Newcomb's paradox

t_w said:

Even if you will never choose it, if you could you would get more. So choosing both would give you more money.

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Your problem is the underlined text...

If you could choose it then the predictor is not omniscient now is he?

You are not playing by the rules...

Well the reason it is a paradox is because we have two logical arguments that are contradictory. So if you concede it isn't illogical.....

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Your argument is not relevant to this problem because it does not address the problem.

You are assuming that the act of choice changes the amount in the box - whether you realise it or not.

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hmm... no, you are the one assumming that.

This is your train of thought:

You pick the 2 boxes.
An omniscient being would leave box 2 empty and put 1,000 in box 1.
You assume that your choice will change the amount of money that the omniscient being already placed in the box. (it doesn't work that way...)

They are impossible but I don't think this changes anything. This isn't a practical experiment.

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A logical contradiction as a result of an assumption is a paradox. E.g. the Grandfather paradox assumes backwards time travel. The logical paradox disproves it.

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You did not address the brownie example I made that parallels Newcomb's paradox.

The grandfather paradox is in no way similar to newcomb's paradox.

t_w said:

Osiris, I've thought of a way to explain why i think you're wrong. I'm using another paradox, the grandftaher paradox.

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Now, you are comparing Newcomb's paradox to an actual paradox by assumming that Newcomb's paradox is an actual paradox...

hmmm... all I can see is that you have created a strawman.

Backwards time travel is assumed. if one goes back in time and kills ones grandfather, then you would'nt be born. If you wouldn't be born then you wouldn't go back in time to kill your grandfather, and he wouldn't die. In which case you would be born. The conclusion is that backwards time-travel is impossible.

Now, your position is analogous to saying, 'but you assumed backwards time travel at the start. So you can't conclude it doesn't exist. You said it existed, so the conclusion cannot be that it doesn't exist!'

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This is what you are saying....

t_w: the predictor is omniscient, but let's say I could choose something where he won't know my choice.

This is exactly what you are doing, you are first starting with a contradiction and when the conclusion fails you say it is a paradox.

This is why I say that you are not playing by the rules.
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Let's go back to the brownie example:

You are starving for a brownie.
I tell you I will give you a brownie ... BUT

[conditions]
1. You can take the brownie only if you don't eat it. [box 2]
2. You can't take the brownie if you will eat it. [both boxes]
[/conditions]

What you want to do is this:

I am starving for a brownie and if I choose the brownie... I could eat it... therefore this is a paradox because I can eat it and at the same time I am told that I can't eat it.

I hope that after this example you are able to see it.

Osiris said:

I don't think you understood what this problem is about...

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It appears that I didn't. Thanks for the heads up.

In that case picking the second box is the only sensible option.

Osiris:

Most of what you say is correct. If the player chooses box 2, they will receive £1,000,000. If the player chooses box 1 and 2, they will receive £1,000. The proof of this follows purely classical lines.

The problem is that the player's two contradictory arguments do not follow purely classical lines. They contain and depend on modal terms and the logic of choice. As such, the arguments are subject to a different analysis under a different system of logic, but whilst the rules for classical logic are almost universally agreed upon, I don't think rules for these other logics are.

Here is another argument the player could employ:

If I knew there was money in box 2, I should pick both.
If I knew there was no money in box 2, I should still pick both.
Therefore, if I want the most money, I should pick both.

This seems intuitively sound and valid (and intuition is all we have here until someone presents us with a system of logic in which to formalise the above statements). However, assuming you agree with the premises, you want to claim that this argument is invalid, because its conclusion is false.

But this is an odd situation. It means that the player's rational choice is completely inconsistent with any kind of more informed choice on the contents of the box. It means that the following argument is also always invalid:

If I knew P was the case, I would do A.
If I knew P was not the case, I would still do A.
Therefore, I should do A.

The question is then: do we give up the validity of arguments like this one (which appears valid to me), or do we keep looking at Newcomb's problem to see if we can identify another source of contradiction? If we keep looking, there are plenty of candidates we can check: the problem is inherently self-referential, and self-reference can yield paradox; self-reference and omnscient prediction is not always possible (suppose the player was shown the contents of each box); or maybe any suitable logic for dealing with the player's arguments requires the assumption of libertarian free-will, which is inconsistent with the omniscient predictor.

If I knew there was money in box 2, I should pick both.
If I knew there was no money in box 2, I should still pick both.
Therefore, if I want the most money, I should pick both.

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As stated by the rule above, the player can not change the contents of the boxes. It seems illogical to not include the very thing which determins the contents of the boxes, (the prediction of the being).

kopilo said:

As stated by the rule above, the player can not change the contents of the boxes.

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What do you mean by changing the contents of the boxes?

At the time of playing the game, the statement "there is money in box 2" is either true or false according as the statement "the player will choose box 2" is true or false (something which the omnscient predictor has determined). So the player can form hypotheticals about knowing the truth of the first statement, and what consequences it will have for what they should do.

t_w said:

Osiris said:

t_w said:

Even if you will never choose it, if you could you would get more. So choosing both would give you more money.

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Your problem is the underlined text...

If you could choose it then the predictor is not omniscient now is he?

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Irrelevant.

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If this is irrelevant than you are not addressing the problem.

You are first creating a contradiction outside the paradox... "the omniscient being won't predict my choice" ... <-problem.

then you use this contradiction into the Newcomb's p. ... when you do you are not addressing the same problem but a different one. The conclusion will fail because you started out with a contradiction, you believe this is a paradox because of this and don't realize that the problem is before you started the problem, not the conclusion.

I'm not claiming you'd make more money by choosing both.

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You're not claiming you'd make more money by choosing both?

I am simply looking at the fact that choosing both gets you £1000 more every time. I'm not assuming my choice would change anything.

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So, you're claiming you'd make more money by choosing both?

t_w, just because there is always more money in both boxes at one time it doesn't mean that you will be able to break the conditions set up by the problem.

If there is 1,000,000 in box 2, you will never take both.

If you will always take both, then box 2 will just simply be empty.

You might say it is backward causality but it isn't, it is simply the being's power. Your problem is that you don't understand the concept of omnisciency. You want to have it and not have it at the same time creating your misconception.

What?!?! How does it parallel it? No assumption is made. No logically contradictory arguments exist that present a paradox.

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Right, same with the Newcomb's paradox... now see that the omniscient being's power are merely a condition... just like

[1] you can take the brownie if you will not eat it... or you can take $1,000,000 if you don't take box 1 along with it.

[2] you can't take the brownie if you will eat it... or you can't take the $1,000,000 if you take box 1 along with it.

what you want to do:
[3] if you take the brownie then you can eat it disregarding the condition... or if there is $1,000,000 in box two, just take both disregarding the condition set by the omniscient being.

W.e. Just answer my question as to whether you can see the error in the grandfather paradox analysis above.

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Yes the grandfather's paradox is a paradox, but you don't understand that you are just creating a strawman.

t_w said:

The being's omniscience is contradicted by the rule that taking both gets you £1000 more every time.

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No. You seem to not understand what a contradiction is in this problem...

The omniscient being states that you will only pick box 2.

How is the fact that the sum of both boxes is always greater than just box 2 a contradiction to the omniscient being's prediction? Do you expect the being's power to somehow make $1,000 + $1,000,000 = $1,000,000?

If the omniscient being states that you will only pick box 2, the only contradiction would be that you pick both boxes.

There being $1,001,000 in both boxes is not a contradiction. A contradiction is that you will get $1,001,000.

The only contradictions in this problem is if you get $0 or $1,001,000

So one can easily(as you do) claim that it isn't a rule because it is contradicted by the already-assumed-omniscience. I could argue vice-versa.

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You could pick both boxes thinking that, you will always get $1,000. I am not say that choosing both boxes is illogical... I am only saying that expecting to get $1,001,000 is illogical.

StrugglingSceptic said:

The problem is that the player's two contradictory arguments do not follow purely classical lines. They contain and depend on modal terms and the logic of choice. As such, the arguments are subject to a different analysis under a different system of logic, but whilst the rules for classical logic are almost universally agreed upon, I don't think rules for these other logics are.

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One argument takes into account the being's omniscient power.

The second argument ignores the being's omniscient power. They think that, since there is always more money in both boxes that they can choose and expect $1,001,000 ignoring the being's omnisciency.

Here is another argument the player could employ:

If I knew there was money in box 2, I should pick both.
If I knew there was no money in box 2, I should still pick both.
Therefore, if I want the most money, I should pick both.

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But this is not the case... the only way you'd know is if you were omniscient yourself.

and I stated this before ... that the only way it could be a contradiction if the predictor and the player are both omniscient.

Osiris said:

I think the paradox may be when both the predictor and the player are omniscient.

- player would pick both.
- predictor knows this and would put only 1000 in A
- player knows this and would pick only B (empty) proving predictor wrong.
- predictor would know this and would put 1,000,000
...

there be no answer unless both come into an honest agreement.

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But the problem as it is assumes that the player is not omniscient. So, you knowing what will happen and choose contrary to the predictor's choice won't happen.

This seems intuitively sound and valid (and intuition is all we have here until someone presents us with a system of logic in which to formalise the above statements). However, assuming you agree with the premises, you want to claim that this argument is invalid, because its conclusion is false.

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But this 2nd argument assumes an omniscient being and expects this omniscient being to somehow predict wrong... does it not? Since this is the case, is it really sound and valid? Remember, the player is not omniscient himself.

But this is an odd situation. It means that the player's rational choice is completely inconsistent with any kind of more informed choice on the contents of the box. It means that the following argument is also always invalid:

If I knew P was the case, I would do A.
If I knew P was not the case, I would still do A.
Therefore, I should do A.

The question is then: do we give up the validity of arguments like this one (which appears valid to me)

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You don't have to give up the validity of arguments like that... the thing is that does not address the problem.

, or do we keep looking at Newcomb's problem to see if we can identify another source of contradiction? If we keep looking, there are plenty of candidates we can check: the problem is inherently self-referential, and self-reference can yield paradox; self-reference and omnscient prediction is not always possible (suppose the player was shown the contents of each box);

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Then the player is omniscient in the sense of knowing the content... both the player and the predictor will be omniscient.

or maybe any suitable logic for dealing with the player's arguments requires the assumption of libertarian free-will, which is inconsistent with the omniscient predictor.

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what's libertarian freewill? that a person's choice can't be determined?

t_w said:

If I am being fallacious(I don't think I am), then it is a false analogy. Not a strawman.

Now, if it were as simple as 'we should always take B2 because we will get the £1,000,000', then there wouldn't be an argument for taking both; that there is always more in both than in only one. It doesn't matter whether or not you can choose both if the million is in B2, the fact remains that there is more money in both,

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t_w,

your confusion is that, since the sum of money is always more than box 2... this means that somehow you will be able to get $1,001,000.

This is like saying...

if I pick the brownie which I can't eat and I am hungry -- by me having the brownie I would be able to eat it too -- therefore I should pick the brownie because I will be able to eat it. (even though the condition is for you not to eat it.)

so the logical choice should be to take both.

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these are the two logical choices:
1. taking both
2. taking only box 2

you can take both... i'm not saying you can't... just don't expect $1,001,000 because that'll be illogical.

Please be reminded that when I first presented this paradox, I was using the predictive power of the being as 90%.

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If the being is capable of error then it is not a paradox...

if the predictor predicts that you will take box 2.
you take both boxes, it does not make it a paradox because you only contradicted the being because he is capable of error.

I have been arguing against a position I am unfamiliar with. To me, the problem remains a paradox if the predictive power is 90% or 100%.

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then you have not understood the problem.

Osiris said:

One argument takes into account the being's omniscient power.

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It doesn't matter what they take into account (neither argument takes into account that it is Sunday today, either). If the logical steps employed in the argument are all valid, then the argument as a whole is valid, and we have a contradiction.

But this is not the case... the only way you'd know is if you were omniscient yourself.

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What is not the case? And how is it relevant whether the hypothetical knowledge can actually be acquired or not? The point is that a more informed rational decision on the contents of box 2, whether or not the knowledge can actually be obtained, will always be to choose both boxes, so the player should choose both boxes.

Furthermore, how does knowing the contents of box 2 cause the player to know everything?

But this 2nd argument assumes an omniscient being and expects this omniscient being to somehow predict wrong... does it not?

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Where is this assumption?

Since this is the case, is it really sound and valid? Remember, the player is not omniscient himself.

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The questions of soundness and validity are distinct. Do you believe that the premises are true, and do you believe that the conclusion is a logical consequence of them?

You don't have to give up the validity of arguments like that... the thing is that does not address the problem.

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But you would have to give up the validity of arguments like that. The new argument I have presented is one of those arguments, and if one of them fails to preserve truth from premises to conclusion, then the general form is invalid by definition.

So if we reject this new argument then we are saying that there are cases where it is logical to take action A, even though any additional information on some question Q would make it logical to not take action A. I find such a scenario bizarre enough to call this a paradox (paradoxes can just be bizarre results -- Skolem's paradox, Banach-Tarski paradox). Otherwise, we should look for other sources of contradiction.

Then the player is omniscient in the sense of knowing the content... both the player and the predictor will be omniscient.

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You are saying that if the player knows the contents of the box, they must know the truth of everything in the universe? How does this follow?

what's libertarian freewill? that a person's choice can't be determined?

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That it is generally not determined (by say, the state of the universe at any time prior to the choice). That would mean the choice cannot be determined by an inerrant prediction either.

Logic and Contradiction Tutorial.
-------------------------------

Statement x: "It will not rain in Madrid today."

The fact that rain exists does not make Statement x a contradiction.

The fact that rain exists does not fully address statement x.

The only contradiction to Statement x is : "It will rain in Madrid today."

--------------------------------

Now to Newcomb's paradox.

Statement x: Omniscient being predicted that you will pick Box 2.

The fact that there is always more money in both boxes does not make statement x a contradiction.

The fact that there is always more money in both boxes does not fully address statement x.

The only contradiction there is to statement x is if "you picked both boxes."

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Now, if the being is not omniscient and he is capable of error... you picking both boxes does contradict his prediction ... but that is because he is capable of error -- no paradox.

Osiris said:

Logic and Contradiction Tutorial.

-------------------------------

Statement x: "It will not rain in Madrid today."

The fact that rain exists does not make Statement x a contradiction.

The fact that rain exists does not fully address statement x.

The only contradiction to Statement x is : "It will rain in Madrid today."

--------------------------------

Now to Newcomb's paradox.

Statement x: Omniscient being predicted that you will pick Box 2.

The fact that there is always more money in both boxes does not make statement x a contradiction.

The fact that there is always more money in both boxes does not fully address statement x.

The only contradiction there is to statement x is if "you picked both boxes."

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Now, if the being is not omniscient and he is capable of error... you picking both boxes does contradict his prediction ... but that is because he is capable of error -- no paradox.

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This is all correct. However, the contradiction is not identified in any of the above statements. The contradiction is identified with the statements:

"The player should choose both boxes."
"The player should choose box 2."

StrugglingSceptic said:

It doesn't matter what they take into account (neither argument takes into account that it is Sunday today, either). If the logical steps employed in the argument are all valid, then the argument as a whole is valid, and we have a contradiction.

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But they are not...

What we have is this:

Statement x: It will not rain in Madrid today.
Statement y: Rain exists.
Therefore it will rain in Madrid and it contradicts statement x.

Such argument does not address the problem. It ignores information, I am not the only that has said this... Mr. David Gould said it from the beginning.

What is not the case? And how is it relevant whether the hypothetical knowledge can actually be acquired or not? The point is that a more informed rational decision on the contents of box 2, whether or not the knowledge can actually be obtained, will always be to choose both boxes, so the player should choose both boxes.

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If you know that there is money in box 2... then you are an omniscient being... or at least omniscient regarding the content of the boxes.

If that's the case, then if could be a paradox where you could choose both boxes when there is money in box 2... or you could choose box 2 when box 2 is empty -- just to contradict the predictor.

But this is the same as if you are cancelling omnisciency out by both of you having omnisciency.

Furthermore, how does knowing the contents of box 2 cause the player to know everything?

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www.dictionary.com
Omniscience: Having total knowledge; knowing everything:

I said:
[being omniscient] regarding the contents of the boxes.

[having total knowledge] regarding the contents of the boxes.

Let's say you don't know everything, but you have this power that allows you to know everything there is to know about tv programming. You will know what aired on channel 4 eight years ago... you will know what will air on channel 4 eight years from now. Will you not be omniscient regarding tv scheduling/programming?

You are not omniscient in the sense that you know everything, but you will have tv probramming omnisciency.

Osiris said:

But this 2nd argument assumes an omniscient being and expects this omniscient being to somehow predict wrong... does it not?

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Where is this assumption?

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here: "you will always get more money by picking both boxes."

The questions of soundness and validity are distinct. Do you believe that the premises are true, and do you believe that the conclusion is a logical consequence of them?

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These are the premises: omniscient being will predict your choice.

These are the rules:
Pick box #2 = $1,00,000
Pick both boxes = $1,000

The conclusion:
picking box #2 will always yield $1,000,000
picking both will always yield $1,000

The flaw:
Thinking that since the sum of both boxes is always more than justone box at one time... picking both boxes will yield more than just picking box 2 (ignoring the premise).

But you would have to give up the validity of arguments like that. The new argument I have presented is one of those arguments, and if one of them fails to preserve truth from premises to conclusion, then the general form is invalid by definition.

So if we reject this new argument then we are saying that there are cases where it is logical to take action A, even though any additional information on some question Q would make it logical to not take action A. I find such a scenario bizarre enough to call this a paradox (paradoxes can just be bizarre results -- Skolem's paradox, Banach-Tarski paradox). Otherwise, we should look for other sources of contradiction.

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As I said... that argument does not address the problem.

Statement x: is that an omniscient being predicted you will take box 2.

The contradiction is not that there is always more money in the two boxes... this does not address statement x.

The contradiction only arises when the being predicted you will take box 2 and you take both boxes... in result getting $1,001,000 ....

You are saying that if the player knows the contents of the box, they must know the truth of everything in the universe? How does this follow?

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I answered this above...

That it is generally not determined (by say, the state of the universe at any time prior to the choice). That would mean the choice cannot be determined by an inerrant prediction either.

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Yes, than if that is the case, the contradiction happens before the Newcomb's P. starts...

t_w said:

It doesn't matter whether you're able to get it or not. The rule still applies that choosing both boxes will always get you more money. Even if it is the case that the only instance where you will choose two is when there is no £1,000,000 in B2, that doesn't detract from the fact that choosing both always earns more money. If you choose both then there can't have been money in B2, and then choosing both is the only logical thing to do.

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I have said this so many times...

Just because the sum of both boxes is always greater than box 2 at one time, it doesn't mean that choosing both boxes will get you more than if you chose box 2 at two different times.

I really don't know what this has to do with anything. I see why you chose this analogy, but unfortunately it is only analogous to your flawed interpretation.

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Osiris said:

these are the two logical choices:
1. taking both
2. taking only box 2

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If they are both logical then we have a contradiction. There should be a 'better' choice.

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There is a better choice.
The better choice is taking only box 2.

You seem to be confused to what it means to be logical.

If I offered you to take either 25 cents or $1... any choice would be logical.

But if you choose both you always take the maximum amount available, because if you choose both there won't be anything in B2. So choosing both yields the maximum profit.

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You are somewhat correct...

If you choose both you always take the maximum amount available. But the maximum amount will always be 1,000...

You are not creating a paradox by picking both boxes and always getting 1,000... the only way it'd be a paradox is if you acquired $0 or $1,001,000

Picking both boxes does not address statement x: the predictor predicted that you will take both boxes... rather it confirms that you would take both boxes.

For the last time, you need to drop your obsession withn the being's omniscience and look at the bigger picture.

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The bigger picture is the being's omniscience. I suggest you look at the bigger picture.

Yet again I don't understand your relevance - because there is nothing relevant to understand about your statement...

I feel I understand this problem. Why would me positing the being as being 90% accurate mean I don't understand the problem?

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given: there is a bag with balls labeled 1 through 10 inside.
statement x: random person says that you will pick ball labeled #7.

case 1. You put your hand in the bag and you draw ball labeled #7.

case 2. You put your hand in the bag and you draw some other ball.

If case 2 happened... would it be a paradox?