This is another example of your mistaking what we from the outside know with what they from the inside know.
The correct statement would be, “And until there are no possible alternatives, we don’t know that the perfect logicians will use that one.”
What we do and don’t know doesn’t affect what they can and can’t use.
I wasn’t talking about what WE know, but what THEY know.
THEY have to know that there is no alternative concerning any method they are using to predict what others on the island are doing, else they cannot depend on that scheme.
Imagine that you find 200 logicians who have never failed a logic test of any kind. You stick them on an island with those rules. There happens to be 100 blue-eyed. But on the 4th day, one of them leaves. The others are thinking, “what the hell?? How did he do that? Now what? Is someone else going to leave tomorrow?”
James, isn’t it clear that given a syllogism,
A - > B, ~B |- ~A
we don’t have to separately prove that A isn’t also an alternative? The syllogism itself proves that A is not an alternative
So, if the canonical solution relies only on knowns and syllogisms built from them, the proof proves that there are no other alternatives. The logic makes the conclusion necessary; any other alternative would produce a contradiction, which must be inherent in the problem statement (thus my previous question; I didn’t understand your answer).
Carleas, anyone on the island or off can easily see that they need only start counting days from a common number. There are two easy to see common numbers; 1 and 200. If by 1, it takes 100 days to know. If by 200, it takes 51 days to know. But using either method, it must be known as to which method everyone else is using. Both work if chosen by everyone. Neither work if not. Why would they necessarily all choose to use 1 rather than the 200?
This is a problem only for your solutions that rely on everyone somehow choosing the same assumptions without explicit communication.
This really isn’t a problem for the correct solution. As I have pointed out, all they are doing is deductively expanding on what they definitely know for sure, and this just so happens to solve the puzzle. Nothing more is needed for it, it just works from logic and certainty. Nothing is left out or gone to waste, nothing is missed, everything that comes from logic and certainty goes towards the one solution and no other solutions - as shown.
Sure, maybe a breach of the conditions of the puzzle might allow for the otherwise illegal assumptions necessary for your solutions, and at least the pier one would work if the problem was altered in order to allow it.
I think I’ve even said already: if you would only realise/admit that your solutions were only appropriate for an altered version of the puzzle, then that would be fine. It’s the fact that you seem to insist that they’re appropriate for the puzzle as it is that’s incurring the criticism of myself and others. You’ve only been exploring alternative solutions to the puzzle if it were altered - and if you do alter it, there ARE alternative solutions.
Nothing is a problem is you ignore the problem in it.
Yes, I can believe you live by that one.
We’re waiting for a proof of that. If you feel you’ve provided one, link to it. Or, correct my version of it (which I truly meant to be a good faith restatement of my understanding of your proposed solution).
Carleas, before I go make some more formal proof for a hypothetical, I need to ensure that you actually understand the hypothetical. If you understand it, it seems blatantly obvious that it would work, so either you do not understand it (which I only give any credit to at all because FJ couldn’t grasp it), or you are doing your political rhetoric thing again where you divert the conversion upon seeing that you might have a flaw in your reasoning. If it is the former, the proof isn’t going to help because you wouldn’t understand what is being proven. If it is the later, it wouldn’t do any good to present a proof anyway because you would just divert from it again.
So before I go put together some kind of unnecessary proof, how about you show me that you actually understand what it is that I am saying with “IF THEY ACTUALLY START WITH THE SAME NUMBER (between 0-99), IT WILL ALWAYS WORK.” What do you think that statement means?
This whole thing is about clarity and verification.
I agree, and I must ask that you be much more clear, as I’ve asked before: when you say they “start with” or “pick” the same number, what do you mean. Just that they have number in their head? We’ve agreed the number must be meaningful, what meaning are you ascribing to it? What meaning are the people who “start with” or “pick” that number ascribing to it?
It may seem obvious to you, but you know what you’re talking about before you even start talking. We can only discern what you’re talking about to extent you tell us. It is frankly poor form to allege that it is the fault of those you’re trying to convince that you have failed to convince them. As I said before, communication is a two way street. I don’t understand, neither it seems does FJ, but you can’t conclude from that that we can’t understand. It’s at least as true that you can’t explain yourself. To be clear, I’m not saying that you can’t, but that in the same way that you can but haven’t explained yourself adequately, we can but haven’t understood what you’re saying.
So, as you said, let’s focus on clarity so that we can verify the canonical solution (or verify your challenge to it). The problem for me is that your words are capable of many meanings. I’ve offered my interpretation of them, which you said was wrong but about which you said nothing more. Say more.
What is clear to me is that when someone says, “IF…”, they are proposing a hypothetical that doesn’t require any understanding of how it got that way.
“If the Earth really was flat, then…” doesn’t require any understanding of how the Earth got flat.
When the guy is thinking, “IF I am brown…”, he isn’t concerned with how he got to be brown.
Granted. So what? What does that tell us about what “start with” or “pick” means? What does that tell me about how my restatement of your case was wrong? Clarity, James.
“Clarity” Carleas, answer the question;
“If they all actually used the same number (between 0-99) would they all properly deduce their eye color?”
You had said “no” but refused to give any demonstration.
If you don’t get that you don’t even get the original solution.
Ok, James, now we have “start with”, “pick”, and “use”, all of which you refer to how their holding some number in their heads leads to their conclusion that they have a certain eye color. You haven’t provided any additional insight into what “start with”, “pick”, or “use” mean in this context, other than to suggest that it doesn’t mean “X islanders with blue eyes know that there are X islanders with blue eyes,” unless that’s not why my earlier restatement of your solution is incorrect (which you’ve still yet to clarify).
I asked for clarification:
Perhaps you would be able to help me get it by actually explaining what you and James are talking about? Make a syllogism, or tell me specifically why mine is wrong.
EDIT: And by “mine”, I mean my restatement of what I think your intended syllogism to be.
Quid pro quo, bro.
“You haven’t provided any insight as to what “know”, “eye”, or “perfect logician” mean in this context.”
The definition of ‘know’ and ‘eye’ are beyond the scope of this discussion. It’s also bullshit that you first mention your objection to them on page 42.
The definition of ‘perfect logician’ is given in the statement of the problem.
No it isn’t. What it states is merely one attribute, hardly a definition.
And you are the one belligerently avoiding the obvious and direct question, “what does ‘start with’ mean???”
As I said, “Quid pro quo.”
I agree with Carleas that you’re being more vague than you realize, and if you put in the effort to make it more clear, it would probably become more clear what’s wrong with your idea.
You’re also just playing games, and as he said earlier, not really arguing in good faith anymore.
So you seriously don’t know what “number to start counting from” actually means in this context??