The Self-Visitation Paradox

The Argument
1. Ted is sitting.
2. Ted is standing.
3. Ted is sitting and standing.

Suppose that, on Monday at noon, Ted was sitting. The next Friday, Ted time travels back to Monday at noon and stands while his younger self is sitting. Can Ted be both sitting and standing? Time traveling seems to have provided us a way in which he can, though it also seems obvious that a person cannot be both sitting and standing at the same time. What is going on?

Property Compatibilism

The compatible-properties solution accepts that the sitting and the standing can occur simultaneously, done by a single person. (It is a solution formulated but criticized by Sider 2001 and supported by Carroll 2011.) On this view, the apparent paradox stems from a failure to recognize that the arguments conclusion is not contradictory. This failure may stem from the natural assumption that, if Ted is sitting, then it is not the case that Ted is standing. But maybe that assumption is only natural because we are so used to thinking about situations that do not involve time travel. (Notice that it is also natural to assume that no one can exist before being born, though that conflicts with the possibility that one could time travel back to a time before one’s birth.) Thus, the compatible-properties solution asserts that sitting and standing are not mutually exclusive properties; one person may do both at one time. While there would be a contradiction if Ted were both sitting and it were not the case that he was sitting, or standing and not the case that he was standing, it is not contradictory that Ted is both sitting and standing. The self-visitation scenario may not be the problem that it first appeared.

Relativizer

Spatial-location relativists1 believe that the locations of the sitting and the standing are the key to finding consistency. According to these relativizers, it is not the case that Ted is sitting (simpliciter) and it is not the case that Ted is standing (simpliciter). It is true, though, that Ted is sitting, say, over here and also that Ted is standing over there. Just as Ted can be sitting at one time and standing at another time, so can he be sitting in one place and standing in a different place. So, Ted’s time travel scenario is not paradoxical.

The relativizer approach, however, takes for granted that an object can exist in two separate locations simultaneously. Ted is supposed to simultaneously be sitting here and standing over there. This is as (prima facie) puzzling as his being both sitting and standing; it is another paradoxical aspect of the situation. But with this aspect of the situation relativization to location won’t help. Perhaps the relativizer must accept a compatible-properties approach to the self-visitation paradox, at least with regard to the property of spatial location.

Spatial Parts

Maybe the trouble arises from the thought that the sitter and the stander are one person. Though they both answer to ‘Ted’, it might be held that, strictly speaking, they are only two parts of Ted. Consider Ted1 (the sitter) and Ted2 (the stander) and don’t assume they are one person. Maybe Ted1 is one spatial part and Ted2 is another spatial part of Ted. Different spatial parts of an object may have different properties without contradiction. Just as Ted’s head might be bald and his chest hairy, a spatial part of Ted (Ted1) may be sitting while another spatial part (Ted2) is standing. The surprising and sudden appearance of a twice as heavy, four-eyed, two-nosed, spread out Ted might be considered an unexpected effect of time travel, but it is not something that is inconsistent. (This view is offered by Ned Markosian (2004) as a parallel endurantist alternative to the perdurantist views discussed below.)

Perdurantism

So far, we have been working from a common-sense perspective about persistence through time known as endurantism. In other words, we have thought of Ted as something that exists wholly at any particular instant at which he exists. Ted endures through time by continuing to exist, just growing and changing as time passes. Endurantism, however, is not the only stance one might take about persistence, and the solution to the self-visitation paradox could conceivably rest in denying endurantism. An alternative stance is perdurantism.

Instead of Ted, let’s consider Elvis Presley for a moment. In 1958, as a rising star, he is good-looking and in shape. Later, by 1975, he is a very overweight man. One might hold that there is something that is slender and something that is rotund, and that they are not identical–that they are not one person. The perdurantist would say that there is a temporal part of Elvis that is thin and a temporal part that is rotund, and that Elvis is the collection of all his temporal parts. Endurantists hold instead that, while Elvis wholly exists at each of those times, and continues to exist from one time to the next, his properties change.

Since perdurantism handles apparently contradictory properties—Elvis’s thinness and his rotundity—in a non-time-traveling situation, perdurantism appears to be an easy way out of our self-visitation problem. Maybe, on Monday at noon, there is a temporal part of Ted, a part that happens to be sitting; maybe there is another temporal part of Ted then too, a standing part.

Sounds good, but that’s too quick. In the self-visitation case, we cannot be concerned with two different temporal parts as we were with the case of Elvis. The pertinent parts of Ted are simultaneous; they both exist on Monday at noon. It looks like the perdurantist must rely on aspects of the relativizer, the compatible properties, or the spatial-parts approach: A perdurantist could hold that the sitting part and the standing part are two distinct spatial parts of one temporal part of Ted—that’s the usual perdurantist way out (e.g., Lewis 1976, 147; Sider 2000, 101). Alternatively, one could hold that this temporal part of Ted is sitting only relative to one location and standing only relative to another. For a third option, a perdurantist could hold that it is not impossible for a (spread out) temporal part to be both sitting and standing.

References and Further Reading

Carroll, John. “Self  Visitation, Traveler Time, and Compatible Properties.” Canadian Journal of Philosophy 41 (2011): 359-370.

Haslanger, Sally. “Persistence Through Time.” Oxford Handbook of Metaphysics. Eds. M. Loux and D. Zimmerman. Oxford: Oxford University Press, 2003: 316-354.

Horwich, Paul.  “On Some Alleged Paradoxes of Time Travel.” Journal of Philosophy 72 (1975): 432-444.

Keller, Simon and Michael Nelson. “Presentists Should Believe in Time Travel.” Australasian Journal of Philosophy 79 (2001): 333-345.

Lewis, David. “The Paradoxes of Time Travel.” American Philosophical Quarterly 13 (1976): 145-152.

Markosian, Ned. “Two Arguments From Sider’s Four-Dimensionalism.” Philosophy and Phenomenological Research 68 (2004): 665-673.

Miller, Kristie “Traveling in Time: How to Wholly Exist in Two Places at the Same Time.” Canadian Journal of Philosophy 36 (2006): 309-344.

Sider, Theodore. Four Dimensionalism. Oxford: Clarendon Press, 2001.

Simon, Jonathan. “Is Time Travel a Problem for the Three-Dimensionalist?” Monist 88 (2005): 353-361.

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1. Spatial-location relativism is just one simple version of relativism. Sometimes the sitting and the standing are relativized to spacetime location (Miller 2006, pp. 315-316), personal time (Keller and Nelson 2001, p. 344) or proper time (Horwich 1975, pp. 434-435).