On 06/03/11 19:24, Bruno Marchal wrote:

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.
Yes but! I have no problem with the idea of a Platonic realm of mathematical structures simply existing, with or without the physical to instantiate them. I am aware this is a deep philosophical debate, but the Platonic concept seems somehow more straightforward than the physicalist concept. But for there to be activity, change, time evolution, 'in' that Platonic realm, seems to me a massive leap. That all possible numbers simply exist seems simple and straightforward. And as Russell S points out, all possible numbers is vastly simpler than 'the numbers we have discovered / used / instantiated / whatever. But to posit the exercise of some computation requires something utterly different. There has to be some kind of changing frame of reference, as in a Turing machine in action. Are you saying you believe in this kind of procedural process as a process active in an abstract arithmetical Platonic realm? For it seems this is required in what you declare.
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.
But whatever physical computation is, or whatever the process we are witnessing is, it requires an ongoing change. The Turing machine moves along the tape, whether it is physical or simply a theoretical construct of a physical machine. In order to actually move, and carry out the computation, step by step, it requres more than to exist, it has to act. There has to be a time evolution of the state of the system.
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.

Irrespective of the existence of a physical universe, something has to explain how change comes about. Or are you saying that in the arithmetical universe change 'just happens', in the same way as all possible numbers 'just happen' to exist?


Bruno


http://iridia.ulb.ac.be/~marchal/




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