On 18 Aug 2012, at 13:41, Stephen P. King wrote:

On 8/18/2012 6:20 AM, Bruno Marchal wrote:

On 17 Aug 2012, at 21:04, Stephen P. King wrote:

On 8/17/2012 10:48 AM, Bruno Marchal wrote:
<snip>

The dreaming number are usually very big concrete number. They dream by encoding computational state of person, relatively to some universal number, which are encoding universal machine relatively to some other one, and the initial one can be chosen arbitrary. Those are not symbolic number, but real encoding number, a bit like the genome if you want.

Dear Bruno,

Could you elaborate as to how you explain the means by which an encoding (which is an equivalence relation of sorts between one set and another)

?

How do you define "encoding"? What kind of mathematical entity is it?

I define it by its program, and its semantics. So you can see encoding as defined by the number k such that phi_k(x) is an encoding function. So its precise definition can be given by a number:

encoding = s(s(s(s(s(s(s(s(s(s(s(s(s......s(0)))))))) ...)

with the right number of parenthesis.

Equivalently I could define encoding by a SK-combinators, or by a lisp program. All those definition are provably (in peano arithmetic for example) equivalent.





is a generative action such that dreams obtain?

I work in the comp theory, so I postulate that consciousness can be manifested through a computation.

I am thinking that the my self-simulation idea of identity requires this, so we agree a tiny bit. I do define computations as *any* transformation of information and information I define as "a difference between two that makes a difference to a third".

Computation is a more easy concept than "information", which is a bit a trash word in which people put usually many different things. Computation admits Church's thesis. Information admits many non equivalent definitions. It is an important cloud of important notion, but I would not use it to define computation, which, thanks to CT, is much more easy to define in a mathematical proper way.

Bruno






I would very much like to better understand how you obtain the appearance of chance from purely static relations. I ask this as I simply do not see how you can claim to explain actions in terms of purely non-active relations. Craig's ideas assume activity at a primitive level and thus puts his considerations at odds with yours in an almost irreconcilable way.

There are different form of chance. A "real randomness" is given by the first person indeterminacy bearing on all computation (aka UD*, AKA arithmetic). Yes, Craig's theory is non-comp. I suspect more and more that you defend also non-comp, but unlike Craig, you seem to want to deny this.

Bruno

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





--
Onward!

Stephen

"Nature, to be commanded, must be obeyed."
~ Francis Bacon


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



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