It appears now that there are many random truths in any given
formal system. This is extremely unfortunate in many ways. With random truths, even if we were able to construct an automatic
proof generator to generate all proofs from the axioms, we would never be able to construct a list of all
truths in any given formal system.
This means that these random truths must be
divinely inspired or the result of a long
meditation. Presumably
Buddha would have known of all the random truths in the Universe.
Godel's Theorem is an extremely important result which really really sucks. Heres why:
Godel's Theorem talks about what is 'random truths', the problem is most of
science,
math, and even
stats (uses
set theory) use formal systems. Therefore there are true statements which cannot be proven. Since our understanding of the
universe hinges on
Physics which hinges on
formal logic systems, there are true things in the universe which we cannot prove.