we agreed that it can't work for 2 people. 2 people don't leave on the 2nd day.

You seemed to understand why that means it can't work for 3 people, so if there are only 3 eyed blue people, we also know they won't leave on the 3rd day.

Do you see why that means it can't work for 4 blue eyed people, why they can't leave on the 4th day?

If you are patient and take this seriously, I'm pretty sure you'll find what I have to say compelling. But we gotta start small.

well then that logic should work when there are just 3 blue eyed people. But it doesn't.

I really want you to consider the lowest possible number this can work at, so we can actually analyse it without being confounded by big numbers.

Why would they commit to 3?

if there were only 99, then no they wouldn't think it's not possible for blues to leave on day 98. That's what we're reasoning about. We're reasoning about "if there were only 99". If there were only 99, they WOULD think it's possible for the 98 they see to leave on day 98, if your logic holds. They would have to

No, that's false. Although both statements are true, neither depends on the other. — Michael

Why would 99 leave on day 99 if they didn't reason that only 98 would leave on day 98?

You're saying 100 would be able to leave on day 100 because they're reasoning that if there were only 99 they would leave on day 99. Why do you think it's different for 99? Surely the proof for 99 leaving on day 99 is the same - surely it relies on it being true that only 98 would leave on day 98, just as much as 100 relies on it being true that only 99 would leave on day 99.

Philosophically physicalism (as a rational position) does not hold all the answers and it is more than reasonable, in many ways, to take other positions seriously — I like sushi

I think they should be taken seriously too! I'm not implying otherwise.

I do see a lot of people not talking physicalism seriously, which I think is odd and getting even more odd every day now that we live in a world where computer simulacrum of neurons are capable of speaking to us.

I'm not saying anybody is going to leave on day 98. I'm saying the statement, "if there were only 99, they would leave on day 99" can only be true if it's also true that "if there were only 98, they would leave on day 98"

Otherwise, how could it be true that "if there were only 99 they would leave on day 99"?

right, and in order for that to be true, that only 99 would leave on day 99, then it must also be true that only 98 would leave on day 98, right?

okay let me rephrase, I thought you would understand my more casual phrasing:

Your logic relies on it being true that if there were only 99, they would leave on day 99. That's what I meant by "If your reasoning works, then it must be true that 99 leave on the 99th day. Right?" Forgive my sloppy wording.

Do you agree with the new wording?

No.

My reasoning is: if the 99 blue leave on the 99th day then I am not blue, else I am blue — Michael

I'm really not trying to be sense here but, doesn't that make the answer to the question "yes"? Yes, if there's only 99, they leave on the 99th day.

well one side has something to do - the physical side has literally every bit of research they've been doing and are continuing to do. They obviously don't have all the answers, but they're also obviously trying and progressing.

The other side hasn't made a single inch of progress in thousands of years.

I know that might sound unfairly dismissive, but I also believe there's at the very least a big dose of truth in it.

Imagine rather, that there are 3 blues, 5 browns, 1 green, and you. You know thus that everyone can see at least 2 blues if they are blue, and at least 4 browns if they are brown and so on. — unenlightened

I was imagining myself as one of the blues though, putting myself in the place of BL1. That's what I was going for

If we assume that the participants are numbered, each participant asks himself "is there some X and Y such that #X does not know that #Y knows that #101 sees blue?".

And just to be clear, we can apply this to 3 blues.

Imagine 3 blues and 5 browns and 1 green.

BL1(#X) sees 2 blues, and looks at one of them (#Y) and knows that he sees at least 1 blue, and because #Y sees at least one blue, #X can reason that #Y also knows that guru sees at least one blue.

So if this is truly the basis of the reasoning, it has to work at 3 blues.

It might not be the explicit premise you're trying to focus on, is what I'm saying, but it's still a direct consequence of the reasoning you're trying to apply. If your reasoning works, then it must be true that 99 leave on the 99th day. Right?

That's not my premise. — Michael

So if the 99 you see leave on the 99th day, on the 100th day you'll conclude you have blue eyes anyway?

Then go through all the numbers and for each number imagine the participants asking themselves "is there some X and Y such that #X does not know that #Y knows that #1 sees blue/brown/green?" — Michael

X knows that everyone knows that guru sees blue at 3 blue. But we've already established that 3 can't leave on the third day.

You're trying to address the problem, but this is a deduction puzzle, and your deduction has a false premise. The premise that's false is 99 blue eyed people would leave on the 99th day.

But for me to show you that's false, I would have to show you that it's false that 98 people would leave on the 98th day.

And to prove that's false, I would have to prove to you that it's false that 97 people would leave on the 97th day.

And so on.

That's a lot.

But here's the deal- you keep counting down, 99 98 97... eventually you get to 3. And we know 3 don't leave on the third day.

It's easier to talk about small numbers than big numbers.

Okay, well I think the answer is that there isn't a difference — Michael

Just to recap, We've already agreed that it does make a difference for the case of one blue eyed person, and two, and three. There must be some number where it starts making a difference. I'm very interested in that number. You want me to accept that it starts making a difference some time before 100 - if I'm going to accept that, I'm gonna need you to show me when.

For every number of blue eyed people x, your reasoning seems to rely on the premise that if there were x-1 blue eyed people, they leave in x-1 days. You're obscuring your logic by jumping to 100 blue eyed people. I'm trying to explore with you the numbers that aren't obscured.

okay so I dare you to not leap to thinking about 100, and think about smaller numbers. We've talked about 2, we've talked about 3, I think we agreed 2 can't leave on the second day, I think we agree 3 can't leave on third. Can 4 leave on the 4th?

But what's the relevant difference between seeing a piece of paper with the words "there is at least one blue" written on it and seeing 99 blue? How and why is it that the former can "cut through this recursive epistemic conundrum" but the latter can't? — Michael

That's what makes this puzzle so interesting. Truly, that's one of the biggest points, and why people find it fascinating. It's weird. It's hard to explain, it's unintuitive, but if you work through the logic from the ground up, it's nevertheless true. For some reason, it makes a difference.

This is the logic being discussed, right?

1. As of right now everyone has come to know, through some means or another, that everyone knows that #101 sees blue
2. If (1) is true and if I do not see blue then I am blue and will leave this evening
3. If (1) is true and if I see 1 blue then if he does not leave this evening then I am blue and will leave tomorrow evening
4. If (1) is true and if I see 2 blue then ...
...

And it bears repeating (if any reader missed the previous comment), that even though as a practical matter (1) is true in counterfactual scenarios (2) and (3) only if someone says "I see blue" isn't that someone must say "I see blue" in every counterfactual and actual scenario for (1) to be true and for this reasoning to be usable.

But we already have a simple, straight-forward case that this logic doesn't work. We know, because he's already acknolwedged, that 2-blue-eyed doesn't work. 2 blue-eyed people cannot leave on the second day.

If it's true that 2 blue-eyed people cannot leave on the second day, then it must also be true that 3 blue-eyed people cannot deduce that there's more than 2 blue-eyed people just because they don't leave on the second day. So 3 blue-eyed people cannot leave on the third day.

But premise 1, "everyone has come to know, through some means or another, that everyone knows that #101 sees blue", is true in the case of 3 -- and yet it still doesn't work.

So we have a tangible, specific case where Michael should be able to apply this logic, and yet can't.

It genuinely feels like these simple cases, for low numbers of blue-eyed people, are being ignored because it's easier to hide the reasoning behind the obscurity and confusion of very large numbers. The beauty of unenlightend's logic is that it clearly unambiguously works for small numbers, and so we can work our way up to large numbers. In contrast, Michael's logic, we know for sure doesn't work for small numbers, so instead of working his way up to large numbers, he just kinda ignores the problems at small numbers and hopes nobody notices the gaps in logic once there's 100 people to talk about. It's easier to hide the cracks with so many blue-eyed people to think about.

If Michael wasn't so worried about getting tortured for eternity, I'd be encouraging him to find the lowest number of blue-eyed people that it works for. Michael it's only a fictional torturing for eternity.

I do not think causation is one, though — AmadeusD

Causation itself isn't even in the category of things we're talking about. It's the meta-category of those categories of things. Minds interacting with bodies is a type of causation. Heat causing x or y is in the category of causation.

I don't know what physicalism of a kind means.

I don't think the mind thing is comparable. There are physical facts that are simple enough to be modelled by an equation - that's the perfect candidate for something being fundamental, and therefore the prefect candidate for something being a "brute fact" as it were.

Minds, on the other hand, seem complex and ever-changing - a human-scale mind is nowhere near a brute fact, and if it interacts with a body, there will be a particular way it interacts with a body. For example, it didn't seem to interface with the toes directly, it interacts with the brain and the brain moves the toes. So "the mind interacts with the body because that's how it is" is many steps removed from a brute fact, in comparison to, say, something like the Schrödinger equation, which because of its relative simplicity is a candidate for being close to a brute fact.

He's been ignoring me since I tortured him for eternity.

In his defense, that's a pretty good reason to ignore someone

he replied to your last reply my brother

the reason I know Michael's answer doesn't work... is related to the recursion you're speaking of, I think, I would phrase it like this:

His logic for 100 relies on the assumption 99 would leave on day 99.

And that in turn relies on the assumption that 98 would leave on day 98.

And you can continue to trace that back, all the way down to:

Logic for 6 relies on 5.
Logic for 5 relies on 4.
Logic for 4 relies on 3.
Logic for 3 relies on 2.

And we KNOW 2 doesn't work if the guru says nothing. Even Michael agrees with that.

If 2 doesn't work, 3 doesn't work. If 3 doesn't work, 4 doesn't work. Trace that all the way back up to 99, then 100.

they are all distinct facts, all the way up — hypericin

Yeah I think that's probably true. I changed my mind

Thinking about it more, I probably am wrong. Maybe it never explodes to infinity

I don't know why, I can't justify it right now, I feel as though it explodes to infinity at some threshold.

Like imagine I know something. Maybe you know I know it, maybe you don't - that doesn't explode.

Now imagine I know something and you know I know it. Now, that also doesn't explode - maybe you know I know, but I don't know you know I know.

Now imagine I know you know I know.

And then imagine you know I know you know I know.

If I know the fact, and you know I know, and I know you know I know, and you know I know that, then... at that point, can't we realistically add as many "I know you know"s as we want and it still remain deductively true, assuming we're perfect logicians and both know each other are perfect logicians?

That's my intuition. I could be wrong.

at two blue, everyone sees a blue

at three blue, everyone knows everyone sees a blue

at four blue, everyone knows everyone knows everyone sees a blue. But, at this stage, you can add as many "everyone knows" as you want, I think. Can't you? At four blue, everyone knows * infinity that everyone knows that everyone sees a blue.

I think

Or maybe at 5?

Idk I'm lost

The elder learns they do not have brown eyes — Philosophim

How do they learn that? The elder could easily have brown eyes, as far as she's concerned.

Again, fun puzzle. :) — Philosophim

I think so too. I wanted to spark some debates.

But, since all 99 don't leave the next day after blue eyes leave, that's because they each brown eyed person realizes 'I must have brown eyes, otherwise they all would have left'. — Philosophim

Why would they have?

I don't think so. I only think blue eyed people can leave. Anybody else can have any possible eye colour, they have no way of knowing

that gives us an easy way to measure bullshit in this thread. See which group is having an easier time defending their position - the group that's having a harder time of it must be right

That's might be taken as a suggestion that there is no interference in the world we experience — boundless

I take it as a suggestion that maybe you experience the consequences of interference constantly, as a matter of course, but they're just... normal. They don't look particularly different from anything else you experience.

We live in a quantum world. Quantum IS normal. Everything normal you experience is the consequence of many quantum interactions. So maybe... interference is just happening all the time, and you experience it all the time, and it's just a normal part of this quantum world we're in.

Note however that our experience does seem about definite outcomes without any interference, i.e. our experience suggests to us that there is no interference, period. Of course, it can be wrong. — boundless

Do you have a solid concept of what the experience of interference would be like? What kinds of experiences would you be expecting, if there were interference?

For instance, MWI supporters generally claim that decoherence is enought to have 'classicality'. But IIRC, interference isn't eliminated. The terms relative to interference become very, very small but not zero — boundless

That doesn't seem like a downside to me. Who says interference at classical scales needs to be anything other than very very small?

After all, we've put relatively large objects in superposition...

But how? *sigh*. — AmadeusD

At some level it's going to be fundamental. There's not going to be a deeper "how" sometimes, eventually it's gonna be "because those are the rules".

Like when one object hits another object and the interaction causes both to change speed - equal and opposite reaction, conservation of momentum - the "how" might not really satisfy you. Are you okay with "because that's just how it works"?

don't start at 100. Start at the minimum possible number of blue eyes.

It's gotta be something like 3 or 4 right?

that's my take, for the "guru says nothing" scenario. I have no reason to think that logic doesn't hold all the way to to 100, or any other number

in his defense, he did learn that the logic he laid out doesn't work for 2 blue eyed people, nor 3. I think he's teachable but just impatient. He keeps trying to skip right to the final conclusion without taking his time building up solid premises