Non-Backtracking Backward Counterfactuals
If Tina is a time traveler who is free to change the past, it must be true that
1) if Tina had chosen 1928, a time traveler would have appeared in 1928.
Moreover, this must be true on a "non-back-tracking" interpretation. A back-tracking interpretation is one on which we consider how past events would have had to be in order to cause some later event. Let's see how (1) fares on Lewis' conditions for non-back-tracking counterfactuals (in "Counterfactual Dependence and Time's Arrow").
Assume in fact Tina decides (in 2025) to travel to 1927 and does so. These are the worlds we have to consider:
| Tina... | chooses 1928 | doesn't choose 1928 |
|---|---|---|
| appears only in 1927 | w1 | @ |
| appears only in 1928 | w2 | |
| appears in 1927 and 1928 | w3 | |
| doesn't time travel | w4 |
For (1) to be true, either w2 or w3 has to be closer to @ than both w1 and w4.
Since @ is a world with genuine time travel, we can assume that in @ her decision to travel to 1927 causes her appearance in 1927. Hence if that decision were absent, it would be miraculous if she nevertheless appeared in 1927. So w1 and w3 require something miraculous in this respect. (Would this be a "big" miracle? See below.)
In all of w1 through w4 a small miracle makes Tina choose 1928 instead of 1927. In w2 and w3 the time machine works, but in w1 and w4 another small miracle prevents it from working.
As for matching spacetime regions, w1 is closest to @: their histories perfectly match until 2025. w2 and w4 only match @ until 1927, w3 until 1928. So we get:
| Miracles | Perfect Match | |
|---|---|---|
| w1 | 3 | -2025 |
| w2 | 1 | -1927 |
| w3 | 2 | -1928 |
| w4 | 2 | -1927 |
So w2 is the most promising candidate. It clearly wins the competition if the multiple miracles required in each of the other worlds always count together as a "big and widespread" miracle.
One more note. So far I have assumed that Tina's world is a world that displays the same asymmetry of overdetermination as our world: events leave lots of traces in the future but not in the past. Shouldn't time travel worlds contain local breakdowns of this asymmetry? Well, Tina's 2025 decision certainly leaves lots of traces in the past. But it does so only indirectly: wouldn't a small miracle suffice to cover up all these past traces, e.g. a small accident breaking the time machine? Moreover, the past traces are quite limited: for one, in an ordinary time travel world, Tina's decision to travel to 1927 doesn't affect any time before 1927. What's more, the 1927 she appears in is very much like the actual 1927. It is not a 1927 completely different from the actual 1927 due to all the accumulated traces left by the 2025 decision. Luckily, these limitations of the past traces make it easier to get time travel even in worlds without much breakdown in asymmetry of overdetermination:
As I mentioned above, I take it that in a world of genuine time travel, Tina's appearance in 1927 depends counterfactually upon her decision in 2025. That is,
2) if Tina hadn't decided to go to 1927, she wouldn't have appeared in 1927.
This requires that the closest worlds where Tina doesn't decide to go to 1927 are worlds where she doesn't appear in 1927. In all these worlds a small miracle prevents her decision. If the worlds are otherwise like our world, a big and widespread miracle would be necessary to fake all the traces the actual decision leaves in the future. Such big and widespread miracles trump perfect match of future spacetimes and thereby make the future depend counterfactually upon the present. But would it take a big, widespread miracle to fake all the past traces of the actual decision? Perhaps not. Perhaps another small miracle would suffice. (That's not obvious: e.g. Tina's memories of her decision would have to be faked as well.) Even if so, (2) might still be true. For big and widespread miracles are only needed to trump extensive match of spacetime. But in Tina's case the smaller miracle would be traded in for merely 98 years of perfect match. Somewhat oddly, this shows that genuine time travel to the near past is simpler to achieve than genuine time travel to the remote past. The latter might require a greater breakdown of the asymmetry of overdetermination. But at least time travel to the near past could occur in worlds that are not too different from our world.