What is the definition of  "a machine"?  I have a sense that there
is an intuitive one but not an explicit one, appropriate to the
discussions here.


----- Original Message ----
From: Bruno Marchal <marc...@ulb.ac.be>
To: everything-list@googlegroups.com
Sent: Tuesday, June 2, 2009 12:29:47 PM
Subject: Re: The seven step-Mathematical preliminaries

The beauty of all this, Brian, is that the correct (arithmetically)  
universal machine will never been able to answer the question "are you  
a machine?", but she (it) will be able to bet she is a (unknown)  
machine. She will never know which one, and she will refute all  
theories saying which machine she could be, unless she decided to  
identify herself with the virgin, never programmed, universal one.

There is a way to attribute a first person view to a machine, but  
then, from that first person view, the machine will be correct in  
saying "I am not a machine".

The consequence of computationalism are so much counterintuitive that  
"even" machines cannot really believe in comp. Yet, those machine  
which believe in the numbers and induction will be able to explain  
exactly all this. Machines can prove that if they are a correct  
machine, then they cannot "believe" that they are a correct machine.

It is related to the incompleteness phenomenon and the logic of self- 
reference which is exploited in the AUDA.

Actually it works also for Turing hypermachines, and a vast collection  
of machine extensions, and even self-aware structures completly  
unrelated to machine, which unfortunately needs a lot of model theory  
to be described (like "truth in all transitive model of ZF", if this  
rings a bell).

But here we anticipate a lot. Hope this can open your appetite.


On 02 Jun 2009, at 21:08, Brian Tenneson wrote:

> Thanks for the links.  I'll look over them and hopefully I'll  
> understand
> what I see.  At least if I have questions I can ask though maybe not  
> in
> this thread.
> I don't yet know precisely what you mean by a machine but I do have
> superficial knowledge of Turing machines; I'm assuming there is a
> resemblance between the two concepts.  I surmise that a machine can  
> have
> an input like a question and if it halts then the question has a
> decidable answer, else it has no decidable answer.
> What about posing the following question "am I a machine" or the
> statement "I am a machine" and maybe some machines halt on an answer  
> and
> some don't.  Ie, if X is a machine, then have it attempt to compute  
> the
> statement "X is a machine."  (I know I'm a bit fuzzy on the details.)
> For machines X that return "X is a machine" I would be inclined to  
> think
> such machines possess at least some form of self-awareness, a kind of
> abstract self-awareness devoid of sensation (or so it would appear).
> -Brian
> Bruno Marchal wrote:
>> On 02 Jun 2009, at 18:54, Brian Tenneson wrote:
>>> Thank you for starting this discussion.  I have only joined recently
>>> and
>>> have little knowledge of your research.  To see it laid out in the
>>> sequence you describe should make it clear to me what it is all  
>>> about.
>>> I'm particularly interested in the interaction between consciousness
>>> and
>>> computation.  In Max Tegmark's Ensemble TOE paper he alludes to a
>>> self-aware structure.  I take structure to be an object of study in
>>> logic (model theory, in particular) but am not at all sure how
>>> consciousness, which I envision self-awareness to be deeply tied to,
>>> connects to mathematics.  It seems you're going to build up to a
>>> statement such as "consciousness is computable" OR "consciousness is
>>> not
>>> computable," or something about consciousness, at least.
>> In UDA, I avoid the use of consciousness. I just use the hypothesis
>> that consciousness, or first person experience remains unchanged  
>> for a
>> functional substitution made at the correct comp substitution level
>> (this is the comp hypothesis).
>> Then the UD Argument  is supposed to show, that physicalism cannot be
>> maintained and that physics is a branch of computer science, or even
>> just number theory.
>> In AUDA, I refine the constructive feature of UDA to begin the
>> extraction of physics.
>> You can read my paper here, and print the UD slides, because I
>> currently refer often to the steps of that reasoning:
>> http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
>> I have written a better one, but I must still put it in my webapge.
>> It seems to me that Tegmark is a bit fuzzy about the way he attaches
>> the first person experience with the "universes"/bodies. Like many
>> physicists, he is a bit naive about the mind-body problem. The
>> computationalist hypothesis is not a solution per se, just a tool
>> making it possible to reformulate the problem. Indeed it forces a
>> reduction of the mind-body problem to a highly non trivial body
>> problem. It is my whole point.
>> UDA shows that if I am a machine then the universe, whatever it may
>> be, cannot be a machine. An apparent physical universe can, and
>> actually must emerge, from inside, but this one too cannot be  
>> entirely
>> described by a machine.
>>> In light of that it seems a prudent fundamental step would be to
>>> define
>>> what it means for one structure to be aware of another.
>> In AUDA, the arithmetical and more constructive version of UDA,
>> consciousness, like truth, will appear to be undefinable, except by
>> some fixed point of the doubting procedure. It is then show  
>> equivalent
>> to an instinctive bet on a reality. It has a relative self-speeding
>> role.
>>> This would
>>> apparently be some relation on the aggregate of all structures  
>>> (which
>>> may be the entire level 4 multiverse in Tegmark's theory).  Perhaps
>>> some
>>> basic fundamental step would be to provide some axioms on what this
>>> relation could be but I'm almost convinced this can't be done in a
>>> non-controversial way.
>> Computationalism is not controversal, nor is my deduction, but few
>> people get both the quantum difficulties and the mathematical  
>> logic. I
>> am more ignored than misunderstood, and then I don't publish so much.
>> But I love to explain to people with a genuine interest in those  
>> issues.
>>> I know I'm putting the cart before the horse here so I don't expect
>>> all
>>> to be revealed for some time when it occurs in your exposition.  If
>>> there is some literature by yourself or others on the particular
>>> subjects and issues I mentioned, I'd appreciate links to them.
>> Almost all my papers dig on that issue. See my url
>> http://iridia.ulb.ac.be/~marchal/
>> or search in this list for explanations. What is new, and
>> counterintuitive is that computationalism entails a reversal between
>> physics and machine's biology/psychology/theology .... See my paper  
>> on
>> Plotinus for a presentation of AUDA in term of Plotinus  
>> (neo)platonist
>> theology.
>> We cannot define consciousness (nor the notion of natural numbers),
>> but we don't have to define those things to reason about, once we
>> agree on some principles (like the "yes doctor" and Church thesis).
>> Welcome aboard on the train Brian,
>> Bruno
> >


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