On 10/7/2012 4:26 AM, Bruno Marchal wrote:
On 06 Oct 2012, at 21:27, Stephen P. King wrote:
On 10/6/2012 2:51 PM, Bruno Marchal wrote:
On 06 Oct 2012, at 17:40, Stephen P. King wrote:
On 10/6/2012 4:25 AM, Bruno Marchal wrote:
On 06 Oct 2012, at 09:35, Stephen P. King wrote:
Hi Bruno,
You wrote:
As the cow-boy guessed right this is assuming too much, both for
the formalism used (which is OK), and the ontology, so it uses
implicitly non-comp hypothesis, which is less OK, as comp is
also assumed implicitly. IT is not uninteresting for possible
progress, but it is unaware that matter as to be explained by
statistics on computations "seen from inside". The role of
"Russell operator" is played by the Kleene second recursion
theorem, which encapsulates the "non foundation" well enough.
I disagree. His operators are "looking from the outside" at A
(the physical universe).
What do you mean here by "physical universe"?
What do you think it means? The common subject of observation by
a collection of observers.
What are observers? Where do they come from?
Hi Bruno,
It depends on what feature you wish to find an explanatory model
of. My point is that "what is an observer" depends on the features
that one wishes to explain.
The context is the search of a TOE, which does not avoid the problem
of explaining consciousness and matter, and the relation between, or
put in another way the relation between first person views and third
person views.
You mentioned the "physical universe", but this is something that we
cannot take for granted in such a context. You defined it by using the
notion of observer, that's OK ... if you define the notion of observer
without mentioning "physical universe" (or if you do it, you have to
solve the recursion, with the second recursion theorem, or, if you
want, with Set Theory + non foundation, à la Barwise, but this must be
eliminable in comp, or put in the machine's epistemology).
In my thinking, a physical world = a reality = that which is
incontrovertible (free of contradictions = Boolean Satisfiable) for some
finite collection of observers, where observers are defined as "bundles
of computations". Physical worlds are not actual in the absence of
observers. I also stipulate that there are an infinite (uncountable)
number of physical worlds. This demands that there exists an uncountable
infinity of observers <=> an infinite number of bundles of computations.
Please recall how I define "exist"; it is *necessary possibility*.
You like the modal logical explanatory model,
This is not correct. I just model "belief" by the "instantional"
manner, à-la Dennet.
One day I might be able to recall your terminology exactly. ;-)
A machine believes p if the machine assert p, which makes sense as I
limit myself to machine talking first order language, ideally
arithmetically sound, and being able to believe the logical
consequences of its beliefs in arithmetic. Then modal logic just
happens to describe completely, at the propositional level, the logic
of provability of such machine, thanks to the work of Gödel, Löb and
Solovay (and others).
I have never choose to use modal logic, I use only machine
self-reference, where a very special modality imposes itself (G).
Sure, you use that is necessitated by non-contradiction principle. ;-)
so there we might think of observers as bundles of computations.
OK. That's nice, but what is a computation?
A computation is *_/*any transformation of information*/_*.
Information = any difference between two that makes a difference to a
third. It is interesting that this definition demand that there exists
at least three entities or processes or whatever for information and
thus computation to exist. I have not considered the further
consequences of this idea so far. It might be completely fallacious.
Your preceding post were using a notion of physical computation, which
would not cut the regress.
I disagree. I am arguing that only if we retain a connection
between computation as a platonic abstraction and the requirement of
physical resources we will have a viable cut off for the regress. A
computer that can only process a finite number of recursions or
iterations of self-modeling will not have an infinite regress for
obvious reasons. What I am trying to do to make this a more formal
statement is to tie together the Kolmogorov complexity of a description
a system <http://en.wikipedia.org/wiki/Kolmogorov_complexity>, abstract
or physical, with the physical degrees of freedom of a physical system
(for example the dimensions of its Hilbert space or Hamiltonian). In
this way we have a way to define a physical system as a bounded bundle
of computations. This would be a lower bound on the necessary physical
resources required to implement an arbitrary computations.
Following this idea we can see that it implies that physical
systems that require infinite computations to be exactly simulated only
can exist is very special circumstances!
But as I answered you can take the original definition of computation
(by Post, Turing & Co.), in which case you can assume only arithmetic,
and the regression is cut, by defining the "bundle of computations"
with the first person indeterminacy. Then you are back to sane04, and
you describe the comp theory.
This is where I agree with comp. I only disagree with your step 8:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.pdf
<http://iridia.ulb.ac.be/%7Emarchal/publications/SANE2004MARCHAL.pdf>
"what if we don't grant a concrete robust physical universe? Up to this
stage,
we can still escape the conclusion of the seven preceding reasoning
steps, by
postulating that a ''physical universe'' really ''exists'' and is too
little in the sense of not being
able to generate the entire UD*, nor any reasonable portions of it, so
that our usual physical
predictions would be safe from any interference with its UD-generated
''little'' computational
histories."
Here you seem to only consider a "physical universe" to be an
entity that "exists" with no observers associated with it and reason
that such is an irrelevant concept that can and should be dismissed from
consideration. I am OK with that! I define a "physical universe"
differently! (see above) I am only asking for a weaker version of a
"physical universe" to exist; one that is not ontologically primitive,
but to demand this is to also demand that arithmetics and numbers are
not ontologically primitive as well. Both abstractions, such as numbers
and their truths, and physical worlds must emerge together from a
primitive ground which is neutral in that it has no innate properties at
all other that necessary possibility. It merely exists.
from your paper:
"It will follow that a much weaker and usual form of Ockham's
razor can be used to conclude that not only physics has
been epistemologically reduced to machine psychology, but that
''matter'' has been
ontologically reduced to ''mind'' where mind is defined as the object
study of fundamental
machine psychology."
But "physics" =/= "physical world". Here is where we diverge in our
agreement! Physics is behavior not "being". Matter =/= "physical world".
Matter is the spatial aspect of sets, once we remove all of the
contingencies of physics explanations. You are claiming to "reduce"
matter (Aristotelian "substance") to "mind" (that which fundamental
machine psychology presupposes) and thus eliminate "matter". But this
seems to be possible only if fundamental machine psychology allows the
existence of a single machine and thus a singular mind. I have tried to
point out that this is exactly consistent with Tennenbaum's Theorem
<http://web.mat.bham.ac.uk/R.W.Kaye/papers/tennenbaum/tennrosser> and
tried to argue that this is a huge problem as it makes comp (or UDA)
into a description of the psychology of a consistent solipsistic machine.
One possibility requires that we "relativize" countable models of
PA using the non-standand arithmetics but in a way that perpetually
"hides" the non-standard component, the constant, of the model from the
machine itself. The inability for a computable model of consciousness to
"know" which computations "it is", is an expression of this property, IMHO.
It might be helpful for you to examine the Zuckerman and Miranker
paper <http://arxiv.org/ftp/arxiv/papers/0810/0810.4339.pdf> and
discuss it with the members of the list. I will defend it against
your critique, as I see the paper as a nice representation of part of
the dual aspect monism (or "process dualism") idea that I have been
advocating.
That's a technical implementation, which assumes too much from the
point of view of foundational studies. It is OK, and rather cliché in
my opinion, and is the kind of thing I let the Löbian machine too
choose. It is not really relevant, given the results in the comp
theory, as the regression cut are based, through comp, to the Kleene
second recursion theorem (the double intensional diagonalization, or
Dx = "xx").
Are you interested in solving the arithmetic body problem or not? I
am interested in solutions! BTW, the regression cut that you are
implementing is not flexible. My work requires a flexible regression cut
to deal the"Heisenberg cut" problem of QM
<http://www.phys.tue.nl/ktn/Wim/qm1.htm#Heis_cut> so we can consider
observers in non-statistical ways (in contrast with the way that
decoherence arguments treat observers). My proposal is to add some fine
detail to Zuckerman''s model, specifically to the definition of
"observation" in his model, in a way that is consistent with Pratt's
model. Pratt's model has some open problems of its own, but these are
solved by the requirement of physical resources for the bound on bundles
of computations (aka observers). But this latter idea demands a weaker
version of computational universality... We fight over that!
I am just trying to understand if your theory contradicts anything in
what has already been done in comp, or if it contradict or is in
opposition as you seem to believe or assert from time to time. Paper
like Pratt, and now Zuckerman are just unaware of the comp reversal
between physics and arithmetic, and completely ignore the mind body
problem.
Why do Pratt and Zuckerman need to be aware of the comp reversal?
Could it be that you are merely complaining that they are ignoring your
work?
They use the term consciousness without motivating its use, or making
clear what axioms they take for consciousness, and seems to build on
the usual Aristotelian paradigm. They are simply unaware of the first
person indeterminacy and its consequences. They are not alone, of course.
"...without motivating its use"? What is a more basic question that
human ask than "what is the nature of my existence?"? Why complain that
they are not stating the obvious?
You seem to accept the first person indeterminacy, and the seven first
steps of UDA, so an interesting work would be to adapt their work (of
Pratt, Zuckerman) to the comp reality, but this does not necessitate
to change the limited arithmetical ontology, as set theory, with or
without foundation, belongs to the number's many possible
epistemologies. If not, it means they are implicitly assuming a
non-comp theory, as it is necessitated by the Aristotelian frame.
Let us see that first and not prejudge the possibilities. Most
people have never questioned the Aristotelian framework as you have; I
appreciate that fact, but we can be OK with that fact. It need not stop
our work.
What Zucker did is a modeling of some aspect of self-reference,
partially coherent locally with comp.
I argue that local coherence is all that is necessary for the
requirements of deriving physics!! In other words, local solutions of
the arithmetic body problem are sufficient. We do not need a global
solution. In fact, I argue that a global solution is impossible as such
would contradict the finding of the Wheeler-DeWitt equation
<http://en.wikipedia.org/wiki/Wheeler%E2%80%93DeWitt_equation>! What I
am arguing for (within physics) is consistent with papers by Peres
<http://arxiv.org/abs/gr-qc/9704061>, Kitada
<http://arxiv.org/abs/gr-qc/0110066> and Dugic
<http://arxiv.org/abs/quant-ph/9810029>.
He seems to ignore the arithmetical self-reference which has to be
used when postulating comp. But what is more annoying is that they use
implicitly a physical supervenience thesis, or are just unclear on
this, and so some correction and adaptation needs to be added.
Maybe Zuckerman is unfamiliar with Lob's work?
Such adaptation is very technical, and I hope you are not using this
to escape the question I am asking you, due to your negative unclear
remark on the step 8.
I am trying to be precise, but I have constraints on my abilities. ;-)
That would be the case if you think that Zucker work contradicts the
arithmetical or Turing universal restricted ontology, which is shown
necessary and sufficient for the derivation of both consciousness and
the matter collective hallucination brought by comp.
But you cannot ignore the open "arithmetical body" problem! We all
have "motes" in our eyes!
By the way, are you sure that Pratt's approach work in set theories
with non-foundation?
Yes. I confirmed this in conversations with Peter Wegner. It was he
that pointed me to the work of Jon Barwise in 1998.
That does not seem entirely obvious to me, and should be justified. In
this case you can point on some references if this has been already
studied. It is not obvious because in the set/boolean algebra duality,
the duality is working, as Boolean algebra are well founded structures.
One thing that I need to point out is that non-foundation theory
works with normal sets. As you might see in the Youtube video of
Zuckerman <http://www.youtube.com/watch?v=WJrhBVTs83o>, the Aczel
Universe <http://www.blutner.de/AFA/liar3.pdf> is an extension of the ZF
universe.
--
Onward!
Stephen
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