Re: A must read paper

2012-10-06 Thread Stephen P. King 

On 10/6/2012 8:54 AM, Platonist Guitar Cowboy wrote:
Yes, but it is also in its infancy. With Aczel's work not 30 years 
old, and this admittedly weak analogy to consciousness only a few 
years old, which Aczel does not seem to be following up on himself:


http://www.cs.man.ac.uk/~petera/papers.html 



My point is, this is very young, what's young is always messy and will 
hopefully tidy itself up, and I can feel some funky aspect, 
specifically the observer aspect of a non-well-founded set defining a 
Russell operator, hinting at quantum physics perhaps in the future.


It should be called the Cantor operator, but as Zuckerman notes: "the 
importance of PR and publishing makes the difference." So, knowing 
this, why doesn't he call it the Cantor operator...




Hi,

I suspect that he named it after Russell because Russell's 
canonical (?) definition of the paradoxical set. I don't know that 
Cantor drew any attention to that set, thus he doesn't get credit for it.




m

On Sat, Oct 6, 2012 at 9:12 AM, Bruno Marchal > wrote:



On 06 Oct 2012, at 02:37, Stephen P. King wrote:


Hi Folks,



http://arxiv.org/ftp/arxiv/papers/0810/0810.4339.pdf


  Mathematical Foundations of Consciousness

Willard L. Miranker
,Gregg
J. Zuckerman

(Submitted on 23 Oct 2008)

We employ the Zermelo-Fraenkel Axioms that characterize sets
as mathematical primitives. The Anti-foundation Axiom plays a
significant role in our development, since among other of its
features, its replacement for the Axiom of Foundation in the
Zermelo-Fraenkel Axioms motivates Platonic interpretations.
These interpretations also depend on such allied notions for
sets as pictures, graphs, decorations, labelings and various
mappings that we use. A syntax and semantics of operators
acting on sets is developed. Such features enable
construction of a theory of non-well-founded sets that we use
to frame mathematical foundations of consciousness. To do
this we introduce a supplementary axiomatic system that
characterizes experience and consciousness as primitives. The
new axioms proceed through characterization of so- called
consciousness operators. The Russell operator plays a central
role and is shown to be one example of a consciousness
operator. Neural networks supply striking examples of
non-well-founded graphs the decorations of which generate
associated sets, each with a Platonic aspect. Employing our
foundations, we show how the supervening of consciousness on
its neural correlates in the brain enables the framing of a
theory of consciousness by applying appropriate consciousness
operators to the generated sets in question.


This is part of what I have been assuming form the beginning
of my conversation with Bruno so many moons ago. Its nice to see
its independent discovery.



As the cow-boy guessed right this is assuming too much, both for
the formalism used (which is OK), and the ontology, so it uses
implicitly non-comp hypothesis, which is less OK, as comp is also
assumed implicitly. IT is not uninteresting for possible progress,
but it is unaware that matter as to be explained by statistics on
computations "seen from inside". The role of "Russell operator" is
played by the Kleene second recursion theorem, which encapsulates
the "non foundation" well enough.

Bruno



--
Onward!

Stephen

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Re: A must read paper

2012-10-06 Thread Platonist Guitar Cowboy 
Yes, but it is also in its infancy. With Aczel's work not 30 years old, and
this admittedly weak analogy to consciousness only a few years old, which
Aczel does not seem to be following up on himself:

http://www.cs.man.ac.uk/~petera/papers.html

My point is, this is very young, what's young is always messy and will
hopefully tidy itself up, and I can feel some funky aspect, specifically
the observer aspect of a non-well-founded set defining a Russell operator,
hinting at quantum physics perhaps in the future.

It should be called the Cantor operator, but as Zuckerman notes: "the
importance of PR and publishing makes the difference." So, knowing this,
why doesn't he call it the Cantor operator...

m

On Sat, Oct 6, 2012 at 9:12 AM, Bruno Marchal  wrote:

>
> On 06 Oct 2012, at 02:37, Stephen P. King wrote:
>
>  Hi Folks,
>
>
>
>  http://arxiv.org/ftp/arxiv/papers/0810/0810.4339.pdf
>
> Mathematical Foundations of Consciousness
> Willard L. Miranker
> , Gregg J. 
> Zuckerman
> (Submitted on 23 Oct 2008)
>
> We employ the Zermelo-Fraenkel Axioms that characterize sets as
> mathematical primitives. The Anti-foundation Axiom plays a significant role
> in our development, since among other of its features, its replacement for
> the Axiom of Foundation in the Zermelo-Fraenkel Axioms motivates Platonic
> interpretations. These interpretations also depend on such allied notions
> for sets as pictures, graphs, decorations, labelings and various mappings
> that we use. A syntax and semantics of operators acting on sets is
> developed. Such features enable construction of a theory of
> non-well-founded sets that we use to frame mathematical foundations of
> consciousness. To do this we introduce a supplementary axiomatic system
> that characterizes experience and consciousness as primitives. The new
> axioms proceed through characterization of so- called consciousness
> operators. The Russell operator plays a central role and is shown to be one
> example of a consciousness operator. Neural networks supply striking
> examples of non-well-founded graphs the decorations of which generate
> associated sets, each with a Platonic aspect. Employing our foundations, we
> show how the supervening of consciousness on its neural correlates in the
> brain enables the framing of a theory of consciousness by applying
> appropriate consciousness operators to the generated sets in question.
>
>
> This is part of what I have been assuming form the beginning of my
> conversation with Bruno so many moons ago. Its nice to see its independent
> discovery.
>
>
>
> As the cow-boy guessed right this is assuming too much, both for the
> formalism used (which is OK), and the ontology, so it uses implicitly
> non-comp hypothesis, which is less OK, as comp is also assumed implicitly.
> IT is not uninteresting for possible progress, but it is unaware that
> matter as to be explained by statistics on computations "seen from inside".
> The role of "Russell operator" is played by the Kleene second recursion
> theorem, which encapsulates the "non foundation" well enough.
>
> Bruno
>
>
>
> --
> Onward!
>
> Stephen
>
>
> --
> You received this message because you are subscribed to the Google Groups
> "Everything List" group.
> To post to this group, send email to everything-list@googlegroups.com.
> To unsubscribe from this group, send email to
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> For more options, visit this group at
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>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
>  --
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Re: A must read paper

2012-10-06 Thread Bruno Marchal 


On 06 Oct 2012, at 02:37, Stephen P. King wrote:


Hi Folks,



 http://arxiv.org/ftp/arxiv/papers/0810/0810.4339.pdf

Mathematical Foundations of Consciousness

Willard L. Miranker, Gregg J. Zuckerman
(Submitted on 23 Oct 2008)
We employ the Zermelo-Fraenkel Axioms that characterize sets as  
mathematical primitives. The Anti-foundation Axiom plays a  
significant role in our development, since among other of its  
features, its replacement for the Axiom of Foundation in the Zermelo- 
Fraenkel Axioms motivates Platonic interpretations. These  
interpretations also depend on such allied notions for sets as  
pictures, graphs, decorations, labelings and various mappings that  
we use. A syntax and semantics of operators acting on sets is  
developed. Such features enable construction of a theory of non-well- 
founded sets that we use to frame mathematical foundations of  
consciousness. To do this we introduce a supplementary axiomatic  
system that characterizes experience and consciousness as  
primitives. The new axioms proceed through characterization of so-  
called consciousness operators. The Russell operator plays a central  
role and is shown to be one example of a consciousness operator.  
Neural networks supply striking examples of non-well-founded graphs  
the decorations of which generate associated sets, each with a  
Platonic aspect. Employing our foundations, we show how the  
supervening of consciousness on its neural correlates in the brain  
enables the framing of a theory of consciousness by applying  
appropriate consciousness operators to the generated sets in question.


This is part of what I have been assuming form the beginning of  
my conversation with Bruno so many moons ago. Its nice to see its  
independent discovery.



As the cow-boy guessed right this is assuming too much, both for the  
formalism used (which is OK), and the ontology, so it uses implicitly  
non-comp hypothesis, which is less OK, as comp is also assumed  
implicitly. IT is not uninteresting for possible progress, but it is  
unaware that matter as to be explained by statistics on computations  
"seen from inside". The role of "Russell operator" is played by the  
Kleene second recursion theorem, which encapsulates the "non  
foundation" well enough.


Bruno




--
Onward!

Stephen

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



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