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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Received on Sat May 23 2009 - 20:02:21 PDT