The reasoning for blue eyed people specifically works because the guru said he sees blue eyes. — flannel jesus

The Guru doesn't need to say it. Him saying it is a red herring. As perfect logicians, every blue-eyed person already knows that the Guru sees at least one blue-eyed person and every brown-eyed person already knows that the Guru sees at least one brown-eyed person.

To be more specific, Unenlightened's first step of reasoning is



This first step of reasoning doesn't work for brown eyed people, because that's not what the guru said.

So if his first step of reasnoning doesn't work, then you can't just swap out blue for brown.

Did they all arrive on the same day, and do they all know that they all know that they arrived on the same day?

Also I think the brown eyed people would not know their eye-colour for another 99 days after the blue eyes left, but only that they themselves didn't have blue eyes.

Also I think the brown eyed people would not know their eye-colour for another 99 days after the blue eyes left, but only that they themselves didn't have blue eyes. — unenlightened

Why do you think that? Imagine the Guru were to have said "I see at least one blue-eyed person and at least one brown-eyed person".

But as I said to flannel, the Guru doesn't even need to say it because everyone already knows that she sees at least one blue-eyed person and at least one brown-eyed person, and so her saying it is a red herring.

But as I said to flannel, the Guru doesn't even need to say it — Michael

You said you base your reasoning on unenlighteneds reasoning. Step 1 of his reasoning completely relies on the guru saying what he said. Can you see that?

So you must have different reasoning. Will you make it explicit?

Step 1 of his reasoning completely relies on the guru saying what he said. Can you see that? — flannel jesus

That's the red herring; it doesn't. Everyone already knows that she sees at least one brown-eyed person, so her expressing this fact verbally provides no new information.

are you sure you know what I'm talking about when I say "the first step of unenlighteneds reasoning"? Because in that first step, in that hypothetical, no, not everyone knows what the guru said.

If you're saying unenlighteneds first step is the red herring, then that's fine, that means you have different reasoning from him, and so your conclusion can't just be "his reasoning but with brown". You're fundamentally disagreeing with his reasoning, doing something different. You have your own reasoning.

The first step in the reasoning is "the Guru sees at least one person with brown eyes". She doesn't need to say "I see at least one person with brown eyes" for this first step to be true. Her saying so is a red herring.

ok so your reasoning is different from unenlighteneds then. Can you tell us what it is?

ok so your reasoning is different from unenlighteneds then. Can you tell us what it is? — flannel jesus

It's the same. Here are unenlightened's exact and complete words:



Notice that he doesn't mention the Guru or what she says at all.

Notice that he doesn't mention the Guru or what she says at all. — Michael

It's implicit in the first sentence. The first sentence of his reasoning clearly depends on the guru saying what she said. Please look specifically at that first sentence, let's at least agree on that.

" there was only 1 person w. blue eyes, that person would see no blue eyes and therefore know they had blue eyes and leave that night."

If the guru doesn't say what she said, then no, the 1 blue eyed person wouldn't leave that night

The first sentence of his reasoning clearly depends on the guru saying what she said. — flannel jesus

No it doesn't. It only depends on "the Guru sees at least one blue-eyed person" being true. It doesn't depend on her saying so.

how? How does the blue eyed person know they have blue eyes in that scenario? What's the single blue eyed persons reasoning in that scenario?

How does the blue eyed person know they have blue eyes in that scenario? What's the single blue eyed persons reasoning in that scenario? — flannel jesus

The reasoning is: if the Guru sees at least one person with blue eyes and if I don't see anybody with blue eyes then I have blue eyes.

but how would he know the guru knows that? The guru didn't say anything. He has no idea what the guru knows

but how would he know the guru knows that? The guru didn't say anything. He has no idea what the guru knows — flannel jesus

Every person on the island already knows that the Guru sees at least one person with blue eyes and one person with brown eyes, whether or not she says so, as explained here. Given this fact:

If I don't see anyone with blue eyes then I have blue eyes, else if I don't see anyone with brown eyes then I have brown eyes.

This reasoning is valid even though I do in fact see others with blue eyes and brown eyes.

Every person on the island already knows that the Guru sees at least one person with blue eyes — Michael

Not in the scenario with one blue eyed person they don't

Not in the scenario with one blue eyed person they don't — flannel jesus

I see 100 people with blue eyes and (unknown to me) I have brown eyes. The Guru says "I see at least one blue-eyed person". Now I imagine a scenario where these 100 blue-eyed people don't exist.

If I can still assume that the Guru says "I see at least one blue-eyed person" then I can still assume that the Guru sees at least one blue-eyed person, but doesn't say so.

what?

If there's only one guy with blue eyes, he would only know that the guru sees blue eyes if the guru told him. There's no way around that.

If there's only one guy with blue eyes, he would only know that the guru sees blue eyes if the guru told him. — flannel jesus

In practice, perhaps, but the logic doesn't require that the Guru say anything. The logic only requires that I know that the Guru sees at least one blue-eyed person and one brown-eyed person.

Given that our reasoning stipulates (contrary to the facts) that I don't see any other blue-eyed person but that the Guru still says "I see at least one blue-eyed person", it can also stipulate (contrary to the facts) that I don't see any other blue-eyed person but that I know that the Guru still sees at least one blue-eyed person.

And I can stipulate all of this even if I in fact have brown eyes.

I have no idea why you're stipulating completely random things. They don't make any sense. Nothing in the description involves any telepathy. You only know what the guru sees if he tells you.

I’m not stipulating random things, as shown by the fact that if the people on the island were to apply my reasoning then they would all correctly deduce the colour of their eyes. That’s not just some happy coincidence; it’s because the reasoning is sound.

but they wouldn't. If the guru didn't say anything, and you don't start adding random things like telepathy, nobody deduces anything. If there's an island with 2 people and the guru and he doesn't say anything, and there's no telepathy, nobody knows anything

If there's 2 blue 2 brown 1 guru and he doesn't say anything, no telepathy, nobody gets off the island.

Right?

No it doesn't. It only depends on "the Guru sees at least one blue-eyed person" being true. It doesn't depend on her saying so. — Michael

No. It does depend on the guru saying so unless everyone already knows that everyone already knows at the same time, as I suggested above and you ignored. This is the extra information that the guru imparts: she doesn't inform them about what she sees, but she puts everyone in a synchronised state of knowing each other's knowing. That is what is required for the nested hypotheticals to begin.

I reason thus:
If there was only 1 person with blue eyes {PWBE} and that person knew that the guru sees blue eyes, then that person would know that they have blue eyes and would leave tonight.

Therefore:
If there were only 2 PWBE and the guru sees blue eyes {GSBE} then neither would leave tonight, and when they see that, they each know they have blue eyes and would leave on the second night.

And so on.

But the factual knowledge that I can see multiple blue eyes and thus already know that the guru can see blue eyes cannot be imported into the counterfactual hypothetical wherein the blue eyed person would know no such thing because he would not himself see blue eyes, and thus could not know therefore that the guru saw blue eyes ... wait for it ... UNLESS SHE SAID SO.

If there's an island with 2 people and the guru and he doesn't say anything, and there's no telepathy, nobody knows anything — flannel jesus

And if in this scenario I have brown eyes then the Guru wouldn’t say “I see someone with blue eyes”, and yet we are allowed for the sake of argument to assume that she does.

Given that the Guru does in fact say it when there are 201 people we are allowed to assume that she still says it in a hypothetical scenario with 2 people.

And given that we all know what the Guru sees without her saying it when there are 201 people we are allowed to assume that we still do in some hypothetical scenario with 2 people.

The reasoning is sound in either case and gets us to the correct answer.

it should be obvious to you now, given unenlighteneds last post, that his reasoning is very much based on what the guru said

No. It does depend on the guru saying so unless everyone already knows that everyone already knows at the same time, as I suggested above and you ignored. This is the extra information that the guru imparts: she doesn't inform them about what she sees, but she puts everyone in a synchronised state of knowing each other's knowing. That is what is required for the nested hypotheticals to begin. — unenlightened

She doesn’t need to say anything for perfect logicians to be in a synchronised state. At every moment they are in a synchronised state and will apply the same reasoning.

And if new people arrive or are killed by tigers during this process they’ll adapt their premises (e.g “the Guru sees either N or N+1 blue-eyed people”) as needed.

But the factual knowledge that I can see multiple blue eyes and thus already know that the guru can see blue eyes cannot be imported into the counterfactual hypothetical wherein the blue eyed person would know no such thing because he would not himself see blue eyes, and thus could not know therefore that the guru saw blue eyes ... wait for it ... UNLESS SHE SAID SO. — unenlightened

She doesn’t need to have actually said something in the “real” world in which I see 100 blue-eyed people for me to stipulate that she said something in this counterfactual hypothetical world in which I don’t see any blue-eyed people.

In the “real” world I know that she sees at least one blue-eyed person even without her saying so, and so if it helps I can just assume that she says so even if she doesn’t.

so just ignore the first scenario and imagine a scenario where there's 4 people on the island, perfect logicians, no guru, just 2 brown eyes 2 blue eyes. If it genuinely doesn't matter if the guru says anything, can these people figure out their eye colour? How?

Oops.