On 28 Jan 2012, at 23:36, meekerdb wrote:

On 1/28/2012 2:48 AM, Bruno Marchal wrote:

On 27 Jan 2012, at 21:02, meekerdb wrote:

On 1/27/2012 9:20 AM, Bruno Marchal wrote:

Pierz, Craig, I disagree. Consciousness can be explained as a non 3p describable fixed point when machine's observe themselves.

Why is this not 3p describable? Your explanation of it seems to imply a description.


Yes, but the explanation is not consciousness itself.

In the UDA, you are supposed to know what consciousness is. You are asked to believe that your consciousness remains invariant for a functional digital substitution.

In the AUDA, consciousness is not mentioned. It is handled indirectly via knowledge, which is defined via an appeal to truth, which (by Tarski theorem) is not definable by the mechanical entity under consideration.

In B'"1+1=2" & 1+1=2, the "1+1 = 2" is a description, but 1+1=2 is not. It is true fact, and as such cannot be described. We cannot translate True("1+1=2") in arithmetic. We can do it at some meta- level, when we study a simpler machine than us, that we believe to be correct, like PA. But then we can see that neither PA, nor any correct machine can do this for *itself*.

Consciousness, knowledge, truth, are concept which does not admit formal definition; when they encompass ourselves.

I wasn't asking for a formal definition, just a 3p description.

I model the 3p idea by formal. "formal" just means having a local finitely describable shape. Consciousness is not a product of any such finite shape.



You are saying that B"1+1=2" is a description of being conscious that 1+1=2?

Not at all. I am saying that B"1+1=2" & 1+1=2, is a description of being conscious that 1+1=2. B"1+1=2" just mean that the machine believes p (using Dennett' intentional stance, or some generalized non-zombie attitude. For correct machine Bp is the same as "the machine asserts p", "the machine proves p", but supposedly express by the machine itself (in general). Knowledge of p is (Bp & p). This related knowledge to an aspect of consciousness: its non formal definablity. By Tarski, we cannot define (Bp & p) is arithmetic, although we can simulate it for each particular arithmetical p (by itself).




This confuses me though because I read B as "provable"; yet many things are provable of which we are not conscious.

Sure. That's why we use Bp & p instead. And this changes everything, even for the correct (a priori) machine, because that machine cannot know that she is correct.

Bruno


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



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