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Time Travel, Double Occupancy, and The Cheshire Cat

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Abstract

The possibility of continuous backwards time travel—time travel for which the traveler follows a continuous path through space between departure and arrival—gives rise to the double-occupancy problem. The trouble is that the time traveler seems bound to have to travel through his or her younger self as the trip begins. Dowe (2000) and Le Poidevin (2005) agree that this problem is solved by putting the traveler in motion for a gradual trip to the past. Le Poidevin goes on to argue, however, that the gradual trip gives rise to the Cheshire cat problem, a concern about whether the traveler survives the gradual trip. We address the Cheshire cat problem by proposing and considering new continuity constraints on identity over time. Along the way, we come upon an endurantist conception of temporal parts.

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Notes

  1. For the purposes of this paper, whether a trip to the past is continuous depends on the spatial locations of the traveler during the temporal interval between the time of the departure and the time of the arrival. There must be a function f(x) from each instant in the temporal interval to a spatial location of the traveler at that particular instant. The trip is continuous if and only if the function, f, is continuous in the usual mathematical sense: for all y, the limit, as x goes to y, of f(x) = f(y).

  2. See Harrison (1971: 13–15), Cook (1982: 52), Macbeath (1982, 426–427), Nahin (1999: 23–25), Grey (1999: 60–62), and Bernstein (2015, 161–162).

  3. A reviewer for Philosophia has correctly pointed out to us that double-occupancy issues arise even if there are no changes of location of any of the parts of what time travels: Imagine a stationary, unchanging Democritean atom, starting to travel backwards in time. The atom is an extended, finite, and indivisible entity that doesn’t change. Presumably, it may cease to exist at a later external time as a result of it somehow departing to the past by being put it in a traveling-to-the-past state that involves no intrinsic changes to the atom. The double-occupancy issue that arises is this: a few seconds in external time prior to its departure to the past, how could the atom be both persisting normally forward in time and traveling backwards in time at one location in space?

  4. We have chosen an arrow for our time traveling object in order to show the object’s orientation. Unfortunately, in doing so, the representation of the arrow in Figure 1 is misleading. Because of the vertical length of the arrowhead and the fletching, it looks like the top half of the arrow is earlier in external time than is its bottom half. Keep in mind that the arrowhead is depicted just to show what end is the front end of the time-traveling object; the fletching is just to indicate what end is the back end.

  5. On this notion of continuity, whether a trip to the past is continuous depends on the spatiotemporal locations of the traveler during the personal time interval between the time of the departure and the time of the arrival. There must be a function f(x) from each instant in the personal time interval to a spatiotemporal location of the traveler at that particular instant. The trip is continuous if and only if the function, f, is continuous in the usual mathematical sense: for all y, the limit, as x goes to y, of f(x) = f(y).

  6. We are simplifying a bit. The arrow is really located at a lot of spatiotemporal locations at each personal time. What we are depicting in Figure 3 is a mapping from personal time of the tip of the arrow to a location of the tip and its co-parts relative to the tip’s location at that personal time, first focusing only on the spatiotemporal locations of the tip to the left of C, and finishing looking at the spatiotemporal locations of the tip just to the right of C. We will continue making this simplification.

  7. In 2008, I (John Carroll) taught an honors seminar on the philosophical paradoxes of time travel at NC State University and assigned an exercise about how to understand a passage in Le Poidevin’s paper. A superb class discussion led to term projects on the double-occupancy problem by Daniel Ellis, Daniel Farrell, David Fenwick, Supun Koralalage, Jennifer Leaf, Brandon Moore, and Jeffrey Vohlers, several with helpful animated graphs, and several with excellent analysis. These projects suggested the plausible solutions to the problem at hand. Among those doing the best projects on double occupancy, Daniel Ellis and Brandon Moore had the time and interest to work with me off and on over the past eight years to produce the present paper. Our thanks go out to the entire class. Versions of the paper were presented to the NC State Philosophy Club in November of 2008, the North Carolina Philosophical Society in February 2009, and the Northwest Philosophy Conference in November of 2011. Thanks also to the participants and audience in these sessions, especially Kenny Boyce, David Robb, and Amy Seymour. We are grateful to Jim Van Cleve for providing helpful comments on an earlier draft.

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Authors and Affiliations

  1. Department of Philosophy and Religious Studies, NC State University, Raleigh, NC, 27695-8103, USA

    John W. Carroll

  2. NC State University, Raleigh, NC, 27695-8103, USA

    Daniel Ellis & Brandon Moore

Authors
  1. John W. Carroll
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  2. Daniel Ellis
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  3. Brandon Moore
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Correspondence to John W. Carroll.

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Carroll, J.W., Ellis, D. & Moore, B. Time Travel, Double Occupancy, and The Cheshire Cat. Philosophia 45, 541–549 (2017). https://doi.org/10.1007/s11406-016-9804-x

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  • DOI: https://doi.org/10.1007/s11406-016-9804-x

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