Newcomb's paradox

[Osiris]

First of all, I don't know where you read that the being's predictive power is 100%. I can say with 100% certainty that this in the version I read about this paradox, from Martin Gardner no less, the being's predictive power was not 100%(in some instances). However, often the predictive power is postulated as 100% to make certain points or draw certain conclusions from the pardox. I actually think a predictive power of 100% makes my point better -

perhaps i misread it... but nevertheless, I would think if this paradox didn't have a predictive power of certainty then it'd be no different if this supreme being didn't have a predictive power at all and was putting money inside the box (because there is room for error).

because such power is impossible(hence the paradox).

Why such power is impossible? Because we can't do it?

Yes, he is.

No, what I meant was this:
You: (concentrating hard) I'll take the second box. I'll take box #2. I'll take the second box. I'll take box #2...
S.Being: (reads your mind) ah! he's going to take box 2. (puts $1,000,000 in box 2)

(week goes by... decision time)

You: eh, I think I'll take both boxes.
S.Being: Doh'!

He will use this information to form a deterministic model which will suggest how you will rationalize. He uses information in your brain at the time of closing the boxes.

right, that is what i've been explaining this whole time.

He doesn't know what you rationalize throughout the week, he guesses based on a deterministic model(of the brain). Remember, he is't always right.

guessing is not predicting...

one could accurately predict the result of a dice roll (using physics) by placing the dice in a controlled environment and rolling the dice according to certain variables(height, force, throw direction, dice position, etc)

The way I interpret this paradox is that nothing can be completely predicted in the future if a conscious rational being(man) is making a decision.

well, the statement is an unsupported opinion.

einstein's opinion was that everything in this universe was deterministic.

Look, you've pointed out another contradiction. It both is possible and isn't. Contradictions really aren't a great way of attacking a logical paradox.

there is no contradiction... the contradiction you are creating it yourself.

if such power of predicting humans is possible... then it is possible. if such power of predicting humans is impossible then it is impossible... I never said or implied that it could be impossible and possible at the same time...

this is what i implied:

A = possible
!A = impossible

if A = true then !A = false
if !A = true then A = false

there is no contradiction...

 

[David Gould]

Then I misunderstood the whole thing.

However, the big mistakes here are these:

1.) unpredictability = free will
2.) a human will make their decision on which box to choose only based on the information in the above.

Umpredictability does not equal free will. All this would indicate is that things are either way too difficult to predict or that there are random elements involved.


Imagine this scenario: a magician holds out a deck of card and says, 'Pick a card, any card.' There is no particular reason to pick card 1 or card 52 or any card in between. However, most people will indeed pick a card. Thus, the reason for them picking any particular card must be far more subtle than anything we can measure - for example, it could be that I pick card 31 rather than card 32 because I glimpsed a bird out of the window on my 14th birthday. In other words, causality is more complex than we think, with human conscious, rational processing only a tiny part of the overall picture.

 

[t_w]

perhaps i misread it...

No, I think you've understood the paradox and raised some interesting objections(well they made me think again about my conclusion, at least).

Why such power is impossible? Because we can't do it?

My reason for saying it is impossible is because if we assume a being has it, and then draw conclusions from this, a logical paradox ensues. A logical paradox shouldn't be possible.

No, what I meant was this:
You: (concentrating hard) I'll take the second box. I'll take box #2. I'll take the second box. I'll take box #2...
S.Being: (reads your mind) ah! he's going to take box 2. (puts $1,000,000 in box 2)

(week goes by... decision time)

You: eh, I think I'll take both boxes.
S.Being: Doh'!

I think that people, when considering this paradox, assume the prediction would be made on what someone will think, or how they will rationalize. I prefer to think of the determinism involved in the prediction as being at a molecular level, if that makes any sense.

guessing is not predicting...

To-may-toe, to-mah-toe. Clearly the being is not making a random guess, and I don't think I argued this.

one could accurately predict the result of a dice roll (using physics) by placing the dice in a controlled environment and rolling the dice according to certain variables(height, force, throw direction, dice position, etc)

And the same could be done for every event(except stochastic and random events). However, when human choice is involved things get a little strange. At least, that's one of the conclusions I draw from this paradox.

well, the statement is an unsupported opinion.

I think it is supported by the paradox. Certainly not confirmed, but vaguely supported....

einstein's opinion was that everything in this universe was deterministic.

Einstein was, without a doubt, wrong. The study of quantum physics completely disproves Einstein's misconception. Einstein was a great man and a gift to mankind, but he was wrong in this instance.

there is no contradiction... the contradiction you are creating it yourself.

I think there are contractions allover the place as soon as we assume the being which this discussion is about.

if such power of predicting humans is possible... then it is possible. if such power of predicting humans is impossible then it is impossible... I never said or implied that it could be impossible and possible at the same time...

Aha, but in some instances, if we assume something, something is impossible and possible at the same time! And if this happens, the assumption is wrong.

this is what i implied:

A = possible
!A = impossible

if A = true then !A = false
if !A = true then A = false

there is no contradiction...

If we assume X, and then A = true AND !A = false as the result of our assumption, then X must be wrong. Do you agree?

 

[t_w]

Deleted

 

[t_w]

Deleted

 

[t_w]

Then I misunderstood the whole thing.

However, the big mistakes here are these:

1.) unpredictability = free will
2.) a human will make their decision on which box to choose only based on the information in the above.

Umpredictability does not equal free will. All this would indicate is that things are either way too difficult to predict or that there are random elements involved.

Unpredictability != free will. Agreed. However, an explanation for unpredictability may well be free will. Of course, this is by no means certain or even fairly certain, but free will is a possible explanation(where there lies no other) for unpredictability.

I don't know what you're addressing with 2). I never argued this, I only argued conflicting logical arguments that prove the paradox. I didn't say they were the only arguments or causes. Of course I realise there are conspicuous causes of events and I haven't overlooked this in this thread(I hope).

I think the most important point is, if everything is completely determined in a long causal chain, then surely the being would be able to predict perfectly(assuming he had all relevant information). However, it appears he can't predict perfectly. If he could, then there would be no paradox. For me, this conclusion is one of the most fascinating.

 

[David Gould]

Unpredictability != free will. Agreed. However, an explanation for unpredictability may well be free will. Of course, this is by no means certain or even fairly certain, but free will is a possible explanation(where there lies no other) for unpredictability.

I don't know what you're addressing with 2). I never argued this, I only argued conflicting logical arguments that prove the paradox. I didn't say they were the only arguments or causes. Of course I realise there are conspicuous causes of events and I haven't overlooked this in this thread(I hope).

I think the most important point is, if everything is completely determined in a long causal chain, then surely the being would be able to predict perfectly(assuming he had all relevant information). However, it appears he can't predict perfectly. If he could, then there would be no paradox. For me, this conclusion is one of the most fascinating.

Determinism does not imply predictibility, either.

Free will is not a possible explanation for other reasons.

 

[Osiris]

No, I think you've understood the paradox and raised some interesting objections(well they made me think again about my conclusion, at least).

okay... cool

My reason for saying it is impossible is because if we assume a being has it, and then draw conclusions from this, a logical paradox ensues. A logical paradox shouldn't be possible.

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

I think that people, when considering this paradox, assume the prediction would be made on what someone will think, or how they will rationalize. I prefer to think of the determinism involved in the prediction as being at a molecular level, if that makes any sense.

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

To-may-toe, to-mah-toe. Clearly the being is not making a random guess, and I don't think I argued this.

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

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.

And the same could be done for every event

right, that is what I was trying to imply in how the Supreme Being would predict humans.

(except stochastic and random events).

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

However, when human choice is involved things get a little strange. At least, that's one of the conclusions I draw from this paradox.

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

The way I interpret this paradox is that nothing can be completely predicted in the future if a conscious rational being(man) is making a decision.

I think it is supported by the paradox. Certainly not confirmed, but vaguely supported....

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.

Einstein was, without a doubt, wrong. The study of quantum physics completely disproves Einstein's misconception. Einstein was a great man and a gift to mankind, but he was wrong in this instance.

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

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.

I think there are contractions allover the place as soon as we assume the being which this discussion is about.

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.

Aha, but in some instances, if we assume something, something is impossible and possible at the same time! And if this happens, the assumption is wrong.

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

we won't assume that A is treu and !A is true as well...

If we assume X, and then A = true AND !A = false as the result of our assumption, then X must be wrong. Do you agree?

I don't see why it'd be wrong...

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

 

[Osiris]

Unpredictability != free will. Agreed. However, an explanation for unpredictability may well be free will. Of course, this is by no means certain or even fairly certain, but free will is a possible explanation(where there lies no other) for unpredictability.

i don't think that unpredictability may be well freewill...

unpredictability is a sign of randomness... would you attribute randomness to freewill? I would think that randomness would be contradictory to the will of the person.

I think the most important point is, if everything is completely determined in a long causal chain, then surely the being would be able to predict perfectly(assuming he had all relevant information). However, it appears he can't predict perfectly. If he could, then there would be no paradox. For me, this conclusion is one of the most fascinating.

It appears that he can't predict it perfectly? or is it that freewill is being applied here while the supreme being's prediction implies a contradiction to freewill?

 

[David Gould]

I think that I need to see the premises that result in this supposed paradox a little more clearly.

I will read back and see if I can make sense of it.

 

[David Gould]

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?

 

[David Gould]

I suppose it could continue. It just depends on how you work through it.

For example, let us say that you have worked through the above progression, and discovered that 1,000 is the best you can hope for.

However there is still a 10 per cent chance that the predictor is wrong. Therefore, it is still better to pick B2, even at the end of this. (10 per cent of a million).

The predictor would also know this. Thus, he would pick B2. And then we are back in the loop.

Is that how the paradox works?

 

[Osiris]

I suppose it could continue. It just depends on how you work through it.

For example, let us say that you have worked through the above progression, and discovered that 1,000 is the best you can hope for.

However there is still a 10 per cent chance that the predictor is wrong. Therefore, it is still better to pick B2, even at the end of this. (10 per cent of a million).

this is really not a paradox if the predictor is capable of error in his predictions.

a real paradox would imply that the predictor is an infallible being. it becomes a paradox when this scenario implies that a person's freewill will prove the predictor wrong... an infallible prediction being wrong.

There are some different variations, I think that is what t_w picked up on...

 

[David Gould]

this is really not a paradox if the predictor is capable of error in his predictions.

a real paradox would imply that the predictor is an infallible being. it becomes a paradox when this scenario implies that a person's freewill will prove the predictor wrong... an infallible prediction being wrong.

There are some different variations, I think that is what t_w picked up on...

But doesn't the paradox relate to human actions, not to the actions of the predictor?

In other words, if humans always do the thing that they (given the information they have) believe gives them the most advantage - and this is a key prediction of people who do not believe in free will, such as me - then this situation leaves a person unable to make such a choice.

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.

Of course, this assumes that there is no random factor (Asimov's positronic robots had a randomiser that made it very difficult - although not impossible - for them to end up in a brain lock of this sort).


Of course, the probability is that I just simply do not understand the scenario and how it relates to free will.

If it is supposed to be a perfect predictor, then that automatically proves that we do not have free will.

Sigh. I guess I am simply completely confused here.

 

[David Gould]

I guess I cannot see how it is a paradox even if the predictor has 100 per cent accuracy.

 

[Osiris]

But doesn't the paradox relate to human actions, not to the actions of the predictor?

In other words, if humans always do the thing that they (given the information they have) believe gives them the most advantage - and this is a key prediction of people who do not believe in free will, such as me - then this situation leaves a person unable to make such a choice.

Ah, Ok, I see what you mean... but I think this would only work if we assume that the entity doing the prediciton is capable of error... but if the being is infallible the answer is obvious: Box 2.

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.

Of course, this assumes that there is no random factor (Asimov's positronic robots had a randomiser that made it very difficult - although not impossible - for them to end up in a brain lock of this sort).

right

Of course, the probability is that I just simply do not understand the scenario and how it relates to free will.

Wikipedia explains it differently plus other variations similar to this.

http://en.wikipedia.org/wiki/Newcomb's_paradox

If it is supposed to be a perfect predictor, then that automatically proves that we do not have free will.

That's where the contradiction comes in... that man's freewill will somehow prove this super being's infallibility wrong. Making freewill exist in a hypothetical where freewill is impossible.

 

[David Gould]

That's where the contradiction comes in... that man's freewill will somehow prove this super being's infallibility wrong. Making freewill exist in a hypothetical where freewill is impossible.

But how does this scenario do this? I cannot see it.

 

[Osiris]

But how does this scenario do this? I cannot see it.

By choosing both and expecting to get $1,001,000 (man's unpredictable choice)... but this will never happen because of the being's infallible power.

These are some views of this paradox from other people :
from www.wikipedia.org
Thoughts on the paradox

Some argue that Newcomb's Problem is a paradox because it leads logically to self-contradiction. Reverse causation is defined into the problem and therefore logically there can be no free will. However, free will is also defined in the problem; otherwise the chooser is not really making a choice.
Other philosophers have proposed many solutions to the problem, many eliminating its seemingly paradoxical nature:
Some suggest a rational person will choose both boxes, and an irrational person will choose the closed one, therefore rational people fare better, since the Predictor cannot actually exist. Others have suggested that an irrational person will do better than a rational person and interpret this paradox as showing how people can be punished for making rational decisions.
The rationality of the person who chooses the closed box depends upon facts concerning the Predictor. If, as posited, the Predictor is 100% accurate, and is completely reliable to put the million dollars in the closed box, and the chooser knows this, then the only rational choice is to pick the closed box. If the players knows the Predictor is unreliable, then the only rational choice is both boxes.
Others have suggest that in a world with perfect predictors (or time machines because a time machine could be the mechanism for making the prediction) causation can go backwards. If a person truly knows the future, and that knowledge affects his actions, then events in the future will be causing effects in the past. Chooser's choice will have already caused Predictor's action. Some have concluded that if time machines or perfect predictors can exist, then there can be no free will and Chooser will do whatever he's fated to do. Others conclude that the paradox shows that it is impossible to ever know the future. Taken together, the paradox is a restatement of the old contention that free will and determinism are incompatible, since perfect predictors require determinism. Some philosophers argue this paradox is equivalent to the grandfather paradox.

 

[David Gould]

Still can't see the paradox. If you know the guy is a perfect predictor, then you know that whatever you pick, he predicted it.

This is their table:

Predicted choice / Actual choice / Payout
A and B / A and B $1,000
A and B / B only $0
B only / A and B $1,001,000
B only / B only $1,000,000

If you pick A and B, you know with absolute certainty that he picked A and B.
If you pick B, you know with absolute certainty that he predicted B.

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

In other words, I cannot see how this possibly results in paradox, as you cannot thwart someone who is 100 per cent accurate in their predictions.

 

[Osiris]

Still can't see the paradox. If you know the guy is a perfect predictor, then you know that whatever you pick, he predicted it.

This is their table:

Predicted choice / Actual choice / Payout
A and B / A and B $1,000
A and B / B only $0
B only / A and B $1,001,000
B only / B only $1,000,000

If you pick A and B, you know with absolute certainty that he picked A and B.
If you pick B, you know with absolute certainty that he predicted B.

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

In other words, I cannot see how this possibly results in paradox, as you cannot thwart someone who is 100 per cent accurate in their predictions.

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.