On 06 Mar 2011, at 14:16, Andrew Soltau wrote:
On 07/02/11 15:22, Bruno Marchal wrote:
You say "And the result is easy to describe: physics is not the
fundamental branch.". This is the leap of yours I never understand.
Do you posit that a mathematical universe with no physical content
somehow automatically computes?
Comp makes precise that saying to be a machine is equivalent with
saying that there is a level of functional substitution where my
(first person) consciousness is invariant for a substitution made
at that level. Comp can show that we can never known our level of
substitution, and my reasoning works whatever I mean by my brain
(it could be the entire galaxy or the entire observable universe if
someone asks for it). CTM is vague on the level, and miss the point
that we cannot know it, if it exists.
Comp is also much more general than CTM, which relies usually on
some amount of neurophilosophy, or on representationalist theory of
the mind, and CTM is often criticized by 'externalist', like brent
Meeker for example. But comp is not annoyed by externalism, given
that it defines the (generalized) brain by the portion of universe
you need, like possibly the matrix above.
So comp is a very weak, and thus general, hypothesis. And the
result is easy to describe: physics is not the fundamental branch.
Computations have been discovered by mathematicians, in mathematics.
Models of Sigma_1 complete theories automatically computes indeed. It
is a theorem, even without Church thesis. In physics people usually
bets that some physical devices can approximate such computation. But
apart from Landauer and some others, the notion of physical
computation is not yet even well defined.
My leap is a consequence of step seven already, in case the apparent
universe is robust. Then the MGA eliminates the assumption of the
existence and of the robustness of a physical universe.
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