Hi Jerry, List,
On 17 Mar 2017, at 22:29, Jerry LR Chandler wrote:
List, Bruno:
(My response to theMarch 13 message are interwoven in a red font.)
While I appreciate the flow of concepts emerging from Bruno’s
“poetry”, its guidance appears to exclude chemistry and biology.
We have something like:
Number(with + and *) => Number's dreams statistics => Physics =>
human biology
Thus, Bruno’s associations are not so clear to me.
This provides evidence you have a sane mind :)
So, I will be a “spoil sport” and look toward a more “life-
friendly” flow of both symbols and numbers with only a tad of
poetry.
On Mar 3, 2017, at 11:51 AM, Bruno Marchal <marc...@ulb.ac.be> wrote:
The tensions between the computational natures of discrete and the
“continuous” numbers haunts any attempt to make mathematical
sense out of scientific hypotheses. I am uncertain as to the logical
implication of the “computationalist’s hypothesis" in this
context.
If you are aware of the notion of first person indeterminacy, it is
not so difficult to understand how the appearance of the continuum
can be explained to be unavoidable in the digital-mechanist frame.
The physical reality will emerge from a statistics on infinities of
computations (including many with Oracles). Amazingly, in the
digitalist frame, it is the digital which remains hard to understand
a priori, but the mathematics of self-reference gives important clue.
In my view, this is philosophy not related to the logic of the
physics of the atomic numbers.
Each atomic number has an identity.
That identity infers both mass and electricity and the corresponding
set of predicates that respect the attributes of the individual form
of matter.
The computational logic of the chemical sciences is based on the
coherence of the relations that couple these physical attributes
into the metrology of chemical sciences.
The success of chemical computations on the atomic numbers is based
on compositions of atomic numbers (generating functions) and the
metrology of the emergence molecules, cells, organisms, human
individuals.
Bruno: How do you relate your methods of calculations to your
identity? Can you construct a clear narrative that states the
necessary premisses? propositions? consequences? Causal pathways?
The premise is a weak form of Cartesian Mechanism. It is the
assumption that I could accept a brain or body digital transplant.
Precisely, it is the assumption that my consciousness is invariant for
a functional digital susbtitution made at some level. That hypothesis
is much weaker that the neurophilosophers hypothesis, because I put no
bound on the substitution level: it can be the enire observable
universe at the level of quarks and gluons. That hypothesis is used in
evolution theory, and many think that Nature has already bet on
computationalism in developing the genetic code. But I am not claiming
that hypothesis to be true, only that it entails logically that the
physical reality is an appearance in the relative state of the numbers
engaged in (Turing) universal relations.
In fact, I do not assume that there is a primary physical universe,
and I show that if we take the digital mechanist assumption, we
*can't* assume it.
Is the reference grounded in Curry’s combinatorial logic or
otherwise?
It does not. The reasoning is independent of any basic universal
theory chosen.
Both chemistry and biology are based on the chemical table of
elements and the combinatorial compositions.
I thought so too but I changed my mind when I discovered Gödel's
proof of its incompleteness theorem, where I realized that there is an
abstract (or more concrete according to the philosophical position we
can have) biology independent of its physical implementation. That is
what decides me to study mathematics instead of biology and chemistry.
I explain this with some details in my old paper "Amoeba, Planaria and
Dreaming Machines" (in Bourgine Paul, Varela F.J. (eds), Artificial
Life, Toward the Practice of Autonomous Systems, ECAI 91, MIT press,
pp. 429-440),
or in my more recent papers:
The computationalist reformulation of the mind-body problem. Prog
Biophys Mol Biol; 2013 Sep;113(1):127-40
The Universal Numbers. From Biology to Physics, Progress in Biophysics
and Molecular Biology, 2015, Vol. 119, Issue 3, 368-381.
Provably so if we assume mechanism. Contrarily to a widely spread
opinion: mechanism is not compatible with even quite weak form of
materialism, or physicalism.
The connotations of the term “mechanism” varies widely from
discipline to discipline.
The sense of “mechanism” in chemistry infers an electrical path
among the discrete paths of illations that “glue” the parts into
a whole. By sublation, this same sense is used in molecular biology
and the biomedical sciences.
Bruno, could you expand on your usage in this context?
I always meant "mechanism" in the sense of the mathematical logicians
who discovered the universal machine. It has been shown as being a
purely arithmetical notion. You can define such machine in terms of 0
and its successors, together with addition and multiplication.
Elementary arithmetic is "Turing universal", so whatever you can do
with a computer is "already" realized in any model of a simple
axiomatization of arithmetic.
I can explain more, but of course, this is not obvious nor well known,
apart by logicians and theoretical computer scientist.
Mechanism, as I use it, is the hypothesis that a level of digital
substitution exist…
The events and processes of the chemical sciences are based on the
atomic numbers.
The “digits” of the atomic numbers are NOT substitutable for one
another.
This means that you assume atoms. I do not. If they exists as
appearances, we have to justify them from a statistic on computations
realized in arithmetic. up to now, only the quantum propositional
formalism has been derived.
How do the senses of “computationism" and “mechanism” refer to
the material world, if at all?
The notion of computation is born in pure mathematics,
Historically, it was just the opposite - computations gave rise to
(im)pure mathematics?
Babbage guessed it before the logicians, that is right. But then,
independently of Babbage, the logicians isolated the concept when
working on the paradox of set theory.
The "universal dovetailer argument" ---that you can found here for
example:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
explains how the appearance of the material world has to emerge from
all relative computations.
This explanation is not extensible to chemistry and biology because
of the perplexity of Coulomb’s Law.
You might elaborate on this.
God created the natural numbers, and saw that it was good.
Would it be more accurate to that “"God" created the internal
creativity of the atomic numbers."
I was just saying, albeit poetically indeed, that the "theory of
everything", (still in the frame of the digital mechanist
hypothesis), can't assume more than classical logic + the following
axioms:
0 ≠ (x + 1)
((x + 1) = (y + 1)) -> x = y
x = 0 v Ey(x = y + 1)
Together with (just below):
Then she said: add yourself, and saw that is was good.
x + 0 = x
x + (y + 1) = (x + y) + 1
And:
Then she said: multiply yourself.
x * 0 = 0
x * (y + 1) = (x * y) + x
And nothing else.
These sorts of “computations” are not possible with atomic
numbers because the atomic have a tri-partite semantic meaning.
“zero” is not defined. “1” is hydrogen. Physical
conservation laws negate the possibility of multiplication of 6*8 =
48 (Carbon related to oxygen as carbon monoxide.)
You seem to assume some physical reality. I do not. I prefer to be
theologically neutral and not commit an ontological commitment.
Physical conservation laws is explained by the disappearance of
irreversibility in the basic quantum formalism (not the one inferred
from observation, but the one implied by the mathematics of number
self-reference).
With Digital Mechanism, even if a primary physical universe exists,
you need to confer to it some magical, or infinite, power to be able
to select a "physical computation" from all computations realized in
elementary arithmetic.
I think these counter-arguments are sufficient to justify my
assertion that the logic of the atomic numbers differs from your
views of numerical logic and your interpretation of
computationalism from chemical and biological computations,
including brain dynamics.
The pragmatism of the chemical sciences is the basis of its success
in biology, evolution, and indeed, consciousness. This pragmatic
perspective respects the physical law of conservation of electrical
particles.
So, our world views are radically different from one another.
No problem. Just say "no" to the surgeon who would propose to you an
artificial digital brain.
My point is logical: contrary to a widespread belief, mechanism and
(weak) materialism are logically incompatible.
If you are right, then the brain is an actual infinite, substantial
and analog object, and we can't be emulated by any computer, physical
or not. My point is that digital mechanism is testable, and quantum
mechanics (without collapse) confirms (≠ proves, of course) it
spectacularly: the evidence is that the physical do emerge from the
interference of many computations.
(By weak materialism I mean the assumption that there is some primary
physical reality).
Best,
Bruno
http://iridia.ulb.ac.be/~marchal/
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