# Re: Bruno's mathematical reality

```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. My approach is to closely examine reality 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. 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 example, reality is clearly a computational process, 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. How that computational
process works must be determined by examining reality itself. 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.

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 GĂ¶del 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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