On 17 May 2017, at 20:49, Brent Meeker wrote:
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.
Well, self-consistency *is* an interesting theorem of the super-theory
(assuming it correct). It might not be an interesting statements in
term of numbers, but it is interesting in term of the machine
theology. G* minus G is quite interesting in that regard.
Bruno
Brent
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