On 07 Nov 2012, at 21:07, Stephen P. King wrote:
On 11/7/2012 10:39 AM, Bruno Marchal wrote:
On 07 Nov 2012, at 13:48, Stephen P. King wrote:
On 11/5/2012 1:49 PM, Bruno Marchal wrote:
[SPK] You are considering only one entity.
This is incorrect. For example the first person plural is defined
in term of duplication of populations of machines sharing
universal numbers/computations.
Dear Bruno,
I would like to restrict my discussions to just a few
questions about the comp hypothesis. I do not understand how the
AUDA explains the "duplication of populations of machines sharing
universal numbers/computations". Could you elaborate on this? I
asked previously if there exists an index set or some other way to
identify differences between populations. You didn't seem to know
what an index set is...
Then read the post more cautiously, please, and quote that part. My
specialization is recursion theory, and I was pointing that your
use of "index set" was irrelevant, and did not apply to the 1p.
Dear Bruno,
Can you explain exactly what distinguishes one 1p from another
in a way that does not refer to some Platonic Ideal?
?
One 1p has headache. Another one as toothache. For example.
My confusion is that I see only a single equivalence class of
machines allowed by Tennenbaum's theorem.
When I ask you to explain what is the role of Tennenbaum here, you
escape in even more 1004 fallacies.
Tennenbaum's theorem tells us that there is only one countable
model of Peano Arithmetic that can be recursive. This makes, in my
opinion, a Universal Machine to be a single entity
There is an infinity of different universal machines in the standard
model, or any model, of arithmetic, for example a LISP interpreter, a
prolog interpreter, the GOL, etc. All constitutes different universal
numbers.
and any copy of it is identical to it. This prevents multiple copies
of it having different identities unless the copies are all embedded
in a space such that each copy has a different location.
They have different "locations" in the sequence 0, 1, 2, 3, ...
Explain it informally so that everyone can get the idea, if there
is one. Avoid any links.
OK.
Take the time to explain what is a non standard model,
If we allow for non-standard models of PA to be countable and
recursive models that individually 'imagine' themselves to be in
compliance with Tennenbaum's theorem by hiding the constant that
makes them non-standard from themselves, as if they are allowed to
forget that they are actually non-standard (as seen from some
hypothetical 3p) and thus fool themselves into believing that they
are standard models.
Too much metaphorical. I don't think a model is a good metaphor for a
thinking being (doubly so assuming comp). A model is a better metaphor
for a reality than a thinking being.
and why "2+2=4" is universally true,
"2+2=4" is universally true because any collection of at least 3
observers of tokens that represent {2, +, =, 4} can agree that it is
true.
It is simpler to grasp that 2+2=4, than to grasp that 3 observers
agree that "2+2=4" is true.
that is true in both standard and non standrad model.
What I am trying to explain covers both instances, no?
Then explains what role you see in those non standard model, and
why they would change something in the comp results, which I have
proved in arithmetic, and so are valid also for the non standard
models.
All that comp needs to add is something like a Blum complexity
measure, as you suggest, to act as the unique decoration of the
instances of the model that are associated with a given observer.
Where am I going wrong?
You are already in the "not even wrong" territory. You make
statements which are too much unclear, and this is worsened by your
constant appeal to technical jargons.
You are trying to understand my words too literally.
If you use technical terms, I think that I have no choice.
You must treat what you read as signals whose code you do not
entirely know. We each speak different languages and are trying to
communicate with each other via crude analogies. I just ask that you
truth that I have some coherent idea of what I am trying to say and
I will do the same for you.
That is the root of your constant 1004. You make crude analogies with
technical concepts. This can't work.
My problems center around your ideas about 3p-truth!
This, on the contrary is clear but weird, as you refer all the time
to papers using that 3p truth notions. But then for comp, you seem
to use philosophy to resist following a reasoning.
My argument is that all of those texts tacitly assume that the
3p truth can be verified by some physical means, how ever remote it
might be.
It is not an argument. It is a confession of aristotelianism. It begs
the question addressed by the comp theory.
The texts you refer too does not make that tacit assumption, even if
at another non relevant level, the authors of those paper assumes
there is some world in which they can publish the paper, but that is
not part of the theory they are studying.
There has to be at least one way to physically represent a theory
for it to be communicated between two or more observers! My thesis
is that the "physical means" is defined only by the computations
that the observers have in common.
OK.
There is not really a separate physical world in my thinking, only
the illusion that there is one.
OK, but then comp is handy to explain how and where the illusion come
from.
In the comp theory the 3p truth is the truth of the arithmetical
sentences. You should have develop the intuition of it in high
school. It is the simpler known 3p realm. In QM, an example of 3p
would be Everett universal wave function.
I don't like the MWI model of QM. It assumes too much.
I disagree. It assumes less. In fact Everett did not invent a new
interpretation of QM. he proposed a new formulation, which is the old
QM minus the collapse of the wave. In that theory, using comp, he
explains where the belief in collapse can be explained by the SWE. MWI
assumes less. It is even the main motivation for everything type of
TOE. You need less assumption for getting an "all" than any sub-
particularization.
Most of science is based on 3p mathematical truth, simple like in
economy and classical physics, and more sophisticated in quantum
mechanics and theoretical physics.
I understand that is the case. My argument is that the 3p can be
defined by the mutual agreements about statements between many
observers, the 3p is just another way of talking about an illusory
physical world..
That is terribly confusing. Once you agree that the physical worlds is
dream sharing, it becomes 1p plural. It is simple to keep the 3p for
what we assume to be objective, like elementary arithmetic.
Of course I cannot explain comp, nor QM, nor GR, nor anything in
science to someone who stops at "2+2=4", by doing what I feel to be
only premature philosophical resistance.
You assume that Plato solved all problems of many minds
I don't do that. Anything related to Plato is in the consequence, not
in the assumptions. That is why I use "arithmetical realism" in place
of "arithmetical platonism".
and I am trying to explain to you that Plato's idea has an open
problem. You know this problem as the 'arithmetic body' problem.
It is not in Plato. And the "body problem" is the result of reducing
the mind body problem in computer to science. It is a mathematical
problem, no more a philosophical one. But philosophically, it is a
logical refutation of aristotelian metaphysics.
Bruno
http://iridia.ulb.ac.be/~marchal/
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