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You stand before an omniscient being. It is either God, who always tells the truth, or the Devil, who always lies. You don't know which. Your task is to figure out whether Heaven is real. You may ask the being one yes-or-no question in English. (Coercive logic is not permitted.)

Jeff is also here. He knows all the rules in the preceding paragraph and will hear the question and answer. You hate Jeff and do not want him to know whether Heaven is real.

What do you ask?

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    $\begingroup$ What exactly is coercive logic? $\endgroup$
    – Victor Stafusa
    Commented Aug 6 at 19:26
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    $\begingroup$ @VictorStafusa An example would be "Is is true either that heaven is real, or that you will answer no to this question?" God would be unable to answer if heaven isn't real, and the devil would be unable to answer if it is. $\endgroup$
    – Nuclear Hoagie
    Commented Aug 6 at 19:56
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    $\begingroup$ @Parrotmaster I used to play a game called Afterlife where you had to build an afterlife for humankind. In that game you could decide that the afterlife has no Heaven or no Hell (actually the Devil even reminds you that making a Heaven is not necessary at all). So in this situation, if it happens that you are talking to the Devil then you cannot imply that Heaven exists. $\endgroup$
    – Cincinnatus
    Commented Aug 7 at 10:54
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    $\begingroup$ @Parrotmaster en.wikipedia.org/wiki/False_dilemma Christianity or nothing supernatural are not the only options, there are infinite possibilities $\endgroup$
    – JollyJoker
    Commented Aug 9 at 8:56
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    $\begingroup$ @Apostolos I guess every question you can't answer is likewise "flawed"? $\endgroup$
    – no comment
    Commented Sep 5 at 18:26

4 Answers 4

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The question that you would ask, if there was no Jeff out there is:

If I were to ask the opposite omniscient being about if Heaven is real, what would he say?

God would answer:

Whatever the Devil would say, which is a lie.

The Devil would answer:

The opposite of what God would answer, hence, a lie.

So:

The correct answer is the opposite of the given answer.

This works so far without Jeff and is the classic solution of the Jeff-less problem. To work around Jeff, there is a boolean operator that is handy in cryptography to add confusion:

XOR

Mix the question with something that only you and an omniscient being know:

Does my gmail password has an odd number of lowercase letters?

So what you should ask is:

If I were to ask the opposite omniscient being about if Heaven is real XOR my gmail password has an odd number of lowercase letters, what would he say?

Hence, the given answer:

Is the correct answer if your password has an odd number of lowercase letters and the opposite of the the correct answer if your password has an even number of lowercase letters.

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    $\begingroup$ ...and then, ideally, change the "something that only you and an omniscient being know" afterwards so that Jeff can't go try to work out what it was. $\endgroup$
    – Ryan M
    Commented Aug 6 at 22:34
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    $\begingroup$ My answer was similar but I tried to avoid the use of the XOR: rot13(Bs gur fgngrzragf "Lbh ner Tbq", "Urnira vf erny", "V'z jrnevat juvgr haqrecnagf", ner gurve na rira ahzore bs gehr fgngrzragf?) $\endgroup$
    – Tyler Seacrest
    Commented Aug 7 at 0:50
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    $\begingroup$ That's still essentially an XOR. $\endgroup$
    – Lucenaposition
    Commented Aug 7 at 1:58
  • $\begingroup$ To expand on Lucenaposition's comment: rot13(N KBE O vf vqragvpny gb, "Qbrf [N,O] pbagnva na bqq ahzore bs gehr fgngrzragf?"). $\endgroup$
    – Brian
    Commented Aug 7 at 14:22
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    $\begingroup$ @TylerSeacrest It is an English abbreviation for "exclusive or" and any omniscient being would understand it very clearly. $\endgroup$
    – Victor Stafusa
    Commented Aug 7 at 18:50
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You

hold firmly in your mind either the question "If I asked you whether heaven is real, would you say yes?" or the question "If I asked you whether heaven is real, would you say no?", choosing between them as randomly as you are able

and then

ask: "What is the answer to the question I was thinking about immediately before asking you this question?".

Then

if your question was the "would you say yes?" question, then -- supposing for the moment that heaven is real -- God would say yes if asked whether heaven is real and will truthfully say so, whereas the Devil would say no if asked whether heaven is real and will falsely say he'd say yes; if heaven is not real then God would say no and hence will say no, whereas the Devil would say yes and hence will say no.

But

Jeff, who unlike God and the Devil does not know what you have been thinking, will have no way to learn anything from the answer since he has no idea what question it is answering.

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  • $\begingroup$ Just barely beat me to it! $\endgroup$
    – Deusovi ♦
    Commented Aug 6 at 18:57
  • $\begingroup$ Sorry! (Second time in a few days...) $\endgroup$
    – Gareth McCaughan ♦
    Commented Aug 6 at 18:57
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    $\begingroup$ I feel this is a loophole in the question. You might as well write it on a piece of paper since "Jeff" only hears what's going on, or use sign language. $\endgroup$
    – infinitezero
    Commented Aug 8 at 13:00
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    $\begingroup$ I don't think I agree. The point is to make what's happening depend on something Jeff doesn't know but you and these omniscient beings do, or equivalently on something Jeff doesn't know but you do. You only need one bit of this "shared secret" to make the thing work, but the most obvious ways to get it all give you a lot more, so I thought it made things clearer and simpler to push the whole question into the "shared secret". $\endgroup$
    – Gareth McCaughan ♦
    Commented Aug 9 at 16:11
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    $\begingroup$ (The first thing I thought of did only use one bit of shared secret; I made the deliberate decision to do it this way instead because I thought it was neater.) $\endgroup$
    – Gareth McCaughan ♦
    Commented Aug 9 at 16:11
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You can ask:

Are you glad that the place I am thinking of exists?

If Heaven does exist, God will answer:

God is glad that heaven exists = YES

If Heaven does exist, the devil will answer:

Devil is not glad that heaven exists, but lies = YES

If Heaven does NOT exist, God will answer:

God cannot be glad that heaven exists, because it does not = NO

If Heaven does NOT exist, the devil will answer:

Devil is glad that heaven does not exist, but lies = NO

Meanwhile:

Jeff does not know of where you are thinking.

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Ask the being:

Is the boolean operation true: “Is heaven real” XOR “You are God” XOR “Is my middle name James”?

This makes use of a logical operation that helps us negate the truth of a statement. Some examples:

The operation is called "XOR". We can use it as follows:

A XOR True = NOT A
A XOR False = A

Let's start with a simple question we can build upon:

Is the statement true: “Is heaven real”?

Let A be the answer to this question. God will answer A, truthfully. The Devil will lie and answer NOT A. Since we don't know the identity of the being, whether we hear a "yes" or "no" doesn't tell us anything about Heaven.

So let's simplify the lying problem:

If God says "yes" but the Devil says "no", we don't know which is lying. This means their answer should be conditioned on their own identity. Let's add XOR "You are God" to our question.

Our boolean operation is now “Is heaven real” XOR "You are God".
- God will answer A XOR True = NOT A
- The Devil will answer (NOT A) XOR False = NOT A

The answer is unanimous. If either being says "yes", Heaven is not real. If either says "no", Heaven is real.

Unfortunately, Jeff has all the information we have, and learns whether Heaven is real. Let's take care of that:

We add a personal question into the mix. For example: "My middle name is James". Our true middle name is only known to us and the omniscient being. So if we add XOR "My middle name is James" to our equation, there are 2 possibilities:

- Our middle name IS James, which means we negate the entire equation.
- Our middle name ISN'T James, which means we interpret the answer as before.

We know our middle name, so we know if we need to flip the being's answer. Jeff doesn't know, so the answer is useless to him.

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