On 22 Dec 2013, at 19:20, Edgar Owen wrote:
Bruno,
Thanks for your comments. However I think you are coming at Reality
from the POV of human logico-mathematical theory whose results you
are trying to impose on reality.
See previous answer to this. Church thesis makes computations as solid
as numbers, and those does not depend on humans at all, or show me the
dependence (and define "humans").
My approach is to closely examine reality
Physical reality, mathematical reality, arithmetical reality? They all
kicks back.
and then try to figure out how it works and what ITS innate rules
and structures are.
I would probably agree with much of what you say, if you were saying
it about human logico-mathematical structures, but the logico-
mathematical structure of reality is not bound by human rules.
That's my point.
It runs according to its own logic and science is the process of
trying to figure out what those rules are and how they work...
For this we have to agree on some "independent truth". Mine are simple
and precise; basically logic + the axiom of elementary arithmetic.
For example, reality is clearly a computational process,
That is refuted by the UDA.
and it runs against pure information which is the fundamental stuff
of the universe. There is simply no other way current information
states of reality could result from previous ones other than by a
computational process.
Some solution of differential equation can be non computable. then
with comp, some physical facts emerge in a non computable manner.
How that computational process works must be determined by examining
reality itself.
How could we examine reality itself. We measure numbers and
correlation between some of those numbers, the rest is in big parts in
our (real) imagination.
We may try to make sense of it in terms of traditional human math
theory, but when there are differences then reality always trumps
human math theory, which applies to human math rather than reality's
logico-mathematical system.
You seem to be anti-realist in math. This means comp should not even
have any sense. I am not sure what you mean by "computational". I use
it in its standard sense of Turing computable. I delete "Turing" using
Church Turing thesis.
Bruno
Edgar
On Dec 22, 2013, at 6:44 AM, Bruno Marchal wrote:
On 21 Dec 2013, at 00:52, Edgar Owen wrote:
All,
The fundamental nature of reality is examined in detail in my
recent book on Reality available on Amazon under my name.
Marchal is on the right track, but reality consists not just of
numbers (math)
Arithmetic is not just numbers, but numbers + some laws (addition
and multiplication).
but is a running logical structure analogous to software
When you have the laws (addition and multiplication), it can be
shown that a tiny part of arithmetic implement all possible
computations (accepting Church thesis). Without Church thesis, you
can still prove that that tiny part of arithmetic emulates
(simulate exactly) all Turing (or all known) computations.
that continually computes the current state of the universe.
You mean the physical universe. Have you read my papers or posts?
if we are machine, there is no physical reality that we can assume.
the whole of physics must be derived from arithmetic.
Just as software includes but doesn't consist only of numbers and
math, so does reality.
It depends on your initial assumption.
In fact the equations of physical science make sense only when
embedded in a logical structure just as is the case in
computational reality.
The computational reality is a tiny part of arithmetic. Logic is
just a tool to explore such realities.
Modern science has a major lacuna, the notion that all of reality
is mathematical,
Most scientists do not believe this, and indeed criticize my work
for seeming to go in that direction.
Then term like "reality" and "mathematical" are very fuzzy.
Now, if we are machine, then it can be shown that for the ontology
we need arithmetic, or any equivalent Turing universal system, and
we *cannot* assume anything more (that is the key non obvious
point). Then, it is shown that the physical reality is:
1) an internal aspect of arithmetic
2) despite this, it is vastly bigger than arithmetic and even that
any conceivable mathematics. That is why I insist that the reality
we can access to is not mathematical, but "theological". It
contains many things provably escaping all possible sharable
mathematics.
That arithmetic is (much) bigger viewed from inside than viewed
from outside is astonishing, and is a sort of Skolem paradox (not a
contradiction, just a weirdness).
that prevents science from grasping the complete nature of
reality. In truth all of reality is logical, as is software, and
the mathematics is just a subset of the logic.
I disagree, with all my respect. Even arithmetic escapes logic. It
is logic which is just a branch of math, but math, even just
arithmetic, escapes logic. Arithmetical truth escapes all effective
theories (theories with checkable proofs).
After all, modern science with its misguided insistence that all
of reality is mathematical,
I really do not believe this. Except for Tegmark and Schmidhuber, I
doubt any scientist believes this. But its is a consequence of
computationalism, for the ontology. Yet, the physical is purely
epistemological, and go beyond mathematics. I show that all
universal machine, when believeing in enough induction axioms, can
discovered this by introspection only.
has had nothing useful to say about the nature of either
consciousness or the present moment, the two most fundamental
aspects of experience.
I suggest you read my sane paper.:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
It explains the present moment by using Gödel form of indexical
(with explicit fixed points), including the non communicable part,
the qualia, and also the quanta (making computationalism testable).
In fact machines have already an incredibly rich and complex
theology, and it is testable, as it should contain physics.
However I present a computational based information approach to
these in my book among many other things.
The second clarification that needs to be made to the post on
Marchal's work is that human math and logic are distinct from the
actual math and logic that computes reality.
With computationalism, reality is not computed. Most of the
arithmetical reality is already highly not computable.
The (partially) computable part of arithmetic is the sigma_1 part
(the sentences having the shape ExP(x) with P decidable). Abobe it
is no more computable.
The whole of the arithmetical reality is the union of all the
sigma_i and pi_i parts, and is far beynd what we can compute or
emulate with a computer.
The the human arithmetic and arithmetic are well distinguished in
my presentations, so I am not sure to what you allude too.
For computation, Church thesis makes it a *very* general human
independent notion.
The human version is a generalized and extended approximation of
the actual that differs from the actual logico-mathematical
structure of reality in important ways (e.g. infinities and
infinitesimals which don't actually exist in external reality).
You seem to assume a primitive physical universe. ("primitive"
means that it would have to be assumed).
I can explain further if anyone is interested, or you can read
about it in my book...
I might take a look, but, with all my respect, I am not sure you
grasp modern logic, as you seem to confuse computation, logic, and
math, and to confuse digital physics (there is a physical reality
and it is computable) with computationalism (3-I is a machine),
which entails that physics emerges from computations in a non
computable way. Do you take into account the First person
indeterminacy? This is not well known, but is really the basic
block needed to see why the physical reality emerges non computably
from very elementary computable arithmetic. Let me insist on that
fundamental point: If my body can be emulated by a machine, then
neither mind nor matter appearance can be entirely emulable by a
machine.
Above our comp substitution level, we are confronted with
enumerable sets of universal numbers, and below the substitution
level, we are confronted with a continuum of different computations
involving all universal numbers simultaneously. In fact the problem
of comp relies in the justification of the apparent computability
of the known physical laws (the white rabbit problem).
Bruno
http://iridia.ulb.ac.be/~marchal/
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