On 11 Sep 2009, at 17:45, Flammarion wrote:

>
>
>
> On 4 Sep, 22:12, Bruno Marchal <marc...@ulb.ac.be> wrote:
>> On 04 Sep 2009, at 19:21, Flammarion wrote:
>>
>>> ...  Bruno has been arguign that numbers
>>> exist because there are true mathematical statements asserting their
>>> existence. The counterargument is that "existence" in mathematical
>>> statements is merely metaphorical. That is what is being argued
>>> backwards
>>
>> I have never said that numbers exists because there are true
>> mathematical statements asserting their existence.
>
>> I am just saying that in the comp theory, I have to assume that such
>> truth are not dependent of me, or of anything else. It is necessary  
>> to
>> even just enunciate Church thesis. A weakening of Church thesis is 'a
>> universal machine exists".  In the usual mathematical sense, like  
>> with
>> the theorem asserting that 'prime numbers exists.
>
> There is no usual sense of "exists" as the material I posted
> demonstrates.
>
> You have to be assuming that the existence of the UD is literal
> and Platonic  since you care concluding that I am beign generated by
> it and
> my existeince is not merely metaphorical. The arguemnt doesn't go
> through
> otherwise.


Once you say "yes" to the doctor, there is a clear sense in which  
"you" (that is your third person relative computational state, the one  
the doctor digitalizes) exist in arithmetic, or exist arithmetically,  
and this in infinite exemplars, relatively to an infinity of universal  
numbers which executes the computation going through that state, and  
this in the arithmetical sense, which implied a subtle mathematical  
redundancy.

Then the MGA enforces that all universal machine first person future  
experience is statistically dependent of a sum on all those  
computations.

You may read books by Boolos and Jeffrey, or Epstein & Carnielli, to  
see this. It is related to the representability of the computable  
functions in Robinson Arithmetic together with Church thesis.


>
>> I just make explicit that elementary true arithmetical statements are
>> part of the theory. You are free to interpret them in a formlaistic
>> way, or in some realist way, or metaphorically. The reasoning does  
>> not
>> depend on the intepretation, except that locally you bet you can  
>> 'save
>> your relative state' in a digital backup, for UDA.
>
> IF formalism is true  there is no UD. It simply doesn't exist
> and doesn't genarate anything.

If formalism is true, there is no matter, either.
I am still waiting your formal definition of "primary matter", and of  
"ontological existence".
I am not sure I understand how you can both believe to be a formalist  
and believe in *primary* matter. To be honest.

Both in the West and the East we known since the dream argument that  
*primary* matter is a metaphysical notion. That is the main difference  
between the Platonist (in my sense) and the Aristotelicians. Atheists  
and Christians are usually Aristotelicians, and their opposition hides  
the deeper opposition between (weak) materialist Aristotelician and  
(neo)-Platonist.

It is here that the scientific attitude remind us to not commit  
ontological commitment, and to be agnostic, except on refuted  
statements.

I am agnostic on both Matter and God. With "B" = believe, "~" = not,  
"m" = "Matter exists" and "g" ="God exists", taking in mind that I am  
open for large sense of those words, I am agnostic in the sense that  
~Bm & ~B~m & ~Bg & ~B~g. That's why I do research. (Matter with a big  
"m" = primary matter. In Plotinus the "One" and "Matter" are both  
beyond being/existence. That fits very well with AUDA.

  I am not agnostic about consciousness, and persons, though.

>
>> And you don't need
>> really that for the 'interview' of the universal machine.
>
> Of course I need a real machine for a real interview.

You should avoid the use of 'real". In our context, this is the notion  
which we are discussing, or (re)defining.
I have personally less doubt about my consciousness, and about my  
believe in the prime numbers than in anything material. Physicists  
avoid the question, except when interested in the conceptual problems  
posed by QM.

Bohr was ready to decree sometimes ago that the notion of reality did  
not apply to the microscopic. Nowadays we apply QM in cosmology, and  
we accept the price, that is the multiverse, but this still avoid the  
consciousness/reality relationship problem, when we assume comp. The  
MGA shows that we have to be a little more radical than Everett if we  
want to keep the CTM/comp idea.
As I just said on another forum: 'real' is a tricky notion.



>
>> All theories in physics uses at least that arithmetical fragment. But
>> fermions and bosons becomes metaphor, with comp.
>
> Mathematical existence is metaphorical if mathematical existence is
> literal.

In your theory. I have no problem with that. I just refer you to an  
argument showing that such theories are epistemologically incompatible  
with the comp hypothesis, or CTM.


>
> Their existence is literal  if mathematical existence is metaphorical.
>
>> May be very fertile
>> one. Like galaxies and brains.
>>
>> Scientist does not commit themselves ontologically. They postulate
>> basic entities and relations in theories which are always
>> hypothetical.
>
> False. There is nothing hypothetical about ingeous rock.

This is either mere wishful thinking, or you are not a machine. If you  
are a machine, then you confuse stable hypothesis with truth. "de  
mémoire de rose, je n'ai jamais vu mourir un jardinier" said the poet  
Fontenelle (from a rose's memory "I have never seen a gardiner dying".  
A possible misquote!

Of course, we can play with words. Comp does provide an explanation of  
the existence of relatively stable patterns, already similar to  
quantum mechanics, so there is a sense, in the comp frame, that some  
rock are not hypothetical relatively to some observer. They are just  
not composed of little material definite things, they are singular  
maps on the local accessible probable computational histories. Why  
this is described by a wave? Probably because things get symmetrical  
and linear on the border of the universal machine ignorance, as the  
logic of "sensible" and "intelligible" matter suggests (already, cf  
AUDA).

With the SWE, you get a phenomenological account of the wave packet  
reduction through a comp subjective differentiation (that's mainly the  
work of Everett). But UDA shows that once you do that, you have to  
pursue the differentiation up to the justification of the SWE itself,  
from the numbers (or combinators, etc.).

You are stuck at step 0 (you told me) by irrelevant philosophical  
considerations, I'm afraid. My point is mainly technical. UDA  
transforms the mind-body or consciousness/reality problem into a  
problem in mathematical computer science. If you are formalist, there  
is a complete formalist reading on what I do, indeed that's AUDA. A  
strict formalist can read UDA as a motivation for AUDA. But I have to  
insist that formalists are in general arithmetical realist ... in the  
formal sense of using the third excluded middle. I don't need more,  
and I can technically recast the whole thing with less (by using  
Markov intuitionistic principle).

The consistency of all this eventually resides in subtle aspects of  
the incompleteness phenomena in theoretical computer science. "Comp"  
is also for "computer science". Once you accept the excluded middle  
principle, like most mathematicians, you discover there is a  
"universe" full of living things there, developing complex views.

You can say everything is metaphor but your consciousness: it is up to  
*your* work to make some things less metaphorical than others.
We share, "obviously" long histories, and we are deep objects which  
can explain usual confusions about tokens and types.

And all this leads to a very elegant theory of everything. The  
ontology is defined by "p is true" if "p" is provable in Robinson  
Arithmetic. The epistemology is defined by "p is believed" if "p" is  
provable by Peano Arithmetic, or by any Löbian Machine described by  
Robinson Arithmetic. It is very concrete and a formalist should  
appreciate. Perhaps you should forget UDA for a while, and come back  
later, and study the "formal" AUDA part. It is my modest part in  
theoretical computer science, relying on key theorems by Gödel, Löb,  
Solovay, and many others. It is also a sequence of open problems, but  
the contrary would have been surprising. And there is an heroin there:  
the (classical) universal machine. And its little brother the  
(quantum) universal machine plays some key role too. AUDA shed some  
light on a two way road between those two notions.

To be sure other part of math shows that, like the relation between  
braids and quantum computations, or Abramski's combinators algebra.  
The advantage of the "self-referential" approach, with the (formal)  
interview of the universal machine which introspects itself is that,  
by the Solovay G/G* splitting, we get the difference between the true  
(theological part) and the provable (the 'scientifically communicable'  
part).

A correct Löbian machine can study correctly (formally) the whole  
theology (which extends the science here) of a simpler Löbian machine.  
She cannot lift it correctly to herself, without falling in  
inconsistencies, but she can lift it in the interrogative and informal  
way, be it by hope, fear, bets, prayers or whatever. (or she can  
accept some 'truth' as new axioms and transform herself, but that's  
necessary risky).


Bruno


http://iridia.ulb.ac.be/~marchal/




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