From: Stathis Papaioannou (stathisp@gmail.com)
Date: Tue Mar 04 2008 - 06:43:36 MST
On 04/03/2008, Bryan Bishop <kanzure@gmail.com> wrote:
> On Monday 03 March 2008, Stathis Papaioannou wrote:
> > Yes. This is sometimes called "failure of induction" and it's a
> > problem for any ensemble theory in cosmology, such as Max Tegmark's.
> > (In fact, the idea that every possible computation is necessarily
> > implemented is one way of justifying Tegmark's modal realism).
>
>
> That's interesting, I must have missed this when I first learned of
> Tegmark. Leibniz would say that all unnecessarily nonexistent programs
> would exist, and that there are some that can become unnecessarily
> nonexistant or become existing through various means, but does Tegmark
> directly mean to say that all possible computations are platonically
> eternal and already implemented?
Not exactly: he says that all mathematical structures are eternally
and necessarily implemented, and that mathematical structures are all
there is (eg. see this recent short paper:
http://arxiv.org/pdf/0709.4024). One obvious objection to this idea is
that that physical objects seem to be *different things* compared to
mathematical objects; a physical circle is the same shape as its
platonic counterpart, but that's about all they have in common. On the
other hand, if we look at computations as one subtype of mathematical
object, the situation seems to be reversed. The computation as seen
from the inside (consciousness) seems to be a different thing compared
to the substrate of its implementation: it is nothing like the neurons
or semiconductors or gears and cogs, and it can produce its own
solid-seeming physical objects which need bear no relationship to the
substance of the computer. Indeed, multiple realisability and the
arguments presented in this thread (as well as other arguments such as
in this paper by Tim Maudlin:
http://links.jstor.org/sici?sici=0022-362X%28198908%2986%3A8%3C407%3ACAC%3E2.0.CO%3B2-A)
suggest that consciousness is necessarily a property of the
computation as platonic object, and only contingently a property of
physical objects that happen to be isomorphic to this platonic object.
This is analogous to roundness being necessarily a property of circles
as platonic objects, and only a property of physical objects insofar
as they happen to be isomorphic with a circle.
-- Stathis Papaioannou
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