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June 25, 2004
Predictive Prophecy and Counterfactuals
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 Jeremy at June 25, 2004 11:10 AM
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» Predictive Prophecy and Counterfactuals from Parablemania
In line with our discussions of time and time travel, the Gnu brings up a related issue 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... [Read More]
Tracked on June 25, 2004 11:18 AM
» Predictive Prophecy and Counterfactuals from Prosblogion
I've just posted some reflections at OrangePhilosophy about predictive prophecy and how to deal with counterfactuals in such a case. It isn't about God's foreknowledge of the future but takes its start from a fantasy role-playing case, but it raises... [Read More]
Tracked on June 25, 2004 11:23 AM
Comments
Wow, D&D *and* reverse causality! How could I *not* respond! ;∋
What messes me up about these stories is not veridical foresight, but rather assumed veridical *counterfactual* foresight a la Minority Report.
Veritical non-counterfactual foresight is really not as cool a power as is typically assumed. So here's how it might help: It tells you the exact future trajectory of the dwarf through your obsidian castle. So you think: a ha! I'll put the sword in a room where the dwarf won't tread. But it's not that simple. The dwarf navigates according to the way things in the castle are when he's there. Much of what he responds to are objects arranged by the Liche. But the specific arrangement of everything, including the location of the sword, must be settled if the dwarf's path already is.
It reminds me of a line from a talk I'm preparing to give in Oswego next semester:
"Prophecy is a poor guide for action, because what is prophecised either will happen or it won't. You don't need to worry about prophecies that won't come true. And there is no hope of acting in a way that prevents prophecies that are. The truly-prophecised thing *will* happen. Suppose a prophet told me "a child born of Oswego this week will blow up America in 2020." There is not much sense in a rampage of preventative infanticide. If the prophet is wrong then it's just senseless killing, and if he's right, the guilty party won't be stopped anyway (though many innocents will)."
The Liche is in a similar situation. There are interesting complications... I could go on, but that's not the main topic.
About the Lewis thing, because he takes counterpart relations to vary according to principles of relevance, I think he allows that closeness relations also depend on similar things. So take the counterfactual "If I were showering right now, my clothes would be wet." (I am actually wearing clothes as I write this!) Well, that's not a mystery - if you're holding fixed my psychology, this is false, and if you're holding fixed something else, it might be true. I know he has that stuff about miracles and maximizing the similarity in property instantiation patterns. I'm not enough of a Lewis scholar to sort this out. He needs counterfactuals to be solid to make sense of causality, and it's in the context of figuring out what causes what that minimizing departuers in property instantiations is the right ordering scheme for closeness of worlds. But counterfactuals like the "shower" sentence don't seem like they should be treated that way. So Liche stories should be dealt with like the "shower" sentence. Somebody help!
Posted by: Dave H. at June 26, 2004 6:12 PM
I'm worried about your argument because it sounds too much like the lazy argument. It's different in that he also foresees his own actions, whereas the lazy determinist doesn't foresee that he will, say, fail his exam because of his accepting of the conclusion of his arguyment but wouldn't have done so if he'd studied. But then maybe the seeing of his own future actions is what undermines his sense of freedom here.
Posted by: Jeremy Pierce at June 27, 2004 2:27 PM
I take the "lazy argumnet" is *not* the following:
"If my failing the test is correctly prophecised, then whatever action I will undertake to pass the test will not succeed."
There is a separate question of what I *can* or could do, and that requires some subtlety. Whatever I do (suppose I don't yet know how I will respond to the sad prophecy), it won't result in passing the test, but *could* I have done something different that did lead me to pass it? I think so. If you're a compatibilist it's easy. If you're a Libertarian, you can analyze abilities as as sets of worlds with the right relevance relation to α, something like "worlds that I have the ability to make actual." In some of those worlds the prophecy is false (you pass). But it's not weird that you can make a true prophecy false. It only sounds weird.
Btw. I think there are good arguments not far from the bad "lazy argument". Consider that reacting with laziness to any true prophecy will put its truth in danger. If an knowably infallible prophet tells me I will have a long, healthy, fulfilling life full of wealth, friendship and stimulation, it is perfectly rational for me to drive recklessly, swim with sharks and not study anything that bores me.
Posted by: Dave H. at June 29, 2004 9:58 AM
Ooh, I left out a "not" from the last paragraph:
...reacting with laziness to any true prophecy will *not* put its truth in danger.
Posted by: Dave H. at June 29, 2004 10:02 AM
Ah, but it isn't rational. The prophecy only told you that you'd have a long, healthy, fulfilling life full of wealth, friendship, and stimulation. It didn't tell you whether a short part of that life before all those things would be spent in prison for killing someone while driving recklessly or whether your arm would be present during all the fun and fulfillment.
There was a great X-Files near the end of the time David Duchovny was still doing it full-time about a genie who had to take people's requests literally while making it as bad as possible in every way consistent with the literal request. Mulder asked for world peace, and everyone except him and the genie disappeared. A guy wished to be invisible, and he got killed walking across the street. His friend wished for him to be alive again, and he was restored half-decayed and still invisible. Prophecies can be like that. If you don't have all the information, you can't rule out a number of things that you still need to avoid.
Posted by: Jeremy Pierce at June 30, 2004 9:07 AM
Oh, come on... so let's say the prophet added "without unpleasant interludes". Also, even without that, it's rational for you to volunteer to diffuse bombs that either explode fatally or do nothing.
Posted by: Dave H. at June 30, 2004 3:40 PM
Oh, and about that X-files episode - I saw that one, and it reminded me of my old D&D days when I used to DM. Players learned quickly to not try doing too much with their wish spells! It's interesting to think about which wishes and which prophecies are really safe.
Posted by: Dave H. at June 30, 2004 3:47 PM