## Reversible Sobel Sequences

A Sobel sequence is a sequence of conditionals with increasingly strong antecedent. Lewis used Sobel sequences to motivate his "variably strict" analysis of counterfactuals.

For example, intuitively (1) and (2) might both be true, which seems to contradict a simple strict analysis:

(1) If the US had destroyed its nuclear weapons in 1965, there would have been war.
(2) If every country destroyed its nuclear weapons in 1965, there would have been peace.

A problem with this argument (pointed out in von Fintel 2001), is that the intuition about (1) and (2) depends on the order in which the sentences are considered. If we consider (2) first, and judge that it is true, then (1) looks at best doubtful.

Intuitively, once we pay attention to the possibility that every nation might have destroyed its weapons, we no longer think that it is certain that there would have been war if the US had destroyed its weapons.

The effect doesn't require uttering a counterfactual like (2). Instead, one could make the relevant possibility salient by saying that every country could have destroyed its nuclear weapons in 1965. One could also make it salient by simply asking if it is really guaranteed that there would have been war if the US had destroyed its weapons, if there is absolutely no chance that a different outcome might have resulted. Either way, (1) then seems problematic.

But all this, I think, depends on the choice of example. Here is a different case. Suppose I was walking north at 10am today, with the Sun to my right, in the east. In that scenario, consider (1*) and (2*).

(1*) If I had turned right today at 10am, I would have turned towards the Sun.
(2*) If I had been walking south today at 10am and then turned right, I would not have turned towards the Sun.

These are both intuitively true. It's a Sobel sequence. But I think it's reversible: (1*) still seems true to me even after I've considered (2*), provided I'm evaluating it in the originally described scenario where I was walking north at 10am.

More generally, unlike in the previous example, I don't think there is any way of casting doubt on (1*) by drawing attention to unlikely eventualities. Given that the Sun was to my right at 10am, it is not merely likely that I would have turned towards the Sun if I had turned right. Turning right would have constituted turning towards the Sun. If someone asked, "isn't there a chance that you might not have turned towards the Sun?", I would answer "no".

Another example. Suppose you promised to pick me up at the station. On that supposition, consider (1') and (2').

(1') If you had not picked me up, you would have broken your promise.
(2') If you had not promised to pick me up, and then you had not picked me up, you would not have broken any promise.

Cases like these arguably pose a more serious challenge to strict analyses than cases like (1)-(2).

Another possibly interesting fact about these cases is that they don't easily transfer to indicative conditionals, unlike ordinary Sobel sequences like (1)-(2).

Suppose you know that I was walking north today at 10am, and you don't know if I continued walking north from then on. You might reasonably say:

(3) If you turned right today at 10am, then you turned towards the Sun.

But could you reasonably say (4)?

(4) If you walked south today at 10am and then turned right, then you didn't turn towards the Sun.

I think you couldn't. (4) is only assertable if you're not sure whether I walked north or south at 10am. In any such context, (3) is unassertable. No such problem arises for the subjunctive cases (1*)-(2*) and (1')-(2').