Actually you turned it around in your answer (marked in red). I had defined the e and c in terms of received, not owed (and underlined it several times).
You turned it around by multiplying by 100 in one equation and dividing by 100 in the other. If you define it in terms of cents then both equations would have multiplications by 100.
It was only a matter of defining âeâ as what was received versus what was owed.
I defined it as what was received.
You ignored that and redefined as what was due.
That is the only difference (other than me leaving out a later division operation).
I mentioned the exact mistakes that I made. He denied the ones that he made (possibly still unaware).
Neither of us are claiming to be perfect.
Get your shit straight if you are going to get into the middle.
NOTE!: Phyllo made a mistake in his original complaint because he didnât realize the definition of âeâ that was being discussed. He intruded, unaware of the details. End of that story. He later provided the answer ⌠fine. I have no disagreement with his answer. I provided just short of that answer (trying to not give it all away). In doing that, I made one division error that I pointed out and corrected.
This is NOT an issue of either one of us being egotistical. It is an issue of phyllo not seeing that he had overstepped into an already established discussion (thus redefining the terms). After that point, there was no right and wrong, merely two rights that were different in their nature (due to differently defined terms; specifically âeâ and âcâ). And then you stepping in, completely blind and making an ⌠of yourself.
Just put your answers in reverse, into the equation that I provided. You will get the same result. I merely had e and c defined (before you intruded) to be the opposite of what you chose ⌠no big deal. It works either way.
By the way, Iâm not sure how you defined DS. Does it stand for dipstick, dip shit, dumb shit or something else? I would like to know in case you use it again in the future.
First, itâs important to note that this premise is not that same as âIf everyone is thinking this âŚâ Itâs not logically equivalent, and the former does not implicitly assume the latter.
Second, this is a given. We know this because 1) they must deduce anything deducible, and 2) they have been on the island for an infinite number of days prior to the Guru speaking. If there were a way for them to deduce their eye color prior to the Guru speaking, they would have. The problem goes to length to rule out other means of learning their eye color: there are no mirrors, they canât otherwise communicate, they donât already know it. In infinite time before the Guru speaks, nothing has let them learn their eye color, and nothing else happens on the island that could communicate their eye color to them.
Similarly to the above, this is not logically equivalent to âIf we assume that only the colors we see apply, thenâŚâ
But to address the objection, I think it must be a failure of communication. Each color of headband that any logician can see is the correct answer for at least one logician in the circle to the question âwhat color is my headband?â Thatâs tautologically true. Each color of headband that any logician can see is worn by at least one logician: the logician that is wearing it. Sorry if I was unclear in expressing this premise, but properly stated, it cannot be false.
Never said that it was. It is a new presumption. Your next presumption was âif he is thinking blue, thenâŚâ.
Ummm⌠no. The only way something is a âgivenâ is if it is GIVEN. If there is a âbecause we know thatâŚ.â, then it was obviously not a given, but rather a deduction/assumption.
That is why you failed to solve it. They had many deducible things other than the one you presumed them to start with (ref: âIf he is thinking blue, thenâŚâ). They MUST immediately deduce anything deducible and there really are many things deducible (I showed some at the time).
And that was merely a fallacy of the puzzle. The intent was that they could not deduce until the guru spoke, but that was not the reality of how it was setup (similar to the master saying âit is solvableâ when it actually is not).
But they did not rule everything out. They merely attempted to. They didnât rule out that the âperfect logiciansâ already knew that puzzle and thus already knew how to deduce far ahead of the timing. Obviously if you were there today as that scenario began, you would know when most of the people would be leaving long before your proposed turn. And so would they. The only thing that the guru provided was a moment to begin, and I am not sure that they necessarily needed that.
I donât think it said anything about an âinfinite timeâ, but like I said, there was a solution already there. Perfect logicians would have already figured it out before the guru spoke. The puzzle wasnât stated properly for what they wanted. And I donât know that it could have been.
And similar to above, I never said that it was. The way that is worded is begging the question of whether you meant âknown by everyoneâ or merely âknown by the othersâ. The word âknownâ infers an erroneous premise.
Yes, but that is kind of irrelevant unless you were intended to use it in an erroneous way. As you said, it is tautologically true if you meant it that way, so why even bring it up.
This tells me that you donât understand the logic of the problem. The Guruâs statement does not âonly [âŚ] provide a moment to beginâ, it provides crucial information that makes a logical deduction possible that was impossible before (in the proof by mathematical induction, her statement provides the base case).
Again, take the situation of 2 islanders who donât know their eye color, but are familiar with this problem. Without the guru telling them that she sees at least one islander with some eye color, neither islander can deduce his eye color. Unless when you say they âalready knew the puzzleâ you really mean they âalready possessed the information that the Guru providesâ.
EDIT: alternatively, replace the Guruâs statement with, âBegin deducing your eye color now!â If the Guru had said that, no one could deduce their eye color.
Donât reintroduce your blindness on that one too. Again, it is irrelevant that the syllogism part of your proposal works. Other syllogisms work even better.
James, it looks like your position is based on the possibility that someone can logically deduce the color of their eyes based solely on the color of the eyes of the people around them. Is that right?
OK, James. Not like itâs been half of the discussion for 10+ pages now or anything. Not like youâve provided a whole lot of awfully confident objections in your last few posts to an argument you âdonât rememberâ and arenât interested in discussing. Not like your interest faded when you were backed into acknowledging that your best argument is that it might be possible for a person to deduce their eye color by looking at a group of other people with eyes.