On 22 May 2009, at 18:25, Jason Resch wrote:

>
> On Fri, May 22, 2009 at 9:37 AM, Bruno Marchal <marc...@ulb.ac.be>  
> wrote:
>>
>>
>> Indeed assuming comp I support Arithmetic -> Mind -> Matter
>> I could almost define mind by intensional arithmetic: the numbers  
>> when
>> studied by the numbers. This does not work because I have to say:
>> the numbers as studied by the numbers relatively to their most
>> probable local universal number, and this is how matter enters in the
>> play: an indeterminacy bearing on an infinity of possible universal
>> machines/numbers.
>>
>>
>
> Bruno, I was wondering if there are anyn concrete examples to help
> clarify what you mean by numbers studied by numbers.  Are there things
> for example, that 31 could know about 6, or are such things only
> possible with or between very big numbers?




Do you remember that the partial computable functions are recursively  
enumerable?
Do you remember the phi_i: computing partial functions from N to N.

phi_1, phi_2, phi_3, phi_4, ....

You can associate a computation to a proof in Robinson Arithmetic of a  
statement like phi_31(6) = 745.
The idea is to use the original Robinson Arithmetic as the basic  
universal machine.

A description of a computation would be a representation of that  
computation in arithmetic. And Robinson arithmetic is already Sigma_1- 
complete and thus, if there is a computation of phi_31(6) = 745, there  
will be proof of that fact in Robinson Arithmetic.

The difference is really a question of level, and is basically  
(simplifying a little bit) the difference between the fact that

phi_31(6) = 745, is true and provable in RA, and the fact

provable(phi_31(6) = 745) is true and provable in RA

The numbers involved will not be so great, but can hardly be very  
little.


>
> I still have a confusion as to what you label a computation and a
> description.

A computation is an abstract object. It is what is usually described  
by a description of a computation. It is a sequence of step of a  
universal machine. Remember that you can also enumerate the partial  
computable functions from NXN to N, noted with P capital:

Phi_1, Phi_2, Phi_3, Phi_4, ....

Let me say that a number u is universal if   Phi_u(x,y) = phi_x(y) for  
all x and y. x is the number-program, and y is the number-data. By  
chosing RA as basic system, all those numbers are well defined. It can  
be shown that there will be an infinity of such universal number u1,  
u2, u3 ... (enumerable but not recursively enumerable!).

A computation is a finite or infinite sequences of step of some u_i on  
some input x.
A description of a (finite piece of) a computation is a nummber code  
for an arithmetical description of such a computation.

The difference between computation and description of a computation is  
similar to the difference between 1+1=2, and the Gödel number of the  
formula "1+1 =2".




> Do you believe if we create a computer in this physical
> universe that it could be made conscious,

But a computer is never conscious, nor is a brain. Only a person is  
conscious, and a computer or a brain can only make it possible for a  
person to be conscious relatively to another computer. So your  
question is ambiguous.
It is not my brain which is conscious, it is me who is conscious. My  
brain appears to make it possible for my consciousness to manifest  
itself relatively to you. Remember that we are supposed to no more  
count on the physical supervenience thesis.
It remains locally correct to attribute a consciousness through a  
brain or a body to a person we judged succesfully implemented locally  
in some piece of matter (like when we say yes to a doctor).  But the  
piece of matter is not the subject of the consciousness. It is only  
the "abstract person" or "program" who is the subject of consciousness.
To say a brain is conscious consists in doing Searle's'mistake when he  
confused levels of computations in the Chinese room, as well seen  
already by Hofstadter and Dennett in Mind's I.



> or do you count all
> appearance of matter to be only a description of a computation and not
> capable of "true" computation?

"appearance of matter" is a qualia. It does not describe anything but  
is a subjective experience, which may correspond to something stable  
and reflecting the existence of a computation (in Platonia) capable to  
manifest itself relatively to you.


> Do you believe that the only real
> computation exists platonically and this is the only source of
> conscious experience?

Computations and their relative implementations exist only in  
platonia, yes. But even in Platonia, they exist in multiple relative  
version, all defined eventually through many multiple relations  
between numbers.


>  If so I find this confusing, as could there not
> be multiple levels?

But they are multiple levels of computations in Platonia or  
Arithmetic. Even a huge number of them. That is why we have to take  
into account the first person indeterminacies.




> For example would a platonic turing machine
> simulating another turing machine, simulating a mind be consicous?


A 3-machine is never conscious. A 3-entity is never conscious. Only a  
person is. First person can only be associated with the infinities of  
computations computing them in Platonia.




>  If
> so, how does that differ from a platonic turing machine simulating a
> physical reality with matter, simulating a mind?


You will have to introduce a magical (assuming comp) selection  
principle for attaching, in a persistent way, a mind to that "physical  
reality" simulation. The mind can only be attached to an infinity of  
such relative simulations, and this is why if that mind look at itself  
below its substitution level he will find a trace of those  
computations. Comp says you have to make the statistic on all the  
computations. So the Physical has to be a sum on all those computations.
That such computations statistically interfere is not so difficult to  
show. That the comp interference gives the apparent quantum one is not  
yet discarded.

I think you are not taking sufficiently into account the first person  
(hopefully plural) indeterminacy in front of the universal dovetailer,  
(or arithmetic) which defined the space of all computations.

Does this help a bit?


Bruno


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




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