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 <http://en.wikipedia.org/wiki/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?
My confusion is that I see only a single equivalence class of
machines allowed by Tennenbaum's theorem
<http://web.mat.bham.ac.uk/R.W.Kaye/papers/tennenbaum/tennrosser>.
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 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.
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.
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.
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. 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.
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. 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. There is not really a separate physical world
in my thinking, only the illusion that there is one.
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.
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..
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 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.
Bruno
http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/>
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Onward!
Stephen
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