Topic: GENERAL LOGIC
Predictive Prophecy and Counterfactuals
by Jeremy Pierce
Source: Orange Philosophy June 25, 2004
In line with the discussions of time and time travel at my blog and to some degree here also, our own Gnu has a related puzzle using a fun fantasy role-playing kind of example for a philosophical puzzle about conditional predictive prophecy (i.e. predicting what someone will do and then telling him that A will have already happened if he ends up doing P but B will have already happened if he turns out to do Q). I think this case is interesting in terms of its view of time and of the relation of guaranteed prediction to time, but it also has some relevance to how to evaluate counterfactual statements. Read the case first at Gnu's blog, then read on here for my analysis.
The Liche Lord has predicted what Thurvan would do. That means he knew that Thurvan would go to all the rooms. Therefore, assuming he isn't lying, he hasn't placed the sword in the room he said it would be in if Thurvan had chosen not to go to the other rooms. Thurvan was correct to say that the sword is either there or not, but he was wrong to think that it was there independent of his decision. It was there because of what he would do. If Thurvan had chosen otherwise, and the Liche Lord had still set up the same deal, the sword would have been there. But unless he's lying, the sword can't be there as things stand. Given that the Liche Lord can take the shape of any object and enjoys taking people to be his undead slaves, you might expect that what the dwarf sees as the sword is probably the Liche Lord himself waiting to trap him.
Of course, the Liche Lord can see the future, so this is probably only the case if the Liche Lord has predicted that the dwarf will take the sword. He may well have predicted that the dwarf would reason through all this and leave without going for the sword, in which case he may have lied and put the sword there anyway. What's great about this is that the sword might really be there but only if he doesn't try to get it, and it's not there if he does. So he can't get it one way or the other. The only way to get the sword would have been to do what the Liche Lord knew he wouldn't do, and that would have been to avoid the other rooms.
In working through this, I had a hard time thinking about what the Liche Lord would have done if Thurvan had chosen otherwise, because it may well be that the Liche Lord would not have chosen to set this scenario up at all without the knowledge of Thurvan choosing the way he did. It's hard to think about counterfactual possibilities where the thing that would have been different depends on knowledge of the future in the counterfactual world.
According to David Lewis' semantics of counterfactual statements, 'if Thurvan had chosen to go straight to the sword room, the sword would have been there' is unclear to me. Lewis says to go to the nearest possible world where Thurvan goes straight to the sword room, meaning that you should find the world most like the actual world except for that detail and then see what's true. So if we change nothing in the world except that and what changing it will require, what happens? I can think of three kinds of candidate worlds for the closest:
1. My first thought would be to say that if Thurvan had chosen differently, and if you kept as much intact as possible, then the Liche Lord would have predicted differently and as a result put the sword in the chamber to honor his deal. This world holds the Liche Lord's honesty and abilities constant and changes the state of the world for the entire time between the writing of the letter and the present so that the sword has been there all along.
2. Lewis prefers to find a world intrinsically as much like the actual world as possible. That would require keeping the tomb , just as things are in the actual world. But then the Liche Lord would have to have told something false to Thurvan. Either he was lying (2a), or his predictive abilities failed in this one case (2b). I think Lewis has to favor 2b, because even 2a has intrinsic changes with the Liche Lord's beliefs and intents, whereas 2b could be just a surprising failure of his abilities, something like the miracle worlds Lewis discusses in his paper on whether free will requires breaking the laws of nature.
3. Lewis wouldn't like this at all, because it requires even more of a change of the intrinsic state of the world so far than 1, but some might argue that if Thurvan had chosen to take the sword and not go to the other rooms, the Liche Lord would not have set up the case this way at all and wouldn't have given a deal that would mean he'd end up losing. I'm bring this up only to argue against it as a legitimate near possibility. Seeing this as a near possibility of what would happen given Thurvan's choice to go only for the sword assumes something false. It assumes the Liche Lord is predicting what Thurvan would do given that the Liche Lord sets things up a certain way. According to Gnu's setup, the Liche Lord predicts what Thurvan will do, period. He doesn't consider all the possibilities and make things go his way. His ability only tells him what will happen. So this one requires a difference in the intrinsic state of the world and in the abilities of the Liche Lord. 1 has a difference only in the state of the world (and not even as much of a difference), and 2 has a difference in the abilities or intent of the Liche Lord (and not as much of a difference -- either a one-time failure of the same ability rather than a completely different ability or a different motivation rather than a whole change in the nature of his abilities).
So I think 1 and 2 are the real options for which world is closest to the actual one Gnu has constructed. This is a particularly vivid example of those who agree with Lewis on nearness of worlds based on intrinsic likeness and what I think is the more commonsense view of nearness of worlds based on preserving the abilities of the Liche Lord that related causally to the future in certain guaranteed ways. Lewis' view is required for those who reduce causality to relations between instrinsic properties of things across time, and my intuitions against his view on this case are therefore intuitions against his reduction of causality to such things. The causal relations between the Liche Lord and the future that he sees are an important part of the structure of the world, and a world seems to me to be much further from the actual one (of the case) if the Liche Lord has to have different abilities or failure of his abilities to keep the world intrinsically as close as possible. Simply changing some more intrinsic facts seems to me to be less of a change.
Posted by Tony Marmo
at 15:17 BST
Updated: Monday, 9 August 2004 07:59 BST
