You have only the choices of logical deduction, spontaneity, and pot luck.

The only one of those that always works is logical deduction.

You can't think of a single number that they could all choose that would not work because any number they all choose will work every time. As logicians, they know what always works because they can deduce what always works. I didn't try every number, I deduced that any number would work. So if I can deduce what always works, why can't perfect logicians?

Silhouette wrote: James S Saint wrote: Was there ever only one person on the island when the guru said there was one?

Noooo.

It is irrelevant.

The Guru never said that there was

only one person on the island.

Who said anything about the guru saying that there was ONLY one??

Carleas wrote:Again, James, what you're saying suggests that you don't understand the logic behind the canonical solution.

What it suggests to me is that You do not understand logic.

Carleas wrote:But the counterfactual, "if there were only 1 he would leave on day 1", is still necessary to reach the conclusion.

You should explain that to Sil.

Carleas wrote:For some reason, though, when we get to 4, you and Fixed Cross discount the value of the same information, and suppose that the 1 would just spontaneously know that he has blue eyes. What is the difference between the case of 3 blue islanders and the case of 4 blue islanders such that the guru is necessary in the former but not in the latter?

What FC and I know is that it is not spontaneous, else it could not work

every time they do it. Why don't you know that?

Carleas wrote:If we use your example for the

case of 4 blue eyed islanders, I think what Silhouette is saying becomes even clearer:

James S Saint wrote:I am blue out of 100 blues;

A) They all know [that they all know] [that there are at least 1 blues].

B) They all know [that they all know] [that they don't know their own color].

C) They all know [that they all know] [that they will leave if they could deduce their color].

D) They all know [that they all know] [that if there were only 1 and (A) were true, they would leave the 1st day].

E) They all know [that they all know] [that if there were only 2 and (A) were true, they would leave the 2nd day].

F) They all know [that they all know] [that if there were only 3 and (A) were true, they would leave the 3rd day].

G) They all know [that they all know] [that if there were only 4 and (A) were true, they leave the 4th day].

.

.

N) They all know [that they all know] [that if there were only 100 and (A) were true, we leave the 100th day].

You have trouble with patterns, I take it..?

Carleas wrote:We are given that no one knows their eye color, and D requires that there is at least 1 who does.

(D) does NOT require that anyone know their own eye color. It makes the

exact same hypothesis as the canonical version, "

IF there were only one and he knew there was one."

Carleas wrote:The contradiction, as Silhouette has repeatedly explained, is that you're taking the knowledge out of context. 4 know there is at least 1. But if there were only 1, he would not know that there is at least 1 - until the guru speaks.

I haven't taken any more out of context than you;

"

If there was only one when the guru said that was one" (which

never took place).

But the question, still incorrectly answered was simply;

"IF everyone chose the SAME number to start counting the days before deducing their color, would it always lead to an accurate deduction of their color?"So far, you have each said "no", yet you cannot come up with a single number that doesn't lead to an accurate deduction of the color, every time they do it.

It is a yes or no question with a request for what number that would be if your answer is "no".

Let me guess, you guys took an oath to ban yourselves if you turn out to be wrong...??

Seems it has to be something like that for you to go to such extreme lengths to avoid such a simple question.