## A fork time puzzle

According to a popular view about counterfactuals, a counterfactual hypothesis 'if A had happened…' shifts the world of evaluation to worlds that are much like the actual world until shortly before the time of A, at which point they start to deviate from the actual world in a minimal way that allows A to happen. 'If A had happened, C would have happened' is true iff all such worlds are C worlds. The time "shortly before A" when the worlds start to deviate is the fork time.

Now remember the case of Pollock's coat (introduced in Nute (1980)). John Pollock considered 'if my coat had been stolen last night…'. He stipulates that there were two occasions on which the coat could have been stolen. By the standards of Lewis (1979), worlds where it was stolen on the second occasion are more similar to the actual world than worlds where it was stolen on the first occasion. Lewis's similarity semantics therefore predicts that if the coat had been stolen, it would have been stolen on the second occasion. This doesn't seem right.

An obvious solution, adopted, for example, in Bennett (2003), assumes that if the antecedent A describes a time interval ("last night"), then the fork time tends to be before that interval. That is, Pollock's counterfactual directs us to worlds that are much like the actual world until shortly before last night, and then deviate in some way to allow a theft of Pollock's coat.

I used to think that this solves the issue. But the solution leads to trouble, twice over.

The first kind of trouble is that it seems to invalidate certain inferences that are patently valid.

Let A be the hypothesis that Pollock's coat was stolen last night. Let A1 be the hypothesis that the coat was stolen on the first occasion, and A2 be the hypothesis that it was stolen on the second occasion. Let C be some ordinary consequent.

The following inference looks patently valid to me:

(1)A1 > C, A2 > C ⊨ A > C.

If the earlier and the later thefts would both have led to C, and there are no other theft possibilities, then a theft last night would surely have led to C!

The "early fork time" response does not validate this inference. It assumes that the fork time for A is more or less that of A1, while the fork time for A2 may be later. It follows that the worlds to which A2 directs us need not be among the worlds to which A directs us.

The inference (1) is valid according to the familiar similarity semantics of Lewis and Stalnaker. It follows that the "early fork time" response is incompatible with these accounts. It requires an antecedent relative account, discussed and rejected, for example, in Stalnaker (1984, 129ff.) and Bennett (2003, 298ff.). As Stalnaker points out, such accounts also invalidate, for example, the inferences (2) and (3):

(2)A > B, B > A, A > C ⊨ B > C.
(3)A > B, (A∧B) > C ⊨ A > C.

That was the first kind of trouble. To see the second, I need to bring in backtracking counterfactuals. Recall Lewis's adaptation of an example from Downing, in Lewis (1979, 33):

Jim and Jack quarreled yesterday, and Jack is still hopping mad. We conclude that if Jim asked Jack for help today, Jack would not help him. But wait: Jim is a prideful fellow. He never would ask for help after such a quarrel; if Jim were to ask Jack for help today, there would have to have been no quarrel yesterday. In that case Jack would be his usual generous self. So if Jim asked Jack for help today, Jack would help him after all.

The final counterfactual ('…Jack would help') is a backtracking counterfactual. Informally, backtracking counterfactuals direct us to worlds where the antecedent becomes true in a way that is consistent with salient regularities about the world, such as Jim's pridefulness.

What's important for my purposes is that one can often generate a backtracking reading by moving the fork time back in time. (I think Khoo (2017) suggests that this is how backtracking counterfactuals always work.)

Consider a world that is much like the world in the Downing-Lewis example, until shortly before yesterday's quarrel, and then deviates in a minimal way to allow Jim today to ask Jack for help. Given Jim's pridefulness, the world will plausibly deviate in a way that prevents the quarrel. And so Jack will help Jim.

Now let's return to Pollock's coat and the proposal that the relevant fork time for 'if my coat had been stolen last night…' lies at around the start of last night. If the second occasion for theft was towards the end of the night, we should expect backtracking effects when we consider thefts on that occasion. I claim that no such effects can be observed.

Of course, it's not clear what the relevant effects would be in this case. But take a variant of the Downing-Lewis example. Same story as before. Let's not emphasize Jim's pridefulness etc., and consider the statement: 'if Jim had asked Jack for help yesterday morning or today, Jack would have helped him'. Intuitively, this is false, because Jack wouldn't have helped if Jim had asked today, after yesterday's quarrel. But if the fork time for the counterfactual is yesterday morning, we should expect that the counterfactual is true.

What are we to make of this?

One could get around the logic problems by suggesting that the fork time is not semantically sensitive to the antecedent, but only to the conversational context. This would lead to a strict conditional account, in which 'if A' quantifies over all A-worlds that deviate at the contextually determined fork time.

OK. But this doesn't seem to help with the backtracking issue. And I worry that the move is not available for deontic conditionals, where analogous issues arise.

Another idea is that our judgements about conditionals like Pollock's are distorted by whatever gives rise to the Simplification of Disjunctive Antecedents effect – the appearance that 'if A or B, C' entails 'if A, C' and 'if B, C'. It has often been suggested that this is an implicature. Perhaps there is a general mechanism by which conditionals with unspecific antecedents implicate corresponding conditionals with more specific antecedents. This might explain why A>C seems to entail A1>C and A2>C, in the case of Pollock's coat.

But then what is the literal meaning of A>C? Was Lewis (1979) right about the similarity standards after all? I don't think so. 'If my coat had been stolen, it would have been stolen on the second occasion' sounds robustly false, unless a theft on the second occasion was somehow more likely.

So I'm not sure what to think.

Bennett, Jonathan. 2003. A Philosophical Guide to Conditionals. New York: Oxford University Press.
Khoo, Justin. 2017. “Backtracking Counterfactuals Revisited.” Mind, fzw005. doi.org/10.1093/mind/fzw005.
Lewis, David. 1979. “Counterfactual Dependence and Time’s Arrow.” Noûs 13: 455–76.
Nute, Donald. 1980. Topics in Conditional Logic. Vol. 20. Springer Science & Business Media.
Stalnaker, Robert. 1984. Inquiry. Cambridge (Mass.): MIT Press.

# on 22 March 2024, 10:11

Thanks Wo, really interesting! Does it follow from Bennett's solution to Pollock's coat that the divergence event happens around the start of the interval described in the antecedent? He uses the phrase "a latest admissible fork" (p.220) which, I assume, is compatible with both an early and a late coat theft. It seems to me that in your revised Jack-Jim backtracking case, we only get the intuitively wrong result if the closest ask world is one where Jim asks yesterday morning, but I'm not sure this follows from Bennett's revision. Perhaps "a latest admissible fork" would be compatible with a post-quarrel ask, as well as a pre-quarrel ask (although I'm not entirely clear how to unpack "a latest admissible fork").

# on 22 March 2024, 14:35

Thanks Stephan. I'm thinking that if the latest admissible fork is after the first theft occasion then we'd get the false result that if the coat had been stolen then it would have been stolen at the second occasion. So I assume Bennett's idea is that the latest admissible fork, in the Pollock case, lies before the first occasion.

Similarly in the revised Jack-Jim case: We don't want to say that if Jim had asked yesterday or today then Jim would have asked today (or: ...then X would have happened, where X would only have happened if Jim asked today). To avoid this, the latest admissible for must be yesterday.

# on 23 March 2024, 08:28

Yeah, but I take Bennett to be saying that in cases like Pollock's coat involving a vaguely defined temporal interval in the antecedent, there is no unique latest admissible fork. He writes, "The ‘latest admissible fork’ constraint, then, if taken strictly is too strong to fit our practice. I shall use the phrase ‘a latest admissible fork’, stipulating that two forks can both count as ‘latest’ if their times of occurrence are not considerably different" (220). So among the closest theft worlds, some fork times occur earlier and some occur later.

# on 25 March 2024, 14:48

Ah! You've read Bennett more carefully than I have. Thanks.

I don't think having the early and the late fork tied for closeness helps, though. You still invalidate the three inferences, and you still run into a version of the backtracking problem. For example, suppose Jim and Jack quarreled yesterday and today. We want 'if Jim had asked yesterday or today, Jack wouldn't have helped' to be true. But the closest worlds that deviate yesterday to allow Jack asking for help *today* are plausibly worlds where there's no quarrel today. So the counterfactual isn't true.

In essence, the problem is that if we don't seem to *allow* for worlds that deviate before the earlier opportunity when we evaluate what would happen if the later opportunity were realized.

# on 26 March 2024, 10:22

Ah I think I see that a version of the backtracking problem remains. And you're right about it not helping with the first problem. Thanks!

# on 07 May 2024, 19:47

>>
Lewis's similarity semantics therefore predicts that if the coat had been stolen, it would have been stolen on the second occasion. This doesn't seem right.
<<

Are the closest worlds the most probable worlds? That's not so obvious. But if so, then I can see how Lewis' semantics would make such a prediction. But if not, the it is hard to see why L-semantics would predict the second occasion.