On 5/17/2017 5:08 AM, David Nyman wrote:
As a (very) rough and partial analogy, if I am on deck, and you are observing me from aloft, I can grasp that you are in a position to command an entire domain of such personally "unprovable" facts about me, despite my not being in a position​ to access them. Such personally unprovable facts might also bear directly on questions of my own consistency, for example if I were forced to rely on them in some crucial sense. Say you offered from your superior perspective to "be my eyes" in guiding my survival through some risky predicament below. I might choose to trust that guidance under hazard despite being in no position to prove independently the correctness of such a critical viewpoint. So in such a situation I might be unable to be unambiguously convinced of my own consistency but nonetheless choose to trust in it implicitly in order to promote my survival.
I think this is a common but misleading way of thinking about incompleteness...that a super-theory, in which consistency of a sub-theory is provable, is more truthful and comprehends more knowledge. The incompleteness has been proven not by finding some horizon beyond which vast new knowledge is found; it has beer proven by showing that some self-referential sentences cannot be proven on pain of inconsistency. Whether there are any interesting new theorems in the super-theory is a separate question.
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