Given a subjective interpretation of reality, can we show that some beliefs cannot be identified as encodings in physical reality?
My gut feeling is that the answer is likely yes, and even if the answer is not as interesting as I thought it would be, the process of exploring it would yield interesting results.
For example, if we had a machine that, somehow purported to accurately decipher your brain neurons and tell you what you (objectively) believed, what would it be like?
Perhaps there would be instances in which the machine would claim you believed in X, but you actually believe you honestly believe in Y. Assuming the machine is really reliable due to some physical law or whatever... is this possible to have a belief that isn't encoded in physical reality, something that the machine cannot detect or will contradict you? This might be a parallel with free will vs determinism, in the objective interpretation of reality the two might not be that different, but in the subjective interpretation, beliefs seem to have more power than mere "will".
Perhaps it is useful to imagine something slightly different -- a machine that can tell you what color you perceive. It doesn't do so by just asserting the colors it displays on the screen, but rather, in addition to displaying colors on the screen, probe into your brain to try to figure out which neurons are firing. Is it possible for such a machine to misreport what you perceive?
This goes back to the question of whether we perceive the color "red" in the same way. While most people (those without a colorblind situation) can usually agree whether an object is objectively "red", there seems to be nothing physical that ensures one's perception of "red" is the same as another's. What if there is the same thing for belief?
Another funny thing about the a "belief probe" is that it might actually be able to probe the brain for "beliefs", and might actually be accurate in doing so for the overall person. But if it were only one belief, it might still not be able to accurately probe the subjective beliefs within a person. What if multiple "consciousnesses", with conflicting beliefs, were within the same physical body (as in the case of multiple personality disorders). The "tsundere" factor might also come into play, where while the probe might accurately predict behaviors, the subjective consciousness might dismiss it as superficial, because thoughts might not necessarily translate to concrete action. Is it necessary for a mere subjective feeling to always have a physical basis?
There is also the issue of meta beliefs, i.e. "belief of belief of belief ... ". Do they complicate the picture? I don't know.
It feels as if sorting this out properly could make way for identifying room that metaphysical entities might theoretically reside, if they exist.
