A. Wolf wrote:
>> So universes that consisted just of lists of (state_i)(state_i+1)...
>> would exist, where a state might or might not have an implicate time value.
> Of course, but would something that arbitrary be capable of supporting
> the kind of self-referential behavior necessary for sapience?
"Capable of supporting" implies some physical laws that connect an
environment and sapient beings. In an arbitrary list universe, the
occurrence of sapience might be just another arbitrary entry in the list
(like Boltzman brains). And what about the rules of inference? Do we
consider universes with different rules of inference? Are universes
considered contradictory, and hence non-existent, if you can prove X and
not-X for some X, or only if you can prove Y for all Y?
You see, that's what I like about Bruno's scheme, he assumes a definite
mathematical structure (arithmetic) and proposes that everything comes
out of it. I think there is still problem avoiding wonderland, but in
Tegmark's broader approach the problem is much bigger and all the work
has to be done by some anthropic principle (which in it's full
generality might be called "the Popeye" principle - "I yam what I
yam."). Once you start with all non-contradictory mathematics, you
might as well let in the contradictory ones too. The Popeye principle
can eliminate them as well.
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