In Four Dimensionalism, Ted Sider briefly presents an argument against three-dimensionalism from the metaphysical possibility of time travel.
Time Travel Argument Against Three Dimensionalism
- If time travel is metaphysically possible and three dimensionalism is true, then it is metaphysically possible for a person to be wholly located in two different places at the same time.
- It is not metaphysically possible for a person to be wholly located in two different places at the same time.
- Therefore, it’s not true that time travel is metaphysically possible and three dimensionalism is true.
- Time travel is metaphysically possible.
- Therefore, three dimensionalism is not true.
One option for the three-dimensionalist is to reject (2). I don’t want to get into that (just yet). In this post, I simply want to note something odd about Sider’s response to another possible three dimensionalist reply.
The three dimensionalist could reject (4). In fact, they could reject (4), precisely because they recognize the same (apparent) incompatibility between three dimensionalism and the metaphysical possibility of time travel that Sider exploits.
Sider passes the buck to David Lewis’ Paradoxes of Time Travel defense of the metaphysical possibility of time travel. However, there is something dialectically odd about this move. Doesn’t Lewis explicitly assume four-dimensionalism in his defense?
I’ve got some more thoughts on the option to reject (2) – but I need to get back to grading.
UPDATE: Here’s the passage from the beginning of paradoxes of time travel that I had in mind.
The world – the time traveler’s world, or ours – is a four-dimensional manifold of events. Times is one dimension of the four…Enduring things are like timelike streaks: wholes composed of temporal parts, or stages, located at various times and places. Change is qualitative difference between different stages – different temporal parts – of some enduring things, just as a “change” in scenery from east to west is a qualitative difference between the eastern and western spatial parts of the landscape. If this paper should change your mind about the possibility of time travel, there will be a difference in opinion between two different temporal parts of you, the stage that started reading and the subsequent stage that finishes. (p.68-69)