Newcomb's paradox

[David Gould]

Now imagine that yourself have this special power of unpredictability or that no one can predict your choices... let's call this freewill.

introducing freewill, an uncertainty to this infallible being ... well, at least that is how I understand it.

But that means he is not infallible.

In other words, you cannot set up this paradox by saying:

'This dude is infallible. Except that he isn't.'

The only way that this can be a paradox is by using the assumption that he is infallible you prove that he is fallible - you cannot assume the paradox from the get go.

 

[David Gould]

In other words, I thought this whole thing was about proving the existence of free will, not assuming it.

 

[Osiris]

I think this is on the same supposition of :

an unstoppable force/object meets an immoveable object.

 

[kopilo]

I think this is on the same supposition of :

an unstoppable force/object meets an immoveable object.

Personally when I hear this I imagine the unstoppable force going through the object. Hence the unstoppable obejct/force does not stop and the immoveable object does not move.

 

[t_w]

the logical paradox arises when you assume the Supreme Being's prediction will be wrong. Perhaps such even is not possible...

If you read the OP, there is a clear paradox.

The way I was thinking of this determinism was something like "physics of human brain and genetics"...

Of course, but this essentially boils down to molecular movement.

predict: To state, tell about, or make known in advance, especially on the basis of special knowledge.

guess: 1: a message expressing an opinion based on incomplete evidence 2. an estimate based on little or no information

They do have different meanings. I suppose that I was using guess to mean predict. I thought it was obvious from the context this is what I intended, but if not, then I concede my error.

A guess would imply that the being isn't certain about his decision... a prediction, an infallible prediction would imply that his predictions are certain.

Ok.

there is no certainty in that... random events only seem unpredictable.

Wrong. The location of a quark in an atom is genuinely random. It doesn't just seem that way. To add to the confusion, it's location appears to change when measured.

I don't see anything strange when human choice is involved...

I do. Hence our lengthy discussion

what i meant about it being unsupported was that such statement is just an opinion without any emperical evidence... even if it is stated or implied in the paradox.

I wasn't aware of much empirical evidence in the free will debate, or even in the realm of philosophy for that matter.

I wouldn't think that Einstein was "without a doubt wrong"....

I'm afraid he was. It is generally accepted in the scientific community that quantum mechanics destroyed complete determinism. Sadly, Einstein wasted the last few years of his life refusing to accept quantum physics.

the randomness and unpredictability of quantum physics is because to us it seems random/unpredictable. subatomic particles could be switching back and forth between parallel universes(which have different laws of physics) - hence such unpredictability would only lie because of the difference of physics.

Now we really are in the realm of unsupported assertion, methinks. Don't forget the possiblity that the IPU swallows subatomic particles and regurgitates them every so often.

The contradiction doesn't arise on the supreme being(if he were to exist) and his power of infallible human predictability. Problems arise when you assume that humans actions will never be predictable -- which is what you are creating.

I think you're thinking of a different contradiction. I certainly did not assume such a thing though! I concluded it from the paradox. There is a huge chance I am wrong, however I stand by my conclusion and feel I commited no logical fallacy.

we won't assume that something is impossible and possible at the same time.

I didn't assume that. I concluded that such a situation is a paradox.

[ A = true AND !A = false ] is a logical statement as defined by me above...

Sorry, they were supposed to both be A. Now do you agree?

 

[t_w]

This is the prgoression of the paradox (from my understanding):


On a flat probability analysis, it is clear that it is most likely that the being will predict that you will pick B2.

But that means that it is actually better for you to pick both boxes.

But the being would know this, and is therefore likely to predict that you are going to select both boxes.

Which means that selecting B2 would give you nothing.

Which means that you would select both boxes to get the 1,000.

Paradox resolved. Isn't it? Am I missing something here?

I think you're missing quite a lot. This isn't a game of paper, scissors, stone; a battle of reverse-psychology(I think you are thinking along these lines). I suggest you read it through again.

It is easy to see that if the being is 100% accurate, then you should always take box 2 and take the million, as if you take box 2 he will have predicted it.
However, why not take both. As I stated earlier, anyone who knows what are in the boxes(who doesn't communicate with you) and wants you to win big, will want you to take both. Whether or not the million is there, you will get more if you take both.
This is without a doubt a paradox.

 

[t_w]

In other words, it is set up such that a human without free will would be paralysed into indecision. Free will is the thing that enables a choice to made, even though there is no reason to tip the choice one way or the other.
.

Exactly. From my perspective, you've hit the nail on the head here. I hadn't thought of expressing it this way.

 

[t_w]

Therefore, the only rational choice is to pick B. (If you pick A and B, you will only get $1,000).

the explanation that allowed me to see it was this:
Imagine a person who wants you to win as much as possible is watching, and can see into the boxes. It becomes clear that whatever is in them, he wants you to take both. If the million is there he wants you to take both. If the million isn't there, he wants you to take both. So an equally logical choice is to take both everytime. Important: remember that there is no backward-acting causality. Once the amount is sealed( a week prior to choosing), the being is essentailly out of the situation.

 

[kopilo]

I think you're missing quite a lot. This isn't a game of paper, scissors, stone; a battle of reverse-psychology(I think you are thinking along these lines). I suggest you read it through again.

It is easy to see that if the being is 100% accurate, then you should always take box 2 and take the million, as if you take box 2 he will have predicted it.
However, why not take both. As I stated earlier, anyone who knows what are in the boxes(who doesn't communicate with you) and wants you to win big, will want you to take both. Whether or not the million is there, you will get more if you take both.
This is without a doubt a paradox.

Unlike our capital society, it is not just about attaining the most amount of money but also us trying to guess the beings prediction, which is based on our own actions.

 

[Osiris]

the explanation that allowed me to see it was this:
Imagine a person who wants you to win as much as possible is watching, and can see into the boxes. It becomes clear that whatever is in them, he wants you to take both. If the million is there he wants you to take both. If the million isn't there, he wants you to take both. So an equally logical choice is to take both everytime. Important: remember that there is no backward-acting causality. Once the amount is sealed( a week prior to choosing), the being is essentailly out of the situation.

If this is the case... the predictor will know about this second person... there won't ever be $1,000,000 in Box 2... Box 2 will always be empty -- unless no matter what this person tells you don't decide to listen to him.

 

[t_w]

If this is the case... the predictor will know about this second person... there won't ever be $1,000,000 in Box 2... Box 2 will always be empty -- unless no matter what this person tells you don't decide to listen to him.

Come on! I've stated countless times that this other person is purely to demonstrate a point. His existence has no bearing on the paradox. He does not talk to you. He is just hypothetical. He is there to make the point that it seems to be logical to take both boxes.
The existence of the other person makes no difference at all, I think this is blindingly obvious. If he never existed, the logical argument for taking both would be the same. He is just a way of expressing the argument.

 

[StrugglingSceptic]

I would hazard a guess that this paradox has spawned a whole load of doctoral theses and other research papers around Anglo-American philosophy departments. As to how it should be resolved, I am not really sure, but it has me thinking about an interesting result in formal logic that may be of relevance. Here are some sketchy thoughts on the matter:

In formal logic, there is no valid rule of inference which allows you to deduce from the statement "I can prove P" the conclusion P. Such a rule of inference would just produce rampant inconsistency.

So imagine the person playing this game is a computer which churns out the statements of some formal system. We take P to be the statement "I will open box B2", and say that the computer's ultimate goal is to churn out one of P or ~P. If it fails to do this after a specified time, then it will automatically puke up one of the theorems anyway, say P. We take the workings of the game to form some of the axioms of the formal system, thus modelling a person trying to rationally deduce whether or not to open the box. We assume that in the formal system, the statement "the superior being says I will eventually churn out P" proves the statement "I will eventually generate P" which we call Q.

Now the theorem-prover cannot validly deduce a whole lot from Q on the way to deciding P, because neither P nor ~P are logical consequences of "I will generate P" (see above). Perhaps this observation goes some way to resolving the paradox, at least from the perspective of formal logic. The player cannot come up with any valid argument based on hypothetical predictions of the superior being, and so shouldn't bother trying. They would do just as well to say "I will pick both boxes because I feel like doing so."

 

[Osiris]

Come on! I've stated countless times that this other person is purely to demonstrate a point. His existence has no bearing on the paradox. He does not talk to you. He is just hypothetical. He is there to make the point that it seems to be logical to take both boxes.

It would only be logical if the supreme being is capable of error.

If he's capable of error, this whole thing is not a paradox. It is not a paradox by the same reason it is not a paradox if I was the predictor and you were the person making the choice.

Your error is that you still view this supreme being as someone that is capable of error. If the being is infallible/omniscient, then it'd always be illogical(in expecting to get 1,001,000) to pick both boxes because the being will always know that. So, picking both boxes would be the dumbest move to make if the predictor is infallible.

The existence of the other person makes no difference at all. I think this is blindingly obvious. If he never existed, the logical argument for taking both would be the same. He is just a way of expressing the argument.

The existance of this other person is important because he is letting you know what the predictor predicted.

This external person is making you omniscient regarding the predictor's choice.

If this person does not exist, then there's no way for you to get this information unless you are omniscient yourself.

But we are not omniscient. The player would never choose contrary to the predictor's choice and there will never be a paradox.

The paradox may arise when the omniscient supreme being is trying to predict the choice of another omniscient being.

My opinion is that Newcomb's paradox is only a paradox if the boxes are made of glass(making the player omniscient regarding the predictor's choice)... but still I don't think an omniscient person would put himself in such situation .... or if he does, in Newcomb's paradox (where the boxes are made of glass) box 2 would always be empty(for people that would choose both if they see both boxes with money) unless a person honestly would choose box 2 and ignore box 1.

 

[t_w]

Your error is that you still view this supreme being as someone that is capable of error. If the being is infallible/omniscient, then it'd always be illogical(in expecting to get 1,001,000) to pick both boxes because the being will always know that. So, picking both boxes would be the dumbest move to make if the predictor is infallible.

This is no error. it is illogical to take both for the reason you stated. it is logical to take both for the reason I stated - whatever the being has done, you will get more by choosing both. This is a difficult point to grasp, and I think you've missed it. Such a situation, when something is completely illogical and completely logical, is what we name a paradox.
Most people, when seeing this paradox, quickly side with one of the above arguments. They affirm it strongly and feel that the other side is wrong. Notice that when you attack the argument above, you don't acutally attack its content, you just repeat your argument. That's because there is no argument against either argument. I hope you realize that both sides are equally logical.

 

[Telephone]

a) no being.

b) people with a religious bent think with a reduced clarity.

 

[David Gould]

I still cannot see the paradox.

 

[David Gould]

Can someone take me through this step by step in order to show me what the paradox is? The wikipedia article did not really help.

1.) There exists a being that is 90 per cent accurate in its predictions.

Correct?

 

[Osiris]

This is no error.

It is an error if the predictor is omniscient.

it is illogical to take both for the reason you stated.

right

it is logical to take both for the reason I stated - whatever the being has done, you will get more by choosing both.

It isn't....

The predictor is omniscient, what makes you think he won't know your choice? If you take both an omniscient being will know that...

This is a difficult point to grasp, and I think you've missed it. Such a situation, when something is completely illogical and completely logical, is what we name a paradox.

This will never happen as it is in the paradox...

it could be a paradox perhaps if both the predictor and the player are both omniscient as I stated in my previous post.

Most people, when seeing this paradox, quickly side with one of the above arguments. They affirm it strongly and feel that the other side is wrong. Notice that when you attack the argument above, you don't acutally attack its content, you just repeat your argument. That's because there is no argument against either argument. I hope you realize that both sides are equally logical.

As far as logic goes... picking both boxes does not contradict logic... but expecting to get $1,001,000 out of this would be illogical...

could you answer this: how could you choose something where an omniscient being won't know your choice? if you could then as David Gould said, the predictor was not omniscient to begin with...

 

[Osiris]

Can someone take me through this step by step in order to show me what the paradox is? The wikipedia article did not really help.

1.) There exists a being that is 90 per cent accurate in its predictions.

Correct?

No... if that being is capable of error, it wouldn't be a paradox.

Just like it isn't a paradox if I were to be the predictor...

I still cannot see the paradox.

Perhaps because there isn't one.

 

[David Gould]

Okay, I have read back a little.

From doing that, I have reached this point:

There are two potential strategies for choosing here.


1.) Ignoring whether the predictor guessed right or not:

If the predictor guessed that you would pick box B, then it is best to select both boxes.

If the predictor guessed that you would pick both boxes, then it is best to select both boxes.

Thus, you should pick both boxes.

2.) However, if you take into account the fact that the predictor is likely going to guess right, it is best to pick box B.


This to me still does not look like a paradox, as the premises used in each strategy are different. If the being is 90 per cent accurate, a strict probability analysis tells you that the 2nd strategy is the best one in terms of maximising your money.

In other words, if you pick box B, 90 per cent of the time you will get $1,000,000 and 10 per cent of the time you will get nothing.

If you pick both boxes, 90 per cent of the time you will get 1,000 and 10 per cent of the time you will 1,001,000.

In other words, if you exclude from your consideration the predictor, on average you will lose.