On 06 Mar 2011, at 14:16, Andrew Soltau wrote:

On 07/02/11 15:22, Bruno Marchal wrote:

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.
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?

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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