date:20121108

Re: Plurality

2012-11-08 Thread Bruno Marchal



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

Re: Communicability

2012-11-08 Thread Bruno Marchal

On 08 Nov 2012, at 01:38, Stephen P. King wrote:

On 11/7/2012 12:44 PM, Bruno Marchal wrote:

On 07 Nov 2012, at 17:13, Stephen P. King wrote:

On 11/7/2012 9:41 AM, Bruno Marchal wrote:
Arithmetic explains why they are observers and how and why they
make theories.

Dear Bruno,

This is a vacuous statement, IMHO. Absent the prior existence of
entities capable of counting there is no such thing as Arithmetic.
Your belief to the contrary cannot be falsified!

In the same sense that 2+2=4 cannot be falsified.

Dear Bruno,

You are missing my message. 2+2=4 is universally true only
because there does not exist a counter-example that can be agreed
upon by 3 or more entities. You continue to only think from the
point of view of a single entity. My reasoning asks questions from
the point of view of many entities

But even with that criteria, your point will not go through, as it is
obvious that nobody will find any counterexample to the fact that
observer exists in arithmetic (assuming comp). In the same sense
that 2+2=4.

It just mean that you have never grasp the proof of Gödel's
incompleteness theorem, which does that, almost in passing. This is
proved in all good introduction text to logic.

Ha! OK, but you are wrong.

If you stiudy and grasp by yourself Gödel's prrof, you should see why
the prior existence of comp-counting entities is a theorem of
arithmetic, and have the same reality as 2+2=4. You would not have the
remark above.

We can prove, in Peano arithmetic, that there exist entities
capable of counting.

If we follow the orthodox interpretation of Tennenbaum theorem
there can only be one entity that can count; the standard model of
PA. I am thinking of the uncountable infinity of non-standard models
of PA that have a condition imposed on them: each thinks that it
alone is the standard model as it cannot know that it is non-
standard. In this way we can get an infinity of standard models of
PA instead of just one. I think that this gives us a modal logical
form of general relativity!

By Gödel's completeness those entities exists in the standard model
of arithmetic (arithmetical truth), and in all model, and thus
also in all non standard model.

Yes, but each model must be able to truthfully believe that it
alone is the standard model; it cannot see the constant that defines
it as non-standard from inside itself.

It is confusing to use models for modeling thinking entities.

So arithmetic assures the prior existence of entities capable of
counting.

Sure.

Ah? But it is a key point that you seem to avoid in many of your post.

You have the Matiyasevich's book. A (more complex) proof is given
there. It is more complex as it proves this for a much more tiny
fragment of arithmetic.

It is impossible for me to write my ideas in Matiyasevich's
language. :_(

I am not sure why. I have taught computer science to disabled people,
and unless severe disability, it is always possible to overcome any
technical limitations.

Forgive me, but I need to let others explain my argument as I have
run out of patience with my inability to form sentences that you
will understand. This article (which I cannot asses completely due
to the paywall) seems to make my claim well: http://www.springerlink.com/content/052422q295335527/

Nomic Universals and Particular Causal Relations: Which are Basic
and Which are Derived?

Armstrong holds that a law of nature is a certain sort of
structural universal which, in turn, fixes causal relations
between particular states of affairs. His claim that these nomic
structural universals explain causal relations commits him to
saying that such universals are irreducible, not supervenient upon
the particular causal relations they fix. However, Armstrong also
wants to avoid Plato’s view that a universal can exist without
being instantiated, a view which he regards as incompatible with
naturalism. This construal of naturalism forces Armstrong to say
that universals are abstractions from a certain class of
particulars; they are abstractions from first-order states of
affairs, to be more precise. It is here argued that these two
tendencies in Armstrong cannot be reconciled: To say that
universals are abstractions from first-order states of affairs is
not compatible with saying that universals fix causal relations
between particulars. Causal relations are themselves states of
affairs of a sort, and Armstrong’s claim that a law is a kind of
structural universal is best understood as the view that any given
law logically supervenes on its corresponding causal relations.
The result is an inconsistency, Armstrong having to say that laws
do not supervene on particular causal relations while also being
committed to the view that they do so supervene. The inconsistency
is perhaps best resolved by denying that

Re: On the ontological status of elementary arithmetic

2012-11-08 Thread Bruno Marchal

On 08 Nov 2012, at 01:42, Stephen P. King wrote:

On 11/7/2012 12:46 PM, Bruno Marchal wrote:

On 07 Nov 2012, at 17:16, Stephen P. King wrote:

On 11/7/2012 9:43 AM, Bruno Marchal wrote:

On 06 Nov 2012, at 17:05, Stephen P. King wrote:

On 11/6/2012 8:33 AM, Bruno Marchal wrote:

snip

This is not convincing as we can make statical interpretation
of actions. In physics this is traditionally done by adding one
dimension. The action of throwing an apple (action) can easily
be associated to a parabola in space-time.
This invalidate your point, even if you say that such parabola
does not exist, as you will need to beg on the real action to
make your point.

Dear Bruno,

So do you agree that the relation goes both ways, which is to
say that the relation is symetrical? If the action of throwing
an apple implies a parabola, does the existence of the parabola
alone define the particular act of throwing the apple?

Throwing an apple === a parabola

But throwing a banana a parabola, too.

Dear Bruno,

Can you not see that these two relations are not in a
symmetrical one-to-one relation? There are many actions that can
be represented by one and the same parabola.

Then why do you ask me if it is symmetrical. You make my point here.

Hi Bruno,

That is not my question. If you agree that the relation is not
symmetrical, then how can you use the existence of the parabola to
necessitate the particular case (throwing an apple) without further
explanation as to how that one special case is selected?

The parabola is only one feature of a complex event. But my code saved
by the doctor does contains all the relevant information for my
survival, in the comp theory. And the computation in arithmetic does
singularize my mind from the 3p view. Then form the 1p view I have to
take into account all computation.

Your analogy simply does not work.

We can show the existence of a general class of entities far easier
than the existence of a particular entity!

Just what I said to say that the MWI assumes less than non-Everett QM.
And comp assumes still less than Everett as it forces to derived QM
(the SWE) from arithmetic, in a precise way (if we want exploits the G/
G* distinction to get both qualia and quanta).

Bruno

--
Onward!

Stephen

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