On 23 May 2009, at 18:54, Brent Meeker wrote:


>
> I think it is related.  I'm just trying to figure out the implications
> of your theory for the problem of creating artificial, conscious
> intelligences. What I gather from the above is that you think there  
> are
> degrees of consciousness marked by the ability to prove things.


Hmm ... It is more a degree of self-reflexivity, or a degree of  
introspective ability. RA, although universal (in the Church Turing  
thesis sense) is a *very* weak theorem prover. RA is quite limited in  
its introspection abilities. I am open to the idea that RA could be  
conscious, but the interview does not lead to a theory of consciousness.
It is not a lobian machine like PA (= RA + induction). Lobianity  
begins with weaker theory than PA though, somewhere between RA and PA,  
and Lobianity is persistant, it concerns all sound extensions of PA,  
even hyperturing extension actually.

Also, I don't think I have a theory. I work in a very old theory:  
mechanism. It is not mine, and I use it because it makes possible to  
use computer science to prove things. Enough things to show mechanism  
empirically refutable.
For AUDA you need to accept the Theatetical approach to knowledge, all  
right.

I recall that in Smullyan "Forever Undecided", which introduces to the  
logic of self-reference G, a nice hierarchy of reasoners is displayed  
up to the Lobian machine.



>  To
> consider another view, for example, John McCarthy thinks there are
> degrees of consciousness marked by having narratives created and
> remembered and meta-narratives.  Either of these ideas is definite
> enough that they could actually be implemented (in contrast to many
> philosophical ideas about consciousness).

It is not bad. PA has the meta-narrative ability, and RA lacks it. You  
can see this in that way.



> I have some reservation
> about your idea because I know many people that I think are conscious
> but who couldn't prove even the simplest theorem in PA.

Because they lack the familiarity with the notations, or they have  
some math trauma, or because they are impatient or not interested. But  
all human beings, if you motivate them and give them time, can prove  
all theorems of PA, and, more importantly believe the truth of those  
theorems.

I have to add this last close, because even RA can prove all theorems  
of PA, given that RA is turing universal. But RA, without becoming PA,  
cannot really understand the proofs, like the guy in the chinese room  
can talk chinese, yet cannot understand its talk. It is the place  
where people easily make a confusion of level similar to Searle  
confusion (described by Dennett and Hofstadter). I can simulate  
Einstein's brain, but this does not make me Einstein. On the contrary  
this makes possible to discuss with Einstein. It is in that sense that  
RA can simulate PA without becoming PA. Likewise, all theories can  
simulate all effective theories. PA is probably still very simple  
compared to any human, except highly mentally disabled person or  
person in comatose state of course.




> Are we to
> suppose they just have a qualitatively different kind of  
> consciousness?

I don't think so, but in the entheogen forums people can discuss at  
infinitum if under such or such plants people experience a  
qualitatively different kind of consciousness. Given the hardness to  
just discuss on consciousness you can understand that this is a bit of  
a premature question.

Many estimate that to be conscious is always to be conscious of some  
qualia. In that case I could argue that even "me today" has already a  
qualitatively different kind of consciousness compared with "me  
yesterday".  Now, my opinion (which plays no role in the UDA- 
reasoning) is that consciousness can be qualia independent, and is  
something qualitatively stable, as opposed to the content of  
consciousness, which can vary a lot.

Now, if you compare RA (non lobian) and PA (lobian), then it is far  
more possible that they have a different kind of consciousness, and  
even lives in a different kind of physics, as a consequence. RA could  
be closer to a "universal consciousness notion". It would mean that PA  
could already be under some illusions ...
I don't know. Real hard questions here.

Bruno


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




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