In my view, thinking too much about whether one can prove that a system
is friendly or not is getting a bit ahead of ourselves. What we need first
is
a formal definition of what friendly means. Then we can try to figure out
whether or not we can prove anything. I think we should focus on the
problem of definition first.
Shane
But, it may be that one can prove a theorem of the form
"For any definition of Friendliness fulfilling properties P1, in any
universe satisfying properties P2, it is impossible for a system of
complexity < K1 to prove Friendliness about a system of complexity >
K2"
(for an appropriate computation-theory-relevant definition of "complexity")
In this case, the problem of definition of Friendliness is sidestepped...
I think this is the right approach, because I don't think that
Friendliness, to be meaningful, needs to have a compact definition.
My personal definition of what a Friendly universe is like is quite
complex and difficult to formalize, in the same manner that the rules
of English are complex and difficult to formalize.... But that
doesn't mean that it's meaningless, nor that it's unformalizable in
principle....
I think the argument in my recent pdf file could probably be turned
into such a proof, where the property P2 of the universe has to do
with its dynamical complexity. But I don't seem to have the time to
turn my heuristic argument into a real proof...
-- Ben
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