we possess spatial and temporal parts, but that we possess exclusively spatiotemporal parts (e.g., “my hand yesterday” and “my hand today” are not my hand with different temporal coordinates, they are parts of the whole four-dimensional object that is my hand).
One common critique of perdurantism is what I will refer to as the ontological argument. It is the claim that perdurantism leads to ontologically unsound particulars and, due to this, is unable to constitute a valid theory of time. This is explained by Michael Loux as the fact that “for perdurantists, there are infinitely many ways of cutting up the four-dimensional spread that is the material world. No one of those ways of cutting it up is ontologically privileged”.[vi] While we may intuitively understand common sense spatiotemporal divisions of a particular (such as breaking down myself into the parts of James-of-yesterday, James-of-today, and the James-of-tomorrow), for perdurantists this is simply one possible configuration of temporal parts. What endurantists find problematic about this tendency is that it leads to the existence of implausibly composed particulars. An example of this would be Loux’s Athanasius, a particular which is composed of the following parts: “the Loux of yesterday; Big Ben from noon, January 15, 1914, to midnight, February 13, 1916; Wembley Stadium from 2 p.m. to 3 p.m., May 12, 1954; and the top two-thirds of the Sears Tower on Christmas Day, 1994”.[vii] According to perdurantists, Athanasius is every bit as real and valid a particular as I am when I am broken down into the sum of the spatiotemporal parts of my body from my birth to my current state. Their view asserts that, while not particularly meaningful to discuss, Athanasius is simply another possible composition of real spatiotemporal parts into a larger identity. However, unlike the relationship between my parts, Athanasius’ parts appear disparate and without any unifying element, which gives rise to the endurantist critique that perdurantism is fundamentally flawed, as it gives rise to nonsensical objects such as Athanasius.
The restructuring of identity into a collection of discrete spatiotemporal parts without any apparent connection to one another becomes jarring to our experience of diachronic sameness in ourselves and our environment. In order to justify their views, the perduantist must be able to respond to the enduranist critique that Athanasius’ validity is incongruent with our experience of how things exist in time.
The possibility of particulars such as these pose a significant challenge to the perduantist account of identity. For the endurantist, particulars are composed solely in three dimensions and the ways of dividing and understanding them into their parts are all readily apparent to us. The endurantist will see the very notion of accepting an object such as Athanasius – which has unrelated parts split across unrelated times forming something which we fail to intuitively recognise as a thing – as real as the height of perdurantist folly. This claim is not one which is as absurd as it initially seems. Rather, it highlights the absurdity of our attempts to configure parts into things. While we may see Athanasius as counterintuitive due to its lack of a coherent relationship between parts, we freely ignore this when it comes to three-dimensional objects. Take, for example, myself.[viii] We can say without question that I am a coherent object under any normal account. This would mean my parts are able to constitute an object (myself) and, unlike Athanasius, this relationship is coherent. However, what we are doing here is not really talking about the relationship between my parts, but my parts’ ability to fit an idea of myself. If shown to an alien lifeform with no similarities to myself (and thus not possessing any idea of what I should look like), it would fail to recognise my parts as forming the object known as myself. Unless we privilege my cognition as truer or more accurate than the alien, we are left with an interesting idea: the configuration of an object’s parts is arbitrary.
If we accept this, then connections between parts are not required for an object. However, this remains problematic to endurantists, who see this as an endorsement of the existence of nonsensical objects composed of unconnected parts. To them, these perdurantist objects are unlike our familiar particulars (such as a sofa), which we can understand intuitively as composed of connected parts. While they will allow physical separation between parts (such as for a stereo system having a spatially detached remote as a part of itself), they will justify this claim by saying its parts are all causally related.[ix] However, the difference they find between these objects’ relationship with their parts is that, unlike Athanasius, the stereo system’s parts have shared causal relationships with each other, which they argue to be the condition for ontological validity. Put formally, their argument is:
(1) If an object is ontologically valid, it will have causally related parts. (P → Q)
(2) Athanasius does not have causally related parts. (¬Q)
(3) Therefore, Athanasius is not an ontologically valid object. (1, 2)
From this, as Athanasius lacks causally related parts it cannot be considered ontologically valid.
However, the argument of plausibility through parts’ causal relationships remains problematically rooted in subjectivity and is prone to revision. To see this, we can consider this scenario: I am living in a house (H1) and there is another house (H2) immediately next door to me. One day, I discover a new room which contains a passageway (P) which connects H1 to H2. Following my discovery, my perceptions of H1 and H2 shift from distinct objects into unified parts of a larger house (L) which is composed of the sum of H1, H2, and P. Despite no change occurring outside of my perceptions, the apparent composition of these two houses has shifted. From this, we can arrive at two possible positions to explain how this change occurred: (1) there are objective causal connections between things and their parts which we can discover, however we are unable to prove them beyond all doubt, or (2) there is no way to constitute objective connections between parts in a way which transcends subjectivity. The shared conclusion between these two positions is that there is a reliance on subjectivity to understand an object’s composition. Following this, we can revisit the endurantist’s argument against Athanasius’ validity: if an object has causally related parts, then it will be ontologically valid. From the previous conclusions about causal connections, we can dissolve the endurantist argument in two ways. The first is to use a reduction ad absurdum by pointing out the now contradictory nature of the argument. By affirming subjectivity as a valid form of determining ontological validity, the endurantist loses the objectivity which their argument was based on. The second option is to perform a modus tollens on the endurantist argument. In the face of the fact that subjectivity does away with the independent and pre-existing status of causal relationships between parts (rendering it false), ontological validity is no longer dependent on this relationship. We can see this as:
(1) If an object is ontologically valid, it will have causally related parts. (P → Q)
(2) No parts have definite causal relations. (¬ Q)
(3) The ontological validity of an object is not defined by the causal relationship between its parts. (1, 2)
(4) Athanasius is a valid object. (3)
What we are then left with, then, is a reality in which causal relationships are dependent on subjectivity and can be freely assigned.
Under this view, Athanasius becomes mereological junk, an object which is almost meaningless to discuss. Despite this diminutive classification, I believe the perdurantist will find no problem with agreeing with this classification of Athanasius. While Athanasius may be of no use in discussions and prove to be more of a hazard than a boon to know about in everyday life, these facts are ultimately irrelevant to its ontological status. Privileging the realness of common-sense particulars such as myself over Athanasius then can be understood to be a naturalistic prejudice.
If we accept this, then spatial connections between parts are not required for an object. And, unless endurantists deny that time is a spatial dimension, arguing against Athanasius’ legitimacy cannot be accomplished by arguing against its coherence as a concrete particular.
Though perdurantism does not appeal to our intuition, I believe that it explains change to a level which endurantism is unable to. To explain this, I will use David Lewis’ problem of temporary intrinsics. In this, Lewis concerns himself with a persisting thing’s intrinsic properties (that is, its current properties which it possesses independently of anything else) and the problem of how “Persisting things change their intrinsic properties [over time]”.[x] Put more directly, this is the way in which a concrete particular can have incompatible properties at different times despite maintaining the same identity (such as a banana being unripe one day and ripe the next). For this, Lewis proposes three possible solutions: (1) intrinsic properties are, in reality, unchanging properties which only change in their relation to time, (2) the only true intrinsic properties are a particular current properties, and (3) incompatible intrinsic properties belong to a different temporal parts of the same object.[xi]
Of the three, the first two are immediately rejected by Lewis. For the first, Lewis describes the idea that change in temporary intrinsics must be “reinterpreted as relations that something with an absolutely unchanging intrinsic nature bears to different times… simply incredible, if we are speaking of the persistence of ordinary things… If we know what shape [Lewis’ example of an intrinsic property] is, we know that it is a property, not a relation”.[xii] The second is rejected on the grounds that it denies identity and history. This is due to it rejecting persistence as a whole – if my past self is not real, then no identity has persisted through change (this similarly applies to the future). Obviously, this is an untenable option to the normal person. The third option, however, is of keen interest to Lewis.
Unlike the previous two options, the idea that we have different temporal parts is an unproblematic explanation. Under this explanation, “we are made up of temporal parts, and our temporary intrinsics are properties of these parts, wherein they differ one from another. There is no problem at all about how different things can differ in their intrinsic properties”.[xiii] This option explains change as variation between our temporal parts. Similarly, temporal parts allow us to explain the persistence of a particular’s discernible identity through time despite change in intrinsic properties. Rather than being a series of disconnected parts with no relation to one another, a particular’s later state is fundamentally inclusive of its earlier parts in its constitution. In the case of a cup (Cup) which is initially unbroken (Hcup) which later loses its handle (Tcup), we can say Tcup includes the temporal parts of Hcup.[xiv] While it is a divergence from Hcup’s intrinsic properties, Tcup is still inclusive of Hcup’s parts and a state of Cup and a development of Tcup. The problem of incompatible intrinsic properties then proves no more problematic for temporally extended objects than spatially extended objects. In the same way a poker can be hot at one end and cold at the other, a banana can be unripe in one temporal part and ripe in another.
Lewis’ explanation of change through the inclusion of temporal parts is the view which I believe to be true. However, the perdurantist account of change which Lewis sets out does have a common objection: the no change argument which holds that perdurantism doesn’t allow for real change. There are two versions of this argument with different focuses: I will refer to the version proposed by Roderick Chisholm as the unity argument, and the version proposed by D. H. Mellor as the variation argument. I will explain these arguments before offering my own responses to them.
The unity argument as given by Chisholm focuses on what he takes to be a major flaw of perdurantism: its lack of unity between temporal parts. Chisholm proposes the idea that temporal parts do not permit change due to their lack of unity in identity. The identities of the temporal parts, according to Chisholm, are all distinct.[xv] An example we can use is a modified version of Theseus’ Paradox: suppose I was sailing a ship and, unknown to me, an omnipotent demon had intervened and swapped one of the planks out with a slightly rotting one. I notice this, but continue sailing, continue sailing. The demon continues to swap that same plank out with slightly more rotting ones. By the time I notice, the plank is entirely rotten, and I falsely conclude that the plank has rotten while it has actually been replaced by a series of different objects. This, following Chisholm, is the problem of perdurantism: nothing is changing, parts are simply being replaced by ones with incompatible properties.
A version of this is the variation argument. It is essentially the idea that variation between spatiotemporal parts is incompatible with the identity of indiscernibles. This is best articulated by D. H. Mellor, who states that change is “a thing having incompatible real properties at different times… But events, as well as things, can have incompatible properties at different times [but this does not constitute change]”.[xvi] This is due to the way in which Mellor alleges perdurantist particulars fail to maintain a persistent identity as is required for change. To explain Mellor’s view, I will use an example: we have an object (x) which possesses two mutually exclusive properties (+1 and -1) at two different times (t1 and t2). This is such that,
x is +1 at t1, and
x is -1 at t2.
If x is a temporal object, it will have parts at t1 and t2. I will call these x1 and x2. Then, following Mellor, we can understand the change as
x1 is +1, and
x2 is -1.
The problem here is the loss of identity of x. The change in properties no longer occurs in x, but in x1 and x2, which, as Mellor puts it, “stops this being a change, since change needs identity as well as difference. That is, it needs a single particular for the difference to be a change in; and here there is no such particular”.[xvii] While the x1 and x2 may be the same in every way other than temporal location and a single property, Mellor does not believe this can be considered real change.
In defence against the no change argument, I believe Mark Heller provides strong responses to both forms of the no change argument which I have outlined. In response to the unity argument, Heller points out the endurantist view of parts does not take into account the shape of four-dimensional parts. While the proponent of the succession argument will claim that perdurantists argue for persisting objects “as a series of very short-lived three-dimensional objects”, this is a mistake on their part.[xviii] Instead of thinking of spatiotemporal parts as successive three-dimensional parts, Heller points out that four-dimensional parts have extension not only in conventional space, but time (which we experience as duration) as well: “The parts, like the whole, are just the material contents of filled regions of spacetime. I am not composed of a series of short lived people; I am composed of bits of matter that fill sub-regions of the region of spacetime that I fill”.[xix] Maintaining the succession argument would then require extending of the criticism of the connectedness of temporal parts to spatial parts as well. However, I believe this would prove too odd a move for most endurantists to endorse.
Heller offers similar reasoning against the variation argument. He does not deny that difference in parts is not real change, but that these parts’ properties can be extended to the whole at a given time. In the same way we can predicate a property of a three-dimensional particular within its boundaries (such as a road being hilly in New York but flat in Illinois), there should be no problems with doing so from a four-dimensional viewpoint.[xx] By making four-dimensional particulars equivalent to three-dimensional particulars, perdurantists are able to adopt “just about any account of what it is for an object to have a property at one time while lacking it at another”.[xxi] In this way, the objection to perdurantism – its apparent inability to constitute real change – are able to be discarded. From this, we can return to the strength of Lewis’ argument that temporal parts offer the cleanest explanation of how change in properties can occur whilst maintaining a single identity.
The notion of change is one which is naturally divisive. How does something persist through time, whether it has the same identity as before, and whether either of these are valid questions? I, however, believe that the perdurantist account of temporal parts offers an elegant solution to the problem of persistence. The difficulty we face when confronted with the idea that we are composed of different temporal parts with different properties lies, I would argue, mostly in perspective. By focusing on our experience as one grounded in time, as a process and experience rather than a spatial dimension, we are naturally led to endurantism. However, if we understand it more clearly as a spatial dimension (albeit an unintuitive one), then many of the difficulties of temporal parts can be dissolved. By shifting our perspective from three-dimensional space to four-dimensional space, I believe we are able to elegantly understand the problem of persistence of identity.
I am a final year student studying philosophy and literature. My primary areas of interest in philosophy are aesthetics, ethics, the philosophy of language. Outside of philosophy, I’m interested in art, fashion, and architecture.
ENDNOTES
[i] Katherine Hawley, “Temporal Parts,” The Stanford Encyclopedia of Philosophy (2020), ed. Edward N. Zalta, https://plato.stanford.edu/archives/sum2020/entries/temporal-parts/.
[ii] Michael J. Loux, Metaphysics: a contemporary introduction (New York: Routledge, 2006), 231.
[iii] Hawley, “Temporal Parts”.
[iv] Loux, Metaphysics, 231.
[v] Loux, Metaphysics, 231.
[vi] Loux, Metaphysics, 240.
[vii] Loux, Metaphysics, 238.
[viii] For the sake of my argument, I will restrict this to my physical parts.
[ix] Achillie Varzi, “Mereology,” The Stanford Encyclopedia of Philosophy (2019), ed. Edward N. Zalta, https://plato.stanford.edu/archives/spr2019/entries/mereology/.
[x] David Lewis, On the Plurality of Worlds (Oxford: Blackwell, 1986), 203.
[xi] Lewis, On the Plurality of Worlds, 204.
[xii] Lewis, On the Plurality of Worlds, 204.
[xiii] Loux, Metaphysics, 240.
[xiv] Andre Gallois, “Identity Over Time,” The Stanford Encyclopedia of Philosophy (2016), ed. Edward N. Zalta, https://plato.stanford.edu/archives/win2016/entries/identity-time/.
[xv] Roderick Chisholm, “Problems of Identity,” in Identity and Individuation, ed. Milton K. Munitz (New York: New York University Press, 1971), 19.
[xvi] D. H. Mellor, Real Time II (London: Taylor & Francis Group, 1998), 89.
[xvii] Mellor, Real Time II, 89.
[xviii] Mark Heller, “Things Change,” Philosophy and Phenomenological Research 52, no. 3 (1992), 700.
[xix] Heller, “Things Change,” 700.
[xx] Heller, “Things Change,” 700-701.
[xxi] Heller, “Things Change,” 702.
WORKS CITED
Chisholm, Roderick. “Problems of Identity.” In Identity and Individuation, edited by Milton K. Munitz, 3-31. New York: New York University Press, 1971.
Gallois, Andre. “Identity Over Time.” The Stanford Encyclopedia of Philosophy (2016). Edited by Edward N. Zalta. https://plato.stanford.edu/archives/win2016/entries/identity-time/.
Hawley, Katherine. “Temporal Parts.” The Stanford Encyclopedia of Philosophy (2020). Edited by Edward N. Zalta. https://plato.stanford.edu/archives/sum2020/entries/temporal-parts/.
Heller, Mark. “Things Change.” Philosophy and Phenomenological Research 52, no. 3 (1992): 695–704. https://doi.org/10.2307/2108216.
Lewis, David. On the Plurality of Worlds. Oxford: Blackwell, 1986.
Loux, Michael J. Metaphysics: a contemporary introduction. 3rd. New York: Routledge, 2006.
Mellor, D. H. Real Time II. London: Taylor & Francis Group, 1998.
Varzi, Achillie. “Mereology.” The Stanford Encyclopedia of Philosophy (2019). Edited by Edward N. Zalta. https://plato.stanford.edu/archives/spr2019/entries/mereology/.
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