On 12 Feb 2013, at 03:22, Stephen P. King wrote:

On 2/4/2013 11:57 AM, Bruno Marchal wrote:

On 01 Feb 2013, at 20:25, Stephen P. King wrote:

On 2/1/2013 5:20 AM, Telmo Menezes wrote:

On Thu, Jan 31, 2013 at 11:38 PM, Stephen P. King <stephe...@charter.net > wrote:
On 1/31/2013 4:46 PM, Telmo Menezes wrote:
What's an entity?

Any system whose canonical description can be associated with some kind of fixed point theorem.

Ok, do you figure that a human being can be considered an entity under that definition?

Hi Telmo,

Recall the phrase "I think therefore I am." The "I" is a fixed point under variations of content of experience.

Yes. And Descartes limited to the doubts experiences. He tried to doubt all propositions, but then he has to doubt the proposition asserting that he doubts all propositions, that is conceiving certainty.
Dubito ergo cogito. (I doubt thus I think)
Cogito ergo sum.  (I think thus I am).

Hi Bruno,

I would add the temporal tense and state: Cogito, ergo eram, "I think, therefore I was".

But that does not follow.

This is Löbian, with the classical definition, making Dt such a fixed point.

I agree. I believe that this is exactly how the ambiguous self of self or "I" obtains.

I don't see the ambiguity. Unless it is the usual "ambiguity" between truth and provability, G* and G. Cf G* proves Bp equivalent with Bp & p, and G does not.

But neither Descartes, nor any correct Löbian machine, can prove Dt, although the reasoning above validly confirm, from the first person point of view, consciousness as undoubtable, with consciousness being something like Dt?, a sort of basic, automated, instinctive, elementary faith in a reality.

Could you elaborate on what would happen *if* any correct machine could indeed prove Dt? What would be the implications?

The machine would eventually prove that 0 = 1, implying that you are the pope, notably.

Thomas Slezak made a similar analysis of the cogito of Descartes. References in the general biblio of "Conscience and Mecanisme".

This need the classical definition of knowledge, which is given here by Thaetetus definition in arithmetic, thanks to incompleteness (the machine cannot know that Bp and Bp & p are equivalent).

I am not happy with this negative type of proof. I would like to see some kind of constructive argument or even an approximation.

The proof is not negative. And it is constructive, even if bearing on an impossibility. The machine can build the conterexample. The result can be said to be negative, but math is full of such non go theorems. We can't change that at will.

This entails the fact that we can be genuinely aware that we dream, but we can never be genuinely aware that we are awake, (as the usual Turing emulation thought experiences illustrate).

This seems to me to be analogous to "we can know for sure that X' is a fake or simulation of X and not the real thing", but it presupposes a 3p judgement. If one only allows 1p judgements and finite computational resources, then one must be a fallibist in one's claims.

Usually the 3p discourse is always fallible. Only a part of the 1p discourse (our own consciousness) is not fallible.



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