On 21 Dec 2013, at 00:52, Edgar Owen wrote:


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.:

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).



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