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rhinoceros
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Newcomb's paradox
« on: 2004-11-19 11:50:47 » |
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This is a thought experiment which can take many forms and pose interesting problems to different fields.
http://en.wikipedia.org/wiki/Newcomb's_paradox
Let's see the first form, which has to do with timelines, free choice and determinism.
There are two players: the Chooser and the Predictor.
The Chooser is presented with two boxes. An open one which contains $1,000 and a closed one which contains either $1,000,000 or $0. He can choose to take either only the closed box or both. "Why, both, of course!" you might say. But there is a catch.
The Predictor can see the future with 100% certainty. He is the one who puts the money in the boxes the previous day, and he knows what the Chooser is going to do. He decides to do the following:
- If he predicts that the Chooser is going to take both boxes, he will leave the closed box empty and the Chooser will get only $1,000.
- If he predicts that the Chooser is going to take only the closed box he will put the $1,000,000 in it, so the Chooser will get $1,000,000.
The Chooser knows the rules but he does not know the prediction. "Easy. It is obvious from the rules that he should take only the closed box and put the $1,000,000 in his bank acount", you might say.
But this is where it becomes interesting. When the Chooser stands before the boxes, the Predictor has finished his part. The money either are in the box or not. Nothing is "quantum" or "Schroedinger-ish". The chooser gets to act, and he thinks: "If the prediction was that I will take only the closed box, the million is already there, so I will just take both boxes to get one thousand more".
The paradox becomes even more weird if both boxes are transparent and the Chooser sees what's in them.
Questions about determinism, timelines and choice arise from here. Discuss?
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David Lucifer
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Re:Newcomb's paradox
« Reply #1 on: 2004-11-20 16:11:32 » |
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Quote from: rhinoceros on 2004-11-19 11:50:47
Questions about determinism, timelines and choice arise from here. Discuss?
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It looks to me like the paradox is due to logically inconsistent assumptions:
1) The Predictor can see the future with 100% certainty.
2) The Chooser has a choice.
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hell-kite
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Re: virus: Re:Newcomb's paradox
« Reply #2 on: 2004-11-21 04:17:05 » |
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Sunshine!
I see the problem, but in a way, the answer came intuitively:
IF Chooser takes both boxes, THEN Predictor WILL HAVE PREDICTED IT, thus,
the closed box will be empty.
The same applies to choosing only one box. In this game, it seems logical to
me that Chooser CANNOT win the 1000000.
This intuitive argumentation seems congruent with what David noted, that
<snip>the paradox is due to logically inconsistent assumptions:
1) The Predictor can see the future with 100% certainty.
2) The Chooser has a choice.</snip>
By the way, some very similar argument is contained in my thoughts about the
incompatibility of god's supposed omnipotence and our supposed free will.
Cf.
http://virus.lucifer.com/bbs/index.php?board=32;action=display;threadid=2556
4;start=15.
Regards
Björn
p.s.: Interesting - maybe even evolutionary - implications contained in the
last paragraph on Newcomb's paradox:
In this case, the problem rapidly devolves into an analysis of statistical
preferences for risk avoidance and tolerance. This can be seen more easily
if the dollar values are changed. For example, if the amount in the open box
is reduced to $1, essentially all Choosers will select the closed box - the
incremental value of the dollar does not justify the risk. On the other
hand, almost all Choosers will select both boxes if the amount in the open
box is raised to $900,000.
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rhinoceros
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Re:Newcomb's paradox
« Reply #3 on: 2004-11-22 11:36:37 » |
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[rhinoceros]
http://en.wikipedia.org/wiki/Newcomb's_paradox
Questions about determinism, timelines and choice arise from here. Discuss?
[David Lucifer]
It looks to me like the paradox is due to logically inconsistent assumptions:
1) The Predictor can see the future with 100% certainty.
2) The Chooser has a choice.
[rhinoceros]
I agree, but I wonder what is the cause and the implications of this inconsistency.
Is this so because at least one of the two assumptions is wrong? Which one?
Or is the whole model which brings them against each other broken?
(a) What are the implications if assumption (1) is wrong (perfect prediction not possible)?
a1) That there is a determinist timeline but it is logically impossible to predict, for a fundamental reason?
a2) That there is no determinist timeline, and Laplace's Demon (see Note) is fundamentally absurd?
To retain determinism, one could think of alternative determinist timelines, as in Everett's hypothesis of many worlds. This is a neat trick to preserve determinism, but still a trick: It allows the Chooser to escape the Predictor by jumping onto another world, but another Predictor would be waiting for him there...
(b) What are the implications if assumption (2) is wrong (choice not possible)?
If both boxes are transparent and the Chooser decides to prove the Predictor wrong even against his own interests, what would stop him from doing so? A migrain? A cosmic effect pulling his limbs against his voluntary control?
(c) Perhaps there is a way to show that bringing these assumptions against each other at the same conceptual level is absurd?
*Note to (a2): Laplace's Demon
http://en.wikipedia.org/wiki/Laplace's_demon
<quote>
Laplace strongly believed in causal determinism, which is expressed in the following quote from the introduction to the Essai:
"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes."
This intellect is often referred to as Laplace's demon
<end quote>
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rhinoceros
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Re:Newcomb's paradox
« Reply #4 on: 2004-11-22 11:37:37 » |
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[rhinoceros]
http://en.wikipedia.org/wiki/Newcomb's_paradox
[hell-kite]
Sunshine!
I see the problem, but in a way, the answer came intuitively:
IF Chooser takes both boxes, THEN Predictor WILL HAVE PREDICTED IT, thus, the closed box will be empty. The same applies to choosing only one box. In this game, it seems logical to me that Chooser CANNOT win the 1000000.
[rhinoceros]
See the "transparent boxes" version in my reply to Lucifer.
[hell-kite]
By the way, some very similar argument is contained in my thoughts about the incompatibility of god's supposed omnipotence and our supposed free will. Cf.
http://virus.lucifer.com/bbs/index.php?board=32;action=display;threadid=25564;start=15
[rhinoceros]
True. The way out of your argument for the religious folk would be "God made logic, hence he can be exempt". Or, according to their own usual terminology, "See? It's a mystery!".
[hell-kite]
p.s.: Interesting - maybe even evolutionary - implications contained in the
last paragraph on Newcomb's paradox:
In this case, the problem rapidly devolves into an analysis of statistical
preferences for risk avoidance and tolerance. This can be seen more easily
if the dollar values are changed. For example, if the amount in the open box
is reduced to $1, essentially all Choosers will select the closed box - the
incremental value of the dollar does not justify the risk. On the other
hand, almost all Choosers will select both boxes if the amount in the open
box is raised to $900,000.
[rhinoceros]
This is a very different version of Newcomb's paradox. Here, the Predictor is not clairvoyant at all -- he is just a player who puts the money in the boxes on the previous day and his goal is to be proven right. Changing parameters, such as the amounts of money, gives rise to very interesting cases of rational choice and cooperative/adversarial behavior for both the Predictor and the Chooser.
This version does not pose "big philosophical problems" but it is an excelent tool for game theory and rational choice, same as the "Prisoner's dilemma" (http://en.wikipedia.org/wiki/Prisoner's_dilemma). We could discuss that one next.
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Re: virus: Newcomb's paradox
« Reply #5 on: 2004-11-23 06:00:39 » |
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Gloomy tuesday greetings!
[David Lucifer]
It looks to me like the paradox is due to logically inconsistent
assumptions:
1) The Predictor can see the future with 100% certainty.
2) The Chooser has a choice.
[rhinoceros]
(...)
(b) What are the implications if assumption (2) is wrong (choice not
possible)?
If both boxes are transparent and the Chooser decides to prove the Predictor
wrong even against his own interests, what would stop him from doing so? A
migrain? A cosmic effect pulling his limbs against his voluntary control?
[hell-kite]
The answer is - as already stated -, CHOICE IS NOT POSSIBLE: The Chooser has
no degrees of freedom left to alter his actions. [If we accept the
determinist viewpoint,] The Predictor predicts the Chooser's BEHAVIOUR,
thus, whatever his motivation, the Chooser will "cross the Rubicon" where
predicted.
It does not matter whether the Chooser thinks, "I will proof the predictor
wrong", because the Predictor WILL HAVE PREDICTED this. Thus, nothing like
migraine or armageddon will stop the Chooser from acting the way he [thinks
he] wants to, but the Predictor knows what the Chooser will want, or think
he wants, or, more to point, MUST.
[rhinoceros]
(c) Perhaps there is a way to show that bringing these assumptions against
each other at the same cognitive level is absurd?
[hell-kite]
As I see it - as I was trying to say before - as I was trying to say
above -, there is no logical, only a terminological conflict (regarding the
word "choice"). There are "rules" of the "game", and GIVEN these rules, the
outcome is determined as: the Chooser cannot win the million. In a
determinist world, the "Chooser" has no choice, no degrees of freedom.
Besides, prediction implies prediction of motives and motivations, too
(although this is not necessary, since only the behaviour is of interest -
yet, one cannot predict behaviour without the motivation except, maybe, in
extremely strong situations).
All in all, I don't see the problem here (two wrongs made right? a paradox
in a paradox turns the former into... what?).
<snip>This [rational choice/cooperation] version does not pose "big
philosophical problems" but it is an excelent tool for game theory and
rational choice, same as the "Prisoner's dilemma"
(http://en.wikipedia.org/wiki/Prisoner's_dilemma). We could discuss that one
next.</snip<
Yeah, why not.
Regards
Björn
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Re:Newcomb's paradox
« Reply #6 on: 2004-11-23 10:54:31 » |
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[rhinoceros]
[...]
(b) What are the implications if assumption (2) is wrong (choice not
possible)?
If both boxes are transparent and the Chooser decides to prove the Predictor
wrong even against his own interests, what would stop him from doing so? A
migrain? A cosmic effect pulling his limbs against his voluntary control?
[hell-kite]
The answer is - as already stated -, CHOICE IS NOT POSSIBLE: The Chooser has no degrees of freedom left to alter his actions. [If we accept the determinist viewpoint,] The Predictor predicts the Chooser's BEHAVIOUR, thus, whatever his motivation, the Chooser will "cross the Rubicon" where predicted.
It does not matter whether the Chooser thinks, "I will proof the predictor wrong", because the Predictor WILL HAVE PREDICTED this. Thus, nothing like migraine or armageddon will stop the Chooser from acting the way he [thinks he] wants to, but the Predictor knows what the Chooser will want, or think he wants, or, more to point, MUST.
[rhinoceros]
It seems to me that the *transparent* boxes make lots of a fifference. You (the Chooser) stand in front of them and look:
If you see the million dollars in the second box, then you know that the Predictor predicted that you would choose only this box, and this is why he put the million there, according to the rules. You decide to take both boxes. You end up with $1,001,000 and you have proven the Predictor wrong!
If you see the second box empty, then you know that the Predictor predicted that you would choose *both* boxes, and this is why he left the second one empty, according to the rules. You decide to take only the second box (the empty one), forfeiting $1,000 (it is possible if you are rich enough) but proving the Predictor wrong again!
In both cases, if the boxes are transparter, the Chooser can easily prove the Predictor wrong. This counts as one point for free will and against the feasibility of determinism which was in the assumption.
I am now coming back to Lucifer's initial statement. This discussion revealed another interesting thing:
<quote Lucifer>
It looks to me like the paradox is due to logically inconsistent
assumptions:
1) The Predictor can see the future with 100% certainty.
2) The Chooser has a choice.
<end quote>
After some though, it seems to me that the first one must be revised, at least for this problem. The inconsistency is not caused by the certain prediction itself but by the fact that the Predictor *acted on* that prediction in a way affecting the Chooser and the Chooser was able to figure out that action and respond to it.
Apparently the Chooser would not be able to draw any conclusions about determinism or free will if he didn't know the result of Predictor's intervention. Whatever he did, it might be the predicted outcome or not -- he wouldn't be sure. But the "transparent boxes" version seems to show that *there is* an issue to resolve.
By the way, I found this PDF where the author supports that there is no paradox at all, does the math, and concludes that the Chooser in the initial version should choose only the second box:
http://www.math.chalmers.se/~kyle/pub/newcomb.pdf
He also mentions an interesting opinion by Isaac Asimov:
<quote>
On a personal note, I think that the Newcomb Problem is nothing at all of a
paradox. [...] the only contradiction involved is incurred because of a disparity regarding views of free will. Isaac Asimov presents an interesting analysis: "I would without hesitation take both boxes . . . I am myself a determinist . . . Suppose that you take both boxes and it turns out . . . that God has foreseen this and placed nothing in the second box. You will then, at least, have expressed your willingness to gamble on his nonomniscience and on your own free will and will have willingly given up a million dollars for the sake of willingness" (2Gardner 104). Although I disagree with his conclusion to take both boxes, I believe that Asimov has struck upon the essence of the Newcomb problem – the question at stake is that of free will and determinism. It simply is a "litmus test" of sorts to determine one's position on free will. Those who are determinists will take both boxes (I suppose on their view, they have no choice but to do so, seeing as it has been predestined anyhow). Those who are "free-willists" – those who believe that there exist free choices that one can make – will take only B2 , believing that their choice will affect the situation and that the expected-utility principle seems more plausible than does the dominance. Thus, I feel, the problem can be reduced to the age-old philosophical arguments of free-will and determinism – it is better left for the philosophers to debate ad infinitum rather than to be considered by logicians. I, personally, however, think that such debate will never be resolved – for if the world is, indeed, deterministic, then those who believe in free will were willed to be so; if free-will is ours then those who believe in determinism should be free to do so: "if we make an exhaustive study of that problem [that is, the problem of determinism and free-will], and finally arrive at the result that our will is free, we still will not know whether our mind is of such a nature that we have to find our will to be free, although it is not, in fact, free" (2Gardner 106).
Irresolvable discussion of free-will aside, were I the chooser, I should most decidedly choose to take only B2 and walk away with the million.
<end quote>
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Re:Newcomb's paradox
« Reply #7 on: 2004-11-23 11:24:06 » |
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Quote from: rhinoceros on 2004-11-22 11:36:37
(c) Perhaps there is a way to show that bringing these assumptions against each other at the same conceptual level is absurd? |
Yes, an analysis of the assumptions reveals logical inconsistencies.
1) The Predictor can see the future with 100% certainty.
2) The Chooser has a choice.
3) If (1) then the Predictor cannot be wrong in the prediction.
4) If (3) then it is impossible for the Chooser to select the option the Predictor does not predict.
5) If (2) then it is possible for the Chooser to select either option at the time of the choice.
(4) and (5) are clearly incompatible.
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Re: virus: Newcomb's paradox
« Reply #8 on: 2004-11-23 11:33:17 » |
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Right back!
[rhinoceros]
It seems to me that the *transparent* boxes make lots of a fifference.
You (the Chooser) stand in front of them and look:
If you see the million dollars in the second box, then you know that the
Predictor predicted that you would choose only this box, and this is why
he put the million there, according to the rules. You decide to take
both boxes. You end up with $1,001,000 and you have proven the Predictor
wrong!
[hell-kite]
My guess is your premise is wrong: Of course it is sensible and
well-nigh "determined" that the Chooser, seeing both boxes filled, will
take both. But, given his clairvoyant abilities, the Predictor WILL KNOW
how the Chooser will behave. If under the circumstance of both boxes
filled, the Chooser will always choose both, THEN THE PREDICTOR WILL
NEVER FILL BOTH BOXES.
He foresees that IF he DOES, THEN the Chooser will take both, so he DOES
NOT. He cannot, as a matter of fact, or else we had a logical
inconsistency: You CANNOT prove the Predictor wrong, because the
Predictor is, by definition of 100%-TRUE-PREDICTION, ALWAYS RIGHT!
[This was my initial answer, but things got more complicated as I
considered your second possibility]
[rhinoceros]
If you see the second box empty, then you know that the Predictor
predicted that you would choose *both* boxes, and this is why he left
the second one empty, according to the rules. You decide to take only
the second box (the empty one), forfeiting $1,000 (it is possible if you
are rich enough) but proving the Predictor wrong again!
[hell-kite]
It occured to me that the transparent box-game is flawed regarding an
imbalance of the Predictors and the Choosers options. In the closed
box-game, both have only two choices: The Predictor can put the million
in the box or not. The Chooser can take only one box or two. In the
transparent version, the Predictor still has only two options, but the
Chooser has his two basic options, plus the option to defect or
cooperate, thus, he has 4 options. Thus, the Predictor cannot adequately
react according to his prediction. Thus, the rules of the game do not
fit anymore.
BUT, note that the Predictor still can predict correctly: He knows how
the Chooser will behave, even though he only has two suboptimal choices.
Thus, this is, imho, not at all an argument for free will. In the closed
box-case, the Predictor never was the cause of the Chooser's behaviour
(except in the sense that his existence constitutes one aspect of the
game). In the transparent box-game, he becomes a causal force because
the decision of the Chooser becomes dependent on his actions.
Again, I believe the transparent box-game is not valid for deterministic
or anti-deterministic argumentation.
Hopefully coherent,
Björn
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Re:Newcomb's paradox
« Reply #9 on: 2004-11-24 11:07:12 » |
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[hell-kite]
It occured to me that the transparent box-game is flawed regarding an
imbalance of the Predictors and the Choosers options. In the closed
box-game, both have only two choices: The Predictor can put the million
in the box or not. The Chooser can take only one box or two. In the
transparent version, the Predictor still has only two options, but the
Chooser has his two basic options, plus the option to defect or
cooperate, thus, he has 4 options. Thus, the Predictor cannot adequately
react according to his prediction. Thus, the rules of the game do not
fit anymore.
[rhinoceros]
The Pedictor does not make any choice at all. He just *sees* the future (either by solving equations or by travelling to the future, taking a look, and coming back or in any other way). Then he just applies the simple rule of the game and puts the money in the box or not. No options and no choice for him. He can either see what will happen or not.
And then, if the Chooser can figure out what the prediction was (this is the only difference in the "transparent" version), he can just do the opposite.
[hell-kite]
BUT, note that the Predictor still can predict correctly: He knows how
the Chooser will behave, even though he only has two suboptimal choices.
Thus, this is, imho, not at all an argument for free will. In the closed
box-case, the Predictor never was the cause of the Chooser's behaviour
(except in the sense that his existence constitutes one aspect of the
game). In the transparent box-game, he becomes a causal force because
the decision of the Chooser becomes dependent on his actions.
Again, I believe the transparent box-game is not valid for deterministic
or anti-deterministic argumentation.
[rhinoceros]
He can't predict the Chooser's *action*. Do you mean that he can predict that the Chooser will do the opposite of what he predicted? Then either logic or determinism is broken.
I think that the "transparent" version of the paradox only leaves us two options: Either (a) free will exists and determinism does not exist, or (b) determinism does exist but making an 100% certain prediction about an agent's actions, by any means, is fundamentally impossible.
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Re:Newcomb's paradox
« Reply #10 on: 2004-11-24 11:32:32 » |
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[Lucifer]
Yes, an analysis of the assumptions reveals logical inconsistencies.
1) The Predictor can see the future with 100% certainty.
2) The Chooser has a choice.
3) If (1) then the Predictor cannot be wrong in the prediction.
4) If (3) then it is impossible for the Chooser to select the option the Predictor does not predict.
5) If (2) then it is possible for the Chooser to select either option at the time of the choice.
(4) and (5) are clearly incompatible.
[rhinoceros]
Your inference is valid, of course. Perfect prediction and free choice are incompatible. So, which one is wrong? Or is it a false dilemma?
Using the two concepts within the same framework seems tricky. Since both have served us well in their appropriate contexts, I suspect that if we assign ontological status to either one we'll run in trouble. Perhaps it is safer to see them as modelling concepts (same as a timeline in space-time with all its peculiarities).
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hell-kite
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Re:Newcomb's paradox
« Reply #11 on: 2004-11-24 15:24:41 » |
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Hello rhino,
I suppose I am being stubborn here, but I am determined to be.
[rhinoceros]
He can't predict the Chooser's *action*. Do you mean that he can predict that the Chooser will do the opposite of what he predicted? Then either logic or determinism is broken.
[hell-kite]
Yes, that's what I meant [nb to do something=action is what I meant]. Though, neither logic or determinism needs to be broken. I repeat,
Predictor sees EXACTLY what will happen, and that is one of four possibilities
Box 1: $1000-Box (always filled)
Box 2: $1000000-Box (conditionally filled)
I. BOX 2 filled
a) Chooser takes Box 2 (within the game concept)
b) Chooser takes Box 1+2 (NOT within the game concept: "defect")
II. Box 2 not filled
c) Chooser takes Box 2 (NOT within the game concept: "defect")
d) Chooser takes Box 1+2 (within the game concept)
One of these actions will happen, for the future is determined. BUT, in the case of the transparent box, the Predictor becomes, as I said, a causal force, i.e., part of what determines the future. Thus, he has to "reconsider" the impact of his action, and granted that he can continually look into the future and doesn't do the math just once, change his action IF:
IF the Predictor sees the Chooser "defect" [and the game DEMANDS he still MUST continue the game (put something into Box 2 or not and leave Chooser to "choose"), even though the Chooser breaks the rules] we enter some sort of evil retro-causality loop which will probably result in nervous breakdown (a computer would break down anyway):
If he foresees b) would happen [if he filled Box 2], Predictor will not fill the box, which might lead to c) to happen [which Predictor foresees, if so]. Both are violations of the rules, so Predictor can, or must, "freely" choose to fill Box 2 or not, because neither will do. The loop is broken only if either I. or II. lead to within-the-rules-behaviour.
Thus, I still don't think that
<snip>the "transparent" version of the paradox only leaves us two options: Either (a) free will exists and determinism does not exist, or (b) determinism does exist but making an 100% certain prediction about an agent's actions, by any means, is fundamentally impossible.</snip>
Regards
Björn
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rhinoceros
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Re:Newcomb's paradox
« Reply #12 on: 2004-11-24 16:27:49 » |
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[hell-kite]
Hello rhino,
I suppose I am being stubborn here, but I am determined to be.
[rhinoceros] No problem, its ok. I saw at least one case that I had not covered before.
[rhinoceros]
He can't predict the Chooser's *action*. Do you mean that he can predict that the Chooser will do the opposite of what he predicted? Then either logic or determinism is broken.
[hell-kite]
Yes, that's what I meant [nb to do something=action is what I meant]. Though, neither logic or determinism needs to be broken. I repeat,
Predictor sees EXACTLY what will happen, and that is one of four possibilities
Box 1: $1000-Box (always filled)
Box 2: $1000000-Box (conditionally filled)
I. BOX 2 filled
a) Chooser takes Box 2 (within the game concept)
b) Chooser takes Box 1+2 (NOT within the game concept: "defect")
II. Box 2 not filled
c) Chooser takes Box 2 (NOT within the game concept: "defect")
d) Chooser takes Box 1+2 (within the game concept)
One of these actions will happen, for the future is determined. BUT, in the case of the transparent box, the Predictor becomes, as I said, a causal force, i.e., part of what determines the future. Thus, he has to "reconsider" the impact of his action, and granted that he can continually look into the future and doesn't do the math just once, change his action IF:
IF the Predictor sees the Chooser "defect" [and the game DEMANDS he still MUST continue the game (put something into Box 2 or not and leave Chooser to "choose"), even though the Chooser breaks the rules] we enter some sort of evil retro-causality loop which will probably result in nervous breakdown (a computer would break down anyway):
If he foresees b) would happen [if he filled Box 2], Predictor will not fill the box, which might lead to c) to happen [which Predictor foresees, if so]. Both are violations of the rules, so Predictor can, or must, "freely" choose to fill Box 2 or not, because neither will do. The loop is broken only if either I. or II. lead to within-the-rules-behaviour.
Thus, I still don't think that
<snip>the "transparent" version of the paradox only leaves us two options: Either (a) free will exists and determinism does not exist, or (b) determinism does exist but making an 100% certain prediction about an agent's actions, by any means, is fundamentally impossible.</snip>
[rhinoceros]
My first remark is that the Predictor is not expected to make any choise. Just to see the future and apply the simple rule (which was not violated at all). If that breaks his prediction or creates a paradox... well, bad for him.
I see your point. We can insist that the Predictor, by definition, will actually see the future, whether he likes it or not, and then we can check what breaks (if anything). I'll make it a narration, for simplicity.
The Predictor peeks into the Future. He sees the Chooser standing in front of the two glass boxes. Let's say they both contain money, the first one $1,000 and the second one $1,000,000. The Predictor hears the Chooser thinking aloud:
Chooser: Hmm... the predictor put the million in the second box. That means that, according to the rule, he thought that I would take only that box, not both. I will take both and prove him wrong. And he takes both.
The Predictor returns to the past day scratching his head.
Predictor: I saw him taking both boxes. The rule is clear, I'll leave the second box empty. Hmm... but I saw that they both contained money... This is strange... Well, my business is not to make the future happen -- it is to predict the future, and I did. I'll follow the rule and leave the second box empty.
(Notice that, if the Predictor puts money in the second box too, not following the rule, then the future which he saw would happen, but only because he cheated for this purpose: he didn't just see the future -- he chose to cause it.)
So, the Predictor leaves the second box empty. But the next day, for some strange reason, the Chooser sees two boxes with money... and takes them both, as predicted.
The deterministic timeline is broken. This is definitely a paradox. What was the false assumption? That the future is fixed and lies on a timeline? That it is logically possible for a perfect Predictor to see the future? That it is logically possible to inform a Chooser about what a perfect Predictor saw? One of these must be wrong.
Also notice that free choice was not questioned at any point in this particular version.
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hell-kite
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Re: virus: Re:Newcomb's paradox
« Reply #13 on: 2004-11-25 03:30:25 » |
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Good morrow!
[rhinoceros]
My first remark is that the Predictor is not expected to make any choise.
Just to see the future and apply the simple rule (which was not violated at
all). If that breaks his prediction or creates a paradox... well, bad for
him.
[hell-kite]
Well. It seems I have a different understanding of the word "prediction".
You are right, if what the Predictor foresees MUST happen (I think even I
said something to his regard). The strange thing is, then the future would
determine the past as well as the past the future. In my understanding, if
the actions of the Predictor, including his prediction (to consider
something is an action, too), BECOME A CAUSAL FACTOR of the future, one
cannot follow any simple rules of decision anymore. As I understand
"prediction" under these circumstances, it enables one to RECONSIDER one's
actions (actually, one of the main features/advantages of prediction),
creating some sort of feedback loop (I am repeating myself, but in other
words):
1. Predictor puts money in Box 2 (or considers this action)
1.1 Predictor predicts what WOULD happen now that money is in Box 2
1.1.1 IF Chooser took only Box 2, EXIT (perform this action)
1.1.2 IF Chooser took Box 1+2, perform 2.
2. Predictor does not put money in Box 2 (or considers not to)
2.1 Predictor predicts what WOULD happen now that no money is in Box 2
2.1.1 IF Chooser took Box 1+2, EXIT (perform this action)
2.1.2 IF Chooser took Box 1, perform 1. (entering an inescapable loop as
mentioned before)
This seems related to the oft-quoted paradox of time-travelling...
[rhinoceros]
The deterministic timeline is broken. This is definitely a paradox.
[hell-kite]
The timeline is not broken, but it could well be the game becomes impossible
if the Predictor MUST decide, for he will still remain in the
retro-causality-loop the day after: the Chooser will probably encounter a
deeply disturbed and desperate individual...
[rhinoceros]
What was the false assumption? That the future is fixed and lies on a
timeline? That it is logically possible for a perfect Predictor to see the
future? That it is logically possible to inform a Chooser about what a
perfect Predictor saw? One of these must be wrong.
[hell-kite]
I think it is logically impossible for a perfect Predictor to foresee the
future IF he must act on it and IF by his action he causes an event in the
future to happen (the Chooser's action) and IF this event again causes him
to alter his causal actions regarding that event (this is the case with the
possibilities b & c of my former reply).
Best regards
Björn
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Re: virus: Re:Newcomb's paradox
« Reply #14 on: 2004-11-25 03:35:27 » |
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post scriptum
[rhinoceros]
My first remark is that the Predictor is not expected to make any choise.
Just to see the future and apply the simple rule (which was not violated at
all). If that breaks his prediction or creates a paradox... well, bad for
him.
[hell-kite]
Yes, this model applies either if the Predictor has no causal effect or if
you restrict him to looking into the future just once. The former is not the
case in the transparent-box-version, while the latter should be explicitly
stated as one of the rules of the game...
Björn
-----Ursprüngliche Nachricht-----
Von: owner-virus@lucifer.com [mailto:owner-virus@lucifer.com]Im Auftrag
von rhinoceros
Gesendet: Mittwoch, 24. November 2004 22:28
An: virus@lucifer.com
Betreff: virus: Re:Newcomb's paradox
[hell-kite]
Hello rhino,
I suppose I am being stubborn here, but I am determined to be.
[rhinoceros] No problem, its ok. I saw at least one case that I had not
covered before.
[rhinoceros]
He can't predict the Chooser's *action*. Do you mean that he can predict
that the Chooser will do the opposite of what he predicted? Then either
logic or determinism is broken.
[hell-kite]
Yes, that's what I meant [nb to do something=action is what I meant].
Though, neither logic or determinism needs to be broken. I repeat,
Predictor sees EXACTLY what will happen, and that is one of four
possibilities
Box 1: $1000-Box (always filled)
Box 2: $1000000-Box (conditionally filled)
I. BOX 2 filled
a) Chooser takes Box 2 (within the game concept)
b) Chooser takes Box 1+2 (NOT within the game concept: "defect")
II. Box 2 not filled
c) Chooser takes Box 2 (NOT within the game concept: "defect")
d) Chooser takes Box 1+2 (within the game concept)
One of these actions will happen, for the future is determined. BUT, in the
case of the transparent box, the Predictor becomes, as I said, a causal
force, i.e., part of what determines the future. Thus, he has to
"reconsider" the impact of his action, and granted that he can continually
look into the future and doesn't do the math just once, change his action
IF:
IF the Predictor sees the Chooser "defect" [and the game DEMANDS he still
MUST continue the game (put something into Box 2 or not and leave Chooser to
"choose"), even though the Chooser breaks the rules] we enter some sort of
evil retro-causality loop which will probably result in nervous breakdown (a
computer would break down anyway):
If he foresees b) would happen [if he filled Box 2], Predictor will not fill
the box, which might lead to c) to happen [which Predictor foresees, if so].
Both are violations of the rules, so Predictor can, or must, "freely" choose
to fill Box 2 or not, because neither will do. The loop is broken only if
either I. or II. lead to within-the-rules-behaviour.
Thus, I still don't think that
<snip>the "transparent" version of the paradox only leaves us two options:
Either (a) free will exists and determinism does not exist, or (b)
determinism does exist but making an 100% certain prediction about an
agent's actions, by any means, is fundamentally impossible.</snip>
[rhinoceros]
My first remark is that the Predictor is not expected to make any choise.
Just to see the future and apply the simple rule (which was not violated at
all). If that breaks his prediction or creates a paradox... well, bad for
him.
I see your point. We can insist that the Predictor, by definition, will
actually see the future, whether he likes it or not, and then we can check
what breaks (if anything). I'll make it a narration, for simplicity.
The Predictor peeks into the Future. He sees the Chooser standing in front
of the two glass boxes. Let's say they both contain money, the first one
$1,000 and the second one $1,000,000. The Predictor hears the Chooser
thinking aloud:
Chooser: Hmm... the predictor put the million in the second box. That means
that, according to the rule, he thought that I would take only that box, not
both. I will take both and prove him wrong. And he takes both.
The Predictor returns to the past day scratching his head.
Predictor: I saw him taking both boxes. The rule is clear, I'll leave the
second box empty. Hmm... but I saw that they both contained money... This is
strange... Well, my business is not to make the future happen -- it is to
predict the future, and I did. I'll follow the rule and leave the second box
empty.
(Notice that, if the Predictor puts money in the second box too, not
following the rule, then the future which he saw would happen, but only
because he cheated for this purpose: he didn't just see the future -- he
chose to cause it.)
So, the Predictor leaves the second box empty. But the next day, for some
strange reason, the Chooser sees two boxes with money... and takes them
both, as predicted.
The deterministic timeline is broken. This is definitely a paradox. What was
the false assumption? That the future is fixed and lies on a timeline? That
it is logically possible for a perfect Predictor to see the future? That it
is logically possible to inform a Chooser about what a perfect Predictor
saw? One of these must be wrong.
Also notice that free choice was not questioned at any point in this
particular version.
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This message was posted by rhinoceros to the Virus 2004 board on Church of
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60>
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Othello. Thou dost conspire against thy friend, Iago,
If thou but think'st him wrong'd, and mak'st his ear
A stranger to thy thoughts.
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