Is Newcomb's Paradox really a paradox

Discussion: Newcomb's problem

Equivalent problem

The paradox is similar to the prisoner's dilemma

The difference seems to be that in the prisoner's dilemma the choice of the other has not yet been made.

Newcomb's problem is no longer a paradox if one allows for the possibility of misjudgment or inaccuracy.

It is also possible that the higher being is lying.

In the other case the being corresponds (at least partially) to the Laplace demon. Because it knows what I'm doing. Anything I want to do would be irrelevant. For him, the only thing that counts is the result.

In practice, the problem does not arise because there is no Laplace demon. As soon as even a tiny bit of lie or chance goes into it, it becomes the prisoner's dilemma. The task becomes irrelevant. I have to take both boxes if I definitely want to win, otherwise I can take the one where the money is supposed to be. What's really in it doesn't seem relevant in either case. - Hutschi

Now please someone explain it to me - as if I were 4 years old ...

The supreme being seems to be kind to me and puts a million euros in box 2. Why shouldn't I then take box 1 and increase my wealth by 1000? And why should this decision move the being to remove the million from box 2?

Sure, 1000 more is relatively little, but you can buy a nice suitcase for a million of them.

So I don't quite understand the problem - why don't I just take the second box when I know that there is a million waiting for me there ??? --Derbrain 02:31, Apr 19, 2005 (CEST)


"This is exactly what the being could have foreseen and left the second box empty. After that, it would be better to only take the second box." doesn't really make sense to me. Why should it be better to only choose the second box when I assume that the being has left it empty?

This results from the paradox in the question. I tried to explain it in more detail and added the sentence. --Hutschi 08:26, Jan 6, 2006 (CET)


Where did the name "Newcomb" come from? 18:25, Feb 2, 2006 (CET)

Quote from the lemma

An omniscient being foretold how you will decide. Its reliability in making predictions is absolute. If this being foresees that you will only take the second box, it has put the million dollars in the box. On the other hand, if the creature foresees that you will take both boxes, the second box remains empty.

Ever since I first read Newcomb’s Paradox, I've been annoyed every time I come across it. It is completely incomprehensible to me how it is possible that these clothes have been discussed among serious humanities scholars for decades. This "paradox" is not such a (and therefore completely superfluous), and such a pseudo problem does not deserve to be mentioned in the series of classical paradoxes. Paradox (in the figurative sense) is at best to discuss it (what I am doing myself, however, closes the circle ...)

A paradox is characterized by internal contradictions, always under the condition that such a paradox can be derived from the (to be respected) premises. In no case can a paradox arise from negating or relativizing the premises, or at least not taking them seriously as a result.

If the task involves the action of a being with absolute predictive reliability, then the paradox, in order to be such, would have to result from the consequences of strictly observing THIS premise. If the being accordingly has the abovementioned ability, the answer to the decision question is free from any hint of doubt and free from that inner contradiction that a paradox inevitably presupposes.

You negate the given rules - and this of course leads to a completely different and therefore irrelevant configuration! - if the premise is initially applied in accordance with the rules, but in the next step it is suddenly overridden by simply changing the rules and now without worrying about the Foreknowledge of the being relates only to the FIRST decision. According to the rules, prior knowledge relates unconditionally to the decision that immediately leads to the opening of one or both boxes. And these Decision knows the essence - and that's it!

If there can't be such a fairy-tale-like being with quasi esoteric abilities (which speaks for all sorts ... * grin *), then it is just not suitable for the opposite role intended for him in a paradoxical mind game.

MfG Wilbert

-> This is not about profit, but about the question of free will. An omniscient being necessarily implies the non-existence of free will. This is actually only a paradox if one believes in omniscient beings and free will at the same time (and there are supposed to be some who do exactly that).

A paradox arises when the negation of the premises can be derived, doesn't it? (unsigned post byNinjamin (Discussion | Posts) 01:10 AM, Apr 3, 2010 (CEST))
A paradox also arises when there are two legitimate ways of arriving at the result, but the two results contradict each other. - In this paradox there are two possible types of case distinction that can be made:
1. Case distinction: Do I choose both boxes or do I just choose the 2nd box?
2. Case distinction: Is there money under both boxes or is there only money under the first box?
Both case distinctions are legitimate. But depending on which one I use, I come to a different result. Hence it is a paradox. --Eulenspiegel1 13:09, Jul 6, 2010 (CEST)

Quantum-like consideration

Both quantities may be in the box at the same time. The state is only established through the type of observation. Depending on how you measure, either one or the other result comes to light. The type of measurement is determined by the type of observer. --Hutschi 10:24, May 31, 2006 (CEST)

See the problem of the paradox from a human point of view, but why should there be no solution?

Assuming that the higher being can really make the decision and has already made it, there are three possibilities due to the rule that no wrong things can exist in reality:

1. I cannot freely decide which box I choose, because my thoughts are influenced by the entire universe and the fact whether the money is in the box affects the entire (rest of) universe.

2. The being can put the money in and not in it at the same time. (-> Schrödinger's cat) This can be described abstractly by imagining two parallel worlds which are "created" (or can be distinguished) at the point in time in which the being makes a decision from our point of view. For one of the two, I decide by the act of choosing the box.

3. There is no such thing as time and conclusions are deceptive by ourselves, which only appear like some kind of pattern

The idea of ​​several worlds in my mind leads to further expirations that all worlds already "exist" insofar as one can say so and one not only continues in the dimension of time but "jumps back and forth" between them at any point in time. Personally, I like the last option best because you can use it to explain everything, it is unimaginable and therefore the most interesting. But I'm also just a stupid student, whoever can't do anything with my solutions should rather continue to understand it as a paradox. -- 01:02, Jul 29, 2006 (CEST)

Quote by ??

-> "This is not about profit, but about the question of free will. An omniscient nature implies imperative the non-existence of free will. This is actually only paradoxical if one believes in omniscient beings and free will at the same time (and there are supposed to be some who do just that). "

Is the mentioned implication really compelling, or isn't that also a question of the respective "philosophical" point of view - just like the question of 'free will or determinism' itself? The only thing that really matters is that the being (according to the problem) can see into the future. Although it makes sense to associate this subordinate ability with a priori unchangeable (and thus calculable in advance) causal chains, I do not consider it imperative to define this as an exclusive possibility. The fact that "someone" is able to see into the future as the result of 'configurations' which are currently beyond our current knowledge and knowledge (which would ultimately still be the case if the strictly deterministic explanation of the world were correct) can also be seen independent mechanisms are based, which, for example, enable a "journey through time", which thus bridges randomly and / or will-controlled historical processes exclusively on the level of time.

With all such considerations, one is ultimately moving on the terrain of speculation, which today cannot withstand the demands of sufficient verifiability or falsifiability.

Mfg Wilbert

What's the problem?

If the player takes both boxes, he gets the smaller price because the being didn't put the bigger one in. So the player just takes the hidden box and gets the bigger one. What's the problem? 217-125-121-169 8:36 PM, Nov. 18, 2006 (CET)

It's a pseudo-problem: At the time when I assert my decision, the boxes are already stocked and cannot be changed. Regardless of how the boxes are equipped, it always applies that there is more in both together than in the second alone. So, one might conclude, it is reasonable to take both. The paradox here is that this argumentation no longer works. It doesn't work because the creature only populates the boxes after I've made my choice. By means of clairvoyance, the course of time, but not cause and effect, is twisted. The joke is that once you've made the best decision, you'll know for sure that both boxes contain money but still only take one. --Montezuma 10:48 p.m., Mar 17 2007 (CET)

I have a basic question.

Do I actually know about the being's prediction? If I know about the fact that the being has foreseen my decision and I also know how it then distributed the money into the boxes, then it is probably clear that I always take the second box. So what's the problem?

So can someone explain to me how this paradox works when I know how the being acted in the cases of its respective predictions?

Box 2 transparent or not ?!

In the English version both are "opaque"! And even through googling, I have not yet found a majority opinion. --The Hawk 15:47, Jun 22, 2007 (CEST)

opaque = uncoated!

it doesn't matter whether you see the 1st, the 2nd must always be opaque

Nonsensical paragraphs

The last four paragraphs in the "The Problem" section seem nonsensical to me ... I would honestly delete them or at least move them to a single section. The problem is defined by the fact that the "Higher Being" is firstly omniscient and its reliability is absolute and secondly it bases its action on its prediction. So it makes no sense to calculate over probabilities. And Hutschi with "Besides, the being could lie" - wonderful thing, only the "paradox" is not formulated that way. The Higher Being puts the million dollars in the second box if you only take the second box, and not when it has seen that you only take the second and it wants to annoy you ... At least in the wording like it there stands the paradox is not a paradox, because you just take the second box. Effectively it's the same as having the second box in a hole in the ground and when you say "I'll only take the second one" someone from below is secretly putting a million dollars in it.

Equivalent transformation?

If I have understood the problem correctly, it is equivalent to the following game (assuming that the existence and infallibility of the being are known to the player before making his decision): I have 2 cans again and can choose which one to take: I choose I get both € 1,000, if I choose only one I get € 1,000,000. So you choose, completely logically, only one can (in the original can 2).

Because, according to the article, all paradoxes are based on the fact that this being knows my will before I have made a decision (or before I have gained knowledge of my decision), but this itself is not relevant for the game (and in my eyes too not paradoxical), since the state of the money distribution is completely irrelevant before my choice, since I make the choice myself and also get the money myself. Something different would be, for example, if the money distribution still depends on my decision, but someone else names his choice and receives the money (which was only influenced by my decision). Another possibility would be, if I am not convinced of the existence of such a being, and should the being not exist, find nothing in the second box, but of course that is just another possibility to the chance that the being is wrong.

Happy New Year everyone;) ---

No. This is not an equivalent transformation. Because in your example, it depends on your decision how much money is in the second box. As you describe it, the money is basically only put in the second box after I refrain from taking the first box as well.
In the original, however, the money is already in the box. No matter how I choose, the being cannot reverse its decision.
See it this way:
1st case: There is nothing under the 2nd box.
If I choose both boxes now, I will get € 1000 more than if I only choose the first box.
2nd case: Under the 2nd box there are € 1 million.
If I choose both boxes now, I will get € 1000 more than if I only choose the first box.
After the task, one of the two cases is fulfilled. That means: Regardless of whether there is money under the 2nd box or not: If I choose both boxes, I will get € 1000 more.
From this point of view, it is intelligent behavior to take both boxes. Because I get a thousand dollars more from it. The being can no longer go back into the past and reverse the decision.
Many people assume that by giving up the € 1000, € 1 million will suddenly appear in the 2nd box. That's not the case. - The money is already there or it is not there.
That said, from this point of view, it makes the most sense to take both boxes. And that also makes sense if we take the clairvoyant nature into account. Because the clairvoyant being is now unable to change the boxes.
In theory, I could also ask the creature to open the boxes. Since the being can see into the future, it knows how I will decide anyway. - And if there is a million euros under the 2nd box, then I regret it and take both boxes. And if the being lifts the 2nd box and nothing is underneath, then out of spite I only take the 2nd box. Either way, the being suddenly predicted wrongly. --Eulenspiegel1 04:04, Jan. 7, 2008 (CET)
It also only depends on my decision how much money is in the second box, that guarantees me the infallibility of the essence, if I only choose box 2, it will be 1 million below that (always), but I will both boxes choose, the being would not have placed a million under the second (also always) and I only get 1000 €.
By the way, in your case distinction you have just ignored the infallibility of the essence, if you take this into account then this is as follows:
1st case: There is nothing under the second box.
Only occurs if I choose both boxes, so I get € 1000 and choose both boxes.
2nd case: Under the second box is € 1 million
Only enter if I only choose the second box, so I get € 1 million
Let's see if we can trick the creature into somehow going empty-handed, or to get more than a million €:
Go empty: I only choose the second box (only this can be empty) and find nothing in it, but this is a contradiction to the infallibility of the being, because for the second box to be empty, the being would have anticipated that I would take both boxes which I didn't do. Ergo, this case cannot occur.
Got more than € 1 million: I have to choose both boxes (there is a maximum of € 1 million in each individual box, but I want more) and find € 1 million in the second box, here too there is a contradiction to the requirement of infallibility of the essence, because there was a million euros under the second box, it foresaw that I would only take the second box, but I took both, so the essence was wrong ...
Personally, I think that the rules of the game in the article contain a mistake, or that the behavior in the game is clear, but one has problems with the infallibility of the being when it comes to predictions and that the actual paradox relates to it, although there is nothing paradoxical about that would come up ... (same author as above, only this time different IP :)) ---
I'll bring you 5 explanations that show why it is a paradox:
1) It doesn't matter when the cases occur: In both cases it makes more sense to use both boxes. In the first case it makes more sense to take both boxes and in the second case it makes more sense to take both boxes.
When exactly which case occurs does not matter, because one of the two cases will always occur. And in both cases it makes more sense to use both boxes. (The paradox here is indeed very similar to the prisoner's dilemma: Actually, it is best if I trust my partner. - Regardless of my fellow prisoner's decision, it is better to betray him. My partner is likely to be accurate the way I think - although overall it is best if both trust each other, it is immediately best if one betrays each other.)
2) Imagine I'm a person who either wants everything or nothing. Either I get € 1.001 million or I don't want any money at all. I am not satisfied with € 1000 or € 1 million. Besides, you are a good friend of mine that I trust. So I'm telling you that I don't want to get € 1000 or € 1 million, I want all or nothing. As a good friend, you look under the 2nd box while I decide: If there are € 1 million, then you recommend me to take both boxes. - And if there is no money there, then you recommend that I only take the 2nd box.
3) And no, you cannot classically outsmart the omniscient being. That is not what the paradox is about. The point is that there are two contradicting behavioral strategies by which to choose the boxes. First of all, it is the best idea to take both boxes, because there is ALWAYS more money under both boxes than just under the 2nd box. (No matter what the being has foreseen: Under both boxes together there is ALWAYS more money than just under one box.) And on the other hand, it is a better behavioral strategy to only take one box, because the being then puts more money BEFORE.
I make my decision AFTER the entity has put the money under the boxes. That means whether I trust the being or not doesn't matter. My decision can no longer change the contents of the boxes, because the money is there. That is, it doesn't matter what the being foresaw. It doesn't matter whether I trust the being or not. I know: Under the 2nd box there is € 1 million or nothing. And no matter how I decide, in 5 minutes there will be just as much money as there is now. Money can neither suddenly appear in the 2nd box, nor can money disappear there. This means that if I now start to think about it and develop a strategy for how I can get as much money as possible, it has no effect on the money in the box. (Because by changing my mind my money doesn't suddenly disappear.)
And I also know: No matter how I turn it: there is ALWAYS more money under both boxes than under one box. That means, if I only take the 2nd box, I ALWAYS get less money than what lies under both boxes together.
4) Another explanation: Imagine the same experiment, but the omniscient being has not yet looked into the future.
That means, you have 2 boxes there and you have to think about whether you only use the 2nd box or both boxes. At this point you realize: No matter how you decide: There is more money under both boxes than just one box. So it is ALWAYS better to use both boxes than just one box. (At this point the being has not yet looked into the future.)
So, after you have thought about it, suddenly the omniscient being appears and looks into the future, communicates the result to you and gives you the opportunity to reconsider your decision.
Why is now the result that has ALWAYS been the best result up to now (namely taking both boxes) suddenly no longer the best result? The being has the possibility to see into the future, but it has neither the possibility to exchange the money in the boxes, nor to change the future. - The information that the being has given you is practically useless information, since you already knew beforehand that in all possible cases it would be better to take the two boxes. - And although there are no more additional cases, on the contrary, some cases disappear, is it suddenly better to change your mind? (Assuming the being has looked into the future and has seen € 1 million under the 2nd box. Then it makes you with its statement to only take the 2nd box without the being having to lie. - Quite sensible, if that omniscient beings can't stand the candidate, but don't want to lie either.)
5) Before you insinuate with the omniscient being, you hardly have any information about the 2nd box. But that's not necessary either. Because no matter what is under the 2nd box, it is always better to take both boxes. There is not a single case in which it would be better to only take the 2nd box.
And now the omniscient being comes and looks to the future. It is important that the being only looks into the future, but cannot change the future. And because of the information that the being gives us, a case suddenly arises in which it is better to take the 2nd box. How can a case arise through the being's future vision that did not exist before? (Of course, by seeing the future of the being, probabilities can change because I get additional information. However, situations cannot still arise that did not exist before.)
Before the being looked into the future, it looked something like this:
Probability that it is better to take the 2nd box instead of the 1st box: 50%
Probability that it is better to take the 1st box instead of the 2nd box: 50%
Probability that it is better to use both boxes instead of just one box: 100%
So, with additional information you can now change the probabilities that are really greater than 0% and really less than 100%. It goes without saying. But you can never change probabilities that are 0% or 100%. (Disclaimer: OK, if the 0% thing is a non-empty zero set, its probability can grow. - But the case where before talking to the entity it was better to only take one box instead of both before the empty lot.) --Eulenspiegel1 21:36, Jan. 7, 2008 (CET)
Thank you for putting in so much effort, I think I have found a starting point where we differ in the argumentation, so I'll go through your first case as an example:
1) You write here "It doesn't matter when the cases occur", and you draw the conclusion that you should take both boxes, but that is not really correct, in fact you also assume that you are, for example, before you speak and so make your decision final, you can change your decision again, and the being does not know this decision, because then it is actually better to take both boxes, or to take up the thought that then also appears in the article, you have to start for to think the being as it has chosen.
The only problem here is: the being doesn't think, it knows. In my opinion, it knows your final decision, i.e. the one that you then also express and that therefore occurs. Therefore, it does matter when the cases can occur at all, because since the being already knows your final decision beforehand, the intuitive time sequence is canceled (someone [the being] makes a decision in the past [1 million in box 2 or not], according to premises [your final decision] that will only be verifiable in the future [look], but this is always correct [omniscience of the being].) That is, he makes the decision as if he would only make your choice Put in the 1 million and orientate yourself on this choice.
When I read through the remaining cases again, a second point struck me, by the way, you often say: "The being can look into the future, but cannot change it." In my opinion, however, it is based on the knowledge in the future and, according to the rules of the game, it cannot change my decision, but the result of it (do I get 1000 or 1 million?) And of course it also influences my decision.
Furthermore, you assume 4 cases that can occur (0.1k, 1M, 1M + 1k), but as shown above, two of these cases are impossible, which the player also knows (he is rational), i.e. before his Decision or something else, there are only two cases (1k, 1M) and he now has to decide which of the cases he would like to have :) (again, same user as the other two times) ---
Yes, I am assuming 4 cases. But I never make it a condition that a case occurs with a probability greater than zero. When considering the case, I allow a case to occur with probability 0.
And yes, the being can decide how to put the money into it before I decide. But not after I've made up my mind.
And the paradox is not necessarily that I want to trick the creature. (In return, you could make things much easier by not locking the 2nd box, but rather glass. If the 2nd box is glass, it is very easy to outsmart the omniscient being by only choosing the 2nd box, if There is no money in there and both boxes if there is € 1 million in the 2nd box - but that's not what the paradox is about either.)
What is the paradox about:
Since you get the contents of the 2nd box one way or another, you can take the 2nd box and stow it in your backpack. You then only have to decide whether you will also take the 1st box or whether you will leave it where it is. So now you could turn around and leave. You would know that you would be a millionaire then.
You turn around and want to leave with the 2nd box. Then the test leader opens the 1st box and holds the € 1000 banknote out to you.
Now the paradox is: if you take the bill, you are no longer a millionaire.
You're actually a millionaire. But by taking even more money, you are de facto losing money. - Sure, if the guy had a promissory note in his hand, that would be logical. But that one rejects money because one is afraid of losing money is a paradox. Or that you suddenly lose even more money by taking the thousand euros, is also paradoxical.
The paradox is practical that in fact there is more money in a single box than in both boxes combined. (It is as if someone were only buying one canister of gasoline because they could go further with it than with two canisters of gasoline.) So we have: The 2nd box is a subset of the union of both boxes. And through the oracle of the omniscient being, the subset is suddenly more powerful than the total. (The 2nd box is worth more than both boxes together.)
It's not about outsmarting the being. It's about the fact that we receive: A box is worth more than two boxes together. - And that's paradoxical. (If we assume that there is no promissory note in either of the boxes.) - Eulenspiegel1 01:21, Jan. 9, 2008 (CET)
Ah, so now I know where the whole paradox is supposed to be (and at the same time why it is equivalent to Braess' paradox). But I would say that your explanation of exactly where the problem is, should be incorporated into the article (can also be adopted as it is), and the section on free will (which has nothing to do with it) should be deleted. Because the paradox then lies in the fact that I get less if I have another choice. (At the beginning there is only box 2, in which if I only take it there is 1 million. But since there is only one box, the condition is automatically fulfilled, and I will always be a millionaire. Now comes the transparent box 1 with the 1k € added, but if I consider this new option, I suddenly lose a million, only if I ignore the option to take box 1 will I continue to be a millionaire.) Thank you very much for the detailed explanation :) ---
@ Eulenspiegel1: That is actually not a paradox: If you also take the first box, it contains, so to speak, the negation of the contents of the second box, i.e. a negative amount of money. Of course, it can then make more sense to use fewer boxes. In addition, being able to see into the future is a time travel of information from the future (into the past or the present does not matter), and there are enough paradoxes to prove the impossibility of time travel .-- Ninjamin 01:08, Apr 3, 2010 (CEST)
The first box does not contain a negative amount of money. On the contrary: the first box always contains a positive amount of money. (That you imagine that the first box contains a negative amount of money, even though it contains a positive amount of money, is paradoxical - to be precise, the paradox that is being alluded to here.)
And to say it again very clearly: It's the newcomb problem Not about the paradox of time travel.
It's best to read through my example with the accomplice again. That illustrates the paradox at issue here even better. --Eulenspiegel1 04:35, Apr 3, 2010 (CEST)
The friend would stick his recommendation to his hat, because, due to the omniscience of the being from the filling of the boxes, he would already know which boxes the test subject would take .-- Ninjamin 17:17, Apr. 3, 2010 (CEST)
1) The voter knows that the essence is omniscient. The accomplice doesn't necessarily know. (The accomplice could also have been told: "Look at how you put the money here and then recommend your friend which boxes to take. But do not reveal anything about the contents of the boxes.")
2) Suppose the accomplice knows that the being is omniscient. Then he also knows which boxes his friend is choosing. But that doesn't change the fact that he (doesn't) have to consider his friend's decision to be correct. And you can also make recommendations, even though you know that the other will not stick to it. (Just to be able to say: "You see, I told you.")
But this is not about psychology. Why the accomplice now makes a recommendation is irrelevant to the paradox. The only important thing is: he makes a recommendation. (Although he may know his friend will not follow this recommendation.)
3) You did not respond to my remark that it is paradoxical to imagine that there is a negative amount of money in the first box, although there is a positive amount of money in it. Do you agree with me on this point? --Eulenspiegel1 2:45 p.m., Apr. 4, 2010 (CEST)
No, because whether the millions are subtracted from the contents of the second box when you take the first box, or the millions are subtracted from the contents of the first box so that you only get the negative amount when you take the first box, is irrelevant. And since there are only a thousand positive but one million monetary units in the first box, there is a total of a negative amount in it .-- Ninjamin 15:37, Apr. 4, 2010 (CEST)
Correct: It doesn't matter what I subtract the amount from. Either way, an amount is subtracted. And that contradicts the fact that there is a positive amount in both boxes. Ergo a paradox: you subtract something even though you only have two nonnegative numbers. --Eulenspiegel1 00:18, Apr 5, 2010 (CEST)
That is not a paradox, but only very abstract - negative money that is contained in it cannot of course be seen .-- 14:59, Apr. 5, 2010 (CEST)
Why is negative money abstract? If the box contained a promissory note or something similar, it would be negative money and very concrete. But there is no negative money in the box. There is positive money ($ 1000) in it. If there were negative money in the box, it would be neither paradox nor abstract. But that's not the case: there are 1,000 positive dollars in there. --Eulenspiegel1 4:06 p.m., Apr 5, 2010 (CEST)

"Newcomb's Problem" or the "Newcomb's Problem"

"Newcomb's problem" or the "Newcomb's problem" - which term is better (more common)? --Hutschi 11:35, Jan. 25, 2008 (CET)


Am I right that Newcomb's problem will go away as soon as I assume that there will be a repetition? --NeoUrfahraner 1:50, Feb. 11, 2008 (CET)

Box 1

Why is the possibility of ONLY taking Box 1 not addressed at all? Or is this step too illogical? 23:19, Feb. 11, 2008 (CET)

Because it comes to the same thing as if you take box 1 + 2 1000 = 1000 + 0.
It doesn't come to the same thing at all. While the amount of money received is the same, there is a significant difference psychologically. --Hutschi 14:06, 28 Mar. 2008 (CET)
Because the requirements say "You only take the second box or you take both boxes". If you change the premise, it is no longer Newcomb's problem. A paradox is supposed to derive a contradiction from seemingly harmless assumptions and thus show that there must be a mistake there .-- Ninjamin 00:45, Apr. 3, 2010 (CEST)


Is there anyone here who thinks it makes sense to use both boxes? --NeoUrfahraner 1:40 p.m., Feb. 15, 2008 (CET)

Since the answers are so numerous: Who thinks it makes sense to only take the second box? --NeoUrfahraner 04:23, Feb. 17, 2008 (CET)

Wrong task

As already mentioned several times here, the "problem" makes no sense if one assumes that the being inviolable is omniscient (see Internet source 1 below chapter 8). Because then it doesn't matter how I decide, there is always only the case that is available for selection (Box 1 + 2 = 1000, -; Box 2 1M) The possibility of 1,001. Mill. Is not given because the essence is omniscient. No matter how many milliseconds I change my mind beforehand, the being knew. The thought experiment only makes sense if one assumes that there is a possibility (however small) of fallibility in the being. Indeed, Robert Nozick, who was the first to publish and present the problem, did not assume an inviolable omniscient being, but left the possibility of fallibility open. Other treatises on the problem also assume a percentage probability that the being is fallible. And only in this way does the thought experiment make sense. Compare the text by Nozick in "Essays in Honor of Carl G. Hempel" -Reidel, Dordrecht 1969 or "Paradoxes of Rationality and Cooperation" - The University of British Columbia Press 1985 and the texts on the Internet: 1. "http: // "2." "3." http: // www. "(recently offline ...)

OK; I'll try another attempt to explain what the paradox is about the problem.
1) Imagine if the boxes were made of glass. That means you can see the money that is in box 1 and box 2. Now there are two options: Either box 2 is empty or Bos 2 contains 1 million euros. Certainly, the being knows how to make a decision. - But after all, you also know what's in the boxes. (After all, the boxes are made of glass.) If you now see an empty box 2, you just take box 2 out of defiance and leave the 1000 €. If, on the other hand, you see € 1 million in box 2, you are happy about it and take both boxes. No matter how you decide: BEFORE you decide, you have to see something in the boxes. And then you can always change your mind so that the essence is wrong. (Again for clarification: The paradox is not about the fact that the essence could be wrong. - But the idea that the container is transparent can also be helpful in the following.)
2) OK, assuming the test person distrusts the being and wants to make sure that the being really leaves the suitcase unchanged and does not take anything out of the suitcase afterwards. So she sends a friend who can look under both suitcases (before the test person decides) and also checks that everything is there.
The friend can now determine two things: Either there is a total of € 1000 under both boxes or € 1.001 million under both boxes. But no matter what is below, the friend will think: "Hmm, if she takes both boxes now, then she will get more money than if she took one box."
1. Question: "Since this is the test person's best friend: Should he tell her how much money is under the boxes?"
Suppose the friend had to promise the omniscient being not to reveal what was in the 2nd box. However, he may either advise the test person to take both boxes or only the 2nd box.
2nd question: "What advice should he give the test person if there is no money under the 2nd box?"
3rd question: "What advice should he give the test person if the second box is € 1 million?"
3) The omniscient being gives the test person a choice: Either it blindly decides to take both or only the second box, or it can look at the contents of the boxes before deciding whether to only take one or both boxes.
The paradox here is that it is better for the test subject to decide blindly than to get all possible information first before making a decision.
4) Not necessarily a paradox, but at least astonishing is that there is a discontinuity: If the being can predict the future with 99.999 ...% certainty, it is better to take both boxes. But as soon as the being can predict the future 100%, it is suddenly better to only take one box.
As I said, this is not a real paradox, but a discontinuity in the expected values. And that seems pretty strange here too.
The paradox is that there is more money in one box than in two boxes. (Or that there is more money in both boxes, but you should still only choose one box. So you get more money if you opt for the option with less money.) --Eulenspiegel1 13:55, 28. March 2008 (CET)
@ Eulenspiegel1: is there a paradox if a second round is played afterwards? --NeoUrfahraner 17:58, 28 Mar. 2008 (CET)

"" As mentioned several times here, the "problem" makes no sense if one assumes that the being inviolable omniscient " - on the contrary. The paradox only makes sense if one assumes that the being, at least in the case mentioned, is omniscient and is neither wrong nor violating the rules. As soon as one deviates from it, it is no longer a paradox, but simply a problem that mathematical and psychological considerations are relatively easy to access. --Hutschi 14:01, 28 Mar. 2008 (CET)

To 1) Sure, when both boxes are transparent, it becomes paradoxical. But the task says very clearly: The second box is opaque.

Regarding 2) At no point does the task mention a friend whom I can send. So, I'm just me and the creature and the two boxes alone.

To 3) This premise is not an option either!

To 4) “The paradox is that there is more money in one box than in two boxes. (Or that there is more money in both boxes, but you should still only choose one box. So you get more money if you opt for the option with less money. ”Exactly. or for 1,000, - 1,001 million is out of the question, even if I logically conclude that there is money in both boxes.

Conclusion on this: Either I stick to the rules and premises or I take the game ad absurdum, so I would not act according to the rules. The latter, however, would not correspond to the purpose and aim of the thought experiment. In this respect, it only makes sense to assume a fallible being, since, as already mentioned, all the thought processes described (about getting 1,001 million, etc.) cannot come into play in this way. I can't play a game without obeying the rules. If I play chess and don't stick to the pace of the pieces, I don't need to play chess. Or I agree with my counterpart about the new pace of the characters, but then we would have new rules about which there must be a consensus! I cannot arbitrarily change the rules during the game, otherwise my opponent would stop the game. (03/28/2008)

One of the explicit rules is that the being is infallible. Therefore it only makes sense to assume a fallible being if one changes the rules. That would be the case if I assumethat the being is lying. Incidentally, an infallible being can also lie. In this case, however, I don't know anything about the game. I only know that there seem to be 1,000 coins in one of the boxes, I don't know if it's counterfeit money, I don't know if I'll get a blow if I take the money, nor if the creature will rob me afterwards if it does lying to me before. If I can assume that the being is lying, the safer option is to take both boxes, but then the rules have already changed. (According to the task, the being is infallible, but it is not said that it always tells the truth, that would be an implicit additional assumption that is assumed in most solutions. But if an infallible being begins to lie, it is better without money to disappear immediately .-- Hutschi 3:21 p.m., Mar 28, 2008 (CET)
To 1) That's why I also wrote that the paradox is not about the fact that the being could not be infallible. (If Newcomb was interested in the infallibility paradox, he would have used transparent boxes - but for good reason he did without transparent boxes and used opaque boxes.) My point 1 should only lead to the preliminary consideration: "Why was Newcomb against transparent ones Boxing? Why did Newcomb explicitly say that the boxes should be opaque? " The reason is that we would have two different paradoxes: With clear boxes we get a rather boring paradox. With opaque boxes, on the other hand, we get an interesting paradox. Newcomb was probably aware of this and that's why he decided not to use transparent boxes and made it important that the boxes are opaque. (I will work out the subchapter glass box in the article in more detail to point out that in this variant you also come across a paradox, but that nothing has to do with the paradox desired by Newcomb.)
To 2) The task explicitly states that the being can indeed look into the future (i.e. it is omniscient), but cannot manipulate the boxes. This difference is hard to understand. The friend serves practically only as an introduction to the difference between "can manipulate the contents of the boxes" and "can look into the future".
The test person himself can still not look into the boxes. She also doesn't know if her best friend is lying to her or not. Therefore, in principle, nothing changes in the rules when you introduce this friend. (The decision of the test person should be one way or the other: "I only take the 2nd box. No matter what my friend advises me.")
The friend who looks at the boxes beforehand is therefore not used to change the rules, but only to illustrate the rules.
to 3) Would it be a paradox if this fact was introduced? The reasoning is rather the following: We take this variant of the Newcombs problem. Realize a paradox. Now we cancel the change and find that the paradox remains.
To 4) So you agree with me: We have a paradox: "Because you get more money if you choose the option with less money." This is clearly a paradox imho.
to your conclusion) Of course, in chess I can't just change the rules and move a piece, for example, twice in a row. But when playing chess it makes perfect sense to ask yourself: What could I achieve if I now move two pieces in a row? This doesn't change the rules (because I don't move two pieces in a row, I just imagine what if I could move two pieces in a row), but I sometimes make the game easier for myself. (Many chess programs, for example, work with an algorithm after they first move two pieces in a row to see whether this move variant makes sense at all. - In the actual game, of course, they only move one piece.)
And with that in mind, you should see the "rule changes" too.
Furthermore: When I stand in front of the two boxes, I know exactly that the two boxes total € 1.001 million. (Of course I only take the 2nd box. That is out of the question. But I do Whitethat put € 1.001 million under both boxes and still do not take them.)
The € 1.001 million is therefore not a possible case that never occurs, but rather a case that always occurs with a logically thinking person. (Because if he thinks logically, he only takes the 2nd box. That means that both boxes total € 1.001 million. But since he voluntarily refrains from using both boxes, he foregoing € 1.001 million take. Because he Whitethat put € 1.001 million under both boxes. He knows that because he trusts the omniscient being and because he also knows that he will only take the 2nd box.)
@ Hutschi
In my examples, I have assumed the following:
a) The being is infallible.
b) The being always tells the truth.
c) The test person knows that the being is infallible and always tells the truth.
None of this changes the question: "What should my friend advise me after looking under the two boxes and seeing the money there?" (This question is also relevant if you start from a) to c).)
That with the "I mistrust the creature, so I send my friend out", was just a rather funny expression. You could also say: "I'm curious how the creature does it and I send my friend over to see how the creature does it." or: "I want to earn as much money as possible and send my friend over to give me a few tips." or "my friend is curious and would like to be there from the start". The reason why the friend is now with the open boxes is completely irrelevant.
The € 1.001 million is not a possible case that never occurs, but rather a case that always occurs with a logically thinking person. - Exactly. --Hutschi 10:58 am, Apr 3, 2008 (CEST)
Suppose there is a second round - what then? --NeoUrfahraner 12:30, 3rd Apr. 2008 (CEST)
Then, as a result of the first round, you can falsify that the other is following the rules. But in itself it is a game without a past. If all the rules are adhered to and you want to maximize your profit, you always have to take box B alone, as long as the rules do not change. Then there is always € 1.001 million in play. If you want to review the game for yourself, you have to make different choices. --Hutschi 1:18 p.m., Apr 3, 2008 (CEST)
It's not about the past, but about the future. Why should I take 1,000 more in the first round when I have 1 million less in the second round? --NeoUrfahraner 1:27 p.m., Apr 3, 2008 (CEST)
Actually, each game has to be viewed as a single game. Here it is true: Why should I take 1000 euros when I have to forego 999000 euros? If the task is correct, I have the choice between 1000 euros and one million euros. One million plus 1000 euros are excluded. --Hutschi 1:40 p.m., Apr 8, 2008 (CEST)
Why do you have to view the game as a single game? Does the world end after the game? --NeoUrfahraner 16:04, Apr. 8, 2008 (CEST)
No. But with the given games, each individual game is independent of each other. But if you won a million and a thousand, the world would actually end. That would be a kind of singularity if all the rules are followed. --Hutschi 4:07 p.m., Apr 8, 2008 (CEST)
Why independent? The "omniscient being" will of course base its future prognoses on my decision. "Since at the time of the election the decision as to whether the million is in the second box has already been made, you could take both boxes." Sure, but no matter which boxes I use, that of course has consequences for the future. Once these consequences are taken into account, the paradox disappears. --NeoUrfahraner 16:30, Apr. 8, 2008 (CEST)
If the being is omniscient, it does not need to build prognoses on the basis of decisions of the past, since it already knows all decisions. Otherwise it is not omniscient. Which box you take, of course, has personal consequences for the future, at least if you take the money. But it has no consequence on the being's knowledge. This already knows whether and how further games will take place. --Hutschi 16:35, Apr 8, 2008 (CEST)
Then what is the problem / paradox? --NeoUrfahraner 16:40, Apr. 8, 2008 (CEST)
I don't see any either. There is no real paradox unless you bring free will into play. Because in the specified world there is no free will. Since this world does not exist, there is no paradox in the sense of a mathematical contradiction, but one in the sense of an unexpected result - at least I think. --Hutschi 17:12, Apr 8, 2008 (CEST)
There are basically two paradoxes: The first is that if you choose to box less, you get more money. (There is more money in both boxes than in a single box.Still, you get more money if you just choose a single box.) That is the first paradox.
With the second paradox one has to realize that the being can foresee the future, but still cannot manipulate the boxes. That means, when I stand in front of the boxes and think about whether I should meet both or just one, there are two options: Either in both boxes there is a total of € 1000 or in both boxes there is a total of € 1.001 million. Of course, the being knows how much money is in the boxes. And the being also knows how to make up my mind. Nevertheless, it is true that there is more money in both boxes together than in one box alone. (Regardless of how I decide.) The second paradox now lies in the fact that my current decision does not change the contents of the box. Regardless of how I decide: The contents of the box will no longer be changed. Nevertheless, you act as if the decision changed him. (That only has something to do with free will to a limited extent.) --Eulenspiegel1 03:55, Apr. 9, 2008 (CEST)
@ Eulenspiegel1: both paradoxes disappear as soon as you think about the future. --NeoUrfahraner 06:15, Apr. 9, 2008 (CEST)
Then why do the two paradoxes disappear? "There is more money in one box than in both boxes combined." is always a paradox.
And even with the second paradox, I don't see why thinking about the future changes anything. It's about what's in the box * now * and not just in the future. --Eulenspiegel1 18:37, Apr. 9, 2008 (CEST)
If you consider the future, the first "paradox" is: "If I only choose one box now, I will later get more money than is currently in both boxes combined." - what is supposed to be paradoxical about it? The second paradox is: "My current decision influences the future contents of the box" - what should be paradoxical about it? - NeoUrfahraner 18:58, Apr. 9, 2008 (CEST)
"There is more money in one box than in both boxes combined." - That already says that it is not so. It's just what some imagine. "Quasi" puts it into perspective, it says "as if, but not really". The paradox is on a level similar to that of Laplace's demon. --Hutschi 09:59, Apr 10, 2008 (CEST)
@ NeoUrfahraner: OK, if you put on two games then the paradox would dissolve. But you don't have two games, just one game.
@ Hutschi: Of course there is no more money in one box than in both combined. But it's kind of like that. I already know that there is less money in one box than in both boxes combined. But the decision is made as if there is more money in one box than in both boxes combined. Hence the word "quasi" in the sentence. --Eulenspiegel1 12:33, Apr 10, 2008 (CEST)
It is not specified whether there will be a second game or not. The assumption that there is no second game is only contained in the "solution" (a short-sighted utility function that only considers the current utility and ignores the future utility), but not in the problem statement. Assuming a future second game, the cause of the apparent paradox becomes obvious; the future benefit can of course also be more subtle (another game, another reward or just the continued existence of the being's "benevolence") --NeoUrfahraner 13:04, Apr. 10, 2008 (CEST)

The statement "The € 1.001 million is not a possible case that never occurs, but rather a case that always occurs with a logically thinking person.”I would like to contradict. I see myself as a completely logical person and if I look at a corresponding truth table, which is well known in logic, the realization is exactly the opposite:

Take ATake B.Get

Possibly the only paradox that should be highlighted here is the ever-present tendency of a not immaculate number of inhabitants of this planet to declare an omniscient, higher being to be the cause of all for things that they can only explain with difficulty due to lack of knowledge, lack of knowledge. :-) --Geri, ✉ 8:19 PM, Jan. 1, 2009 (CET)


if i correct something like that, you can assume that i checked it, in this case with the publication at hand. the article is so in need of revision that an editwar about such trivialities is ridiculous. ca $ e 11:30, 7 Aug 2010 (CEST)


Please formulate the section in an understandable way and, if necessary, provide evidence of the "equivalence" (do you know what the term means in technical usage?), otherwise it will come out! ca $ e 11:31, 7 Aug 2010 (CEST) much better now. however, the "you" formulations should be replaced. ca $ e 13:06, 7 Aug 2010 (CEST)

Incomplete definition of the situation

The omniscient being can evidently also act itself, i.e. not only foresee the future, but also influence it. So when it sees into the future, it must either (1) foresee its own actions as well, or (2) it foresee the future depending on its own actions, in the kind of "If I do this, that will happen" .

Case (1) would mean that the omniscient being is omniscient, but not free in its will. So it couldn't make up and play this nasty game.

So only case (2) comes into consideration. But then the game is incompletely defined. Because what would the essence do if it foresees the following: "The candidate will choose both boxes if I put 1M € in the second, and he will only choose the second box if I put 0 € in there." ?

--hjm 12:29, 28 Mar. 2013 (CET)

The question of free will is one of the things Newcomb's problem deals with. But why should a being without free will not be able to think up such a game? And ultimately, the game doesn't have to have come up with the omniscient being. The omniscient being is used in the game. But that doesn't mean that it made up the game. --Eulenspiegel1 (discussion) 00:30, 29 Mar. 2013 (CET)

Good, that is true with the conception. But the omniscient being decides what goes into the box. How does it decide when it sees the future as described above? --hjm 10:48, Apr 7, 2013 (CEST)

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Omniscient being is mostly correct?

“Assuming that the stated conditions are true, the optimal strategy is to only take the second box and forego the first. You then know that there is a million under the second box. You cannot get a higher value if the given conditions are true. "

That doesn't seem to be true, because the description of the situation says: “His predictions are mostly correct.” But for option 2 to be worthwhile, the being must have a correctness probability of 103+106(1-P) <106P ⇒ P> 50.05%, that is not yet specified with "mostly" (> 50%).

I have neglected here that there is also “an omniscient being” in the situation, because this is not compatible with “his predictions are mostly correct.” The predictions of an omniscient being are always correct, otherwise it is not omniscient (a similar discussion seems to have taken place earlier in 2008/09). The situation was changed in 2015 and has since made no sense, one of the two statements has to be put into perspective. --π π π(D) | list of main missing items 23:45, Dec. 26, 2020 (CET)