okay no problem.

So Tommy can deduce it?

OK, thank you for clarifying that, last time this came up you said "No, because this is one of those n=2 scenarios that I explicitly accept doesn't always work."

So it DOES work.

So if Tommy sees 1 blue, 2 brown, 1 green, Tommy can safely go to the boat on the second day knowing his eyes are blue. Right? That's your explicit position. It's not a "n=2 that doesn't always work" scenario, this is a scenario where you're saying explicitly, the logic DOES work, Tommy CAN deduce his eye color when he sees 1 blue, 2 brown, 1 green, and he sees that the blue eyed guy doesn't leave on day one.

It's clear, explicit, no "maybe sometimes doesn't work", you agree unambiguously that you think Tommy can deduce this.

So just to be clear, this is you saying it works in the case of 2 blue 2 brown 1 green, correct?

I explained it above — Michael

Above doesn't include a specific scenario where it works. A specific scenario looks like "2 blue, 2 brown, 1 green". Does it work in that scenario, if the green eyed guy says nothing? If not that, what specific scenario does it work in?

Sometimes, but not always, as I keep saying. — Michael

When? Everything seems so vague right now. When does it work? What does Tommy have to see for it to work?

so you're switching back to saying it DOES work for n=2?

I said it works if there are 2 brown and 2 blue. I didn't say it works if there is 1 blue, 2 brown, and 2 green. — Michael

But you're Tommy. You don't know ahead of time if there are 2 brown 2 blue or 3 brown 1 blue. That's the point. That's LOGIC. You don't know. Your reasoning has to apply in any case where you see the things you see. You're not magic, you're just Tommy.

Tommy sees the same thing in the 2 brown 2 blue scenario as he does in the 3 brown 1 blue scenario, doesn't he? Your reasoning, as Tommy, has to be based on what he sees. You said it works if he sees 1 blue and 2 brown - so I put that to the test, and your reasoning got you tortured.

You now accept that it doesn't work for n=2 - that's why it doesn't work for n=3. It would only work for n=3 if it did work for n=2. And it doesn't.

For the longest time, you've been riding unenlightend's logical coattails. The thing is, his logic works for n=1 and because it works for n=1, it works for n=2 and because it works for n=2 it works for n=3.

That's not the case with your logic, as we can see. That's why it's so important to work through n=2 before we even begin with n=3. If it doesn't work for n=2, it can't work for n=3.

No, because this is one of those n=2

=
2
scenarios that I explicitly accept doesn't always work. — Michael

This is the exact scenario that you said did work above.

https://thephilosophyforum.com/discussion/comment/1003049

You said the reasoning worked. You're just randomly changing your mind now.

I don't know if you're going to play the game from my previous post, so I'll play it on your behalf using the logic you've given already.

You see Timmy with blue eyes, you see George and Jack with brown eyes, and you see Guru with green eyes. Nobody says anything on day 1, nobody leaves on night 1. It's day 2.

Using all your reasoning that you've said so far, you've "deduced" that because nobody left on night 1, you have blue eyes.

You go to the boat, you ask to board. You tell Charon that you've deduced that you have blue eyes.

He says I'm sorry Tommy (Michael), that's incorrect, now I'm going to torture you and keep you alive in agony for as long as I can, thems the rules.

Unfortunately, you didn't have blue eyes. You had green eyes. Timmy had blue eyes, but he didn't leave on day one because he DIDN'T imagine the Guru saying "I see someone with blue eyes" like you expected him to. Because why would he imagine that? He didn't see anyone with blue eyes. Of course he didn't imagine that.

Your reasoning skills got you tortured. Try again next life.

How about we do a real experiment:

YOU'RE Tommy.

I'm not going to tell you your eye color.

You see Timmy with blue eyes, you see George and Jack with brown eyes, and you see Guru with green eyes. Nobody says anything on day 1, nobody leaves on night 1. It's day 2. It's approaching time to board the boat. Do you board the boat? Have you deduced your own eye color? What is it?

I can't explain this any simpler than I already have, so I'm not going to keep trying. — Michael

Seems like you're not seriously considering the possibility that you're wrong. That's a mistake.

Tommy genuinely thinks Timmy might be the only one with blue eyes, right?

If that's the case, Tommy has NO REASON whatsoever to think Timmy will leave on day 1. You aren't even trying to make a case for it. You're giving up without even trying.

From Tommy's perspective, Timmy doesn't have any reason at all to imagine green eyed guy saying "I see someone with blue eyes". From tommy's perspective, timmy doesn't know that green eyed guy DOES see someone with blue eyes. So from Tommy's perspective, Timmy could be imagining the blue eyed guy saying "I see someone with green eyes" -- Tommy thinks Tommy could have green eyes, right?

So Timmy might be imagining the guru saying "I see someone with green eyes" as far as Tommy is concerned, and Timmy might see Tommy with green eyes, and Timmy might be waiting day 1 to see what Tommy does, to see if Tommy leaves.

When b>=3, you absolutely DO know that. — hypericin

we're not talkinfg about that case though. michael can't prove it for the case of 2.

sure, it's a "coincidence". You're using non-deduction and incorrect reasoning, as an outside observer, to get to the correct conclusion.

If I asked you, what's 2+2, you might say 4. If I asked, how do you know that? You might say, because rhinosceroses have horns.

You're using nonsensical reasoning to arrive at an answer.

Now YOU as an outside observer can do that in this case because YOU have the privilege of knowing Timmy and Tommy both have blue eyes. But Timmy and Tommy don't know that. THEY only have the information available to them. For all Timmy and Tommy know, the other person could be the only one with blue eyes. Tommy thinks, I couild easily have brown eyes, I have no way of knowing. Even on day 2.

The logic puzzle requires correct deductive reasoning, not just using your magic powers as an outside observer to use wrong reasoning to guess at the right answer.

A1 and A2 don't make sense as two separate premises

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

The only reaason you know Green sees blue is BECAUSE you see blue. You see blue, and so you know green sees blue. This step in the reasoning doesn't ever get off the ground.

A3. Therefore, if I see one blue and he leaves on the first day then I must not be blue

This doesn't work either, because the one blue you see, you don't necessarily know that he knows that green sees blue. Right? How would you know that he knows green sees blue?

That's really what this logic puzzle is about - what can you know other people know? A3 only works if you know that the blue eyed person you see knows green sees blue. But you don't know that he knows that.

spell out the reasoning then.

I don't think it "helps", I think it's an entirely irrational thing for Tommy to imagine that.

that's not deductive though. 1 blue wouldn't leave on the first day anyway, right? Why would he?

let's name the blue-eyed people. We're going to talk about Timmy and Tommy. Timmy and Tommy both have blue eyes so let's look at this from Tommy's perspective

Tommy sees that Timmy has blue eyes and nobody else that he sees has blue eyes. So from Tommy's perspective there's really two possibilities: either Timmy is the only one with blue eyes or Timmy and Tommy both have blue eyes.

So you're saying that Tommy would expect Timmy to leave on day one if Timmy was the only one with blue eyes, but why would Tommy expect him to do that? Think about it

If Timmy was the only one with blue eyes, which is the scenario we're thinking about as Tommy, then Timmy wouldn't see anyone with blue eyes. If Timmy didn't see anyone with blue eyes he wouldn't know anybody on the island had blue eyes and therefore he wouldn't know that he has blue eyes and therefore he wouldn't have a reason to leave the island on day one.

This is why I think your n=2 logic doesn't work. Is there anything wrong with my reasoning?

I'm trying to work with you on making your case, but you don't want to take n= 2 to is logical conclusion. Try it. Try reasoning about the case where there's 2 blue, and the guru says nothing. What's the actual logic? We'll move on when it's settled, but I think we can actually come to an agreement on n=2 if you commit to actually working it to its conclusion.

In the case where there's 2 blue, a blue eyed person sees one blue eyed person, 2 brown eyed people, so he thinks what? How does he reason?

why would they imagine someone saying that?

At n=2, I see only 1 person with blue eyes. I see he doesn't leave on day one. This is the scenario where the guru didn't say anything, so IF he's the only person with blue eyes, he wouldn't leave on day 1 anyway, since he would have no way of knowing he or anybody else had blue eyes.

So he wouldn't leave on day 1 if he was the only one, and he wouldn't leave on day 1 if he wasn't the only one.

So him not leaving on day one gives me no new information, because it would have happened regardless, and I can't use that non information to leave on day 2.

That's the state of play, that's how I and unenlightened analyze this situation.

That's why I said: for all n>=3 — Michael

You said it applies to n=2 as well, that's what we're talking about. Here's the context:

https://thephilosophyforum.com/discussion/comment/1002914

He wouldn't, but that's irrelevant. It can be demonstrated that if everyone just follows the rule: for all n>=3

>=
3
, if I see n−1

−
1
people with X-coloured eyes and if they don't leave on day n−1

−
1
then I have X-coloured eyes, then they will correctly deduce their eye colour (unless they have a unique eye colour). — Michael

But if 1 wouldn't leave, then you can't correctly deduce your eye colour at n=2. You already can't.

Either mental events have some kind of directly emergent relationship with physical events and processes - in which case, "mental causation" is simply an interesting instance of physical causation

-or- mental events happen in some mental spirit realm or whatever, and we apparently have no way of discovering anything about how that realm operates, and mental events trigger physical events which then trigger more mental events, and so on.

There are 2 brown, 2 blue, and 2 green.

Each brown reasons that if the 1 brown doesn't leave on day 1 then he is brown — Michael

Just to follow up on this.

In the case if 2 2 2 like you laid out, from the point of view of a brown, here's what he knows:

"There's 1 brown, 2 blue, 2 green and 1 unknown -me"

Now you're saying "if 1 brown doesn't leave on day 1..." But there's no reason for 1 brown to leave on day 1. If he was the only brown eyed person, he would see 5 people with non brown eyes, and nobody is saying anything in this scenario, so... what information is this hypothetical guy supposed to have that his eyes are brown? His eyes don't have to be brown. There's no rule that says "there's at least one brown eyed person on the island". For all he knows, there could be no brown eyed people. His eyes could be green, blue, yellow, grey - anything.

This is why the canonical answer does in fact rely on the guru saying something. You need that to get the logic rolling.

now I get why you got the answer so fast and so cleanly as well. Very cool

thanks!

as philosophers, surely we've known that the whole time anyway. That there can always be an error in our thinking.

Surely you have experienced this as well, that the "clearly" feeling just isn't as reliable as it feels. — hypericin

I actually think that's a good thing. I mean, we already have situations where two groups of people feel clearly that the other side is wrong - having examples where most people's "clearly" feelings are off base at least forces everyone to be a little more rigorous in their reasoning than just "it feels wrong".

course this forum, and philosophy in general, is a quagmire of mistakes. But it is probably much worse than we suspect. If our intuitions are that uncertain, even when they feel totally certain, it seems we are always on logical quicksand. — hypericin

I guess I don't feel that way about this, because this is an especially contrived scenario, deliberately built to be counter intuitive. I don't think my failure here necessarily hints at a more wide, general failure at logic or thinking.

Given that cases like this exist, how do we even trust our own reasoning? — hypericin

You just have to accept that you aren't a perfect logician. Is that so bad?

This is the fundamental part that fails in the logic, Michael.

There's no reason whatsoever for 1 person, brown eyed or blue eyed, to leave on day one unless the guru says something. If the guru doesn't say anyhing, then all you know is there's X blue eyed people, Y brown eyed people, Z green eyed people and absolutely no way to know your own eye color. There's no mechanism in your logic Michael. You keep on riding the coattails of unenlightened's logic, but throwing out the fundamental premise of unenlightened's logic. You're trying to have your cake and eat it too.

Without the guru saying anything, there's no mechanism whatsoever short of magic for a single blue-eyed or brown-eyed person to know what color their own eye is. You can't skip past step 1.

Each brown reasons that if the 1 brown doesn't leave on day 1 — Michael

This is the part that logically fails. Why would 1 brown leave on day 1 anyway, if guru says nothing?

It seems to be a simple mathematical fact that for all n>=3

>=
3
, if I see n−1

−
1
people with X-coloured eyes and if they don't leave on day n−1

−
1
then I have X-coloured eyes. — Michael

And why n >= 3, rather than n >= 2?

you made a post, and then you edited it to say "oh wait", and then you edited it again after that. It's making the whole conversation incredibly difficult to follow.

did you edit the prior post to this one? The fact that you did willingly edited this post makes me wonder if you might have edited the one prior as well...

Don't edit posts, it confuses everything. If you made a mistake just admit the mistake in your next post. I know you edited a post, and that unfairly makes this whole conversation more confusing than it has to be.

why not at b=2? Think about it. At b=2, guru could say I see a blue, and everyone knows guru could say that, because everyone sees a blue who isn't themselves and also isn't guru

I don't see why, at any stage, one can just imagine the guru. If you can't imagine him at stage one or two, then you can't simply imagine him at stage 3 either.

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?