How things persist

Things exist in time. More specifically, they persist. A thing, such as a tree, remains the same object throughout its existence, although it changes some of its properties, loses some of its parts and acquires new ones. The relation that holds between the same object at different times is called ‘diachronic identity’. But the question is: What is this new type of identity? How does it relate to numerical identity? Is diachronic identity reducible to numerical identity, or perhaps to qualitative identity? These questions are answered differently by two major conceptions of how things persist in time: endurantism and perdurantism. Endurantism can be characterised broadly as the position according to which things persist in time by being wholly and completely present at every single moment of their existence. On the other hand, perdurantism assumes that at a given moment only a small part of a thing is present. The whole thing is an object which extends in time as well as in space.

Let us look more closely at both views. Endurantism seems to be in agreement with our pre-philosophical intuitions regarding persistence. When I look at a table in front of me, I believe that no part of it is missing from my view. Things have only spatial parts and spatial dimensions, but no temporal ones. According to endurantists, the expressions “Napoleon at the time of the battle of Austerlitz” and “Napoleon at the time of the battle of Waterloo” refer to one and the same individual: Napoleon. Hence diachronic identity reduces to numerical identity. Things are three-dimensional objects taking up various spatial regions at different times.

Perdurantism, on the other hand, claims that things are four-dimensional objects taking up regions of space-time. The expressions “Napoleon at the time of the battle of Austerlitz” and “Napoleon at the time of the battle of Waterloo” refer to numerically different objects: temporal parts of the four-dimensional entity that we call “Napoleon” and whose temporal dimension stretches from the moment of Napoleon’s birth to his death. Consequently, the relation of diachronic identity is not defined as numerical identity, but instead can be explicated as the relation that holds between any two temporal parts of the same thing: x is diachronically identical with y iff x and y are different temporal parts of individual z. (An alternative interpretation of diachronic identity under perdurantism is that it is reducible to numerical identity after all, when we say that “Napoleon at t1 is identical with Napoleon at t2” means “The four-dimensional object whose temporal part at t1 is Napoleon at t1 is numerically the same as the four-dimensional object whose temporal part at t2 is Napoleon at t2”.) Temporal parts of an object can be divided into stages and slices. A stage of a thing x is a part of x that occupies a non-zero interval (it has a non-zero temporal “width”), whereas a slice of x is a part of x taken in a zero-length moment of time, and thus it has no temporal dimension. Slices are three-dimensional, and they represent what we would usually refer to as objects of our perception. It is noteworthy that the way things persist according to the perdurantist is analogous to the temporal existence of events. An event, such as the battle of Waterloo, is never fully present in an interval that is shorter than its entire duration.
The main motivation for perdurantism comes from the problem of change which threatens the endurantist approach. Things change their properties in time: for some moments t1 and t2 and a property P it is the case that x has P at t1 and x does not have P at t2. But according to endurantism x at t1 is numerically identical with x at t2. If we apply Leibniz’s law, which states that if x = y and Px, then Py, then we have to conclude that an object has P and doesn’t have P, which is obviously a contradiction. Perdurantism avoids this problem by assuming that the properties P and not-P are attributed to numerically different individuals: different temporal slices. But the endurantist is not without options with respect to the problem of property change. One solution is to relativise properties to time. Let us consider a poker which is cold at t1 and hot at t2. We may say that the poker possesses the property of being-cold-at-t1 and being-hot-at-t2, and these properties are not mutually exclusive as long as t1 is different from t2. But an objection can be raised that this approach treats properties as if they were relations between objects and moments, and consequently no property can be intrinsic. And, besides, isn’t it legitimate to speak about properties simpliciter, without any temporal relativisation? Another solution, available to the endurantist, is to relativise the relation of possession between the object and its properties. Objects don’t just possess properties, but they always possess them at certain moments. This position is known as adverbialism, as it amounts to the adverbial modification of the verb “be” (the poker is-at-t1 cold and the poker is-at-t2 hot). One consequence of this approach is that there is no single relation of exemplification between particulars and universals, but an infinite (even uncountable) number of different relations of exemplification. Finally, let us notice that all the above endurantist solutions seem to assume that moments exist independently, and therefore commit themselves to the substantivalist view.

We will now consider an argument against endurantists which employs the notion of change of parts. The argument is due to Peter van Inwagen, with some corrections added by Mark Heller. Suppose that a person X underwent an amputation of his left hand. Let t1 denote a moment before, and t2 after the amputation. Let us also denote by ‘X-minus’ the whole consisting of X’s body without the left hand (regardless of whether the hand is attached to it or not). The endurantist should accept the following identity statements:

(1) X at t1 = X at t2
(2) X-minus at t1 = X-minus at t2
(3) X-minus at t2 = X at t2

But from these three premises we can derive, using the assumption of the transitivity of identity, that

(4) X at t1 = X-minus at t1

This conclusion is clearly unacceptable. My body is not identical at this moment with my body minus my left hand. Now we will have to look closely at the justification of all the premises (1)-(3), to see which one should be rejected. Premise (1) follows from endurantism and the assumption that an object can lose its part without losing its identity. Premise (2) is a simple consequence of endurantism. Premise (3) is implied by the principle according to which two numerically distinct objects cannot occupy the same spatial region at the same time. Now it should be clear that rejecting endurantism and accepting perdurantism solves the problem. If we agree that the expressions “X (X-minus) at t1 (t2)” refer to temporal slices of appropriate four-dimensional objects, then premises (1) and (2) are evidently false, although (3) is unquestionably true. Another possible interpretation of (1)-(3) under perdurantism is that actually these identities are between appropriate four-dimensional objects, identified by their three-dimensional slices. In that case (1) and (2) are true, but (3) becomes false (two distinct four-dimensional objects can nevertheless share their three-dimensional slices).

But the endurantist has some viable strategies of defence. Firstly, he can claim that a thing cannot lose any of its parts without losing its numerical identity. But this is a highly unintuitive supposition, and if it’s true, then with each passing second our bodies are turned into new things, because they are constantly losing old parts and acquiring new ones. Secondly, the existence of X-minus can be called into question. For instance Van Inwagen rejects the doctrine which he calls “the doctrine of arbitrary and undetached parts”. X-minus before the amputation is not a separate, autonomous object, but an undetached part of X, and its existence is questionable. Thirdly, the assumption that two distinct things cannot occupy the same space at the same time can be rejected. It is argued that a sculpture, for instance “The Thinker” by Rodin, is numerically distinct from the lump of material it is made of (bronze) and yet throughout some period of time the two things occupy the same space. Finally, some authors question the transitivity of identity. According to Peter T. Geach, identity is a relative and contextual notion. We can say that X at t1 is the same person as X at t2, and that X-minus at t1 is the same body as X-minus at t2, but from this it doesn’t follow that X at t1 is the same body as X-minus at t1, nor that X at t1 is the same person as X-minus at t2.

One problem for perdurantism is that it does not offer clear criterions of how to distinguish four-dimensional wholes which are genuine things from arbitrary regions filled with matter. A given temporary slice of a four-dimensional object has an infinite numbers of future continuations. Which one is selected as the right one, and why? Yet another difficulty was noticed by van Inwagen. Four dimensional objects are often presented as collections of stages (slices). But a collection of objects possesses its elements necessarily. From this it follows that Napoleon could not have different stages from the ones he really had (for instance, he could not have been born earlier or later).

Endurantism is typically associated with presentism, and perdurantism with eternalism. But other combinations are also possible. Perdurantism can logically coexist with the theory of the growing (shrinking) universe. In such a case things would be four-dimensional wholes that grow or shrink as time passes. It is also possible to have both endurantism and eternalism. It seems that the only combination which is logically impossible is that of perdurantism and presentism (although some authors disagree with that). Perdurantism assumes that things have different temporal parts, so it is essential to admit that moments other than the present one exist. Also, presentism implies that the universe is three-dimensional (as time is not a dimension, because it is reduced to a point). But perdurantism identifies things with four-dimensional objects, and four-dimensional objects cannot exist in a three-dimensional world.

Readings:

E.J. Lowe, Chapter 3 "Qualitative change and the doctrine of temporal parts", pp. 41-58, A Survey of Metaphysics.
M.J. Loux, Chapter 8 "Concrete particulars II: persistence through time", pp. 230-256, Metaphysics: A Contemporary Introduction.