>>>2) If so, should we really limit ourself to this particular kind
>>>of mathematical structures? My concern is that we may be a bit too
>>>narrow-minded if we do.
>> But this sort of narrow-mindedness seems necessary to remain within the
>> formally describable realm. I'd go beyond computable structures only
>> if forced by evidence, e.g., if someone shows our universe somehow won't
>> run without all the real numbers. But for now there isn't any evidence
>> in this vein.
>Wait a sec: there's also no evidence that our particular
>universe has seven spatial dimensions or a proton/electron
>mass ratio different from 1836. But we're considering the whole
Right. Our motivation is that the ensemble is compatible with existing
data yet simpler than the special case. But Occam's razor also motivates
us to consider just the computable universes as opposed to those based on,
say, non-computable real numbers. The ensemble of computable universes is
both compatible with known data AND simple. The ensemble of non-computable
universes is not!