Second, if we assume that there were many things existing before the Global Replacement event and many things existing afterward, how do we pair each entity that existed before the event with the entity which replaces it after the event? We have this pairing problem: which new entities have replaced which old entities?
One solution to both problems would be to introduce space and its parts as a further entity, with each entity susceptible to creation or annihilation occupying some part of space during each moment of its existence. The endurance of space itself would tie the two world histories together into a single history, and we could use the occupation of enduring places as the criterion for saying which new entities have replaced which old entities. New entities x1, … xn have replaced old entities y1, … yn just in case the place occupied collectively by the x's after the change is identical to the place occupied by the y's immediately before the change.
But now it seems that we have an enduring substrate after all, namely, space itself. What we thought was pure substantial change turns out to be identical to a kind of qualitative change in the parts of space, where that qualitative change is a change in what entities or sorts of entities occupy those places. Once again, it seems natural to think that an entity's occupying a place is an intrinsic feature of that place.
Even if one could resist the identification of the putative purely substantial changes with qualitative changes in the parts of space, one would still have to deny the possibility of Global Replacement. Space itself, on this view, is not created or annihilated. Indeed, this solution to our two problems requires the endurance of space, since only if space endures through the Global Replacement event can it provide the continuity needed to unify the two time-lines and pair the created entities with their respective annihilated ones.
Another solution to this pair of problems is to have recourse to relations of cause and effect. Suppose that the annihilation of entity a is a cause of the simultaneous creation of entity b. These causal links could account for the unity of the two halves of world history (before and after the Global Replacement threshold). They do this because there would be a time at which both the entities existing before the Global Replacement event and the entities existing after it exist. In addition, causal links could solve the pairing problem: entities x1, … xn are replaced by entities y1, … yn just in case the annihilation of the x's is causally linked to the creation of the y's.
However, the causal theory will have to survive another thought-experiment. If Global Replacement were possible, then it would be possible for there to be a stretch of world history during which global annihilation and re-creation occurs at every instant. Let's suppose that it is also possible that time is dense:
Def D24.4 Density. The time series is dense if and only if between any two moments of time there always exists a third.
The assumption that time is dense corresponds to Temporal Anti-Discretism (19.4T). If time is dense, then there is never a next moment. There will be an infinite number of intervening moments between any two moments. Let's suppose that the period of dense Global Replacements lasts for exactly one hour; call it the ‘Interregnum’. We now face again the same two problems. (1) What unifies the history of the world before and after the Interregnum into a single history of a single world? (2) How are the things existing before the Interregnum paired with their post-Interregnum replacements? The sort of causal linkage appealed to above will no longer do the work, since we had to suppose that the causes and effects were always simultaneous—the new entity is created at the same moment that the old entity is annihilated, with the creation event linked causally to the simultaneous annihilation event. Simultaneous causal links, by definition, never bridge any span of time, so they cannot link an entity existing at one moment in the Interregnum with a successor existing at any later moment in the Interregnum. Simultaneous causal links can only link an entity annihilated at some time with an entity created at that same time, and during the Interregnum, no entity exists for more than a moment! We cannot solve the pairing problem. But we also cannot connect the world histories before and after the Interregnum, then, either. Simultaneous causal links will do nothing to connect one moment in the Interregnum with any other moment in the Interregnum so as to make them a continuous history of a single world because the way such causal links accomplished that in our earlier case was by linking entities that existed before and after the single Global Replacement event. Again, though, during the Interregnum, no entity exists for more than a moment, so this rationale is unavailable.
To deal with dense stretches of time, the causal theorist must introduce Wesley Salmon's notion (Salmon 1984, 1998) of a real or causal process (see Section 28.6.4). However, if the causal theory makes use of causal processes in place of causal links between discrete events, then once again we have something that endures through the supposed global substantial change, namely, the process itself. Therefore, we have good reason to believe that it is necessarily the case that something persists through all change.
However, there are two responses that we have not yet considered on behalf of Replacementism. First, Replacementists could appeal to irreducibly spatiotemporal relations, relations of the kind that are commonly used in relativistic physics. Physicists (when employing the theory of relativity) make use of such relations as time-like separation. Two events are time-like separated if it would have been possible to send a light signal from one event to the other. The events that are time-like separated from a given event from the forward and backward light cones of that event. If time-like separation is a fundamental relation between events, it could be used to solve the pairing problem through Global Replacement events, and even through the hypothesized Interregnum. Replacementists who rely on spatiotemporal relations to solve the pairing problem are Perdurantists.
If such spatiotemporal relations do not suffice, Replacementists have one last recourse: posit a primitive pairing relation, one that connects two events just in case they belong to the same enduring thing. Metaphysicians call this relation ‘genidentity’. The event of Barack Obama's birth stands in the genidentity relation to the event of his inauguration as President. This version of Replacementism is Primitive Genidentity Theory.
How is Primitive Genidentity Theory different from Substratism? The difference is a subtle but important one. Substratists posit a new kind of fundamental entity, an entity that exists both before and after the intrinsic change. Primitive Genidentity Theorists deny that any such fundamental entity exists. All that exists are quantitively unchangeable fundamental entities, entities that can undergo creation and annihilation, but no other changes. Where Substratists posit a persisting fundamental thing, Primitive Genidentity Theorists posit a fundamental relation between things, the genidentity relation.
24.2 How Objects Change Properties: Substratism vs. Replacementism
We now turn to the question of how things change their intrinsic qualities. We start our discussion of intrinsic qualitative change by considering the paradox of intrinsic change. In his dissertation, Mark Johnston (1983, 1987) argued that there is something paradoxical about cases of intrinsic change. Suppose that some thing x changes from having intrinsic property P to having property not-P or vice versa. Let's say that x is P at t1 and is not-P at t2. The paradox of instrinsic change is that one seems to be committed to the view that x has incompatible properties. Since x is P at one time and not-P at another, then x is both P and not-P (albeit at different times). How could this be?
Some philosophers, reflecting on this issue, have inferred that objects have parts along the temporal dimension in something like the way they have parts along spatial dimensions. Just as, for example, a beach ball can be both red and green by having a (spatial) part that is red and a (spatial) part that is green, so a persisting apple can be wholly green at one time and wholly red at another by having a temporal part or a time-slice that is wholly red and that exists only at one time and another temporal part that is wholly green and that exists o
nly at another time.
Temporal parts are relatively uncontroversial when it comes to processes and temporally extended events. A trip across the English Channel presumably has parts corresponding to the first and second half. An extended event, like the American Civil War, has parts corresponding to its temporal parts (1861, 1862, etc.). Likewise, baseball games have innings as temporal parts. However, some Substratists might deny that there really are such things as processes or events (at least, as fundamental entities). Talk about events could be replaced by talk of objects having properties at various instants or intervals. Anyway, temporal parts are an essential component in the theory of Replacementism.
Def D24.5 Temporal Part. A thing x is a temporal part of y if and only if x is a part of y, and there is no x' such that x and x' exist at exactly the same times, x ≠ x', and x' is a part of both y and x. That is, x is a maximal part of y occupying some temporal interval.
Usually, philosophers who commit to temporal parts at all go one step further by committing to Universal Instantaneous Temporal Parts:
24.3T Universal Instantaneous Temporal Parts (UITP). All persisting things have instantaneous temporal parts (time-slices), one corresponding to each instant during which they exist, and these time-slices are fundamental and not mere logical constructions.
Change can then be handled by claiming that it is fundamentally time-slices that instantiate intrinsic properties, and persisting things only have those properties derivatively, by having temporal parts (the time-slices) that have them non-derivatively.
Replacementists must believe in temporal parts, since anything that changes must have at least two temporal parts, one before and one after the change. Substratists have the option of either embracing or rejecting temporal parts, including time-slices. Historically, most Replacementists have affirmed not only the existence of some temporal parts but also UITP. These Replacementists are Classical Perdurantists and Classical Genidentity Theorists:
24.1T.1T.1A.1T Classical Perdurantism. The only fundamental things exist only for an instant, and the only fundamental relations between such time-slices are spatiotemporal relations.
24.1T.1T.1A.1A Classical Genidentity Theory. The only fundamental things exist only for an instant, and there is one fundamental relation (primitive genidentity) that is not spatiotemporal.
Substratists can also be divided into two classes, depending on whether they affirm the existence of temporal parts, including time-slices. Historically, most Substratists have denied that fundamental and changeable things have temporal parts at all, whether instantaneous time-slices or extended temporal parts. Since most philosophers who believe in temporal parts believe in instantaneous time-slices of persisting things, we can focus on whether Substratists deny the existence of instantaneous time-slices. Those who deny that changing things have any temporal parts are traditionally called Endurantists—we will label them ‘Classical Endurantists’. Substratists who accept UITP are Time-Slice Substratists.
24.1T.1T.1T.1T Classical Endurantism. Fundamental things can undergo qualitative change, existing before, during, and after the change, but they do not have any fundamental temporal parts.
24.1T.1T.1T.1A Time-Slice Substratism. Fundamental things can undergo qualitative change, existing before, during, and after the change, and they have instantaneous temporal parts corresponding to each instant during which they exist.
Classical Endurantists can embrace the existence of temporal parts, so long as they do not maintain that those temporal parts are fundamental entities. (This runs against the traditional use of the label, but maintains, we think, the spirit of Endurantism.) Thus, Classical Endurantists, by definition, commit to the Absence of Temporal Parts:
24.3A Absence of Temporal Parts. Some persisting thing x and some instant of time t are such that x exists at t but has no instantaneous part at t that is fundamental and not a mere logical construction.
However, Time-Slice Substratists do believe in fundamental instantaneous temporal parts. Time-Slice Substratists suppose that instantaneous parts and persisting wholes are both metaphysically fundamental and necessarily interdependent, in the same way that Volume-Boundary Dualists (18.1A.2A) believe that both three-dimensional regions and their zero-, one-, and two-dimensional boundaries are both fundamental and interdependent. However, such a view comes at some cost, from the point of view of Ockham's Razor (PMeth 1.4.1), since it posits two classes of fundamental entities, both persisting and instantaneous, instead of just one.
Incidentally, the issue between UITP and the Absence of Temporal Parts has a close parallel with the issue discussed in Chapter 19 concerning the existence of the instants themselves, namely, the dispute between Strong Intervalism (19.1A.1T) and Moderate Intervalism or Interval-Instant Dualism (19.1A.1A). If one accepts Strong Intervalism, then one would also have to accept the Absence of Temporal Parts and reject UITP. If we were to accept UITP, we could simply identify each instant with a whole composed of all of the instantaneous temporal parts that are simultaneous with any one such part.
However, one could embrace Moderate Intervalism, with its fundamental instants, while rejecting UITP. Just because a persisting thing exists at an instant, it isn't obvious that each thing has a real part that exists at and only at that instant. It seems natural to say that each persisting thing is wholly present at each moment during which it exists. Thus, Substratists who are Moderate Intervalists embrace either Endurantism or Time-Slice Substratism.
Now, there is an important question that Endurantists face at this point: how can they respond to the paradox of intrinsic change? First, Endurantists can opt for Presentism (20.2T.4). This does the trick because one will not be able to move from the fact that x was F and the fact that x is (presently) not-F to the fact that x is (tenselessly) F and not-F. This is because according to Presentism there is just no sense in which it follows from the fact that something was F that it is true to say that it is (tenselessly) F.1 As we have seen, Presentism is a controversial position, and the problems with taking this route to salvage Endurantism are just the problems with Presentism.
Second, Classical Endurantists might say that intrinsic properties are really relations between things and times or that the exemplification relation is time-indexed. In other words, one can say that when something x is F at a time t, what that means is that x is (tenselessly) F-related to t or that x is-a-t F. This does the trick because being F-related to t and not-F-related to t′ is not paradoxical; likewise, being-at-t F and being-at-t′ not-F is not paradoxical. What would be paradoxical is being F-related and not-F-related to the same time t or being-at-t to both F and not-F.
Opponents of Classical Endurantism (like David Lewis 1986a) have argued that this view is dissatisfying because it follows that intrinsic properties aren't really intrinsic after all. Rather, intrinsic properties are relational or only had-at-a-time. For example, suppose that a bar is hot and straight at t1 and cold and bent at t2. Heat, coldness, straightness, and bentness all seem to be paradigms of intrinsic properties.2 If these aren't intrinsic to the bar, all by itself, what is the bar like intrinsically? It would seem that the bar has no properties intrinsically. However, this option asks us to believe that bentness is a relation between the bar and various instants of time. The bar fundamentally bears the bentness relation to t2 and not to t1. How decisive is this objection? Some Classical Endurantist Anti-Tensers, like Peter van Inwagen (1990b), find it utterly untroubling. Perhaps metaphysics reveals that changing things have thinner intrinsic natures than we might originally have thought. Still, the result seems to come at some cost by way of overturning deeply held beliefs of common sense.
Time-Slice Substratists have a third option for explaining intrinsic change. They can appeal, just as Replacementists do, to the qualitative difference between two temporal parts of the changing thing. That is, Time-Slice Substratists can take the fundamental bearer of the changeable or accidental features of the changing thing to be temporal parts of that thing. To cha
nge from cold to hot is to have a cold part located at one period of time and a hot part located at an immediately later period of time. In order to distinguish such Time-Slice Substratism from Replacementism, we have to assume that according to the Time-Slice Substratists, some fundamental substrate exists both before and after the change and that two temporal parts are somehow dependent on this substrate for their existence. In order to distinguish Time-Slice Substratism from Classical Endurantism, we have to assume that the relation between a thing and its temporal parts is supposed by the Time-Slice Substratists to be timeless, eternal, and unchanging. The Time-Slice Substratists can agree with common sense in taking size, shape, temperature, and the other changeable properties to be one-place qualities (of temporal parts) and not as relations between objects and times.
What positive reasons are there for believing in either Enduring Substratism or Replacementism? The relative attractiveness of the two views depends a great deal on one's position on other issues, including the structure of space and time, whether tense is fundamental, and the fundamentality of powers, laws, and conditionals. We look briefly at some of arguments for each of the two positions.
SUPPORT FOR ENDURING SUBSTRATISM FROM OTHER METAPHYSICAL THESES Enduring Substratism seems rather intuitive as an account of persistence and change. Aside from this, though, here are three types of reasons one might have for embracing Substratism.
An argument from Intervalism (19.1A). If temporal intervals are metaphysically fundamental and not mere logical constructions from instants, then it seems natural to assume that at least some temporally extended things are fundamental as well. Consequently, Replacementism, whether Classical Perdurantism or Classical Genidentity Theory, with its commitment to Universal Instantaneous Temporal Parts, is a poor fit with Intervalism (especially with Strong Intervalism). One could, however, combine Intervalism with a non-classical version of Replacementism, one in which all temporal parts are temporally extended but intrinsically unchangeable. Such a non-classical Replacementism will have a quite limited set of options for dealing with the possibility of continuous change. (For the corresponding problem involving space, see Section 18.4.1 on continuous variation.)
The Atlas of Reality Page 87
