Hi Karl,
On 31 Mar 2016, at 17:30, Karl Javorszky wrote:
In the present Interlude after the session chaired by Lou on
Symmetry and before the coming one, allow me to enlarge on something
Bruno raised.
Bruno wrote:
Then this confirms the "computationalist theory of everything",
which is given by any formalism, like Robinson Arithmetic (the rest
is given by the internal machine's phenomenology, like the one
deducible from incompleteness). Indeed, in that theory, the stable
(predictible) observable have to be given by a statistics on all
computation going through our actual state. This (retro-)predicts
that the physical obeys to some quantum logic, and it can be derived
from some intensional nuance on the Gödel self-referential
provability predicate (like beweisbar('p') & consistent('t')).
In quantum mechanics without collapse of the wave during
observation, the axiom 3 is phenomenological, and with
computationalism in the cognitive science (the assumption that there
is a level of description of the brain such that my consciousness
would proceed through any such emulation of my brain or body at that
level or below) the whole "physical" is phenomenological.
Physics becomes a statistics on our consistent sharable first person
(plural) experiences. With "our" referring to us = the universal
numbers knowing that they are universal (Peano Arithmetic, Zermelo
Fraenkel Set Theory, viewed as machine, are such numbers).
An actuality is a possibility seen from inside, somehow, in this
context or theory (QM without collapse, or Computationalism).
Personally, it seems that quantum mechanics, when we agree on the
internal phenomenological of actuality in the possibilities,
confirms the most startling, perhaps shocking, consequence of
computationalism (digital mechanism). Note that it does not make the
physical itself computable a priori.
Of these thoughts, let us focus on the following:
“…. when we agree on the internal phenomenological of actuality in
the possibilities, confirms the most startling, perhaps shocking,
consequence of computationalism (digital mechanism). …”
Now how does “shocking” enter a discourse on quantum concepts and
the idea that there is knowledge and wisdom in them there natural
numbers?
Obviously, and let us thank Bruno for having pointed it out, there
is an element of reticence, unwillingness, resistance and
protracted, unpleasant surprise in the thought that Life, and the
world in general may be much more mechanistic and trivial than
thought before.
The person pre-shock believes in something, the person post-shock
knows that he has been robbed a dream. It is like a child has to
realise that Santa Claus is not a real person, and that little
babies do come about the way they come about.
Many ideas have to be laid to rest during the process of
familiarising oneself to the idea that the glue that holds the world
together – and within it, our ideas about the world – is best
described by the well-known form of a+b=c as known from good old
elementary school.
Discussing what forms and appearances the order can produce which
rules Nature, and within Nature, us and our thoughts, is
unfortunately equivalent to discussing, what kinds of order we can
look into and discover within a+b=c, as this old, well-chewed bone
is the backbone of rational concepts.
The disillusionment will be individually instrumented for each of
us, as Tolstoy had said about the unhappiness of families, each in
their own way. The resulting – remaining – denotation, after having
lost its connotations, will be made up of the simple grey, standard,
industrial units of abstraction, order as a running fight among, and
a compromise between b-a, a-2b, a+b, 2b-3a, and the like.
Please accept my apologies for the shock the insight may cause that
we are indeed just an experiment in combinatorics, and probably the
elves, fairies, trolls and unicorns do not exist neither.
Thanks for this comment Karl. The biggest shock I was alluding, and
which I get myself before I realized that it was confirmed by quantum
mechanics (without collapse) is that not only nature or the material
world does not exist per se, at least not ontologically, but only
phenomenologically (through a notion of sharable first person
experience) but in the fact that the usual mind-brain or consciousness-
matter identity link is broken, and that "my" particular current
experience is related to an infinity of relative brains-
representations existing in arithmetic. Bryce DeWitt explains how
shocking it was for him when he realized that at each instant he is
multiplied/differentiated by 10^100+ copies, and with only the
mechanist assumption that multiplication/differentiation is up into
the infinite (aleph_zero or aleph_one).
That can also be used to show that the physical reality cannot be
entirely computational, although it might remain as a computation *in*
some random oracle (given freely by the first person indeterminacy on
the infinitely many computations going through my state). Digital
mechanism in the cognitive science refutes digital mechanism in physics.
Note also that everything is derived not just from, a + b = c, but we
need also ab = c. We cannot derive ab= c, nor of course the existence
of a computer (universal number or machine) from a + b = c and logic,
we need also ab = c, and then we can prove the existence of all
universal numbers (accepting Church-Turing thesis at the metalevel).
The advantage of this precision is that we can test computationalism
by comparing the physics coming from the "many-world interpretation of
arithmetic" with the physics inferred from measurement, and it fits up
to now (we get a quantum logic for the universal machine observable).
In case it does not fit, we get a tool for measuring experimentally
the degree of non-computationalism, which can take the form of an
inference of some very special oracles.
Note also how much I concur with Lou about the importance of the first
and second type of fixed point (DD = F(DD), DD = F('DD')), which was
what decided me to do math instead of biology, as such fixed point are
directly usable in a number biology, or combinator, programs, ...
biology. There is not one result in my work which is not proved using
the first or second type of recursion. Most are implicit in Solovay's
arithmetical completeness theorem of the self-reference modal logics G
and G*, which are proved through a very ingenuous use of such fixed
points. Now, both fixed points theorems are direct consequence of the
laws of succession, addition and multiplication, or of elementary
lambda calculus.
Somehow, and this can seems shocking for some people, we get an
answer, perhaps a disappointing one, to the question "why there is
something instead of nothing".
Indeed, the failure of logicism explains that we cannot derived 0, +
and * (or the existence of a universal number/program) from anything
less. But then once we assume addition and multiplication, we have to
derive the psychological and physical appearances from them, or we do
the reification error and use some Material Reality as a "god-of-the-
gap". That is sometimes shocking some people: the idea that physics
is not the fundamental science, but that it is in principle a derived
appearance coming from the fact that we cannot know which machine we
are, nor which computations support us among the computations (all)
realized (executed, in the mathematical sense of Church and Turing) in
(a tiny part) of the arithmetical reality.
People knowing french can read "Conscience et Mécanisme(*)" for an
explanation how much computationalism fits well the philosophy of
Bateson and the idea that biology, psychology and theology (in part)
are intensional (modal) variations of the fixed point construction. It
is much in line with what has been said in this discussion.
Some seems to believe that Mechanism is a reductionism, but this comes
from a reductionist conception of Mechanism. After Gödel, we know that
neither computer science nor arithmetic can be completely axiomatized,
and the universal machine itself (once believing in enough induction
axioms) can justify why it has a soul which is not amenable to any
purely third person account (be it mechanical or not). The soul of the
machine escapes the whole of mathematics, and even "God", in some sense.
Bruno
(*) http://iridia.ulb.ac.be/~marchal/bxlthesis/consciencemecanisme.html
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