James S Saint wrote:I explained the problem and I asked for you to prove one particular assertion in your response. Why aren't you doing so?

Sorry, my fault, I somehow missed

this post.

phyllo wrote:The problem that I have is that it seems that the problem is solvable if the Master says so but it's unsolvable if the Master says so. Nothing physically changes, only the declaration of the Master changes and the Master does not seem to give any information.

Needless to say, these kinds of problems feel unsatisfying.

James S Saint wrote:Saying that the person can or cannot solve the problem does not make it so, although it infers something from which one can make a reasonable guess.

The Master has listed a set of premises, one of which is "this is not impossible." This premise

does convey information, in the same way that Bernard and Albert being able to figure out the problem convey necessary information in the

Cheryl's Birthday problem, and Peter and Sarah's solving the problem allow us to solve the

sum/product problem. Does your objection apply there? Albert/Bernard and Peter/Sarah tell us, effectively, "I can solve this problem", and because they do, and only because they do, we too can solve the problem.

Same here: because the Master tells us that the Logicians can solve the problem, we can solve the problem (unless of course we decide to decry the Master as a liar; that is to create a different problem).

James S Saint wrote:For the problem to be solvable there must be one provable, unique pattern from which to deduce

As I said earlier,

I wrote:The problem doesn't have a specific answer, only a general one. We can't say how many logicians there are, but we can say a lot about minimums and how the numbers affect when the logicians leave.

So, we can't say what the 'one unique pattern' is, or how many logicians there are or what color their headbands are, but we can describe how the logicians would solve the problem -- what the problem would look like to them and how it would be solved regardless of what the specific colors involved are, or how many of each color there is.

James S Saint wrote:Each member has to have faith that the Master knows each member's abilities and color perceptions.

Some of your objections are interesting, but I don't think discussing them is useful just yet, because this strikes me as a more fundamental problem. Let's take the paradigm syllogism:

All men are mortal

Socrates is a man

Socrates is mortal.

No argument there, I hope.

What if instead we had the Master say:

"All men are mortal

Socrates is a man

Socrates is mortal."

"But wait!", says James. "The Master has never peered into the Socratic trou to verify the second premise! Clearly no logician could solve this unsolvable logic problem without irrational faith in the words of the Master!" This seems a poor objection, and a hypothetical logician hearing this statement by the hypothetical Master will have no problem certifying that the logic presented is sound.

Similarly here: the Master's statement is a

premise. It's truth is a given. And because it is a given, we know that none of the edge cases that would make it false are solutions to the logic problem. No logician is blind, because if any were, the problem would be impossible. And it is a

given that it is not impossible.

I asked someone this in relation to the Blue Eye problem and I don't recall getting an answer, I wonder if you'd indulge me here: Do you understand the logic problem that this is

attempting to present? Could you reword it to avoid the problems you have with it?

James S Saint wrote:Carleas wrote:If the headbands could be any color other than those that each logician can see, the problem would be impossible to solve.

Prove that one.

Your finite-set-of-colors possibility is an interesting counter. If we assume there are a finite number of colors, there is one logician with each color headband and they all know the entire set of possible colors, it does seem like each could conclude their own headband color, especially given that the Master said the problem was not impossible.

But is that a problem for the problem? Since our answer is general, and just describes the solution space, can't we just say ">1 of each OR one each of all possible colors OR [whatever else we come up with]"? Is there a general defeater that will always introduce ambiguity for the Logicians?

Also, I mentioned before the idea of a "least-necessary assumption". Is there a smaller assumption than that each logician's headband is one of the colors she sees?

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