It’s my honest impression. Should I accuse you of trolling every time you fail to be convinced by some point I want to make?
It is falsely inserted.
“the blue eyed person does not know his eye color”
“the blue eyed person does know his eye color”
Yes, these statements contradict each other.
You (all) seem to think that “Supposing that the guru [speaks and] is to be believed” applies only to step 3. Where, if it is valid at 3., it would also have been valid at 1. which cancels out the content of 1.
Oh wait, I am thinking.
I mean rambling.
It’s simply true. But not to the point here.
Abstract thoughts, when they are in fact a force, insight, always are hard to put into words. Clever word-play is often mistaken for thinking. I’m not of that school, indeed.
I personally doubt that there isn’t. A proof of a biconditional like “the problem is solvable IFF the board has [some property or set of properties]” would necessarily prove both.
On a much smaller board, the mutual solution is easy: A two by two board is solvable if and only if the removed squares are adjacent, because that implies that the remaining squares are adjacent, and the remaining 2-square board is solvable if and only if it is a 2x1 rectangle.
I would guess that adjacency is a special case of some property for which color is a proxy, and that “the board is solvable IFF the removed squares have property X such that X is a superset of adjacency”.
This does not suggest that either is wrong, but that the problem as originally stated is ambiguous. I think your clarification, that the islanders can only see each other during the day, and they disappear during the night if they learn their eye color, resolves the ambiguity.
Right. So saying “just fucking read my posts. My God. Or better yet, think” as though your posts are so obvious (even though nobody gets them), and that I’m the one who isn’t thinking even though what I’ve said has been agreed with on multiple occasions, and even referenced in order to help combat the two trailing contributors who still don’t get it.
What you say doesn’t make any more sense now than it did the first time I read it. Take a leaf out of my book - from the part where I have proactively improved on my original presentation of the correct solution on multiple occasions, just to more clearly rebuke all the presented criticisms of it and how it is the only correct solution. That’s how you gain credibility: proactively showing and improving on the many hours of thought you’ve put into solving a problem and problems with others not understanding it. And when they don’t, try again and harder until they do.
Like I said: your lazy approach of merely claiming correctness without (clear) demonstration - whilst only angrily pointing fingers at others for not being as clever as you think you are “to back you up” will get you nowhere.
I think sau hit the nail on the head: perhaps FC didn’t realize that 3 was taking place after 1? 1, 2, and 3 were a chronological sequence of facts/events.
After about a fucking million time I told you that I GET THE ORIGINAL SOLUTION.
Honestly, dude, if even that is too difficult for you to understand – that I get the original solution, as I’ve repeated and repeated an repeated – it is not much of a miracle that you don’t understand my posts. But I don’t feel that I can do anything about that.
There are four blues and four browns.
All know that all see that there is at least one of each color: The REAL SET of REAL UNITS.
The day/night/ferry things apply.
All reason:
If there was only one blue eyed who knew that there was at least one blue eyed (one REAL UNIT of the REAL SET), he would leave the first day. And:
If there was only one brown eyed who knew that there was at least one brown eyed (one REAL UNIT of the REAL SET), he would leave the first day.
No one leaves the first day. Therefore there are more than 1 of each color, and all know that they might belong to either one, or possibly another color.
Since no one leaves the second day, there are more than 2 of each color.
Since no one leaves the third say, there are more than 3 of each color.
Since all blues see only 3 blues, they leave the 4th day. Since all browns see only 3 browns, they all leave the 4th day.
Wow, FC, you take some serious time out from this place. A good thing. Well, two weeks… I’d hoped it was due to bowing out after realising your error that Sau so sufficiently presented in analogous form, but I guess that was wishful thinking.
You know that’s not an argument, right?
And that it does nothing to defend your strange claim that someone can not be ignorant of something one moment, come to know it, and know it the next moment. Somehow, to you, this is a contradiction - that if they knew it the next moment, they must have known it all along. Yes, that’s what it sounds like you are saying.
Ok. Whilst I hear you say such things, things like this say otherwise:
As I thought, and have said before, your mistake is to say that since 4 blues (or browns) know that everyone else knows that everyone else knows that there is at least 1 blue-eyed islander and at least 1 brown-eyed islander, 1 blue (or brown) must also know that everyone else knows that everyone else knows that there are at least 1 blue-eyed islander and at least 1 brown-eyed islander.
I know why you think this is an ok assumption, because the reality (in this 4blue/brown scenario) is that there ARE 4 blues and 4 browns, and so they can attribute their knowledge to whatever scanerios they are imagining. The problem is that they have to be hypothesising about what 1 blue/brown would know IF there were only 1 blue/brown. In this case, they have to deduce about this 1 blue/brown aside from the knowledge of 4 blues/browns.
The reason you don’t get this appears to be at least one reason why you don’t get the correct solution. You can say you get the solution a million more times, but when you consistently demonstrate that you do not, it just holds no water. You have to do better than just “saying” you get it.
Perhaps it is too difficult for you to understand what I do. It sounds like we both think the same of the other in regard to the validity of one another’s positions. At least one of us has the correct understanding of the problem. How will we decide who this person is? It would be wrong to base my validity on the fact that all other members of this place and the place that hosted the problem side with my explanations, bar the one “I want to be special, even at the expense of sense” person here, and yourself. We must arrive at a much more acceptable measure of validity - any suggestions? Showing you flawless reasoning doesn’t appear to be sufficient so far. I will continue to try.
This question is really the only reason I keep discussing this. It is possibly the most important question I’ve come across in my years of discussing philosophy.
I think the answer starts this way: what would it take to prove you that you’re wrong? For me, I think it would be a logical proof, using explicitly and exhaustively stated premises. I think that I can point to an implied premise that is false, and that thus if all the premises were explicitly and exhaustively stated and did not rely on the implied premise I see, I would be proven wrong.
What about you guys?
Fixed Cross, I have a thought for you: You say that, “If there was only one blue eyed who knew that there was at least one blue eyed (one REAL UNIT of the REAL SET), he would leave the first day,” and we don’t agree. But it is also true that “If there was only one blue, he could not learn that there is at least one blue by looking at the other islanders’ eyes.” And yet, every person on the island knows “there is at least one blue” only because they can see that by looking at the other islanders’ eyes. This distinguishes the knowledge the islanders have before and after the guru speaks: if there were only one blue, he could learn that there is at least one blue by hearing the guru speak.
That is your mistake. You fail at that again and again.
The only proof is one that leaves the absolute lack of alternatives.
The canonical solution is “A solution”. But it is NOT the “Only solution”, and thus is not a proof of anything else being wrong.
You constantly attempt to shoot down a premise by presuming where it is going to lead and thus claim it to be invalid before finding out where it actually leads. You conflate issues in the effort to prevent the beginning of a scenario. That is pure political strategy, not logic.
In order to prove anyone else wrong, you MUST go through their scenario and point out at exactly what point it fails or prove the absolute lack of alternatives to a different argument. But to do that, you must first except the proposed premises that you might LATER shoot down as inapplicable to the final issue. But you refuse to do that. You want to jump ahead and presume your own conclusion; “I think this premise will be a problem later so I am not going to accept it now”. The problem is that you don’t actually know for certain whether it will be or not and refuse to find out. You are “affirming a presumed consequent”.
“I won’t accept the premise of evolution for discussion because that would mean there is no God.”
…Bullshit. “I refuse to discuss the whereabouts of the defendant because I already know who is guilty.”
…Contempt of court.
If I prove a statement A, I know as a corollary that ~~A. If I prove a collection of statements A and A → B, I know as a corollary that B. If a rigorous logical process leads from a collection of premises to a conclusion, I know that the negation of that conclusion can only be true if the premises produce a contradiction. Since you haven’t offered anything to undermine the logic of the canonical solution, the best you’re shooting for is proving the givens to be contradictory.
If I say “Here are the givens. Teddy bear. Therefore, solution,” have I really proved anything? How much do you need to “go through the scenario and point out at exactly what point it fails or prove the absolute lack of alternatives to a different argument”? Your solution has everyone pick the same number from thin air (unless they have brown eyes), turn that number by magic into knowledge, and then deduce from that knowledge. I’ll be honest, I don’t know how to explain logically why the color of my eyes doesn’t follow from the number we all start counting at. It’s a non sequitur. The one thing doesn’t follow from the other.
Related to point #2, you did not identify what would convince you that you are wrong.
Just to repeat:
the lack of alternatives has been covered by the exhaustive nature of correctly following the logic of the correct solution.
To every blue there are ONLY two possibilities: there are 100 blues or 99. The rest of the solution is examining each of these outcomes just as exhaustively, leaving no stone unturned, and leading to only one solution. It works out very nicely if you really do understand it.
You refusing to discuss anything but your own preferred scenario is not helping your case either (and you haven’t answered the question at all… always trying to jump around it like a frog on a hot plate).
That is absurd.
The canonical solution depends, not only on everyone knowing that everyone knows all of those things we listed, but it also depends on everyone knowing that everyone has no alternative but to be thinking exactly the same scenario.
The problem is that there is a different scenario that also works. So how do they all know that all of the others are using the canonical solution rather than another? Does the guru also tell them that there is one person thinking, “If I was brown and saw 99 blues, then…”. That part wasn’t mentioned.
You are each merely following a proscribed trail. There are alternatives. And because of that, they cannot each know that all of the others are waiting for the same reason.
This is false. The canonical solution is not about what everyone is thinking but about what they can deduce. It is a given that if something can be logically deduced, every islander will deduce it instantly, and the islanders know this about each other. There is no choice of “alternatives”: if we are given A and A → B, and we are perfect logicians who will instantly deduce anything deducible, we will instantly deduce B.