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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