On 27 Aug 2012, at 15:32, Stephen P. King wrote:
On 8/27/2012 8:48 AM, Bruno Marchal wrote:
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.
Dear Bruno,
The question that I am asking is how you deal with multiple
minds. SO far all of your discussion seems to assume only a single
mind and, at most, a plurality of references to that one mind.
?
After a WM duplication there is already two minds. The first person
plural handled the many minds.
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.
OK. This seems to assume a background of the physical world...
Not at all. You need only a Turing universal system, and they abound
in arithmetic.
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?
Yes, but that is not my question. When you wrote "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" these seems to
be the implications that the mind of Einstein and the mind of Bruno
are not one and the same mind, at least in the sense that you can be
come him merely by reading a book just changing your name.
Yes. comp has no problem with many minds.
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?
None so far that I know of. This is the problem that I see. We
completely ignore the ubiquitous even to the point of believing that
it doesn't exit at all!
?
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.
That is not my point. Any and all implementations and
interactions must be "emulated in arithmetic" for the symbols of
arithmetic to have meaningful content. I am asking a semiotics
question. Is there a referent to which arithmetic refers to?
? (the model of arithmetics?)
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.
All of which assumes that such can be communicated.
Why? Even if Matiyasevic found this on a desert islands his result
would be true. Even if he did not found it, and was never
communicated, it still would be true, or you defend an arithmetical
idealism incompatible with comp.
But how does it get communicated? I am asking you to consider what
is being taken from granted, that ideas, concepts, representations
are communicated and asking you how that occurs - even as a toy
model explanation.
It happens when a collection of universal machines are supported by
some common universal machine. That happens all the "time" in
arithmetic.
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.
This is not a reduction issue. The symbols string that you are
reading now does not refer to the computer monitor that you are
reading it on, or does it?
?
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.
Yes, of course it is! I claim that it is an open problem for comp
because it assumes that it (physical reality) can be deleted from
the discussion.
I say the exact contrary. If comp is true then the primitive physical
reality is deleted from the ontology, and we have to explain the
physical reality appearance from the ontology we keep, like numbers or
combinators, etc.
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 think that you are simply failing to understand Deutsch' idea.
one does not need to assume physical reality if one can merely
assume that some kind of communication can occur. My claim is that
interaction defines the equivalent to a physical reality;
it is the plenum of commonalities on which we communicate. I am
trying to get you to see this such that you might see the easy
solution to comp's open problem.
Then do it, please.
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.
That is a nice Attaque au Fer! This is exactly why I make the
claim that your result is omega-inconsistent.
You made another claim.
I have no clue with a result being omega-inconsistent.
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.
Its meaningfulness vanishes when the medium which allows
communication is removed. How can it be communicated? This is not an
issue of consistency, it is something else. I would like to see more
of J. Lucas' statement and the refutation.
There is a full chapter on this in "conscience and mécanisme", and
thousand of papers in the literature.
Again, none of this address the issue of the flaw in UDA.
Bruno
http://iridia.ulb.ac.be/~marchal/
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