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).
You like the modal logical explanatory model,
This is not correct. I just model "belief" by the "instantional"
manner, à-la Dennet.
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).
so there we might think of observers as bundles of computations.
OK. That's nice, but what is a computation?
Your preceding post were using a notion of physical computation, which
would not cut the regress. 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.
It might be helpful for you to examine the Zuckerman and Miranker
paper 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").
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.
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.
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.
What Zucker did is a modeling of some aspect of self-reference,
partially coherent locally with comp. 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.
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. 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.
By the way, are you sure that Pratt's approach work in set theories
with non-foundation? 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.
Bruno
http://iridia.ulb.ac.be/~marchal/
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