No. It doesnāt. You keep thinking that just because you have an operable algorithm, you have the only possible solution. For all of that type of problem, you MUST prove that your proposed solution is the only possible solution, else it isnāt a solution.
All of your deductions include an assumption that must be validated by being the only assumption possible in order to cause the puzzle to be solvable.
Proving that you have the one and only possible solution proves that the master is using it.
Iāve presented a logical syllogism, using mathematical induction, which is a method of deductive mathematical logic.
As weāve already discussed, once you have a syllogism, you donāt need to show that there are no other syllogisms (see e.g. the Pythagorean Theorem)
Even if it were the case that I needed to show there were no other solutions, for the MI problem Iāve provided a syllogism that shows that N islanders cannot learn their eye color before day N, so if there were another syllogism, it would produce the same result.
It is true for certain premises. If we assume X and ~X, we can conclude Y and ~Y. Iām saying that āthis problem is not impossibleā is an exotic premise that could similarly produce contradictory conclusions. I donāt think it does, but much of your argument seems to depend on it.
Right, but youāll notice that I only said that the syllogism is āclearly validā. The point being that a valid syllogism can be constructed using āthis problem is not impossibleā as a premise, and challenging you to show that the syllogism shouldnāt be treated like any other.
Do you agree that ācolors donāt bear any logical relation to each otherā is a true premise? Or do you have a similarly true premise that leads to a contradictory conclusion?
Only AFTER you skipped over substantiating your most essential premise (your presumption of colors) as well as your presumption that a faster method of color discovery could not be used.
Carl, that is stupid. Why do you keep saying that? Do you not read criticisms of your propositions? That is just a dumb thing to say and I have explained why. Once AGAIN: [size=150]We are NOT talking about many proofs for the same outcome.[/size]
We are talking about the need to prove that there cannot be any other possible [size=150]outcome[/size], and thus no other possible algorithm/solution.
No, you have NOT. I showed you that everyone could easily leave after the second bell. You are simply not listening.
No, it isnāt.
It would be true if you made sense of it first, but as stated and knowing the context, I have to deny it. Colors have a natural relative ORDER (most often expressed as a frequency). An order isnāt technically āa logical relationā, but it is an association that can be used in a logic argument: āGreen is between yellow and blue. Purple is between red and blue. Orange is between red and yellow.ā
One of the premises is that āit is solvableā, soā¦
And also the presented colors CAN have a displayed order: