> Does Gödel prove that mathematics is infinitely complex, or just
> incomprehensibly so?
I think infinitely complex is the likely choice. I'm not sure I can
prove it (metamathematics is not my strong suit), but given the
results by Chaitin about the random and non-algorithmic structures
in the natural numbers it seems that the complexity of mathematics
is infinite, not just incomprehensible. Which is good news actually -
at least the mathematicians will never run out of new stuff to
discover (and if platonic materialism/Max tegmark's TOE holds, then
there are an infinity of surprising universes out there).
> Would you say this is the limiting factor to omniscience?
Well, omniscience is limited by what is logically possible to know.
So even an omniscient being in our universe would not be able to
learn both the position and momentum of a particle; to do that it
would have to be "outside" the system. But in this larger system
there will be things it cannot know, and so on.
(You can guess that during the moments I'm a theist my idea about
God is rather bizarre :-)
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