Wolfgang Schwarz :: Some tricky counterfactuals

Some tricky counterfactuals

Posted on Saturday, 24 Sep 2005.

Sometimes, a counterfactual is true even though the consequent is false in the closest world where the antecedent is true:

1) If Hurricane Katrina hadn't hit the town with 200 km/h, completely destroying our house, we would be at home now, watching TV.

Presumably, at the closest worlds where Hurricane Katrina doesn't hit the town with 200 km/h and completely destroys the house, it hits the town a little faster or slower, still completely destroying the house. Even at the closest worlds where the hurricane doesn't completely destroy the house, it destroys it almost completely, still preventing the TV event.

Searching "if Hurricane * hadn't" on Google revealed this even more remarkable counterfactual:

2) If Hurricane Steph hadn't gotten us into the Beacon soundcheck where we had a chance to briefly chat with Billy and Grant before the show and to be told that we could get some passes, we probably wouldn't have been able to stay after the show (but it still would have been a great night even if we hadn't gotten backstage afterwards).

Somewhat similar, but with non-negated antecedent:

3) If we had arrived earlier, we would have witnessed the riot.

4) If the president was smarter, he would have signed the Kyoto treaty.

Considering worlds where we arrived just a little earlier and where the president is just a little smarter will not make the consequent true.

In all cases, the rule seems to be that we are to consider the antecedent not just to be true, but to be really quite significantly true (so to speak). We are to consider worlds where the Hurricane almost didn't hit the town at all and where we arrived not just earlier, but a lot earlier. Can this rule be stated more precisely?

Pragmatics and accomodation seems to play a role here, too: We can say

5) Even if Hurricane Katrina hadn't hit the town with 200 km/h, it would still have destroyed the house: the architect says the house would have collapsed even under a 100 km/h storm.

And, in the other direction:

6) If we had arrived earlier, we would have met dinosaurs here.

Other, vaguely related cases:

7) Travelling at 500000 km/s is ruled out by the laws of nature. But if the laws of nature were different, we could travel at 500000 km/s and reach Alpha Centauri in about 4 years.

8) What we had we will never have with anyone again, and if things were different we would probably be together, but we were just young and stupid and now we can't go back. (Source)

Presumably at the closest worlds where the laws of nature are somehow different, travel at 500000 km/s is still impossible, and at the closest worlds were things are somehow different, we are still not together. Here we not only have to assume a higher degree of difference, but also a suitable respect of the difference.

Comments

# Robbie on 24 September 2005, 22:07

Two quibbles and something more serious.

Quibble 1. I'm not sure about the first case---maybe this is just fuzz with the example, but it seems to me that a good candidate for closest world where the antecendent is true is the following. The hurricaine takes a different path, and so avoids the hitting the house altogether. It's not obvious to me that e.g. a world with slightly lower windspeeds but same hurracaine trajectory is closer than this one.

Quibble 2. The dinosaurs counterfactual just sounds false to me.

More seriously, how are you evaluating the closeness of worlds? Suppose in w the president has 1 additional IQ point, and in v he has 50 additional IQ points. Why is w closer to the actual world than v?

w does have greater overall "approximate match" with the actual world: decisions the president makes will diverge far more from the actual ones if the IQ is much much higher. But approximate overall match can't be the right way to think about closeness of worlds, I take it, otherwise we'd already be in trouble with Fine's Nixon-pressing-the-button example. And I need convincing that you can make a case for w being closer to actuality than v in e.g. Lewis's treatment of closeness.

# wo on 24 September 2005, 22:51

Suppose Ted and Fred are aliens from Alpha Centauri, arriving on Earth today after a billion year journey. Couldn't Ted then truly say to Fred: "If we had arrived earlier, we would have met dinosaurs here"?

The question about standards of closeness is fair. In fact, Lewis says that "we must use what we know about the truth and falsity of counterfactuals to see if we can find some sort of similarity relation [...] that combines with [the analysis] to yield the proper truth conditions" ("Time's Arrow", p.43). What I suspect is that at least some of the cases I mentioned are false on *any* similarity ordering that deserves that name. But I agree that this isn't obvious.

In the IQ case, it seems unlikely that 1 additional IQ point would take a larger miracle than 50 additional IQ points. But if the miracle is equally big or even smaller, the +1 world will be closer to actuality than the +50 world. At best, if we *completely* discount approximate overall match and the miracles are equal, v and w will be equally close, and (4) still false.

# Robbie on 25 September 2005, 17:02

Ok---given setup, the dinosaur claim sounds ok. Just thought it sounded false in a more usual setup! Presumably because in standard contexts worlds where we arrive billions of years earlier just aren't in the context set.

I agree that the best outcome we can hope for from a similarity analysis is that w and v are equally close. I was arguing against the claim they were false. You're right that on the Lewis analysis of counterfactuals, ties for closeness between words disagreeing on the consequent make the counterfactual false. I had been thinking about the Stalnaker setup, where you supervaluate over closest worlds, so in case of ties the counterfactual becomes indeterminate. (NB: Stalnaker discusses briefly a similar case on p.141 of Inquiry.)

Interesting the point about things changing if approximate overall similarity has non-zero weighting. Maybe intuitions about these cases give some traction on whether or not approx overall similarity should be given weight.

# Carrie Jenkins on 28 September 2005, 16:37

I wonder whether the best thing to say is that in some of these cases the antecedents should be thought of as elliptical
(and we're using context, background knowledge about the speaker, knowledge of what the consequent is, charity etc.
to fill in the hidden details).
So for instance, when we're tempted to hear:
If we had arrived earlier, we would have met dinosaurs here.
as true, that's because we're really hearing it as something like:
If we had arrived *millions of years* earlier, we would have met dinosaurs here.

In other cases we seem to have the opposite of an elliptical antecedent: one where *more* info is given than we're
actually supposed to take on board. So for instance, maybe when we're inclined to hear:
If Hurricane Katrina hadn't hit the town with 200 km/h, completely destroying our house, we would be at home now, watching TV.
as true that's because we're really hearing it as something more like:
If Hurricane Katrina hadn't destroyed our house, we would be at home now, watching TV.

Wolfgang Schwarz

Some tricky counterfactuals

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