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 <mailto: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?
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).
I would add the temporal tense and state: Cogito, ergo eram, "I
think, therefore I was".
This is Löbian, with the classical definition, making Dt such a fixed
I agree. I believe that this is exactly how the ambiguous self of
self or "I" obtains.
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?
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.
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.
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