Newcomb's paradox

[Osiris]

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."

What needs to be contradicted is the "omniscient's prediction".

What the player should choose does not address to the contradiction.

The amount of money you get based on your choice is a constant condition/function.

It will always be:
Both boxes = $1,000
Box #2 = $1,000,000

Yes, the sum of both boxes will always be greater, but this does not address the constant condition/function.

Just like... rain exists does not address "it will rain in madrid today."

When the sum of both boxes is $1,001,000 you will never pick both boxes.

You saying that you will always get more money by picking both boxes at one time than picking only Box 2 at another time is illogical (like t_w suggests).

 

[StrugglingSceptic]

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.

I see no relation between this and the argument I presented. Not only is this argument not of the same form, but it is a classical argument (it can be formulated in propositional logic), whereas the arguments deriving the contradiction are modal arguments.

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.

And he was wrong from the beginning. Arguments are valid irrespective of what information they address. What you need to do is either point out a formal error in the reasoning, a conclusion which is not a logical consequence of the premises, or demonstrate that the premises are false. The only rigorous way we can do that is to formalise within an appropriate modal logic.

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.

An omniscient being knows the truth value of all propositions. That is the standard usage.

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

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

Not in any reply to me you didn't. You said the player was omniscient, which means they know all true statements. If you want to revise that, you are free to do so.

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

I'm sorry, but this is an absurd usage of the term `omniscience'. Am I omniscient regarding the statement "1+1=2" just because I know it is true? Anyway, I do not see how your rebuttal now amounts to anything. The hypotheses employed in the argument I presented are "Suppose I knew the contents of box 2". You are trying to refute this by saying it means the player has total knowledge of the contents of the boxes, but how is this not just a restatement of the hypotheses?

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.

I'm not going to bother with this new usage of a standard philosophical term. If you want to talk about total knowledge regarding X, just say "total knowledge regarding X."

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

That statement does not appear in the argument I presented.

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,

This is not the argument I presented. The argument you present above is a classical argument, and as I have already said, analysing this problem classically does not yield contradiction. The flaw is with the player's modal arguments.

This is the argument I wanted you to review for soundness and validity:

P1) If I knew there was money in box 2, I should pick both.
P2) If I knew there was no money in box 2, I should still pick both.
C) Therefore, if I want the most money, I should pick both.

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

What do you mean? If both of the player's arguments for choosing box 2 and choosing both boxes are sound and valid then there is a contradiction.

When someone presents you with a logical argument and you are asked to identify the flaw, you must show either that the premises are not all true, or that the general principles of reasoning employed do not always preserve truth. You cannot handwave with a vague statement like "this 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 is not with statement x. The contradiction is with the following two statements:

"The player should open box 2"
"The player should not open box 2".

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

Yes. But I am not sure if it is the case. One of the interesting things about paradoxes is that there is usually controversy over which assumptions are contradicted.

 

[StrugglingSceptic]

What needs to be contradicted is the "omniscient's prediction".

Those are not my needs. All I am wanting to show is that the contradiction is not necessarily the result of invalid argumentation on the part of the player. It is only t_w who thinks the contradicted assumption is the predictor's omniscience. I have already said there are several possible assumptions which could be contradicted.

What the player should choose does not address to the contradiction.

Yes it does. The problem is a paradox with regards to what the player should do in the given situation.

You saying that you will always get more money by picking both boxes at one time than picking only Box 2 at another time is illogical (like t_w suggests).

I have never said this. In fact, I stated earlier that it is completely true that if the player picks box 2, they will earn more money than if they pick both boxes. This is true by classical argumentation alone. The logical contradiction arises in the player's reasoning about what he should do.

 

[t_w]

. It is only t_w who thinks the contradicted assumption is the predictor's omniscience.

If we have a paradox then something has to 'give', e.g. in the grandfather paradox it is backwards time-travel. I propose it is the being's omniscience. What do you think 'gives'?

 

[t_w]

Osiris, the paradox arises not because of two differebt courses of action can be taken that are logically opposed. It is because there is a completely airtight argument for taking both(that you always get more money) and a completely airtight argument for choosing only B2. If this were any old situation, as you claim, then there should be a better choice. The choices should not be equaly logicall, especially when they return different amounts of money.

 

[Osiris]

I see no relation between this and the argument I presented. Not only is this argument not of the same form, but it is a classical argument (it can be formulated in propositional logic), whereas the arguments deriving the contradiction are modal arguments.

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.

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

The player knowing that there is money in box 2 will never happen. This is an absurdity, it is void...

what you have is this:

1. [void]

2. 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 is why I say your argument does not address the problem.

An omniscient being knows the truth value of all propositions. That is the standard usage.

Yes, but that doesn't mean people don't use it the way I did.

Not in any reply to me you didn't. You said the player was omniscient, which means they know all true statements. If you want to revise that, you are free to do so.

This is what I said:
Then the player is omniscient in the sense of knowing the content... both the player and the predictor will be omniscient.

I'm sorry, but this is an absurd usage of the term `omniscience'. Am I omniscient regarding the statement "1+1=2" just because I know it is true? Anyway, I do not see how your rebuttal now amounts to anything. The hypotheses employed in the argument I presented are "Suppose I knew the contents of box 2". You are trying to refute this by saying it means the player has total knowledge of the contents of the boxes, but how is this not just a restatement of the hypotheses?

what you are proposing is that you will know what an omniscient being will do rather than the other way around.

you are creating an absurdity before the problem (Newcomb's paradox) starts.

I'm not going to bother with this new usage of a standard philosophical term. If you want to talk about total knowledge regarding X, just say "total knowledge regarding X."

ern, i'm sorry if you were not aware of such usage... if you want to stop the usage I'd suggest taking it up to universities or institutions that make decisions regarding the Enlish language.

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

That statement does not appear in the argument I presented.

No?

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 is not the argument I presented. The argument you present above is a classical argument, and as I have already said, analysing this problem classically does not yield contradiction. The flaw is with the player's modal arguments.

Such argument does not address the problem.

Before it begins it already has a contradiction... that you will know what an omniscient being will do and contradict him without him(omniscient being) knowing that you will do such thing.

This is the argument I wanted you to review for soundness and validity:

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.

What do you mean? If both of the player's arguments for choosing box 2 and choosing both boxes are sound and valid then there is a contradiction.

The argument you presented for choosing both boxes is not valid... before it starts it has already a contradiction, an absurdity, and when the whole thing fails you assume it is a paradox... but you fail to see it was the contradiction you had before it started.

When someone presents you with a logical argument and you are asked to identify the flaw, you must show either that the premises are not all true, or that the general principles of reasoning employed do not always preserve truth. You cannot handwave with a vague statement like "this does not address the problem".

I have been explaining this for a while now, I would have thought you knew what I meant by now.

1. [ void ]
2. If box 2 is empty, I should pick both boxes.
Therefore I should pick both boxes.

This does not address the problem because it only suggests 2.

The contradiction is not with statement x. The contradiction is with the following two statements:

"The player should open box 2"
"The player should not open box 2".

I think you mean:

The player should open box 2.
The player should open both boxes.

There is no contradiction in that because you are (not knowingly) not applying the same rules to both sides.

You say that the player should open both boxes if he knows what the predictor will choose... now this is the argument for choosing both boxes. Now, if you know what the predictor will choose, what is the argument you have for choosing only box 2? The only argument for choosing only box 2 is if we didn't know what the predictor predicted.

There is no contradiction there... you just failed to apply the same assumptions to both sides.

 

[David Gould]

Yes. An argument can be logically perfect in every detail and still be wrong if the assumptions underpinning it are wrong.

In other words, the hidden premise is that the omniscient being can be wrong, which is obviously illogical.

That is why you end up with an illogical result from a seemingly logical argument.