I think it is very important to ask the reverse question of “Are there some things, that should I come to know them, I would not be ready to accept?”
Also if you have a questionaire there is going to be some threshold of answers that you will count as noise and not as signal akin to lizardman constant. What things do you only think you are asking but are not actually asking?
Do you have some beliefs that if challenged by contrary evidence you would thereby find the evidence unreliable? Are there things your eyes could send you that would make you Aumann disagree with your eyes about them being optical sensory organs (aka not believe your eyes)? Do you have any beliefs which would require infinite amount of evidence to actually challenge (beliefs with less than appriciable doubt, ie infinidesimal openness). Are there any beliefs you are unreasonably hardheaded about (rather than requiring 1000 times the evidence needed to convince the median human you would require 1 000 000 000 times the evidence)?
Bad news is that most of the questions of the form “are there any...” will be answered in the positive. Rather than asking “whether” there are such beliefs we can almost certainly ask “what” are those kinds of beliefs you have.
This issue has become a lot less hypothetical, regards current events and is funny (while simultanoeusly being a very serious issue). Ant is a part of an information processing system more distributed than a single human that doesn’t have wings.
I have a cube maker contact if anyone is interested.