stekp wrote:PeteP wrote:Hmm have you read my last post?
Sorry, Yeah I did it - there are too many replies from everyone for me to keep up with!!
With your group 1,2,3 etc, in my scenario the "group of people who only see 97 blue eyes" would be the empty set. Everyone would be able so determine that set is empty at the start.PeteP wrote:Anyway another try: At the end of the chain it's unknown whether D knows that anyone has blue eyes not just whether a specific individual has blue eyes. Yes the actual people A ,B,C all know that D has the knowledge that there is someone with blue eyes. But the mental construct C created by the mental construct B which both only exist in A's mind doesn't have to share that knowledge. Because the mental construct C is not the real C.
Yes, the mental construct of C is not the same as C.
But - and this is important - because the information being used is globally known about C, anyone constructing a model of C's brain (at any level of abstraction) is able to use globally known facts about C. And one of those globally known facts about C is that he knows there is a lower bound on the number of blues of (N-2). Therefore everyone can use this fact in their mental constructs of C, and mental constructs any level of abstraction can use this information.
spoilered Because I think that my second explanation attempt below it might work better for you.
Or let's put it in terms of global knowvedge. Person A knows there are at least n-1 and that it's globally known that there are at least n-2. However A doesn't know whether it's globally known that it is globally known that there are at least n-2. Because the people with blue eyes might only know that there are at least n-2 but only know that it's globally known that there are at least n-3 people with blue eyes. The knowledge about global knowledge also decreases with each step. That is why you can't use the global knowledge from the first step deeper in the chain because it isn't known anymore that it is known.
My last attempt for now too.