On 26 Aug 2012, at 21:59, Stephen P. King wrote:
On 8/26/2012 2:09 PM, Bruno Marchal wrote:
On 25 Aug 2012, at 15:12, benjayk wrote:
Bruno Marchal wrote:
On 24 Aug 2012, at 12:04, benjayk wrote:
But this avoides my point that we can't imagine that levels,
context
and
ambiguity don't exist, and this is why computational emulation
does
not mean
that the emulation can substitute the original.
But here you do a confusion level as I think Jason tries pointing
on.
A similar one to the one made by Searle in the Chinese Room.
As emulator (computing machine) Robinson Arithmetic can simulate
exactly Peano Arithmetic, even as a prover. So for example Robinson
arithmetic can prove that Peano arithmetic proves the consistency
of
Robinson Arithmetic.
But you cannot conclude from that that Robinson Arithmetic can
prove
its own consistency. That would contradict Gödel II. When PA uses
the
induction axiom, RA might just say "huh", and apply it for the
sake of
the emulation without any inner conviction.
I agree, so I don't see how I confused the levels. It seems to me
you have
just stated that Robinson indeed can not substitue Peano
Arithmetic, because
RAs emulation of PA makes only sense with respect to PA (in cases
were PA
does a proof that RA can't do).
Right. It makes only first person sense to PA. But then RA has
succeeded in making PA alive, and PA could a posteriori realize
that the RA level was enough.
Like I converse with Einstein's brain's book (à la Hofstatdter),
just by manipulating the page of the book. I don't become Einstein
through my making of that process, but I can have a genuine
conversation with Einstein through it. He will know that he has
survived, or that he survives through that process.
Dear Bruno,
Please explain this statement! How is there an "Einstein" the
person that will know anything in that case? How is such an entity
capable of "knowing" anything that can be communicated? Surely you
are not considering a consistently solipsistic version of Einstein!
I don't have a problem with that possibility per se, but you must
come clean about this!
What is the difference between processing the book with a brain, a
computer, or a book? This is not step 8, it is step 0. Or I miss what
you are asking.
That is, it *needs* PA to make sense, and so
we can't ultimately substitute one with the other (just in some
relative
way, if we are using the result in the right way).
Yes, because that would be like substituting a person by another,
pretexting they both obeys the same role. But comp substitute the
lower process, not the high level one, which can indeed be quite
different.
Is there a spectrum or something similar to it for substitution
levels?
There is a highest substituion level, above which you might still
survive, but with some changes in your first person experience (that
you can or not be aware of). Below that highest level, all levels are
correct, I would say, by definition.
If your level is the level of neurons, you can understand that if I
simulate you ate the level of the elementary particles, I will
automatically simulate you at the level of your neurons, and you will
not see the difference (except for the price of the computer and
memory, and other non relevant things like that). OK?
It is like the word "apple" cannot really substitute a picture of
an apple
in general (still less an actual apple), even though in many
context we can
indeed use the word "apple" instead of using a picture of an apple
because
we don't want to by shown how it looks, but just know that we talk
about
apples - but we still need an actual apple or at least a picture
to make
sense of it.
Here you make an invalid jump, I think. If I play chess on a
computer, and make a backup of it, and then continue on a totally
different computer, you can see that I will be able to continue the
same game with the same chess program, despite the computer is
totally different. I have just to re-implement it correctly. Same
with comp. Once we bet on the correct level, functionalism applies
to that level and below, but not above (unless of course if I am
willing to have some change in my consciousness, like amnesia, etc.).
But this example implies the necessity of the possibility of a
physical implementation,
In which modal logic?
what is universal is that not a particular physical system is
required for the chess program.
With comp, to make things simple, we are high level programs. Their
doing is 100* emulable by any computer, by definition of programs
and computers.
I agree with this, but any thing that implies interactions
between separate minds implies seperation of implementations and
this only happens in the physical realm.
No, this is not correct. You fail to appreciate that all
implementations and interactions are already emulated in arithmetic,
as shown by Gödel (in other terms, and implicity in 1931), and made
clear since.
Actually, since matiyasevich, we know that we can eliminite the
"A" ("for all") quantifier from the logic, and that a unique degree
four diophantine polynomial can already do the job.
Therefore the physical realm cannot be dismissed!
Nothing real need to be dismissed. But once an argument show that it
cannot be postulated, the "non-dismissing" takes the form of a
reduction of it to something else.
Bruno Marchal wrote:
With Church thesis computing is an absolute notion, and all
universal
machine computes the same functions, and can compute them in the
same
manner as all other machines so that the notion of emulation (of
processes) is also absolute.
OK, but Chruch turing thesis is not proven and I don't consider it
true,
necessarily.
That's fair enough. But personnally I find CT very compelling. I
doubt it less than the "yes doctor" part of comp, to be specific.
How is Deutsch's version different?
It is not a different version, it is a completely different thesis. It
assume a physical reality (primitive or not), and his thesis is that
there is a physical universal emulator capable of emulating all
physical processes. In the comp theory, this is an open problem.
CT assumes only arithmetic or equivalent, and postulates the existence
of a universal programming language. Actually it postulates that
lambda calculus is universal with respect of the ability to define
computable functions. Since then lambda calculus has been shown
equivalent with Turing machine, algol programs, game-of-life, very
elementary arithmetic, diophantine equations, etc. So the origian CT
is equivalent with
All computable function can be computed by a fortran program
All computable function can be computed by a algol program
All computable function can be computed by a game-of-life pattern
All computable function can be computed by a four degree polynomial
diophantine equation
All computable function can be computed by a current computer
etc.
CT does not involve physics at all, contrary to Deutsch' thesis.
I don't consider it false either, I believe it is just a question
of what
level we think about computation.
This I don't understand. Computability does not depend on any level
(unlike comp).
I don't understand either.
Also, computation is just absolute relative to other computations,
not with
respect to other levels and not even with respect to instantion of
computations through other computations. Because here
instantiation and
description of the computation matter - IIIIIIIII+II=IIIIIIIIIII
and 9+2=11
describe the same computation, yet they are different for
practical purposes
(because of a different instantiation) and are not even the same
computation
if we take a sufficiently long computation to describe what is
actually
going on (so the computations take instantiation into account in
their
emulation).
Comp just bet that there is a level below which any functionnally
correct substitution will preserve my consciousness. It might be
that such a level does not exist, in which case I am an actually
infinite being, and comp is false. That is possible, but out of the
scope of my study.
Bruno, this is exactly my argument against step 8; it fails
exactly at the infinite case.
The infinite case is exactly non-comp, which, as I just said in the
quote, is not the theory I am working on.
COMP is omega inconsistent.
That statement has been made by J. Lucas, and refuted since. The error
comes from a confusion between
"[](ExP(x))", and
"Ex[](P(x))"
That is "I know it exists a number x having the property P true on x"
and "it exists a number x such that I know P is true on x".
But I have no clue why you say that comp is omega inconsistent in the
present setting.
Bruno
Bruno Marchal wrote:
It is not a big deal, it just mean that my ability to emulate
einstein
(cf Hofstadter) does not make me into Einstein. It only makes me
able
to converse with Einstein.
Apart from the question of whether brains can be emulated at all
(due to
possible entaglement with their own emulation, I think I will
write a post
about this later), that is still not necessarily the case.
It is only the case if you know how to make sense of the
emulation. And I
don't see that we can assume that this takes less than being
einstein.
No doubt for the first person sense, that's true, even with comp.
You might clarify a bit more your point.
I am interested in benjayk answer too.
http://iridia.ulb.ac.be/~marchal/
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