I'm not sure what you're saying in this reply. I read your original post as using the island problem to try to demonstrate that there are situations in which using probabilities conditional on all the available information gives the wrong answer - that to get the right answer, you must instead ignore "ad hoc" information (though how you think you can tell which information is "ad hoc" isn't clear to me). My reply was pointing out that this example is not correct - that if you do the analysis correctly, you do get the right answer when you use all the information. Hence your island problem does not provide a reason not to use FNC, or to dismiss the Technicolor Beauty argument.

In the Technicolor Beauty variation, the red and blue pieces of paper on the wall aren't really necessary. Without any deliberate intervention, there will just naturally be numerous details of Beauty's perceptions (both of the external world and of her internal thoughts and feeling) which will distinguish the days. Beauty should of course reason correctly given all this information, but I don't see that there are any subtle aspects to "how" she obtains the information. She looks at the wall and sees a blue piece of paper. I assume show knows that the experimenter puts a red or blue piece of paper on the wall. What is supposed to be the issue that would make straightforward reasoning from this observation invalid?