Smullyan's Paradox

[lovett]

But if B didn't deny C a means of hydration, did he really kill him? Salt water is not a means of hydration. Arguably no poisoned water is.

Well, let's think about about the death C died.

Death caused by lack of water happens via a number of mechanisms. Primarily, we're interested in the fact that water left C's body for a prolonged period, and no water entered C's body. Sweating is the most likely way this happened. C, being in the desert, sweated a certain amount of water and did not intake any water to replace this. This, quite naturally, lead to the amount of water in his body to steadily fall. Eventually, C had so little water left in his body that his vital systems could no longer function. They began to shut down one by one, and he died. This death is individuated by this entire process.

Well, what about the death C would have died if his canteen hadn't been sabotaged, and he had drunk the dehydrating poison within? Well, this death would have involved different mechanisms to that of simple lack of water. Imagine this poison works a little like salt. Salt water dehydrates people because it is hypertonic. It has greater osmotic pressure than do cells, which causes water to flow out of cells. This is not something that happened in C's actual death, but it would happen in this hypothetical death. This poison would cause water to leave C's cells. The amount of water in his body would not actually change, note. But it would no longer be available to his vital systems. Eventually, C would have so little water available to his vital systems that those systems could no longer function. They would begin to shut down one by one, and he would die. Is this death the same death as that described in the first paragraph?

Well, I don't seen any reason that we must say it is. There are patent differences between this death and the previous one. C died the first death, he didn't die this death. He died a death characterized by lack of water, not by dehydrating poison.

So, how does B fit in? Quite straightforwardly. B caused C's actual death. Oh, it's true enough that C would have died whatever B did, and died of dehydration. But this hypothetical dehydrated death would not involve the exact same mechanisms as C's actual death. And as such, we can distinguish between the two deaths. One was the death C actually endured. B caused this death in that, if he had not acted as he did, C would have died a different death. And if you cause someone's actual death, you cause their death. So B caused C's death (and perhaps we can distinguish between causing someone's death and causing someone to die here).

 

[Flying Pig]

A could be prosecuted for attempted murder in the circumstances, given that he tried, but was thwarted by B's efforts.

 

[GhostWriter16]

I see no reason B should be prosecuted for anything more than maybe theft of water. Unless maybe death due to posion were less painful, in which case maybe for causing needless suffering (Torture?) as well. But not murder. B did not cause C's death. That it was "A different form of death" seems unnecessarily legalistic.

I'd say nobody actually murdered. B stole (Perhaps with some quite significant aggravating factors, although those are mitigated by the fact that the canteen was poisoned in the first place), and A committed attempted murder, but nobody actually successfully commited murder. The man died of dehydration, a natural cause.

 

[lovett]

That it was "A different form of death" seems unnecessarily legalistic.

An incisive criticism, as per.

The man died of dehydration. A dehydration caused by a lack of water. A lack of water caused by B's actions. Casuation is transitive. Therefore B caused the man's death.

 

[GhostWriter16]

And also saved him from a different form of death. What if that was his intent? Not to kill him?

This whole argument seems unnecessarily legalistic

 

[Souron]

Well, let's think about about the death C died.

Death caused by lack of water happens via a number of mechanisms. Primarily, we're interested in the fact that water left C's body for a prolonged period, and no water entered C's body. Sweating is the most likely way this happened. C, being in the desert, sweated a certain amount of water and did not intake any water to replace this. This, quite naturally, lead to the amount of water in his body to steadily fall. Eventually, C had so little water left in his body that his vital systems could no longer function. They began to shut down one by one, and he died. This death is individuated by this entire process.

Well, what about the death C would have died if his canteen hadn't been sabotaged, and he had drunk the dehydrating poison within? Well, this death would have involved different mechanisms to that of simple lack of water. Imagine this poison works a little like salt. Salt water dehydrates people because it is hypertonic. It has greater osmotic pressure than do cells, which causes water to flow out of cells. This is not something that happened in C's actual death, but it would happen in this hypothetical death. This poison would cause water to leave C's cells. The amount of water in his body would not actually change, note. But it would no longer be available to his vital systems. Eventually, C would have so little water available to his vital systems that those systems could no longer function. They would begin to shut down one by one, and he would die. Is this death the same death as that described in the first paragraph?

Well, I don't seen any reason that we must say it is. There are patent differences between this death and the previous one. C died the first death, he didn't die this death. He died a death characterized by lack of water, not by dehydrating poison.

So, how does B fit in? Quite straightforwardly. B caused C's actual death. Oh, it's true enough that C would have died whatever B did, and died of dehydration. But this hypothetical dehydrated death would not involve the exact same mechanisms as C's actual death. And as such, we can distinguish between the two deaths. One was the death C actually endured. B caused this death in that, if he had not acted as he did, C would have died a different death. And if you cause someone's actual death, you cause their death. So B caused C's death (and perhaps we can distinguish between causing someone's death and causing someone to die here).

If C found his canteen tasted salty, he would stop drinking from it. So he might die a tiny bit sooner from the gulp of salt he took to discover this, but ultimately the death would be the same as if the canteen had no water. I can invent other ways that A might damage the water in a way that would make it undrinkable, so that C can't event take one gulp. Now that's not precisely the same as the originally stated problem, but It seems like it should have the same ethics.

An incisive criticism, as per.

The man died of dehydration. A dehydration caused by a lack of water. A lack of water caused by B's actions. Casuation is transitive. Therefore B caused the man's death.

That's not the only interpretation. A took C's water and made it into something else. B did not deprive C of hydrating water, but rather of poison. Or salt water.

 

[Cheezy the Wiz]

And also saved him from a different form of death.

So abortion can be justified to you, if the child would be born into a life of pain and suffering, is what I'm getting from this.

 

[GhostWriter16]

So abortion can be justified to you, if the child would be born into a life of pain and suffering, is what I'm getting from this.

No, I don't understand what you're getting at here. How can we tell the future anyways? And do pain and suffering = death?

I never said the guy in question was justified either. He vandalized the water bottle, and in effect stole the poisoned water within. But he didn't kill anyone.

 

[lovett]

If C found his canteen tasted salty, he would stop drinking from it. So he might die a tiny bit sooner from the gulp of salt he took to discover this, but ultimately the death would be the same as if the canteen had no water. I can invent other ways that A might damage the water in a way that would make it undrinkable, so that C can't event take one gulp. Now that's not precisely the same as the originally stated problem, but It seems like it should have the same ethics.

Well, suppose that is how C would have behaved. Is that 'ultimately the same death' as if the canteen had no water? I don 't see any reason to suppose it must be. We clearly can distinguish between this death and C's actual death. This death involves C drinking a little salt water! In ordinary circumstances we don't make this distinction because we never need to, but these are not ordinary circumstances.

Well, as you say we can create scenario's in which A changes C's water such that he doesn't drink any of it whatsoever. These are different situations to the original hypothetical. Will they have the same ethics? Well, the answer to that is 'it depends'; they needn't. I should note that this isn't really a question of ethics, incidentally. It's a question of causation.

So, let's think of one which does have the same ethics. Suppose A turns C's water to gunk. If C sees his water, he wouldn't taste a drop of it. But B, by making a hole in C's canteen, drains this gunk; C never sees it. So is the death C died the same death as the one he would have died if he had had gunk in his canteen? Well, I don 't see why we must say so. In one death, C was disgusted by the gunk in his canteen, in the other he was shocked by the emptiness of his canteen. Certainly these death are going to feel different from the inside out; in one C will be fixated on the gunk in his canteen and in another he will be fixated on the hole in his canteen. As such, we can distinguish them. Nothing forces us to call them the same death (and there not; one can happen without the other!). So this is a situation with the same ethics as the other one.

Well, let's find a situation with a different ethics. Suppose A does nothing to C's water, but he does screw the lid tight. C has no means of getting to the water within. B has actually, unbeknownst to C, put a hole in the canteen so the water seeps out. But everything in C's life -from C's perspective- is the same hole or no hole. In this case it seems plausible to say that the hoe makes no difference to the individuation of C's death. He would have died the same death whatever B's actions. And, in this case, it is A that killed C.

So changing the situation can (unsurprisingly) change the ethics - or more precisely change the causal relations between events. We can invent situations in which it was A who killed C, but this situation isn't one of them (we can, in fact, invent situations in which A and B jointly kill C).

 

[Gori the Grey]

@lovett

I suspect that if you asked me for a glass of water and I gave you a glass of poisoned water, you'd regard me as having given you poison, not water. But more to the point:

@lovett and flying pig

Your method for resolving Smellyan's paradox is admirable, and I take that you don't experience the little puzzle as a paradox because you apply your principle so quickly that there's never a moment in your thinking about the case when it seems to you, for instance, that A is more responsible for C's death because he created a set of circumstances where, whatever B did, C would die.

I suspect you'll stay committed to your method of resolving the paradox, but would you indulge me by answering the following extension of the hypothetical?

Say C is an expert at making this desert passage. It's an 8 hour trip between oases and he always drinks his canteen at hour number 4. He's studied the deaths of other travelers and found that if they drink either earlier than hour 4 or later, they always die of dehydration. He's published articles on the matter. Anyone who has ever traveled with him testifies that he's religious about drinking at hour four.

His canteen is found, thrown to one side of his tracks at the midpoint between the oases. It seems he went to drink it there, found it empty and threw it aside. His body is found just shy of the next oasis. A study is done of the poison A used, traces of which are found in the canteen. It's a poison that kills instantly.

It's likely, then, that B actually extended C's life by almost four hours. (Much good it did him, but still) Do you still regard him as guilty of B's death?

A simple yes or no is fine. Well, if your answer has suddenly become no, then I'd like to hear an explanation. But you're comfortable regarding someone as guilty of someone else's death, even if in all likelihood that person actually extended his life?

 

[Souron]

Well, suppose that is how C would have behaved. Is that 'ultimately the same death' as if the canteen had no water? I don 't see any reason to suppose it must be. We clearly can distinguish between this death and C's actual death. This death involves C drinking a little salt water! In ordinary circumstances we don't make this distinction because we never need to, but these are not ordinary circumstances.

Well, as you say we can create scenario's in which A changes C's water such that he doesn't drink any of it whatsoever. These are different situations to the original hypothetical. Will they have the same ethics? Well, the answer to that is 'it depends'; they needn't. I should note that this isn't really a question of ethics, incidentally. It's a question of causation.

So, let's think of one which does have the same ethics. Suppose A turns C's water to gunk. If C sees his water, he wouldn't taste a drop of it. But B, by making a hole in C's canteen, drains this gunk; C never sees it. So is the death C died the same death as the one he would have died if he had had gunk in his canteen? Well, I don 't see why we must say so. In one death, C was disgusted by the gunk in his canteen, in the other he was shocked by the emptiness of his canteen. Certainly these death are going to feel different from the inside out; in one C will be fixated on the gunk in his canteen and in another he will be fixated on the hole in his canteen. As such, we can distinguish them. Nothing forces us to call them the same death (and there not; one can happen without the other!). So this is a situation with the same ethics as the other one.

Well, let's find a situation with a different ethics. Suppose A does nothing to C's water, but he does screw the lid tight. C has no means of getting to the water within. B has actually, unbeknownst to C, put a hole in the canteen so the water seeps out. But everything in C's life -from C's perspective- is the same hole or no hole. In this case it seems plausible to say that the hoe makes no difference to the individuation of C's death. He would have died the same death whatever B's actions. And, in this case, it is A that killed C.

So changing the situation can (unsurprisingly) change the ethics - or more precisely change the causal relations between events. We can invent situations in which it was A who killed C, but this situation isn't one of them (we can, in fact, invent situations in which A and B jointly kill C).

The point of loosening the definition of poison is to challenge the assertion that the difference in the circumstances of death matters. In this case you're asserting that B is not guilty as long as "everything in C's life" is the same. That's arguably impossible; simply by interacting with C be may make minute changes in what happens to C. At the other extreme we might say B did not change the fact that C won't make it home to see his wife and kids, and compared to spending time with loved ones, the details of how other things happen in C's life are immaterial, and C doesn't value them. Therefore B didn't change anything. So there's a sliding scale here. You choose to draw the line at, I guess, C noticing the difference. How isn't this arbitrary? If it is arbitrary, maybe the distinction is not important.

 

[Leoreth]

And also saved him from a different form of death. What if that was his intent? Not to kill him?

I don't think that his behavior supports this conclusion. Surely there are other actions someone who wanted to save him would have taken. Like, "Hey, I think this guy has just poisoned your water. Don't drink it".

 

[Mise]

@Gori: I can't see any other consistent way of resolving the paradox. Both "yes" and "no" seem plausible answers to your latest (very interesting) question, but since the "distinguishing cause of death" method provides consistency across all cases, I think it should be the preferred method.

Actually, come to that, I can't seen an alternative method produced in this thread at all. I've seen a lot of criticisms and questioning of Lovett's method, but no alternatives that will answer the question in a consistent, predictable manner. A lot of "hmm this doesn't seem right", but no alternative methods. I can't think of one either. So we must use Lovett's.


@Leoreth: Yeah, and "Here, have some of mine, I'm sure we can make it on half a canteen each."

 

[Mise]

Also, consider this different scenario:

A and B are both in C's apartment, while C sleeps. A and B both act independently again, without either of them knowing that they are both in the apartment and both intend to kill C. A is in C's bedroom, about to stab C, when he hears something -- it is B creeping through the hallway to C's bedroom. A gets scared and escapes through the window. B then enters the room, waits around for a few hours for some reason (maybe he's waiting for "the signal" or something) and then stabs C, killing him.

C has his life extended by a certain amount of time. If B wasn't there, A would have killed C. Yet B is undoubtedly responsible for C's death. This scenario clearly doesn't have the added complication of "I'm merely depriving C of poisoned water", but that isn't the point of the scenario. The point is that the fact that "B extended C's life for a few hours" isn't relevant. It doesn't matter that B took a bit longer to kill C than A would have: B is still responsible for C's death. If we accept that "B extended C's life for a few hours" isn't relevant, then we have to accept that, in your latest version of the desert scenario, B is still responsible for C's death.

 

[Flying Pig]

I'd say nobody actually murdered. B stole (Perhaps with some quite significant aggravating factors, although those are mitigated by the fact that the canteen was poisoned in the first place), and A committed attempted murder, but nobody actually successfully commited murder. The man died of dehydration, a natural cause.

Do bear in mind that, under your logic, nobody has ever died from being pushed off a building, or being stabbed, or being held underwater!

 

[Traitorfish]

By Ghostwriter's logic, nobody has ever murdered anybody, or ever could. So what if you die with my hands wrapped around your throat, crushing your windpipe - the actual death was one of suffocation, a natural cause!

 

[Cheezy the Wiz]

Yeah, his position reminds me of Tom Cruise's in Collateral:

Warning about slight language.


Link to video.

 

[EnglishEdward]

C needed the water to survive in the desert.

Both A and B intentionally took a step that was a crime in itself (poisoning and criminal damage respectively) to deprive him of water that would sustain his life and therefore caused his death.

They are both equally guilty.

In much the same way; if A and B had decided to ambush and shoot C, and both shot at him, but the autopsy showed that he had been killed by only one bullet; both would be guilty.

It would not even be necessary to prove which one had fired and hit him and which one had fired and missed.

Doctrines of common purpose and joint enterprise would apply in most jurisdictions.

 

[Flying Pig]

I'm not sure that holds; common purpose means that they were helping each other or egging each other on, which doesn't hold if they both try to murder him independently, I think.

 

[Leoreth]

Do bear in mind that, under your logic, nobody has ever died from being pushed off a building, or being stabbed, or being held underwater!

By Ghostwriter's logic, nobody has ever murdered anybody, or ever could. So what if you die with my hands wrapped around your throat, crushing your windpipe - the actual death was one of suffocation, a natural cause!

Newton's third law of motion has murdered more people than anyone else.