Newcomb's Paradox

[Dunderman]

@Frylock

I just re-read the problem as stated in the OP, and in fact, the problem is ambiguous. It allows you to think of the predictor either as magically able to foresee what you will do, or else as able to predict what you will do based on your present state through scientific means. These are two different problems, though. I think that you’re saying this as well.

No, I’m saying that the means he uses are irrelevant. The problem puts us in a world where accurate predictions exist. That’s what we have to work with.

If the predictor could literally see what I am going to do, and make his prediction based on that, then the two-boxers don’t have a case, I think. But as classically formulated, the problem posits an alien being with very very good predictive capabilities, and his predictions are explicitly not based on any direct knowledge of what you actually will do. They are predictions in the every-day sense: Taking what’s happening now, and using that to figure out what will happen next. In this case, I think the two-boxer has a case, no matter how accurate the predictions are supposed to be.

If he’s that good, he’ll know we’re going to take both boxes (he knew all the other times), so it’s still better to totally and fully intend to take the second box, and just to make sure, we’ll actually do it. But now we’re drifting into that “intend to take the poison tomorrow” problem.

[Dunderman]

@Lumpy

I’ve heard a slightly different version than the one presented in the OP. The version I heard has box 1 and box 2, and the setup is that either box 1 contains $1000 and box 2 contains $1,000,000, if you pick just box 1; OR both boxes are empty if you try to pick both. In other words you can get $1000 and pass up $1,000,000 OR pick both boxes only to find them both empty (if the prescience of the superior being is correct).

That’s even less of a problem than this one. Box 1 is the right choice.

EDIT: Provided the predictor is perfect, of course.

[Chronos]

I don’t. I think he’s going to accurately give me an empty box, just like he’d accurately give you $1,000,000. That doesn’t change the fact that when it comes down to making the decision I’ll be $1000 better off by taking both boxes, regardless of what’s in box 2 and so it is the only logical decision. Hence the ‘glumness’ with which I do it.

What do you mean by “when it comes down to making the decision”? It looks like you already have made the decision, before you’ve even met this very impressive entity. You’re not making his job of prediction very difficult, when you tell him the answer in advance.

When it comes time to make the decision, I can choose between getting a grand and a megabuck. That’s all there is to it. All that the (near) perfect predictor adds to the problem is that its existance implies that I make my decision earlier than it looks like I make it.

[vetbridge]

I would pick box 2.

But I would also place some side bets on the outcome.

[Mosier]

Pick box 2, get a million bucks.

What’s the issue again?

[ForumBot]

A rational actor would want to maximize his gain and minimize loss. This is why it is very important for the boxes to carry a $1 cost of selecting. The problem isn’t “is there a way for the predictor to be right”, but in this instance, can the predictor be wrong?

The OP has poorly worded the paradox and omitted several critical details. Here is the summation given by my friend Corey, who is attaining his PhD in Logic and assures me is the most powerful argument against omniscience. He personally modified it to show the concept of God, in particular, to be logically incoherent, but the general gist is omniscience.

Quote:

1. There is a predictor who can predict action with 100% accuracy
2. There are two boxes, blue and red.
3. An agent X has two options: take one box (either blue or red) or take both boxes.
4. The red box always contains $1,000
5. If the predictor predicts, with 100% accuracy, that agent X will select one box (and one box alone), it places $1M in the blue box
6. Otherwise, it places no money in the blue box
7. The boxes are made of glass (and are transparent)
8. Selecting a box costs $1
9. The predictor makes these arrangements before agent X selects a box

Game theorists (and economists) will note that (1), (3), (7) and (8) deviate from the Classical Newcomb Paradox initially presented by the late philosopher Robert Nozick. Note further that all agents fall into two categories: they will either select one box or they will select two boxes.

If the predictor predicts, with 100% accuracy, that agent X will select one box, he will place $1M in the blue box. Seeing this, a rational agent X will grab both boxes (since it gives him an extra $1,000). If the predictor instead predicts, again with 100% accuracy, that agent X will select both boxes, he will place no money in the blue box. Seeing this, a rational agent X will select only the red box (since it saves him a dollar).

In other words, a perfectly omniscient predictor will generate incoherent (and self-contradictory) predictions in the modified Newcomb’s Paradox - whatever he predicts will be false, and this is a contradiction since he has 100% accuracy.

A fully omniscient being is a universally omniscient predictor (since prediction is a category of knowledge). A universally omniscient predictor will also be (by definition) an omniscient predictor for the modified Newcomb’s Paradox. But this is incoherent! Therefore, a fully omniscient being is conceptually incoherent.

Conclusion: Either God is not omniscient or the concept of God is incoherent.

[brazil84]

People have a hard time accepting the possibility that somebody else might be able to predict their actions better than they can predict their own actions.

You might intend to take action X all along, and then, later, take action Y. Is it possible that another person could have anticipated the switch?

Sure. When your screwup cousin Louie borrows $500 from you, what do you think the odds are you will get paid back? Pretty damn low, but at the time he borrows the money, Louie may very well think the odds are pretty high.

That’s why I would pick just the black box. Even if reverse causality is technically impossible, the “Being” knows me so well that I may as well act as if it exists.

[ForumBot]

You don’t have to be aware of the being’s presence to make your decision. I have a hard time understanding why any of you would take only one million dollars when you could increase your gain by one thousand when you have literally nothing to lose (minus the $1 choosing fee.)

[Dunderman]

ForumBot, that version makes a whole lot more sense, but I disagree with the conclusion. If the predictor is in fact omniscient and 100% accurate, then it is impossible for the agent to do anything other than what the predictor predicted. Otherwise, the predictor isn’t omniscient and isn’t 100% accurate.

[ForumBot]

That is a classic mistake, mistaking omniscience for omnipotence. The act of predicting is purely a mental one, in assessing what will happen in the future. An act of predicting which binds the future and controls actions is an act of power, a function of omnipotence.

[PatriotX]

@Mosier

Pick box 2, get a million bucks.

What’s the issue again?

That’s what I’m sayin.

If I pick just box 2 I get a $1mil and if I do something different I get $1k.

Where’s the deliberation come in?

[Sage_Rat]

Ah, now that’s a paradox.

@ ForumBot

[panamajack]

Let’s set up a few logical statements.

With only two choices and two outcomes, we can say:

I select both boxes = NOT C
I select box 2 = C

B2 has $0 = NOT R
B2 has $1000000 = R

In both cases Box 1 has $1000, but it’s irrelevant to the outcome.

Perfect Predictions:

1.If C, then R
2.If NOT C, then NOT R

If I take Box 2:
3a. C
therefore, R.

If I take both:
3b. NOT C
therefore, NOT R.

ForumBot’s version : I can see the boxes, and choose spitefully:
3c. If NOT R, then C

4c. If NOT C, then R (from 3c)
5c. therefore, R (from 1 & 4c) (I chose an empty box and won a million!)

or the other way:
3d. If R, then NOT C

4d. If C, then NOT R (from 3d)
5d. therefore, NOT R (from 2 & 4d) (Hey! My money’s gone!)

Indeed, a perfect predictor, no matter what I do.

If our alien can’t predict perfectly:
Let p© be the probability from the alien’s perspective of what my choice is:

If p© > .5, then R
If p© <= .5, then NOT R

I decide to take both no matter what:
If NOT R, then NOT C
If R, then NOT C

Therefore NOT C.

If the alien thinks this way, p© = 0, therefore NOT R.

If the alien has no information about me, then why not take both? And the alien can save $1000000 by never putting anything in Box 2.

[Dunderman]

@ForumBot

That is a classic mistake, mistaking omniscience for omnipotence. The act of predicting is purely a mental one, in assessing what will happen in the future. An act of predicting which binds the future and controls actions is an act of power, a function of omnipotence.

I’m not mistaking omniscience for omnipotence. I’m not saying the predictor causes the choice or restricts the choice. I am saying that an omniscient predictor would see the whole situation, including the transparent boxes and their contents, and see what the agent would end up doing. If the agent doesn’t do that, then the predictor obviously isn’t omniscient.

[Frylock]

@ForumBot's Friend

Quote:

1. There is a predictor who can predict action with 100% accuracy
2. There are two boxes, blue and red.
3. An agent X has two options: take one box (either blue or red) or take both boxes.
4. The red box always contains $1,000
5. If the predictor predicts, with 100% accuracy, that agent X will select one box (and one box alone), it places $1M in the blue box
6. Otherwise, it places no money in the blue box
7. The boxes are made of glass (and are transparent)
8. Selecting a box costs $1
9. The predictor makes these arrangements before agent X selects a box

Game theorists (and economists) will note that (1), (3), (7) and (8) deviate from the Classical Newcomb Paradox initially presented by the late philosopher Robert Nozick. Note further that all agents fall into two categories: they will either select one box or they will select two boxes.

If the predictor predicts, with 100% accuracy, that agent X will select one box, he will place $1M in the blue box. Seeing this, a rational agent X will grab both boxes (since it gives him an extra $1,000). If the predictor instead predicts, again with 100% accuracy, that agent X will select both boxes, he will place no money in the blue box. Seeing this, a rational agent X will select only the red box (since it saves him a dollar).

In other words, a perfectly omniscient predictor will generate incoherent (and self-contradictory) predictions in the modified Newcomb’s Paradox - whatever he predicts will be false, and this is a contradiction since he has 100% accuracy.

A fully omniscient being is a universally omniscient predictor (since prediction is a category of knowledge). A universally omniscient predictor will also be (by definition) an omniscient predictor for the modified Newcomb’s Paradox. But this is incoherent! Therefore, a fully omniscient being is conceptually incoherent.

Conclusion: Either God is not omniscient or the concept of God is incoherent.

If the predictor predicts with 100% accuracy, then if it has predicted that you will pick one box, then you will pick one box. Your friend can insist a rational agent will pick two boxes instead, but your friend is simply stipulating that the agent can contradict the predictor. It is not necessarily true that the agent can contradict the predictor–rather, what is necessary according to the hypothesis is that the agent will pick one box just as the predictor predicted. This means that some force or consideration will intervene, making it seem better to the agent to pick one box just as predicted.

-FrL-

[Alan_Smithee]

There is no paradox in ForumBot’s version. The predictor is also an actor whose actions affect the outcome; being omniscient means that the predictor knows what you will do given any action that the predictor takes–it does not mean that the predictor can foresee a given outcome and then act in a way that precludes that outcome, and therefore make himself wrong.

Imagine you are the predictor. You predict with perfect accuracy that IF you put money in both boxes the subject will take both boxes and that IF you put money in only one box the subject will take only that box. You cannot, therefore, logically do what you proposed and place money where I won’t take it, but that means that you cannot do something logically impossible, not that you lack perfect knowledge. Even God is not traditionally said in Christian theology to be capable of doing what is logically impossible.

[Mijin]

Consider this paradox:

A being capable of seeing into the future with 100% accuracy offers you the choice of coffee or tea. She also (truthfully) tells you what your choice will be. But for a laugh, you vow to choose the opposite of whatever she says.
What happens?

---

I think that Newcomb’s paradox boils down to the same thing. All this stuff about the most rational choice is a red herring: a paradox is implied the minute you put a perfect predictor together with an intelligent agent aware of the predictor’s ability.

[Frylock]

@Mijin

Consider this paradox:

A being capable of seeing into the future with 100% accuracy offers you the choice of coffee or tea. She also (truthfully) tells you what your choice will be. But for a laugh, you vow to choose the opposite of whatever she says.
What happens?

---

I think that Newcomb’s paradox boils down to the same thing. All this stuff about the most rational choice is a red herring: a paradox is implied the minute you put a perfect predictor together with an intelligent agent aware of the predictor’s ability.

That’s why the original formulation did not include a (known) perfect predictor.

As for your example, what happens is some consideration intervenes leading you to choose what it was predicted you would choose.

-FrL

-FrL-

[Mijin]

@Frylock

That’s why the original formulation did not include a (known) perfect predictor.

Without a known perfect predictor, what’s the paradox? Any rational agent would take both boxes.

As for your example, what happens is some consideration intervenes leading you to choose what it was predicted you would choose.

There are many ways out of the paradox, but none of which that can be said to be “right” at this time.

To your escape, I would say that there is no known physical phenomenon that would act to prevent me reaching for tea after hearing the prediction “coffee”. If you prefer to believe that there is one, that’s up to you, but I don’t see how you can be so sure about it.

[Dunderman]

@Mijin

Without a known perfect predictor, what’s the paradox? Any rational agent would take both boxes.

Box two is the right choice if the predictor is merely good.

To your escape, I would say that there is no known physical phenomenon that would act to prevent me reaching for tea after hearing the prediction “coffee”. If you prefer to believe that there is one, that’s up to you, but I don’t see how you can be so sure about it.

There is no known physical phenomenon by which anyone could see the future with 100% accuracy. If you prefer to believe that there is one, that’s up to you, but I don’t see how you can be so sure about it.