Angels and Demons

[Six Fingers]

I was thinking the other day about theology, and how christianity says that if you encounter a spirit you should try and determine whether it is good or evil. Whether or not it could actually happen is irrelevent - but it did sound suspiciously like a variation of knights and knaves, so i'm going to post it.

Lets say that a person is believed to be either an angel, or a demon in disguise. If their nature was angelic then they could tell only the truth because to do otherwise would be against God. If their nature was demonic then they could tell either truth or a lie depending on the situation. What question(s) should be asked to determine its true nature?

Knights and knaves, as I understand, operates under absolute conditions. Knights always tell the truth. Knaves always lie. But is it possible to determine the nature of something that only tells the truth sometimes?

[++$_]

Spoiler:

If the demon is allowed to say anything whatsoever then there is no way to tell the difference between an angel and a demon, because the demon can simply ask itself the question "What would an angel say in this situation?" and then say it.

However, if the demon is restricted to making either true statements or false statements and answering yes/no questions with yes or no, then you may be able to trap it. For example, ask "Are you a demon answering this question truthfully?" If the demon decides to answer truthfully, then it says "Yes." If it decides to answer falsely, then it again has to say "Yes." An angel, of course, says "No" without any trouble, but a demon cannot say this either truthfully or falsely.

In any case, I'm told that a more reliable test is to see if it can consume a holy wafer.

[Another]

Spoiler:

For example, ask "Are you a demon answering this question truthfully?" If the demon decides to answer truthfully, then it says "Yes." If it decides to answer falsely, then it again has to say "Yes."

That is a question that exploits backwards in time recursion through its own answer. I think that it directly borders both tricky questions and limits of first-order logic like "a set of all non self containing sets". If you are formally allowed to ask such questions then you are also allowed to ask "Will you answer 'no' to this question?" Do you see a problem if such a question is presented to an angel who is obliged to give a truthful "yes/no" answer?

Requirement for a "yes/no" answer to be either 100% true or 100% false and nothing in-between can sometimes be mathematically impossible to fulfill. Or you can exploit[hack] such a character to do anything for you with a carefully crafted question that leaves only one narrow path that isn't logically contradictory.

[Zalzidrax]

I wonder if there's a question the angel can answer straightaway but the demon would have to think a bit to figure out the answer that would match the angel's.

[Dark Avorian]

Well...um...ask it to sing a series of praise songs to God...

[0rm]

Well...um...ask it to sing a series of praise songs to God...

To which a Demon would sing, since their response is contextual.

Seems to me like it's adding extra depth to the Knights and Knaves problem. The trick here (I think) is to find a line of questioning that would lead to inconsistencies with a Demon and no inconsistencies with an Angel.

[t1mm01994]

Problem with this problem is, there is no way to exclude that Demons always speak the truth too, in which case you'll never find out.

[Cithoge]

Problem with this problem is, there is no way to exclude that Demons always speak the truth too, in which case you'll never find out.

But they have the option of lying, whereas the angels don't. If somehow you can use this do differentiate between them...

Perhaps ask a question whose only non-paradoxical answer is a lie: if the spirit's head explodes, it was an angel...

[t1mm01994]

Witchhunt in the middleages, but then for spirits? If it dies, it wasn't a demon, if it doesn't die, we'll have to kill it? Doesn't seem like a good idea to me... You might as well kill him right away, as that's what you're going to do anyhow.
And it hasn't been said how angels take paradoxes, or how demons take them...
There hasn't been a thing said about their knowledge, so I think we should let them both be omniscient.
But, if you ask the spirit a paradox, what is "the truth" and what is a lie? If I ask you "Is the next thing you say a lie?" what would be the 'truthful' answer?
I don't think you can differentiate between the two sorts of spirits.

[Cosmologicon]

there is no way to exclude that Demons always speak the truth too, in which case you'll never find out.

Uh, yes there is. You just ask "are you a Demon?"

[t1mm01994]

Let me rephrase that: There's no way you can exclude that Demons always give the same answer as Angels would do.
That way, it's true, isn't it?

[Turtlewing]

It's not what I'd call a formal solution but well:

Spoiler:

You could ask it to recite the exact digets of pi. If it's an angel it'll be stuck answering forever, but if it's a demon you'll eventually reach a point where convincing you it's an angel isn't worth the (infinate) time required to answer your question incognito, and abandon it's disguise. If you're lucky the demon is impatiant and this will happen before you die of old age.

[t1mm01994]

It's not what I'd call a formal solution but well:

Spoiler:

You could ask it to recite the exact digets of pi. If it's an angel it'll be stuck answering forever, but if it's a demon you'll eventually reach a point where convincing you it's an angel isn't worth the (infinate) time required to answer your question incognito, and abandon it's disguise. If you're lucky the demon is impatiant and this will happen before you die of old age.

Spoiler:

But will you stand there, listening forever? I guess not. The devil will at least give it a shot, and starts reciting. Where will you lay the border? Where will he lay the border? I don't think this'll work...

[Vesuvius]

As a protestant Christian myself (protestant as in the denomination, it's not as if I'm Christian but unhappy about it), the official test is to determine whether what it says is in line with what the bible says. If it is an angel, it won't say anything different - if it's a demon, and it's giving good advice, so be it. You still have to confirm your correct interpretation, with a minister for preference, but the bible comes first.

At any rate, angels are messengers - as I understand it, you're unlikely to see one until the end times now we have the revelation of God in Jesus in the bible.


However, that's not the scenario here - in this entirely hypothetical situation, there's just truth-tellers and mixed responses. I think the demon would go on reciting decimals of pi to infinity, or at least until you die. That's a life wasted, so it's happy. It's not like it's running out of time.

I'd say that even if you did lay on the restrictions of yes or no answers and complete truths, then the demon would still say whatever the angel would. They're given to cheating.

[jendral_hxr]

At least this reminds me of this:
http://fora.xkcd.com/viewtopic.php?f=7&t=3971&hilit=always+tell+the+truth+stab+tricky+question

Angels kindly answer your questions, Demons stab you! (they stab even harder if you ask tricky question)

[Turtlewing]

It's not what I'd call a formal solution but well:

Spoiler:

You could ask it to recite the exact digets of pi. If it's an angel it'll be stuck answering forever, but if it's a demon you'll eventually reach a point where convincing you it's an angel isn't worth the (infinate) time required to answer your question incognito, and abandon it's disguise. If you're lucky the demon is impatiant and this will happen before you die of old age.

Spoiler:

But will you stand there, listening forever? I guess not. The devil will at least give it a shot, and starts reciting. Where will you lay the border? Where will he lay the border? I don't think this'll work...

Spoiler:

No, I'd wander off, but if I ever see that spirit again and it's not reciting pi I'd know it's a demon. alternatively I could build a roadside Attraction: "come see the spirit that recites pi" and charge admission.

[graatz]

Spoiler:

You could ask a long series of subjective questions (do you like ice cream?), record the answers, and then ask it to meet you again in, say, 20 years. Ask the same questions and see if the answers match. The demon probably won't bother to remember its answers and is bound to give a contradictory one the second time through. Of course, I suppose this is also assuming that the angel's tastes don't change in that time (I think this is a pretty reasonable assumption, though. Would an angel suddenly acquire a taste for ice cream?)

[undecim]

Spoiler:

You could ask a long series of subjective questions (do you like ice cream?), record the answers, and then ask it to meet you again in, say, 20 years. Ask the same questions and see if the answers match. The demon probably won't bother to remember its answers and is bound to give a contradictory one the second time through. Of course, I suppose this is also assuming that the angel's tastes don't change in that time (I think this is a pretty reasonable assumption, though. Would an angel suddenly acquire a taste for ice cream?)

Spoiler:

Why does a demon or angel have human-like memory?

And what's to say that the a demon won't write it down, or simply tell the truth?

[SammyIAm]

Spoiler:

You could ask a long series of subjective questions (do you like ice cream?), record the answers, and then ask it to meet you again in, say, 20 years. Ask the same questions and see if the answers match. The demon probably won't bother to remember its answers and is bound to give a contradictory one the second time through. Of course, I suppose this is also assuming that the angel's tastes don't change in that time (I think this is a pretty reasonable assumption, though. Would an angel suddenly acquire a taste for ice cream?)

Spoiler:

Even that assumes that the demon would somehow change its answers in that time. I mean, if it just answered the way the angel would the first time; what's to stop it from once again answering the same away the angel would the second time?

Personally, I don't think there is a solution without applying some additional rule to the demon. Something like, "demons can't speak the name of God" or "demons get bored really easily and don't like math".

[t1mm01994]

Spoiler:

...

Spoiler:

Even that assumes that the demon would somehow change its answers in that time. I mean, if it just answered the way the angel would the first time; what's to stop it from once again answering the same away the angel would the second time?

Personally, I don't think there is a solution without applying some additional rule to the demon. Something like, "demons can't speak the name of God" or "demons get bored really easily and don't like math".

Spoiler:

I agree, and that additional rule would create an obvious question to ask, so kill the fun.

It's not what I'd call a formal solution but well:

Spoiler:

You could ask it to recite the exact digets of pi. If it's an angel it'll be stuck answering forever, but if it's a demon you'll eventually reach a point where convincing you it's an angel isn't worth the (infinate) time required to answer your question incognito, and abandon it's disguise. If you're lucky the demon is impatiant and this will happen before you die of old age.

Spoiler:

But will you stand there, listening forever? I guess not. The devil will at least give it a shot, and starts reciting. Where will you lay the border? Where will he lay the border? I don't think this'll work...

Spoiler:

No, I'd wander off, but if I ever see that spirit again and it's not reciting pi I'd know it's a demon. alternatively I could build a roadside Attraction: "come see the spirit that recites pi" and charge admission.

That made me lol though.

Spoiler:

Let's do that. Devils would spoil it, because you earn money. Angels would have no choice but to continue. Make sure to somehow lock the spirit first, it might fade!

[HonoreDB]

Edit: Spoiler'd.

Spoiler:

Combine the exploit tactic and the paradox tactic.

Present these questions simultaneously.

Question 1: Is your answer to Question 2 different from your answer to this one (counting all affirmative answers such as "yes" and "yeah" as the same and all negative answers as the same)?

Question 2: Is God great?

Consider the plight of an angel asked these questions. If it answers "yes" to Question 1, it must answer differently for Question 2. If it answers "no" to Question 1, it must answer the same for Question 2. Either way, it is compelled to answer "No" to Question 2. But in doing so, it renounces God and by definition becomes a demon.

So any being that answers the question at all must be a demon. An angel will either find it impossible to answer, or become a demon in the answering (so don't try this at home).

[Turtlewing]

Combine the exploit tactic and the paradox tactic.

Present these questions simultaneously.

Question 1: Is your answer to Question 2 different from your answer to this one (counting all affirmative answers such as "yes" and "yeah" as the same and all negative answers as the same)?

Question 2: Is God great?

Consider the plight of an angel asked these questions. If it answers "yes" to Question 1, it must answer differently for Question 2. If it answers "no" to Question 1, it must answer the same for Question 2. Either way, it is compelled to answer "No" to Question 2. But in doing so, it renounces God and by definition becomes a demon.

So any being that answers the question at all must be a demon. An angel will either find it impossible to answer, or become a demon in the answering (so don't try this at home).

either I'm misreading something or:

Spoiler:

Question one: "I don't know, you haven't asked it yet", Question 2: "yes"

[HonoreDB]

either I'm misreading something or:

Spoiler:

Question one: "I don't know, you haven't asked it yet", Question 2: "yes"

You missed the word "simultaneously". Assume the questions are side by side on a piece of paper, or verbally smooshed into one with a phrase like "What are your answers to the questions..."

[error1954]

Umm Holy Water anyone?
The angles won't be affected however something would happen to the demons.
This is the only logical way out of it. I don't think you could ask a series of questions
that would separate demons from angles.

[Patashu]

Obviously a demon isn't going to want to mimic an angel perfectly forever, because that means it isn't getting up to demony business. Make it look to the spirit as though you're naive and seeking money/power/fortune/whatever, and if it tries to take advantage of the situation to corrupt/gain for itself you know you've got a demon.

[Turtlewing]

either I'm misreading something or:

Spoiler:

Question one: "I don't know, you haven't asked it yet", Question 2: "yes"

You missed the word "simultaneously". Assume the questions are side by side on a piece of paper, or verbally smooshed into one with a phrase like "What are your answers to the questions..."

Then you get:

Spoiler:

Question 1: "That question is a contradiction", "whait, What?", "i plead the 5th", "I can't answer that", etc. Question 2: "yes"

It would work if they had to answer yes/no, but with neutral or free form answers aloud you can't force that sort of contradiction.

[graatz]

Spoiler:

You could ask a long series of subjective questions (do you like ice cream?), record the answers, and then ask it to meet you again in, say, 20 years. Ask the same questions and see if the answers match. The demon probably won't bother to remember its answers and is bound to give a contradictory one the second time through. Of course, I suppose this is also assuming that the angel's tastes don't change in that time (I think this is a pretty reasonable assumption, though. Would an angel suddenly acquire a taste for ice cream?)

Spoiler:

Why does a demon or angel have human-like memory?

And what's to say that the a demon won't write it down, or simply tell the truth?

Spoiler:

True, I first do have to assume that demons don't have some kind of perfect memory. But assuming that they can't instantly recall something they weren't specifically trying to remember, this solution ought to work. Put yourself in the shoes of a demon being asked a question like "do you like ice cream?" What do you do? As I see it, there are three options:

1) Answer truthfully, because there's no way that the asker can determine that I'm the demon through this question.
2) Try to determine if there's a "right" way for an angel to actually answer this question. Do all angels like ice cream? Does the asker somehow know this?
3) Know that there's no "right" way for an angel to answer, but assume that the asker believes there to be. Maybe the asker believes that all angels eat ice cream?

My guess is that the demon isn't likely to use option (1) because it has to convince you that it's actually an angel and wouldn't take that chance. So now it has to decide between (2) and (3), and then actually consider what the "right" answer is, or what the asker expects the "right" answer to be.

Now if I as the asker go through several questions and secretly record the answers, all I have to do is wait a very long time and re-ask the questions. The demon will then realize the true nature of the questions and be faced with the dilemma of remembering the reasoning it used to determine an answer.

An angel, on the other hand, only has one option: answer truthfully. An angel won't be faced with the same dilemma.

[graatz]

It would work if they had to answer yes/no, but with neutral or free form answers aloud you can't force that sort of contradiction.

But not answering is also a form of an answer. If not answering is permitted (so that the angel can still be truthful) then the demon also doesn't answer, knowing the plight that the angel would face. If a yes or no answer is explicitly required, then you've just forced the being in question to be a demon.

[t1mm01994]

So, you know it's a demon. So, what you wanna do? Kill it.
Couldn't you just have killed it right away? Would have saved you hella (no pun intended) lot of time if you did that... Or else you're stuck with a demon... Good luck with that.
When I see a spirit, I'm going to disobey the Bible, and run. Run as hard as I can... Since there's no way to determine the nature of a spirit, without having killed it, or having it turned into a demon.

[Eebster the Great]

Doesn't this puzzle demonstrate that demons are much more powerful than angels? They can answer however they want!

However, couldn't you simply pose questions that a demon won't know the answer to? Assuming demons aren't all-knowing, and assuming angels can always answer your question truthfully, ask things like, "What number am I thinking of?" If the spirit correctly guesses "24125125," it is probably an angel.

[t1mm01994]

Spoiler:

...

Spoiler:

Even that assumes that the demon would somehow change its answers in that time. I mean, if it just answered the way the angel would the first time; what's to stop it from once again answering the same away the angel would the second time?

Personally, I don't think there is a solution without applying some additional rule to the demon. Something like, "demons can't speak the name of God" or "demons get bored really easily and don't like math".

I agree, and that additional rule would create an obvious question to ask, so kill the fun.

Additional rules create obvious questions and are no fun

[oscarlevin]

If we add the assumption that the two will answer any yes/no with either a yes or no (if they can), then you could ask the following single question to either character:

Spoiler:

"If I asked your friend there whether he was an angel, would he answer yes?" If you addressed the demon, he would either say yes (if he wished to tell the truth) or no (if he wished to lie). On the other hand, if you asked the angel, he could not answer truthfully, so would remain silent. Admittedly, we did have to add a rather strict assumption, but without something along those lines, I'm not sure there is a (logical) solution.

[Arancaytar]

Combine the exploit tactic and the paradox tactic.

Present these questions simultaneously.

Question 1: Is your answer to Question 2 different from your answer to this one (counting all affirmative answers such as "yes" and "yeah" as the same and all negative answers as the same)?

Question 2: Is God great?

Consider the plight of an angel asked these questions. If it answers "yes" to Question 1, it must answer differently for Question 2. If it answers "no" to Question 1, it must answer the same for Question 2. Either way, it is compelled to answer "No" to Question 2. But in doing so, it renounces God and by definition becomes a demon.

So any being that answers the question at all must be a demon. An angel will either find it impossible to answer, or become a demon in the answering (so don't try this at home).

either I'm misreading something or:

Spoiler:

Question one: "I don't know, you haven't asked it yet", Question 2: "yes"

It also assumes they don't have precognition.

[gregorwren]

Spoiler:

However, if the demon is restricted to making either true statements or false statements and answering yes/no questions with yes or no, then you may be able to trap it. For example, ask "Are you a demon answering this question truthfully?" If the demon decides to answer truthfully, then it says "Yes." If it decides to answer falsely, then it again has to say "Yes." An angel, of course, says "No" without any trouble, but a demon cannot say this either truthfully or falsely.

Spoiler:

It could easily still lie to that question. Anything with, "Are you a demon" in it will get an automatic no response.

[W_A]

Maybe you could bring in some theoretical anti-demon, that would always say the opposite of whatever a demon would say in that situation, no matter what. I'm not sure how that would help, just throwing out ideas.

Bring in as in say "what would an anti-demon say in blahblahblah case," not actually bring one in.

[ircmaxell]

Simple:

Spoiler:

Say

"By lying on this next question, you will agree to pledge your undying allegiance to me and do my bidding".

"Are you a demon?"

If they reply "Yes", you know they are a demon.
If they don't reply at all, you know that they are a demon.

If they reply "No", then follow up with the following:

"Tell me that my truthful age is 550 years old"...

If they refuse, or give your correct age, they are an Angel since they are incapable of lying. If they tell you that you are they age, they must be a demon since they must now do your bidding. Have fun with your new pet demon...

Idea from: http://xkcd.com/501/

[undecim]

Simple:

Spoiler:

Say

"By lying on this next question, you will agree to pledge your undying allegiance to me and do my bidding".

"Are you a demon?"

If they reply "Yes", you know they are a demon.
If they don't reply at all, you know that they are a demon.

If they reply "No", then follow up with the following:

"Tell me that my truthful age is 550 years old"...

If they refuse, or give your correct age, they are an Angel since they are incapable of lying. If they tell you that you are they age, they must be a demon since they must now do your bidding. Have fun with your new pet demon...

Idea from: http://xkcd.com/501/

Spoiler:

Assuming that you can make that a binding agreement. You would have to make them sign a contract or something. But humans can easily break simple written contracts, so what prevents a demon from doing the same?

[bobleboffon3]

Spoiler:

You can find out if he's a demon easily with a simple question (2 part question) :
Are you an angel or are you lying to this question?

If he's an angel, he tells the truth, and the first part is "yes", second part is "no".
Yes or no = yes.
An angel would anwser "Yes"

If he's a demon, he can lie or tell the truth.
If he lies :
First part = no ( he's not an angel ), second part = yes ( he's lying )
No or yes = yes.
But he's lying, so he'll answer "no".

If he's honest :
FIrst part = no ( he's not an angel ), second part = no ( he's not lying ).
no or no = no.
And he's honest, so he'll answer "no".

An angel will always answer yes.
A demon, honest or lying, will always answer no.

[oscarlevin]

Spoiler:

You can find out if he's a demon easily with a simple question (2 part question) :
Are you an angel or are you lying to this question?

If he's an angel, he tells the truth, and the first part is "yes", second part is "no".
Yes or no = yes.
An angel would anwser "Yes"

If he's a demon, he can lie or tell the truth.
If he lies :
First part = no ( he's not an angel ), second part = yes ( he's lying )
No or yes = yes.
But he's lying, so he'll answer "no".

If he's honest :
FIrst part = no ( he's not an angel ), second part = no ( he's not lying ).
no or no = no.
And he's honest, so he'll answer "no".

An angel will always answer yes.
A demon, honest or lying, will always answer no.

Spoiler:

I don't think this works (although it is a very nice attempt). The problem is that your question is not really a question at all, and as such neither being would answer it.

Consider the statement, "Either I am the Pope, or this sentence is false." Now I am not the Pope, and yet, as soon as I write the previous sentence, I must be him. For either the sentence is true or false. If it is true, then either I am the Pope, or the sentence is false, or both. But the sentence is not false if it is true, so I am the Pope. On the other hand, if the sentence is false, then I must both not be the Pope and the sentence must be true. But this is impossible, since we are assuming the sentence is false. Contradiction, so in fact the sentence is true, and as such, I am the Pope.

So if I said that I am either the pope or am lying, would you say I am telling the truth or lying? I think you should say that I am doing neither -- I'm speaking gibberish. If we assume that both the angel and the demon can only tell the truth or lie (and not speak gibberish, or use any other part of speech for the matter) then I guess the demon would remain silent when asked your question. I'm just not convinced that the angel would answer either. Could the Pope utter my sentence and have it be true or false? Seems like a problem. The exact same string of symbols sometimes being a proper sentence and sometimes being gibberish, depending on who types them? Troubling.

[bobleboffon3]

Spoiler:

So if I said that I am either the pope or am lying, would you say I am telling the truth or lying? I think you should say that I am doing neither -- I'm speaking gibberish. If we assume that both the angel and the demon can only tell the truth or lie (and not speak gibberish, or use any other part of speech for the matter) then I guess the demon would remain silent when asked your question. I'm just not convinced that the angel would answer either. Could the Pope utter my sentence and have it be true or false? Seems like a problem. The exact same string of symbols sometimes being a proper sentence and sometimes being gibberish, depending on who types them? Troubling.

Spoiler:

I understand your point ( this kind of metaquestion gets tricky sometime ) but the point where we differs in our argumentation, is that you suppose the demon is allowed to "speak gibberish" or "remain silent" when asked a question.

From the original poster, tho, we can find out that

"If their nature was angelic then they could tell only the truth because to do otherwise would be against God. If their nature was demonic then they could tell either truth or a lie depending on the situation."

This changes everything. If the devil was allowed to talk gibberish, answer random words without even listening the question, or even remain silent to a valid question, then my question would not work. But the problem clearly states that the demon can either :
-Tells the truth
or
-Lie
Obviously, he could not do any of those if I asked him a question such as "Will you answer "no" to this question"? This question lead to a contradiction, no matter what you answer. So an honest/liar entity could never answer it. Of course a "random" entity could totally answer "yes" or "no" at will, but not only it would not make sense, would only lead to a contradiction/paradox... but it's also not the kind of entity we're playing with : He's only allowed to tell the truth or lie.

With my question, if he tells the truth, I know he's a demon, if he lies, I know he's a demon. If he would answer randomly/talk gibberish, I wouldn't know who he was, but in the situation we're talking about, he's not supposed to be allowed to do this.

I've wrote similar solution to that other "princess" problems, and someone said a similar reply, about "answering randomly"...
But if the demon is allowed to answers randomly, NO solution at all would work.
It's easy to figure it out...
You want, with your question, to be able to figure out if he's a demon or an angel. So you must ask a question where the answer X would say he's an angel, and the answer Y would say he's a demon, lying or not. But if the demon can just disregard truth/lies and answer randomly X anyway, no question will work at all.