## Angels and Demons

A forum for good logic/math puzzles.

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oscarlevin
Posts: 5
Joined: Mon May 24, 2010 3:31 pm UTC

### Re: Angels and Demons

bobleboffon3 wrote:
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.

Spoiler:
I guess I was not being clear. I am well aware that the demon can not answer gibberish. But just as you say that the demon cannot answer "Will you answer 'no' to this question?" so can he not answer your question.

Perhaps our disagreement stems from some dispute on the nature of lying. I am assuming that to lie is to make a statement that is false. In answering a question, "Is P?" where P is some statement, with a reply of "yes," I claim that this is equivalent to making the statement P. A reply of "no" would be equivalent to making the statement NOT P. You claim that the demon cannot make the statement "I am either an angel or this statement is false," because that is gibberish. I agree completely! That is why I don't think he can make the negation of that statement. Surely P is gibberish if and only if NOT P is gibberish.

Incidentally, I'd be curious to hear what you think of my earlier solution to the puzzle: asking either character, "if I ask your companion there whether he is an angel, will he say yes?"

bobleboffon3
Posts: 38
Joined: Fri Jul 16, 2010 7:35 am UTC

### Re: Angels and Demons

oscarlevin wrote:
Spoiler:
Incidentally, I'd be curious to hear what you think of my earlier solution to the puzzle: asking either character, "if I ask your companion there whether he is an angel, will he say yes?"

Spoiler:
Well the only problem I see with this solution, is that nowhere in the problem ( unless I missed it ) there's any mention of a "companion"! I've read a lot of similar puzzles including two, and not just one companion, I assume you've read some of them too and thought this one was the same!

For the sake of argumentation, let's say there's 2 companions.
Asking this to the demon will give you, as you said, a yes/no answer, depending on the demon's mood.

Asking this to the angel... that's where it gets complicated, and we might not have enough information to know for sure what would happen.

First of all, those demons/angels, do they know everything? If they know everything, then the angel could actually answer you, because he'd know what the demon would say.

If they don't know everything... Well, now it's personnal interpretation... You could even ask them "What is 37 + 129" and they could remain silent, if they're not very good at math... Or any question at all really.

To find out who, out of an angel and a "lie/tells the truth" demon, is an entity, you need to include, in your question, some complex logic.
I'd sure like to be proven wrong, but I don't think there's any simple question to ask, that will work.

I'm not 100% sure about my proof... but here we go.

-The angel tells the truth
-The demon can lie or tell the truth, at will
-If a demon choose to tell the truth, his answer will be the same answer an angel would give, UNLESS the question is about himself
(The angel and the honest demon would both answer "4" if you ask them "What is 2 + 2?" but they would not answer the same thing if you ask them "Are you a demon?".

That's the first "key" to find the question. Because that question is actually two questions, not just one. The "you" changes everything.

Let's say there's only one angel and one demon on earth.
The angel name is God, the demon name is Lucifer. ( how original! )

If you ask them "Are you a demon", you're not asking them the exact same question.
You're actually asking to god "Is god a demon?" and you're asking to Lucifer "Is Lucifer a demon?".

In this case, the "you" changes the answer to the question, depending on who you're asking it to ( as long as they're telling the truth ).

God will say "no" and Lucifer will say "Yes", because the question doesn't have the same truth value if you ask them both.

That's why I use this "you" in my question ( in my first post ) "Are you an angel or are you lying to this question?".

It looks like I'm asking them the same question, so you'd wonder how this will help me if the demon decide to tell the truth ( the angel always tells the truth )...
But the question I'm actually asking to the angel, God, is :
"Is God an angel or are you lying to this question?".
and the question I'm asking to the demon, Lucifer, is :
"Is Lucifer an angel or are you lying to this question?".

The question I pronounce is the same, but the question they receive and perceive is not the same.

God will tell "yes" to this question no matter what ( he's an angel ), And Lucifer will answer "no" to this question no matter what.
If he's lying, "no" or "yes" = yes, he lies so it's a "no"
If he's honest, "no" or "no" = no, he's honest so it's stay a "no".

I don't think it would be possible to do it with a simple question ( no "or" or "and", i.e. a single part question ) because there's 3 different possibilities, and a simple yes/no question can only find out between 2 possibilities.

There's always one thing that doesn't work right if you try to find it with a simple question.
it's easy to find a simple question that would sort apart an honest demon and an honest angel ( Are you a demon? )... but it wouldn't work if you ask it to a lying demon ( he would just say "no", like the honest angel ).

It's also easy to find a simple question that would always get the same answer from an honest OR lying demon ( "are you lying?" they would both say no ), but the angel would answer the same.

So you would need to find a simple question where
-The honest demon and the lying demon answer the same
AND
-It must be the opposite answer the angel would say

If the honest demon doesn't say the same thing than the honest angel, then the question must concern their identity ( are you a demon? ) or personnality ( do you lie sometimes? ), but in both cases, the lying demon would not say the same thing the honest demon would, UNLESS the question has 2 parts.

oscarlevin
Posts: 5
Joined: Mon May 24, 2010 3:31 pm UTC

### Re: Angels and Demons

bobleboffon3 wrote:
Spoiler:
So you would need to find a simple question where
-The honest demon and the lying demon answer the same
AND
-It must be the opposite answer the angel would say

If the honest demon doesn't say the same thing than the honest angel, then the question must concern their identity ( are you a demon? ) or personnality ( do you lie sometimes? ), but in both cases, the lying demon would not say the same thing the honest demon would, UNLESS the question has 2 parts.

Spoiler:
I see no problems with your proof, except that you discount the possibility that there might be more than two possible responses. Thus my idea to allow the honest demon and lying demon to answer differently, and have the angel answer a third way ("I don't know"). But you are right that in doing so we would need to make an extra assumption (that then angel does not know the demon's current mood). Oh, and you are right, I must have imagined that both angel and demon were present when you asked the question. Although even if they weren't, you could ask something like, "If I were to ask an angel or demon not of the same type as you..."

Now I am wondering whether you can extend your proof to show that there is no question which can distinguish them. My idea is this: either in asking a two part question, the demon could be truthful on one part and lie on the other, in which case a two part question is no better than a one part question for practical reasons, or the two parts just give the question the appearance of complexity, but it is really a simple question, in which case your previous argument shows it will not work. Your proposed solution requires the demon to answer "no" because if he answered "yes" he would be making a self-contradictory statement. Either making such a self-contradictory statement is a lie, or is meaningless. But the negation of a meaningful statement must still be meaningful, so it cannot be the latter.

That said, given the loose logic usually allowed in these liar/truthteller puzzles, I'm starting to think your solution is "correct."

TheFactoryReject
Posts: 3
Joined: Tue Aug 24, 2010 8:29 pm UTC

### Re: Angels and Demons

Spoiler:
If the answer is always capable of changing without your knowing then this question is unsolveable. unless demons for some reason change their answer every so often and you've got the good old time to wait for that to happen it is impossible to know. Just throw holy water at it, if it burns-demon, if it sings and starts having a shower-angel. Alternatively, walk away. Seeing as you have time to ask questions, neither one is wanting anything from you so it is of no relevance.

voidistant
Posts: 4
Joined: Wed Sep 15, 2010 5:01 pm UTC

### Re: Angels and Demons

LOL... all you need is one question to determine who the demon is. Ask both of them if they accept Jesus Christ as their personal savior, assuming Christianity is the default religion in question. Demons deny Christ, and even if he is a liar he cannot answer yes. Angels on the other hand rejoiced at Christ's arrival, per the Bible.

This only holds true for angels and demons assuming Christianity is the default religion. If this were say, Islam or another random religion with angels and demons, then ?

Corka
Posts: 17
Joined: Wed Sep 15, 2010 2:16 am UTC

### Re: Angels and Demons

Unless you have some magical way to automatically detect a lie, then you will never be able to tell whether the Demon is really a Demon so long as it answers exactly like the Angel would in the same situation. You can ask them both if they love Jesus, but would this really phase the demon if it knew it was lying? The problem is not solvable in the current form.

Xami
Posts: 74
Joined: Tue Sep 29, 2009 8:29 pm UTC

### Re: Angels and Demons

"Hey, could you forgive me for this?"
Then punch it mercilessly.

EricH
Posts: 259
Joined: Tue May 15, 2007 3:41 am UTC
Location: Maryland

### Re: Angels and Demons

voidistant wrote:LOL... all you need is one question to determine who the demon is. Ask both of them if they accept Jesus Christ as their personal savior, assuming Christianity is the default religion in question. Demons deny Christ, and even if he is a liar he cannot answer yes. Angels on the other hand rejoiced at Christ's arrival, per the Bible.

Angels rejoiced, but not because Jesus was their personal savior--angels rejoiced at the salvation of mankind. How could an angel be saved, since they're already without sin? A Christian angel and demon would both answer "No."
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the_man_with_plan
Posts: 1
Joined: Mon Oct 03, 2011 12:33 am UTC

### Re: Angels and Demons

"Hey, could you forgive me for this?"
Then punch it mercilessly.

Spoiler:
If it is a demon, it can just lie and "forgive" you, then, once you've decided it must be an angel, get revenge. or, it could just forgive you.
one thing that you've all missed, and this is important for the pi question, is that demons tend to be immortal, meaning the demons can just recite the digits of pi until you die of old age, then go about it's business.

tomtom2357
Posts: 563
Joined: Tue Jul 27, 2010 8:48 am UTC

### Re: Angels and Demons

Guys, you are assuming here that the demon can't give a paradoxical answer. Your argument works if this is true, but if it is false there is no way to tell between them because the demon could just give the same answer as the angel in every situation. However I do like the quote pi argument, as long as the demon is not omniscient and can tell when you will come back.
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

Posts: 44
Joined: Sun May 01, 2011 5:18 am UTC

### Re: Angels and Demons

Just say something where both a yes and a no lead to a paradox or where it can't be answered truthfully. "Is your answer to this question a negative?"
A Demon will say yes or no.
A Angel will say something.
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Qaanol
The Cheshirest Catamount
Posts: 3069
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### Re: Angels and Demons

Vesuvius wrote: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.

Excellent. So we ask, “Do you support mass murder of innocent children?” If it says “No” then it is disagreeing with God and the Bible, and thus must be a demon. If it says “Yes”, then it’s a horrible, atrocious being that I want nothing to do with.
wee free kings

tomtom2357
Posts: 563
Joined: Tue Jul 27, 2010 8:48 am UTC

### Re: Angels and Demons

Qaanol wrote:
Vesuvius wrote: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.

Excellent. So we ask, “Do you support mass murder of innocent children?” If it says “No” then it is disagreeing with God and the Bible, and thus must be a demon. If it says “Yes”, then it’s a horrible, atrocious being that I want nothing to do with.

I don't know of anywhere in the bible that supports mass murder of innocent children. Also the 6th commandment is thou shalt not murder, so the bible definitely doesn't support murder.
I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.

Qaanol
The Cheshirest Catamount
Posts: 3069
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### Re: Angels and Demons

tomtom2357 wrote:I don't know of anywhere in the bible that supports mass murder of innocent children. Also the 6th commandment is thou shalt not murder, so the bible definitely doesn't support murder.

Allow me to provide curative balm for your ignorance:
Spoiler:
Exodus 12:29
Numbers 31:17
Deuteronomy 2:33-34
Deuteronomy 3:2-6
1 Samuel 15:3,7-8
2 Samuel 12:15-18
2 Kings 2:23-24
Isaiah 13:15-18
Isaiah 14:21-22
Jeremiah 13:14
Lamentations 4:10-11
Ezekiel 9:4-6
Revelation 2:22-23
Psalms 137:8-9
Hosea 13:16
Deuteronomy 28:53-57
Jeremiah 19:6-9
Ezekiel 5:10, 17
2 Kings 15:16

If you only look up one of those citations, make it Revelation 2:22-23, for that is represented as the word of Jesus himself. If you want to see all of them in one place, go to this page, starting from the line “Would God kill or order the killing of innocent children?”

Here is another page listing some biblical atrocities committed by God, by God’s followers under his direction, or prophesied as God’s will. Infant murder is only the beginning. God also has a penchant for ordering mass rape and indiscriminate slaughter. It’s interesting to note that, according to the bible, God killed or approved the killing of over 2 million humans. For comparison, the total killed by Satan was only Job’s children, and that was with God’s permission.
wee free kings

Eebster the Great
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Location: Cleveland, Ohio

### Re: Angels and Demons

Qaanol wrote:It’s interesting to note that, according to the bible, God killed or approved the killing of over 2 million humans. For comparison, the total killed by Satan was only Job’s children, and that was with God’s permission.

Even aside from flooding the entire world and killing nearly 100% of its inhabitants, along with a promise to kill precisely 100% of people at some point in the future.

jestingrabbit
Factoids are just Datas that haven't grown up yet
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### Re: Angels and Demons

I don't think that this is the right place for these sorts of discussions. This question started possibly logic related, and the discussion has found its way to definite non logic puzzle territory. So, I'm locking.

If you think that there is something that hasn't been said that desperately needs to be said, pm me. -jr
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