Hi Nick, hi Quentin,

On 25 Dec 2009, at 04:13, Quentin Anciaux wrote:

Nick Prince wrote

>> I can understand that numbers and arithmetic operations (as well as a
>> whole lot of other stuff) exist as some kind of objective reality
>> (called a platonic reality).  These archetypal “things” are to me
>> clearly discovered by us rather than invented.  But that our dynamic
>> world emerges somehow from this static ethereal repository seems very
>> difficult to see.

And Quentin commented:

> Would it be easier if I said that all of this came from bouncing  
> particle of matter (whatever that is) ?

That is a good point, which I find rather convincing. To attribute  
consciousness to arithmetical (static, ethereal) relations is not more  
intriguing than to attribute it to continuous particle 4D line  
universe in any block universe conception.

But remember the "Peter Jones" type of move. He understands comp as a  
material form of comp. He posits that to be conscious, you need a  
physical primary universe in which the computations are executed. Of  
course this moves seems completely ad hoc. he has to invoke some magic  
in both mind and matter, which is already against the comp idea. But  
unfortunately, with only the first seven steps, you can still believe  
in such "ad hoc" theory. It is enough to believe that the seven steps  
just show that we are living in a small primary physical universe  
(small = not enough big to run the UD),  and that is why the 8th step  
is needed to prevent that type of move, and to conclude the proof.

Nick Prince wrote

> This must be difficult. How can any theory be interpreted without the
> formalisms or some model.

Remember that logicians use the word "model" like the painters. The  
model (the naked person) is the reality. The theory (the painting) is  
the finite piece of crap trying to capture or represent that reality.

A theory is on the side of the machine. It is a finite or finitely  
representable things, like a program. It has a sort of operational  
syntactical "interpretation": it generates mechanically theorems or  
numbers, and it can (and usually have) a (mathematical )meaning called  
model, and which is the thing it compute or prove statements about.

If you want, a brain is already a theory (with reality as intended  
model). The brain is supposed to interpret reality, or to implement  
some higher level interpreter (you, actually) of reality. for example:

reality = a bird flies in the sky (let us assume).
You look at it, and this makes your eyes sending a (giant) bitstring  
to your brain, which, through many (parallel) computations makes your  
self interpreting the bitstring as  (strong evidence that) a bird  
flies in the sky.
Who interpret the working of the brain itself? Well the answer is  
certainly *some reality*. Aristotelian would say it is nature, or the  
physical reality, but by the cartesian dream argument, a  
computationalist will say "some universal machine", but then he will  
eventually understand that below his level of substitution an infinity  
of universal machines have to compete.

> It is often said that with the many worlds
> interpretation it is the mathematics which tends to give us the lead
> on how to interpret Quantum Mechanics.  It was this that made me tend
> to agree with the many worlders.

Then you should love comp :)
Comp forces us to do, in arithmetic, exactly what Everett has done in  
the quantum theory.

I do agree with Bryce deWitt (and Everett) that the "(statistical)  
interpretation of quantum mechanics" is given by the theory itself  
(QM). And this in some precise sense. By QM I mean the high  
dimensional Hilbert space, the tensor product rule, and the unitary  
evolution of states (or observables). I mean, no collapse.
Then you could define the interpretation of QM by the normal average  
talk of the memory-machine described by the wave. This makes really  
the universal wave explanatively close.

But you need comp to do that, as most Everettian accept. But then the  
uda should make understand that this has to  be done for any universal  
machine (not just the universal QM wave), and even that the  
"appearance" of the universal wave has to be explained by the  
competition between all universal machines below some level.

Arithmetic generates its own interpretation, exactly like Everett  
showed for the universal wave. The universal wave can justify the  
"appearance of the collapse" in most observer's mind, and uda shows  
that if QM and comp are correct, then the appearance of the universal  
wave can be explained by the average universal machine intepretation  
of what they observe.

Monist theories, which embed the subject in the object, have to do a  
trick of that kind, in a way or in another.

Note that this is not standard. What I am doing for arithmetic is as  
original for a logician, than what Everett has done for QM is for a  
physicist (or the layman).

To sum up roughly: an interpretation is the doing of a universal  
number, as defined by its additive and multiplicative structure with  
other numbers.

> A map is a kind of (mathematical) model of reality so although there
> is a one to one correspondence between the points on the map to
> reality I still can’t see the trick of how to get through your step
> 8.  Sorry if I am seeming stupid.

Ah ah! Should I deduce you are OK with the seven first steps?

I don't see the relevance of the bijection between the map and the  
territory. The key here is that if the map is embedded in the  
territory (or the subject in the object) there will be a fixed point.  
There will be a point of the map which is superposed to the "real"  
point of the territory. We don't confuse the map and the territory,  
but we do confuse a point of the map with a point iof the territory.
Same with the painting: if the painters describe all what he sees, at  
some point he will paint the brushes itself, and the end point of the  
brush on the paper will, for a moment, be superposed to its painted  
description (at least infinitesimally).
It is the same in computer science, even with "weakly  
representational" theory of mind. Consciousness is a good candidate  
for a universal invariant in self-observing universal machine/number.

But this is just tangentially related to the step 8, and is exploited  
only in auda. Except that some familiarity with some amount of  
theoretical computer science can help to get the "computational  
supervenience thesis". You need to understand here what is a  
computation, mathematically. Church thesis is needed here, to  
legitimate the "universal" character of the universal dovetailer  
(universal in respect to computability). Auda needs provability logic,  
which is something quite different from computability (but they have  
important connections).

UDA is simple, because the concept of universal machine is not to hard  
to grasp. The base of computability theory is simple. You need only a  
few bit of naive set theory, numbers, and the technic of  
diagonalization. AUDA is more difficult because it needs mathematical  
logic, which is a field where the beginning is hard. It is long and  
boring to even give the little examples of formal theories. The  
difficulty consists in understanding that we have to NOT understand,  
nor even give sense, to the formalism. We have to abstract us from the  
meaning, to be able to tackle it mathematically after. I will have  
some opportunity to illustrate this. I have already done this with the  
modal logics.

>> To understand this well, it is necessary to NOT confuse a theory,  
>> with
>> his mathematical interpretation, and to NOT confuse a mathematical
>> interpretation with an interpretation in some reality. Physicists  
>> have
>> not yet this level of sophistication. They usually confuse a theory
>> (the SWE for example) with the mathematical (standard) interpretation
>> (the wave function).  This can lead to many misunderstanding of what
>> the logicians are doing, especially in applied logic.
> I’m struggling with this one as stated above.

If you are interested enough you may think to study a good book in  
mathematical logic, like Boolos and Jeffery, or Mendelson, or Epstein  
and Carnielli. Then you could take a look at some  textbook in the  
logic of self-reference (Boolos 1979, 1993),  Smorynski 1985.

But you don't need to do that to understand the necessity of the  
reversal, that is UDA.
For UDA you need only to understand the math needed to understand  
Church thesis, I would say. A good simple book is the book by N.J.  

Mathematical logic is exploited only in the mathematical AUDA. Yet,  
for some mathematicians, AUDA provides at least a consistent  
arithmetical interpretation of the kind of "reality" the UDA forces us  
(if I am correct) to envisage.

Hope this helped a bit,

Happy Xmas, and happy new year,




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