I agree that there's a distinction here, though it strikes me as one of degree rather than kind.
I would say the same thing about the two dragon-claiming, garage-owning neighbors... in both cases, their minds fail to associate representations of the dragon in their garage with various other representations that would constrain their behavior in various ways. Whether we call that "belief in belief" or "failure to internalize" or "not thinking it through" or "being confused" or "not noticing the implications" or "failing to be a tactical genius" or "being really stupid" depends on a lot of different things.
That said, I don't think the purely labeling question matters much; I'm happy to adopt your preferred labels if it facilitates communication.
If I'm understanding your comment correctly, you're suggesting that the threshold between "belief in belief" and "failure to internalize" in this case has to do with the willingness to make predictions/bets -- e.g., if I'm willing to give someone a large sum of money in exchange for a reliable commitment to give me a much much larger sum of money after I am restored from cryonic suspension, then we say I have a "genuine belief" in cryonics and not a mere "belief in belief", although I might still failed to have an "internalized belief"... is that right?
If so, then sure, I agree... in the situation I describe, I might have a genuine but non-internalized belief in cryonics.
I would argue that the only difference between "belief in belief" and "failure to internalize" is whether the belief in question corresponds to external reality. The state of the brain is exactly the same in both situations.
Today's post, Mere Messiahs was originally published on 02 December 2007. A summary (taken from the LW wiki):
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