On 24 Dec 2009, at 02:13, Nick Prince wrote:

> Thanks Bruno
>
> I want to have a good think about your answers and also the eighth
> step in your paper.  I think it is the most difficult for me and yet I
> sense its somehow. Schmidhuber assumes a great programmer runs the UD
> but you effectively dispense with him. If a universal turing machine
> necessarilly exists platonically which is capable of running UD's that
> can simulate our minds then our experience of reality follows. Yet I
> still feel that somehow this will be confusing the map of the
> territory with the "reality", the equations of physics with the
> physically real.

And here there is a famous difficulty, which is that physicists and  
logicians use very different if not opposite vocabulary.
Logicians distinguish a theory (-usually a finite or recursive  
(mechanically decidable) thing, and its interpretation (usually an  
infinite mathematical structure.

In the comp frame, it is even more difficult, given that we are going  
through a metatheory, where both the theory and its interpretations  
are studied at the theory level, and then we have to consider the  
fixed point of the interpretation function.

Intuitively, you can understand that with comp, we do confuse,  
purposefully, the map and the territory. You can see a brain as a  
theory of reality. But that reality contains a brain. So, at some  
point the brain will accept (or bet)  that it is itself an object in  
that theory, and the computationalist practicers will have to bet that  
is "brain-theory" is well described (relatively to his neighborhood)  
by a finite thing (its own backup in such or that machine).

It is not stranger that Brouwer fixed point in geometry or topology.  
After all, we know that if the map of a territory is continuously  
embedded in the territory, a point of the map will be confused with a  
point in the territory. It is the indexical "You are here" point of  
the map. Likewise, in computer science, the meaning of a program can  
be described by a fixed point of some universal transformation (like  
in Scott denotational semantics, for example).

To understand this well, it is necessary to NOT confuse a theory, with  
his mathematical interpretation, and to NOT confuse a mathematical  
interpretation with an interpretation in some reality. Physicists have  
not yet this level of sophistication. They usually confuse a theory  
(the SWE for example) with the mathematical (standard) interpretation  
(the wave function).  This can lead to many misunderstanding of what  
the logicians are doing, especially in applied logic.

Concerning the existence of platonic Turing Universal Machine, it is  
equivalent with the platonic existence of the prime numbers, or the  
even numbers, etc. With Church thesis you can eliminate the "Turing"  
label.


Bruno

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



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