#146 Causal Paradox

#146 Causal Paradox

I was sorely tempted to try a solution to this paradox using dialetheism. Be grateful that I didn’t.

Also, if anyone can tell me where this fun little paradox comes from, I’d be grateful. Found it, it is apparently known as Smullyan’s Paradox. If you follow the link you can see a lot of discussion that mirrors ours here.

In other news, I found out this morning that the paper I submitted to the FPA Conference won the Outstanding Graduate Paper Award this year, and will be published in the Florida Philosophical Review. Totally crazy, and awesome! So if you’re in the Gainseville area in November, this is your chance to see me in action!

Oh! And I almost forgot, the cool background in the first panel is a modification of a desktop background image from this website here. There are some other neat images there too that are worth checking out.


Discussion (31)¬

  1. Emil says:

    OOooo

    Surely dilatheism can handle this. It’s easy. Both Bob and George are solely responsible, and neither of them are. No problem there. In fact dilatheism solves ALL philosophical problems.

  2. chaospet says:

    heh yes, that is pretty much exactly the solution I almost went with.

  3. Emil says:

    I don’t know about the “paradox”. Do we really need to be able to say who is responsible? It seems to me that such situations will not happen in practice and so it doesn’t really matter what the answer to the question is. Morality evolved because it made the animals that had it survive more / get more children / etc. better than those who didn’t have it (to that degree).

    How hard do you reckon it is to get published in that magazine? I’m looking to attempt to get something published something. Preferably in some net-magazine that is peer-reviewed.

  4. chaospet says:

    Emil: It does strike me as rather paradoxical if two people attempt to kill someone, the person ends up dead (and wouldn’t have if neither of them had acted), and yet we cannot clearly say that either of them is responsible. I don’t know if we “need” to attribute responsibility, but it seems rather unsatisfying if we can’t.

    I don’t know exactly how hard it would be, but I don’t believe that the FPR is a particularly prestigious journal (they are publishing a paper of mine, after all!), so it may be easier to get published there than in many other journals. But that really is just a guess, I don’t know for sure.

  5. LEGION says:

    Its all wrong, I killed Ed.

  6. Wm Tanksley says:

    I’m not seeing this as a paradox as much as I’m seeing it as a question of … perhaps … epistemology (or perhaps probability, which might be the same problem under a subjectivist view of probability).

    We could, I think, say that an omniscient God would be able to judge both parties guilty of murder, but I think the real head-scratcher is trying to come up with a single fairly applied legal system (for us finite beings living on less than perfect islands) that can convict both under reasonably realistic circumstances without posing a danger of convicting innocent people in much likelier situations.

    -Wm

  7. Emil says:

    In my view of morality it’s not a problem to say that no one is responsible. It seems only to be a problem for someone with really metaphysic / transcendental / magic / objective view of morality.

    An action is moral wrong iff most people would find it morally wrong if they viewed the case as disinterested observers.

  8. chaospet says:

    Wm: I think that’s enough to say it’s paradoxical. Saul Smilansky has an excellent recent book on a number of Moral Paradoxes, I think this sort of puzzle fits nicely in that category.

    Emil: Sure, it is a problem for someone with an objective view of morality – but I wouldn’t equate an objective view of morality with any strong metaphysical (or magical) views.

  9. mark says:

    Bob goes to prison for attempted murder. He tried but failed to cause Ed’s murder. George goes away for murder. Preventing a murder doesn’t exculpate committing murder. If the little rascal was going in your room to kill you with his sword, but I cast a fireball and destroyed you both in an orgy of cinders and molten steel , I’d still be guilty of your murder, chaospet. No matter how powerful my magic.

  10. chaospet says:

    Mark: The fireball analogy, while beautiful, doesn’t fit the example. George did not directly cause Ed’s death by thirst (in the way that your mighty magic directly causes my death), for it was already the case that there was no thirst quenching substance available for Ed to drink as a result of Bob’s actions.

  11. Wm Tanksley says:

    Emil, the “disinterested observers” criterion is an indicator of an “objective morality” view.

    chaospet, I don’t see how that makes a paradox. A paradox is a statement that’s neither true nor false, nor obviously nonsense. What statement are you claiming that meets that criterion?

    I think mark’s right; I didn’t even think of attempted murder. And Bob DID directly cause Ed’s death; his action of poking a hole in his canteen was intended to kill him, and actually did kill him; in a very similar way that poking a hole in his heart would have. There’s nothing indirect about either the intent or the action; there’s a delay, but no indirectness.

    And he would have gotten away with it, too, if not for those kids and their dog.

    -Wm

  12. chaospet says:

    Wm: That is one sense of paradox, but there are others. Here it is paradoxical because we have a situation where it seems clear that at least one of them must be responsible, and yet each seems clearly to be able to demonstrate that he is NOT responsible. But let’s not get caught up on the semantics of the word “paradox”; we can call it a “puzzle” instead if you like.

    Back to the main point – again, I don’t see how George directly caused Ed’s death. If he had denied Ed life-saving water, then of course, we would say that he directly caused Ed’s death. But George didn’t deny Ed thirst quenching, life-saving water. He denied Ed poison. Of course he MEANT to deny Ed life-saving water, just as Bob meant to poison Ed, but neither of those things actually happened. The poison would have done nothing to quench Ed’s thirst and save his life (to make this really explicit, let us further suppose that the poison in fact includes a strong dehydrating agent that completely nullifies the hydrating effects of the water). So how then can we say that George caused Ed’s death?

  13. Cake Ninja says:

    …Weren’t they at an oasis? Couldn’t Ed, you know… drink from the oasis? Wouldn’t he, for this reason, survive his canteen being empty? (Sorry if I’m missing some other meaning of oasis, but I’m pretty sure that’s the meaning used.)

  14. chaospet says:

    Cake Ninja: The idea is that he dies much later, after leaving the oasis believing that he has water to survive his trek across the desert.

  15. Emil says:

    Wm,

    I don’t see any reason to call such as view objective, but if you wish we can call it that. It’s much different from. say, intuitionism such as the one this guy holds: http://home.sprynet.com/~owl1/ethics.htm This is the only kind of objectivism that I know about. I have never read any pro-work of utilitarianism or some deontogical theory. That has yet to come.

  16. BG says:

    I generally find philosophers to be pretty skeptical of probabilistic reasoning, but I think it addresses the problem pretty nicely.

    At the start of the story, Ed has clean water in a canteen. The probability he’ll live is 1.
    Bob then poisons Ed’s canteen and doesn’t tell anybody. The probability Ed will live now is now 0.
    George then pokes a hole in the canteen, such that the poisoned water leaks. The probability Ed will live now remains 0. However, if George believed the water to be clean, then he believed his actions would change Ed’s probability of living from 1 to 0.
    Therefore, Bob is guilty of murder and George is guilty of attempted murder.

  17. chaospet says:

    BG: Yup, I see that as one of the possible lines of argumentation; it is essentially the argument Nester tries to make (but much less clearly than you did) in the third panel. However, when your attention is drawn to the fact that the poison plays no causal role whatsoever in Ed’s death (he never drinks it or comes in contact with it, it has no effect on him at all), I think this line becomes much less plausible.

  18. Wm Tanksley says:

    > Wm: That is one sense of paradox, but there are others.

    Interesting. I don’t know how this definition’s supposed to work; a logical paradox (the kind I knew about) can’t be solved; the correct way to address it is to show that it can’t correspond to reality. This thingie can be solved, and obviously could correspond to reality. “Puzzle” is a good name.

    George definitely denied Ed life-saving water. Ed was reasonably relying on his canteen for water, and Ed took advantage of that reliance, damaging the canteen in a way to make it useless for carrying water. At that point, regardless of what happened (aside from some lifesaving action that directly counteracted George’s specific sabotage), Ed was doomed.

    > But George … denied Ed poison.

    So? He also denied him water, which was his intent and his action. Further, he sabotaged Ed’s life support equipment so that it could not possibly function.

    I admit that both sides will attempt to make their arguments as powerful as possible, but these seem like really bad arguments, given the admitted facts.

    Now, change things up a bit so that Ed survives, and imagines himself to be in debt to George for his heroic life-saving actions. Hijinks ensue, and you have all the makings of a highly successful sitcom. Meanwhile, your original plot is relegated to a single episode of CSI: Death Valley. Again we see there is nothing you can possess which I cannot take away.

    -Wm

  19. Wm Tanksley says:

    The label “objective” seems to fit, and in fact the person you link to calls it that; see his second link, “the Subjectivist’s Dilemma”.

    “This is the only kind of objectivism that I know about. I have never read any pro-work of utilitarianism or some deontogical theory. That has yet to come.”

    Oooh, you’re in for some fun :-). Actually, try the paper I just mentioned — it’s not bad.

    I find it odd to refer to a belief in moral reality as “objectivism”, since I think of Ayn Rand when I hear that. But apparently that’s standard terminology.

    -Wm

  20. chaospet says:

    “George definitely denied Ed life-saving water.”

    This is the crux; George did NOT deny Ed life-saving water, for once Bob was done with his actions, there WAS no life-saving water in the canteen. There was instead only a poisonous, deadly substance unfit for drinking – and citing the removal of a substance that is already unfit for drinking as the cause of Ed’s not having life-saving water to drink seems mistaken.

    By the way of analogy, imagine if Mark with his mighty wizard powers turned your lunch into sand, and then later I stole your lunchbox (thinking it contained your lunch and not sand). If you then concluded that I caused you to go hungry at lunch time, you’d be making a mistake. Your lunch was gone before I ever did anything. Though I meant to steal your lunch, all I really took from you was inedible sand.

    I think this plot is worth a whole season of CSI. The final season, to be precise. I can see it now, they go in circles episode after episode, permutations of the same arguments over and over, until finally someone snaps and kills them all. With poison.

    re: objectivism – it is for precisely that reason that I prefer the term ‘moral realism’. Ayn Rand can suck it.

  21. Canuovea says:

    Okay I got one for you. Though you may have seen it already, I dunno. My symbolic Logic Prof brought it up.

    The “Hangman Paradox”

    The Judge says to a convict: “You will be hanged next week, either Monday (M), Tuesday (T), Wednesday (W), Thursday (TH), or Friday (F) at noon of that day.” Okay fair enough.
    “But you will not know which day until 11:00 on that day.” He cannot actually know before 11 on the day.

    But here is the issue. If on TH he is not told at 11 that he will die on TH then the only remaining option is he will die Friday. Buuuuut then he knows beforehand. He is not supposed to be able to. So it cannot be Friday. And apparently it then logically follows that it cannot be Thursday either, because, having ruled F out then the same argument can be made for Th, and then W, T, and even M.

    Therefore the convict concludes that he will not be hanged.

    What is this? Contradicting premises? Or what? And I know the whole thing could be resolved by replacing “know” with “will be told,” but then it changes the whole thing doesn’t it?

    But there is more… sometimes people continue the story….

    So they come to the convict on Tuesday and say “one hour.” The convict freaks out and shows them his elaborate proof. The response is thus: “Well, did you know the day?”
    “Er. No.” “Sucks to be you.”

    Logic fail.

    So, is that even a Paradox?

    Actually writing this out gave me an idea… The convict is taking the result of a theoretical assumption (assume TH after 11 or whatever) and applying the conclusion derived from that assumption to the actual logical argument where that is only an assumption… Hmm, maybe not an actual paradox, just bad logic… Well I’m posting this anyway. What do you all think?

  22. chaospet says:

    Canuovea: I have heard versions of that one before. And as you say, something clearly goes wrong in the reasoning. The argument seems pretty conclusive for it not being Friday… which results in a conclusive argument for it not being Thursday, so on. So yeah, it is difficult to pinpoint exactly where the reasoning goes wrong.

  23. IcarusRisen says:

    Hey, are you coming down for the conference? I’m over here at UF

  24. chaospet says:

    Icarus: If you mean the FPA conference then yup, I will be there!

  25. Wm Tanksley says:

    “This is the crux; George did NOT deny Ed life-saving water, for once Bob was done with his actions, there WAS no life-saving water in the canteen.”

    This doesn’t matter. Ed, entirely independently of George’s actions, could well have discovered Bob’s treachery and washed out his canteen; but George’s skulduggery could only be countered by discovering George’s murderous scheme.

    It’s mere coincidence that Bob’s scheme didn’t work; in fact, the setup for this puzzle explains that it’s a mere coincidence.

    “citing the removal of a substance that is already unfit for drinking as the cause of Ed’s not having life-saving water to drink seems mistaken.”

    No, the cause is the hole knocked in his canteen, rendering it unusable. But let’s modify the puzzle; say that George didn’t damage the canteen, but simply emptied it. Now George would defend himself by saying that he meant no harm; he was simply removing the poison. Here the puzzle is unclear: it states as a matter of fact that we know that George meant to kill Bob. If we know that, George’s defense is an obvious contradiction of known fact, and won’t be accepted. If we don’t know that (but just deduced it from other evidence), we might accept George’s claim — but then we’d simply reduce the charge to negligent homicide, since George knew or should have known that his action, although intended for some good purpose, would result in death.

    “By the way of analogy, imagine if Mark with his mighty wizard powers turned your lunch into sand, and then later I stole your lunchbox (thinking it contained your lunch and not sand). If you then concluded that I caused you to go hungry at lunch time, you’d be making a mistake.”

    In this story, though, you’re guilty of attempted hungermongering. You’re parallel to Bob (who tried and failed through no fault of his own), not George (who tried and succeeded).

    Curse you, Mark, and your mighty wizard powers!

    “I think this plot is worth a whole season of CSI. The final season, to be precise.”

    Well, civilized people can differ courteously over matters of taste and opinion. Shall it be pistols at dawn, then, sir?

    “re: objectivism – it is for precisely that reason that I prefer the term ‘moral realism’. Ayn Rand can suck it.”

    That happens to be my opinion on her, at least as a philosopher.

    -Wm

  26. Wm Tanksley says:

    > “But you will not know which day until 11:00 on that day.” He cannot actually know before 11 on the day.

    This one feels like the gap; I think the prisoner’s correctly deduced a contradiction, but not a paradox. The judge is simply wrong to group Friday’s execution in with all the other days; Friday’s execution date is a special case because of its edge condition.

    -Wm

  27. chaospet says:

    “No, the cause is the hole knocked in his canteen, rendering it unusable.”

    I don’t think it matters if the canteen is usable or not. I think we are supposed to be imagining that canteen slowly leaks and Ed doesn’t discover it is empty until much later and he is in the desert, where the empty canteen is useless whether it has a hole or not. But for the sake of clarity, let’s imagine George empties it without damaging it.

    “In this story, though, you’re guilty of attempted hungermongering.”

    Precisely. I’m guilty of ATTEMPTED hungermongering because I tried to take away your food and failed. And George (like Bob) is only guilty of ATTEMPTED murder (via thirstmongering) because he tried to take away Ed’s viable drinking water and failed (again, because there was no viable drinking water).

    What I think might be driving the intuition that George does cause Ed to die of thirst is the fact that Ed would not have died of thirst if he had drank the poison. So granted, George’s act of poking a hole in the canteen (or emptying it) is a necessary condition for Ed to die of thirst. But it still is not the cause. Again, to CAUSE Ed to die of thirst, George would have to deny Ed access to viable drinking water, and George simply failed to do that. There was no viable drinking water in Ed’s canteen. If Ed had unwittingly been carrying a bomb, removing the bomb would also be a necessary condition for Ed to die of thirst. But we would not (I don’t think) say that the person who removed the bomb from Ed’s backpack caused Ed to die of thirst.

  28. Gray says:

    The main tricky point is that Bob and George’s ignorance prevents us from simply charging them as accomplices.

    1. Ed would have lived if neither action occurred.
    2. Either action was sufficient to cause Ed’s death.
    3. Both actions, together, were still sufficient to cause Ed’s death.
    C: Ed is dead as a result of their actions. Charge both with murder.

    So we have individual and joint sufficiency, actus reus and mens rea, and a result that would not have occurred without the acts. This seems to be enough to condemn both Bob and George of murder.
    Of course, it’s easy to confuse our intuitions by talking about cause and individual responsibility. But I think individual and joint sufficiency means we can assign responsibility to both parties, regardless of our intuitional confusions about individual causation.

  29. IcarusRisen says:

    Well if you need any help or advice about the area, let me know

  30. chaospet says:

    Icarus: Will do, thanks!

  31. Obscure says:

    Sorry to be tardy to the party.
    It seemed worthwhile to mention: George pokes a hole in the canteen, thus removing a supply of fresh, life-saving, water – and by coincidence some poison.
    George wanted to remove the water, and George removed the water. He also removed poison. Poisoned water is still water (delicious and life-saving), just with a solute in it. The life-saving water component of the poisoned water was still in the canteen before George acted. Supposing no hole had been poked, perhaps Ed could have decided to purify his water later on. We will never know, because George killed him before he had the chance.
    Ed died because his body needed H2O molecules that weren’t there for him. George was directly responsible for removing the H2O molecules – the fact that he removed some CN- ions in the process is incidental to the fact that he removed the H2O molecules. If Ed had imbibed the poisoned water, he would have received his precious H2O and would not have died of dehydration – the fact that he WOULD have then died of poisoning does not change his actual cause of death.
    Dehydration means whoever took away the H2O is responsible, and that’s George. The CN- molecules had nothing to do with anything, they were just along for the ride.

    In the much cooler example of Magic Matt’s Lunch-to-Sand Transmogrification, Matt was the party responsible for removal of the lunch (rather than CP), and hence the direct cause of hunger – the disappearance of (sand-filled) lunchbox is coincidental to the disappearance of lunch.
    If, for instance, Bob had drained the canteen, and then filled it entirely with mercury (or another pure liquid poison containing no trace of water), the Bob would be the one who removed ALL water from the canteen, thus causing the dehydration, regardless of whether a hole was poked.