that's why you have to take it one step at a time. Start by ONLY imagining the scenario with two blue eyed people. The case of "what would happen if there are only one?" would naturally occur to them. Right?

But at three people, the Guru may as well not have spoken — hypericin

But here's the trick. You've agreed with the case of two blue eyed people. Which means, unambiguously, if there were two blue eyed people, they would leave on the second day, right?

Which implies, unambiguously, if there WEREN'T only two blue eyed people, they wouldn't leave on the second day.

Right?

fantastic question!! Seriously. That's what makes this such a great puzzle.

That's why you have to break it down into pieces. If everything were the same, (including what the guru says), except only one person has blue eyes, how and when could he figure out his eyes are blue? And then do the same question, but two blue eyed people.

I think you're giving up too quick.

If there's only 2 blues, then each blue DOESN'T have justification to think that if the one blue they see wasn't blue, green would still see blue.

There's a canonical answer, and you're disagreeing with it. You have a bit of a burden of proof here. You can cop out if you want with "agree to disagree", but it is that, a cop out.

A1. Green sees blue
A2. Therefore, if I don't see blue then I must be blue — Michael

These pair of premises don't make sense together. If green hasn't said anything, then the only reason you could possibly know green sees blue is precisely because you see blue.

"Therefore if I don't see blue, I also don't know that green sees blue, so therefore A1 is no longer applicable"

So you say, and yet if blues were to follow this reasoning and browns were to follow comparable reasoning then they would all correctly deduce their eye colour — Michael

What you're not understanding is that they could just add easily incorrectly deduce their eye colour. It's a coin flip at best, because the "deduction" isn't based on sound premises.

yeah that's the canonical solution, and matches yours. I'm still endlessly impressed you figured that out on your own, not everyone can do that. I couldn't.

you keep begging the question. You're just declaring yourself correct repeatedly, with incorrect premises. Premise 2 is incorrect.

P1. I know that green sees blue
P2. Therefore, if I don't see blue then I must be blue and will leave on the first day — Michael

This doesn't work if green doesn't say anything. If green doesn't say anything, p2 isn't the case. If green doesn't say anything, and you don't see blue, your eyes could literally be any colour.

It's the same reasoning — Michael

Same reasoning as unenlightened, who was assuming the green eyed person said something?

Make your reasoning explicit. You're still riding on coattails, you can't have your cake and eat it to. If you want to disagree with his premises, show your reasoning yourself.

Each blue reasons: green sees blue, and so if the two blue I see don’t leave on the second day then I must be blue — Michael

Like this for example. Why do you think this is true? If green eyed person says nothing, what reason would the two blue have to leave on the second day? Without resting on the coattails of unenlightened, why would this be the case?

just because you think you've explained something doesn't make it correct. I've had a lot of wrong ideas explained to me in my life.

You're still basing your reasoning off the words of a guy who explicitly has different premises from you. Until you stand on your own two feet with your reasoning, your explanations are on shaky ground

it doesn't though. You're just insisting it does, but you aren't starting from a reasonable place. There's no reason in your scenario that anybody could figure out their own eye colour.

I could justify unenlighteneds reasoning with actual complete syllogisms. I don't think you can do so for yours.

so are you going to answer why the green eyed person, who doesn't say anything, is relevant?

simplify the question as asked, instead of 100 blue eyes 100 brown eyes, think about the same scenario but 2 blue eyes 2 brown eyes

your reasoning is still based on nothing other than unenlighteneds reasoning, and he's already told you his reasoning is based on the guru saying something. When are you going to apply your own reasoning?

"I don't know" isn't reasoning. Why is the green eyed person relevant in your scenario? If he's not saying anything? For every blue eyed person who relies on the green eyed person, couldn't they just as easily rely on a brown eyed person? For every brown eyed person who relies on the green eyed person, can't they just as easily rely on a blue eyed person? I don't think the green eyed person is doing anything.

well I'm trying to talk to you about it but you have to actually engage lol.

What does the green eyed person have to do with it? Why not just have 3 blue 3 brown?

you haven't justified that it does, is why. You keep begging the question.

I do not believe it allows that. Do you understand that? I don't think it does. I don't think it actually allows anyone to leave.

if it's this one, then the reasoning is incomplete. Why is the green person relevant? "Green sees blue" so what? So does brown. Skip the inclusion of the green person, each blue eyed person could apply the same logic but swap in a brown eyed person for the green eyed person.

So why doesn't your example just include 3 blue 3 brown?

there's many posts above. Which one is the one that demonstrates that?

And yet every blue-eyed person leaves knowing they have blue eyes and every brown-eyed person leaves knowing they have brown eyes. So what do you mean by it “not being correct”? — Michael

You're saying "and yet" as if you've demonstrated that. You haven't

One guy, I don’t know who, it might be Baden, takes one of his eyes out, looks at it, and then leaves the island. — T Clark

Clever. Obviously everyone could do that to their own eye. That's another loophole answer though - the real answer doesn't involve a loophole

I’m not sure, but my reasoning does allow all brown and all blue to leave knowing their eye colour, so either it’s sound or it’s a very lucky coincidence — Michael

I don't think it's sound or a coincidence. I don't think it's correct. I don't think there's any reason why the green eyed person being there, not saying anything, would allow anybody to decide their eye colour, and you haven't explained why there would be.

But as a question to you, why would it require green saying what everyone already knows? — Michael

You have to follow the logic carefully one step at a time to find that out. It's very subtle and honestly strange - that what makes this such a good logic puzzle. It's completely counterintuitive, but also, once you fully grok it, undeniably true. That gives it this really unique flavour as a puzzle.

I don’t think that’s a comparable scenario. I think a minimal example requires 3 blue, 3 brown, and 1 green. — Michael

If it doesn't matter what the green eyed person says, why is his presence required at all?

it's definitely a difficult, and contentious, problem. I think the official answer is correct but we've already got disagreements here. If you don't mind a spoiler, read unenlighteneds answer (which is more or less the canonical answer) and join the debate with us and Michael.

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?

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

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?

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.

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.

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

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

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?

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

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

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.

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.

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?

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.

It's not the same though. The reasoning for blue eyed people specifically works because the guru said he sees blue eyes. He didn't say that about brown eyes. So what's the reasoning?