On 3/17/07, Brent Meeker <[EMAIL PROTECTED]> wrote:
>> But what is Platonia - Tegmarks all mathematically consistent
> >> universe? or Bruno's Peano arithmetic - or maybe Torny's finite
> >> arithmetic (which would be a much smaller "everything").
> >
> >
> > And while we're at it, why exclude non-mathematical structures?
>
> I guess that depends on what you mean by "mathematical structures". I
> would take any non-contradictory set of axioms to define a mathematical
> structure. I'm not sure what it would mean to include self-contradictory
> "structures". If you regard "mathematics" as a game of propositions it just
> means every wff is a theorem. But if you regard "mathematics" as existing
> (even in Platonia) I'm at a loss.

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What I meant was the naive interpretation of "everything exists": cartoon
characters in cartoon worlds *just there* rather than generated by some
computer simulation or set of physical laws, as our universe seems to be. If
you look at only computations in Platonia, you could argue that such
structures (which as a matter of fact could be generated computationally, so
perhaps non-mathematical was a poor choice of words) would be of low
measure. However, what of the ones "outside" the computer? It seems to me
they should have the same ontological status as the abstract computer, but
it is then impossible to assign them a measure which makes the weirder ones
less likely, as has been done with computation.
Stathis Papaioannou
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