Eternalist Recurrence
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Eternalist Recurrence Abstract: In a world of eternal recurrence, history repeats itself infinitely many times over, without beginning or end and without any variation between epochs. In a world of eternal replication, history replicates itself, since there are infinitely many qualitatively indiscernible epochs without an initial or final epoch. But, while you survive across infinitely many epochs in a world of eternal recurrence, you inhabit only a single epoch in a world of eternal replication. In this paper, I argue that familiar forms of four-dimensionalism cannot properly distinguish the possibility of eternal recurrence from the possibility of eternal replication. I then argue that, in order to distinguish these possibilities, four-dimensionalists ought to be dynamic four-dimensionalists and, in keeping with the “moving spotlight” form of eternalism, posit fundamental non-qualitative tense properties. §1. Introduction Eternal recurrence can be a daunting prospect. In a world of eternal recurrence, your life unfolds infinitely many times over, without a first or final recurrence, and without any variation between recurrences. A perhaps less daunting but no less strange possibility concerns, not eternal recurrence, but, rather, eternal replication. In a world of eternal replication, your life unfolds exactly once, but there are also countless lives qualitatively indiscernible from your own, with no first or final replication, and without any qualitative variation between them. So, while the myriad epochs—i.e., repetitions or recurrences of history—involve the very same individuals in worlds of eternal recurrence, epochs are merely qualitative indiscernible in worlds of eternal replication. This is because, in worlds of eternal recurrence, you yourself persist across epochs, while, in worlds of eternal replication, you merely have a plurality of qualitatively indiscernible doppelgangers strewn across other epochs. Your attitudes towards eternal recurrence and eternal replication are likely somewhat different. Since you survive across epochs in worlds of eternal recurrence, you might reasonably believe the normative stakes are higher in worlds of recurrence than in worlds of replication. Regardless of whether this normative assessment is correct, this much is clear: eternal recurrence and eternal replication are distinct possibilities. In what follows, I will argue that four-dimensionalists encounter a problem in distinguishing eternal recurrence from eternal replication. For present purposes, I take four- dimensionalism to be the conjunction of eternalism—the thesis that past, present, and future entities exist—and perdurantism, according to which objects have temporal parts and persist by being partly located at distinct times. 1 Crucially, I will not assume that four- dimensionalism entails a static or reductionist view of tense. This is because, after arguing that the four-dimensionalist model of eternal recurrence presented in Lewis (1986) cannot distinguish eternal recurrence from eternal replication, I will argue that the best four- dimensionalist model of eternal recurrence requires dynamic four-dimensionalism, sometimes labeled “the moving now” theory, rather than static four-dimensionalism, which holds that our perspective on the world is dynamic even while the world itself is static. Since four- dimensionalists must distinguish eternal recurrence from mere eternal replication, I conclude that four-dimensionalists ought to be dynamic four-dimensionalists.2 1 Eternalist perdurantists include Lewis (1986), Sider (2001), Heller (1990), Hawley (2002), and Jubien (1993). Opponents of eternalist perdurantism include Bourne (2006), Merricks (2007), and Haslanger (1989). 2 Sider (2001) claims that the primary challenge with the moving spotlight view is that it is unmotivated. I take what follows to be one route for meeting Sider’s challenge. 2 §2. The Problem Lewis (1986) presents the standard four-dimensionalist model of eternal recurrence as follows: To illustrate, contrast two kinds of eternal recurrence. Some worlds exhibit one-way eternal recurrence: there is a beginning of time and then there is a first epoch, a second epoch just like the first, a third, and so on ad infinitum... Other worlds exhibit two-way eternal recurrence: there is no last epoch and no first, the epoch are ordered like the integers rather than the natural numbers. Then the corresponding inhabitants of different epochs are not only duplicates but indiscernibles. But still they don’t share all their properties, because for any two of them there are sets which contain one without the other.3 According to Lewisian eternal recurrence (hereafter, LER), eternal recurrence is accommodated by an ontological commitment to an infinite number of numerically distinct temporal regions, each of which is a distinct epoch. On the resulting view, worlds of eternal recurrence are infinite in their temporal extent. In addition, the epochs within these worlds are mereologically disjoint yet qualitatively indiscernible from one another. Intuitively, LER envisions the epochs of eternal recurrence as something like infinitely many cut-out paper dolls: each epoch is connected and qualitatively indiscernible from those preceding and following it. Although initially promising, LER faces a serious problem: it cannot distinguish worlds of eternal recurrence from qualitatively indiscernible worlds of eternal replication, where individuals do not persist across epochs. To get a sense of the difference between eternal recurrence and eternal replication, consider Lewis’ own description of worlds of one- way eternal replication where individuals are epoch-bound. (Note, however, that, while Lewis describes this possibility as “one-way eternal recurrence,” the possibility in question concerns replication as understood here. This reflects no deep controversy, merely a lack of Lewis’s attention to the question of present interest.) Suppose, for instance, that ours is a world of one-way eternal recurrence with a first epoch but not last. One of the epochs is ours. Which epoch? There seem to be many possibilities, one of which is the actual one. Perhaps our epoch is in fact the seventeenth; but we might instead have lived in the 137th epoch. So it seems that there is a possible world that is qualitatively just like ours—the same infinite sequence of epochs, all exactly alike, and exactly like the epochs of our world—but that represents de re, concerning us, that we live in the 137th epoch rather than the seventeenth.4 While the various possibilities Lewis notes here are possibilities involving eternal replication (i.e., they are possibilities involving epoch-bound individuals), it should be clear enough that Lewis and other four-dimensionalists ought to accommodate the possibility of eternal recurrence as well. Failure to do so would not only render Nietzsche’s most notable though- experiment to traffic in impossibilities, but do violence to our intuitive modal judgment that 3 Lewis (1986: 63). 4 Lewis (1986: 227). 3 we could relive our lives infinitely many times over or that we could be co-actual with infinitely many doppelgangers.5 For this reason, four-dimensionalists owe an account of what distinguishes eternal recurrence from eternal replication within their preferred ontology of time. With this in mind, I will now present the problem as it occurs within the four- dimensionalist framework. The problem of distinguishing eternal recurrence from eternal replication arises for the following reason: if four-dimensionalism is true, then two worlds—one exhibiting eternal recurrence, the other exhibiting eternal replication—cannot differ qualitatively. Any difference between these worlds must be non-qualitative, concerning either the identity of individuals or some other non-qualitative feature of the world. For endurantists, the difference between eternal recurrence and mere replication is readily explicable: mereological features of the world are non-qualitative, and the worlds in question differ mereologically. Specifically, in worlds of recurrence, objects are temporally extended across myriad epochs, but, in worlds of replication, individuals are wholly located within a unique epoch. Now, since four-dimensionalism entails perdurantism, four-dimensionalists cannot hold that worlds of eternal recurrence and eternal replication differ in their mereological structure as endurantists suggest.6 In order to distinguish between eternal recurrence and replication, the four- dimensionalist might naturally claim that worlds of eternal recurrence and replication differ in terms of the identity of the mereological fusions identified with ordinary individuals. In worlds of eternal recurrence, an ordinary individual, Fred, is identical to the fusion of a plurality of mereological atoms drawn from infinitely many epochs, and Fred’s recurrence is explained by virtue of Fred being partly located at a plurality of epochs.7 In worlds of eternal replication, Fred is identical to the fusion of individuals drawn from only a single epoch. In this way, the non-qualitative difference between eternal recurrence and eternal replication concerns the haecceities of various fusions. In worlds of eternal recurrence, the haecceities of ordinary individuals like Fred are borne by trans-epoch fusions, while, in worlds of replication, the same haecceities are borne by epoch-bound fusions.8 This strategy for distinguishing eternal recurrence from eternal replication requires commitment to what Salmon (1988)