Dear Bruno,

    I agree with your assessment of that Wiki article. In most universities the 
prevalent ontological doctrine is “dialectical materialism” and such has no 
allowance for any competition in the realm of ideas. I have pointed out that 
your result is similar to solipsism but never as an insult. It was just that I 
do not see a means to extend it to being able to consider the appearance of 
interactions between many minds. As far as I have studied, it seems only to be 
able to make statements about itself. Until you can show how it can be 
individuated for many minds this problem will remains, with or without a 
solution to the measure problem.
    The difficulty is that the numbers, alone, do not have any of the 
properties that we would associate with a mind with the notable exception of 
self-referential logical structure. If we might extend comp with the idea of 
the isomorphism with topological spaces (via the representation theorem) then 
we might have a notion of concrete persistence over transitions that allows for 
a notion of memory – since a single logical algebra is isomorphic to an entire 
class of stone spaces when we consider the relation of diffeomorphism. The 
inclusion of topological spaces allows us a coherent notion of “inside” and 
“outside” that can be used to distinguish multiple minds from each other, if 
only by having the possibility of differing positions in space. 
    The self-awareness that you mention would, in turn, allow for the expansion 
of the group of symmetries that can be considered as “internal” that they can 
be broken and mapped (via fiber bundles) onto the set complement of the stone 
spaces, that yields field theories.
    The “glue” that binds them all together is a combination of bisimulation 
chaining ( a form of homomorphism) on the abstract side and various other 
morphisms on the concrete “physical” side, all woven together by the wonderful 
natural contravariance of the stone duality.

Onward!

Stephen

From: Bruno Marchal 
Sent: Tuesday, June 07, 2011 12:31 PM
To: everything-list@googlegroups.com 
Subject: Re: Mathematical closure of consciousness and computation

On 07 Jun 2011, at 16:32, Jason Resch wrote:





  On Tue, Jun 7, 2011 at 5:22 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:


    On 07 Jun 2011, at 04:00, Jason Resch wrote:

    I guess you mean some sort of "spiritualism" for immaterialism, which is a 
consequence of comp (+ some Occam). Especially that you already defend the idea 
that the computations are in (arithmetical) platonia.
    Note that AR is part of comp. And the UD is the Universal dovetailer. (UDA 
is the argument that comp makes elementary arithmetic, or any sigma_1 complete 
theory, the theory of everything. Quanta and qualia are justified from inside, 
including their incommunicability.



  By immaterialism I mean the type espoused by George Berkeley, which is more 
accurately described as subjective idealism: 
http://en.wikipedia.org/wiki/Immaterialism
  I think it is accurate to call it is a form of spiritualism.


Well I am not even sure. Frankly, this is wikipedia's worst article.  It 
represents well the current Aristotelian reconsideration or non-consideration 
of immaterialism. Among the Platonists were the Mathematicians, the ideal 
platonic worlds for them was either mathematics, or what is just beyond 
mathematics (like neoplatonist will distinguish the intelligible (the nous) 
from the ONE behind (and like all self-referentially correct machine will 
eventually approximate by the notion of theories and the (possible) truth 
behind).
The "enemy" of "immaterialism" try to mock it by reducing it to solipsism 
(which is typically "childish), or to the naive believe in angels and fairy 
tales.
But immaterialism is not a believe in an immaterial realm, it is before all a 
skepticism with respect to the physical realm, or to the primacy of the 
physical realm. It is the idea that there is something behind our observations. 
The early academical debate was more to decide if mathematics or physics was 
the fundamental science.

Aristotelian's successors take primitive materiality as a fact, where the 
honest scientist should accept that scientists have not yet decide that 
fundamental question. Today physics relates observable to measurable numbers, 
and avoid cautiously any notion of matter, which is an already undefined vague 
term. The nature of matter and of reality makes only a  re-apparition in 
discussion through the quantum weirdness.

I argue that if we assume that there is a level of description of ourselves 
which is Turing emulable, then, to be short and clear (albeit not diplomatical) 
Plato is right, and physics becomes a modality: it emerges from 
self-observation by relative universal numbers. The quantum weirdness becomes 
quasi- trivial, the existence of Hamiltonians also, the precise form and 
simplicity of those Hamiltonians becomes the hard question. Comp does not yet 
explain the notion of space, although it paves the way in sequence of precise 
(mathematical) questions.

Unfortunately, the computationalist philosophers of mind, as reflected at least 
in wiki, seems to ignore everything of theoretical computer science, including 
the key fact that it is a branch of math, even of number theory (or combinator 
theory, of creative sets, Sigma_1 complete finite systems, ...). Now I see they 
have a simplistic (and aristotelian) view on immaterialism.










      Okay, this makes sense given your solipism/immaterialism.


    I would like to insist that comp leads to immaterialism, but that this is 
very different from solipsism. Both are idealism, but solipsism is "I am 
dreaming", where comp immaterialism is "all numbers are dreaming", and a real 
sharable physical reality emerges from gluing properties of those 
dreams/computations.




  You are right, I should find a less general term.  It is the missing of the 
glue I think that differentiates the immaterialism of comp from the 
immaterialism of Berkeley.


Don't worry too much on the terms once you get the idea. We can always decide 
on vocabulary issue later.

You sum very well the problem. The glue is really provably missing only in 
solipsism. There is just no reason to believe that numbers could miss the glue, 
that is more than quarks and waves. At least before we solve the (measure) 
problem. Math is there to see what happens. People seems to have the same 
reluctance to let math enter the subject than the old naturalists.

Now, the only way for the numbers to win the measure problem is by 
self-multiplication, and coherent multiplication of populations, that is 
sharing stories/computations. The only reason why I can dialog with you must be 
that we share a 'big number' of similar histories, and those have to be 
observable below our substitution levels. If those did not exist, keeping comp 
could lead to solipsism. But then QM, or the MW understanding of QM, shows that 
we do share indeed big sets, if not a continuum of similar histories, saving 
comp, empirically, of solipsism. Gödel-Church-Tarski saves mechanism from 
diagonalization, and QM saves comp from solipsism. Formally, incompleteness 
will give many possibilities for the glue to form, with the risky one based on 
lies (shit happens in Platonia too, that is the bad news, but it is there at 
the start:  G* prove DBf (it is consistent to prove the false).


Comp's message is not "we got the theory of everything". It is more "Oh, even 
if physicists unify all laws of nature, the task is NOT yet finished". Taking 
comp seriously, we *have to* justify those laws from the numbers 
self-observations. 
My work translate the classical mind body problem into a body problem 
mathematically expressed in computer science and in arithmetic.
Thanks to computer science (insolubilities and incompleteness),  (accepting the 
classical theory of knowledge), we get a gift: we are able to separate (in the 
self-referentially correct way) the quanta from the qualia, and to relate the 
two.

When you said that computation are in math, or in arithmetic, are you aware 
that this is explicitly proved in (good) textbook in logic or computer science? 
This is not easy to show. It is tedious and long, and there are always subtle 
points. But it is akin to define a high level programming language in a low 
level language. Matiyasevitch has gone farer than anyone in showing that 
diophantine polynomials are already enough (but that is much more complex to 
prove). This leads to a crazy proposition, which is that all sigma_1 truth can 
be verified in less than 100 operations, that is addition and multiplication of 
numbers. It means that all stopping computations can be given in the form of a 
short sequence of addition and multiplication (on numbers which might be great 
of course(*)). 


Bruno

(*) I can resist to show a version by Jones of that result. If you remember the 
RE set W_i, the set analog of partial computable functions (which are also the 
domain of the phi_i) Matiyasevitch' result can take the shape below. Nu and X 
are the two parameters, and the other letters, and the two characters "letters" 
are variables. Unknowns range on the non negative integers.
By adding enough variable, you could arrive at a degree four unique polynomial, 
but here we allow high degree. Look at that B^(5^60).

X is in W_Nu iff


Nu = ((ZUY)^2 + U)^2 + Y 

ELG^2 + Al = (B - XY)Q^2

Qu = B^(5^60)

La + Qu^4 = 1 + LaB^5

Th +  2Z = B^5

L = U + TTh

E = Y + MTh

N = Q^16

R = [G + EQ^3 + LQ^5 + (2(E - ZLa)(1 + XB^5 + G)^4 + LaB^5 + + 
LaB^5Q^4)Q^4](N^2 -N)
         + [Q^3 -BL + L + ThLaQ^3 + (B^5 - 2)Q^5] (N^2 - 1)

P = 2W(S^2)(R^2)N^2

(P^2)K^2 - K^2 + 1 = Ta^2

4(c - KSN^2)^2 + Et = K^2

K = R + 1 + HP - H

A = (WN^2 + 1)RSN^2

C = 2R + 1 Ph

D = BW + CA -2C + 4AGa -5Ga

D^2 = (A^2 - 1)C^2 + 1

F^2 = (A^2 - 1)(I^2)C^4 + 1

(D + OF)^2 = ((A + F^2(D^2 - A^2))^2 - 1)(2R + 1 + JC)^2 + 1










        >
        > If by representation you mean the representation of consciousness, 
then this
        > is the functionalist/computationalist philosophy in a nutshell.


        Computationalism says that representation *is* something you are.

        I say the opposite.  Representation is something you do, which is so
        natural to you and so useful to you that you’ve mistaken it as the
        explanation for everything.



      You should read this 
http://en.wikipedia.org/wiki/Functionalism_(philosophy_of_mind)

      Functionalism is the idea that it is what the parts do, not what they are 
that is important in a mind.

      Computatalism is a more specific form of functionalism (it assumes the 
functions are Turing emulable)

    I disagree with this. Putnam' functionalism is at the start a fuzzy form of 
computationalism (the wiki is rather bad on those subjects). It is fuzzy 
because it is not aware that IF we are machine, then we cannot know which 
machine we are. That is why it is a theology, you need an act of faith beyond 
just trusting the 'doctor'. In a sense functionalism is a specific form of 
computationalism because functionalist assumes by default some high level of 
comp. They are just fuzzy on the term "function", and seems unaware of the 
tremendous progress made on this by logicians and theoretical computer 
scientists. 

    Note also that comp makes *1-you* different from any representation, from 
you first person perspective. So, the owner of the soul is the (immaterial) 
person, not the body. A body is already a representation of you, relatively to 
some universal numbers.

    In a sense we can sum up comp's consequence by: If 3-I is a machine, then 
1-I is not. The soul is not a machine *from its point of view". He has to bet 
on its own G* to say 'yes' to the doctor. Of course, once we accept comp, we 
can retrospectively imagine that "nature" has already bet on it, given that the 
genome is digital relatively to chemistry, and given the evidences for 
evolution, and our very deep history.

    Bruno


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





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