On 8/27/2012 10:45 AM, Bruno Marchal wrote:
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.
Dear Bruno,
I am trying to get you to explain to us in detail how the copy and
paste operation of a body (as described in your papers) generates copies
of minds that are not identical to each other. BTW, there is a very nice
Google Book of Smorynski's article on self-reference here
<http://books.google.com/books?hl=en&lr=&id=wwXfHT5ka_8C&oi=fnd&pg=PA1&dq=logic+of+arithmetical+self-reference&ots=51rs_0l3Ml&sig=UhcErZpSm4KTECVdkfLfwMF1LBk#v=onepage&q=logic%20of%20arithmetical%20self-reference&f=false>
.
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.
This universality, as you yourself define it, ensures that all
copies are identical and this by the principle of indiscernible are one
and the same mind. There is no plurality generated unless there is a
necessitation of a physical state association to a mind, but this would
contradict comp. I have a solution to this! Use the relativization that
we can get by relativizing the Tennenbaum theorem! Each mind is
associated with a unique constant that it cannot see, as it is its
Kleene fixed point. That way we can have a true plurality of unique and
distinct minds.
Somewhat surprisingly, it was the poker game
<http://en.wikipedia.org/wiki/Blind_man%27s_bluff_%28poker%29> of "blind
man's bluff" and the book by Smullyan "/What Is the Name of This Book?
<http://en.wikipedia.org/wiki/Special:BookSources/0139550623>" /that
gave me the idea. It occurred to me that if consciousness is some thing
strictly internal (subjective, first person only), maybe there was
something that was the conjugate or complementary to that that would be
"external" or objective. The relation between G and G* seems to have
this same flavor. I am still unsure the details of this, but I hope that
you can see at least a vague outline of the idea that I am trying to
explain.
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.
Really!? It does not have a problem per se because it makes all of
the minds that it might consider to be only one particular equivalence
class: the one that can be imagined by one mind. This is to be expected
from a consistent solipsistic mind.
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!
?
"No other minds exist except for versions of my mind". This is the
consistent thought of a solipsist machine. Please understand that I am
not arguing against this situation, I am arguing that it forces certain
thing to be true and necessary. A solipsistic logical system can be
perfectly self-aware and yet cannot interact with anything other than
itself, by definition. For it, nothing exists that is not it, therefore
it simply cannot "see" the other minds problem.
My claim is that this solipsism condition is perfectly fine, true
and consistent, but only at the level of the primitives, at the Divine
Level. If we which to find a connection from it to the physical level we
have to "break it" otherwise it is incapable of making any contact with
the level of this discussion happening here and now.
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?)
One that uses a relativization using a variation on Robinson's
nonstandard model. But I need your help to find the proper formal
language to express the idea.
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.
You are completely missing the point here! Even a desert island or
in some cave deep in the earth, it is not just a human that could be a
witness to the truth. I/t is the mere possibility of communicability/.
The sand on that beach is a sufficient witness of truth. But /if you
remove the possibility of the merely possible witness, then you cause
the degeneracy (and eventual vanishing) of the very thing that you hold
so dear: the truth value/. The mistake in MGA is the ignorance of this
fact. I think that it is a conflation of the actual with the possible...
We see the exact same thing with quantum phenomena, if there is
even a possibility of detection of position information then the
momentum information will vanish to the limit of the uncertainty
principle. You have been living in a classical world too long and think
and have assumption consistent with such. I am trying very hard to be
consistent with facts: we live in a quantum universe, a universe where
the mere possibility of interaction counts as a term in the results.
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.
What exactly distinguishes them from each other? Is it an
absolute? Universality , as you define it, prohibits absolute
distinctions! Have you not read the articles on the non-uniqueness of
Godel numberings?I doubt that! So why can not you see the point here? I
suspect that you have some idea that there is an absolute ultimate
computation at infinity that can, like G* is a witness of G, witness all
truths of sigma_1 sentences. But what I am trying to show you is that
this cannot happen! Recursive enumerable function have to be finite.... NO?
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?
?
You make me cry with that answer. Please, read it out loud so that
you hear your own voice saying the words:
"*/The symbols string that I am reading now does not refer to the
computer monitor that I are reading it on/*."
And ponder the question that it implies. Is it a true or a false statement?
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.
What is with this obsession with physical primitivity? You have
demolished the idea, so why do you cling to it like a mistress that you
never wish to leave?
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 am trying here, now.
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.
What does omega-inconsistency mean, with regard to a theory? You
learned this in your courses. You know exactly what it means.
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.
Alas I can not read and understand French. :_(
Again, none of this address the issue of the flaw in UDA.
You refuse to look through the telescope.
"My dear Kepler, I wish that we might laugh at the remarkable stupidity
of the common herd.
What do you have to say about the principal philosophers of this academy
who are filled with
the stubbornness of an asp and do not want to look at either the
planets, the moon or the
telescope, even though I have freely and deliberately offered them the
opportunity a thousand
times? Truly, just as the asp stops its ears, so do these philosophers
shut their eyes to the light of truth."
~Galileo Galilei
Bruno
http://iridia.ulb.ac.be/~marchal/
--
Onward!
Stephen
http://webpages.charter.net/stephenk1/Outlaw/Outlaw.html
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