>
>
>
>
> Why not take the categories of all categories (besides that Lawyere tried 
> that without to much success, except rediscovering Grothendieck topoi).
>

I'm more interested in the smallest mathematical object in which all 
mathematical structures are embedded but the category of all categories 
will do.
 

>
> But if you assume comp, elementary arithmetic is enough, and it is better 
> to keep the infinities and categories into the universal machine's mind 
> tools. 
>
> Enough for what, in what sense? 

>
>
> To have a single mathematical object that all mathematical structures can 
> be *embedded* would give us an object that, in a sense, contains all 
> structures.  If one follows Tegmark's idea that ME=PE, then a definition 
> for universe just might be a mathematical object (which by ME=PE is a 
> physical object) that contains, in a sense, all mathematical objects (i.e., 
> all physical objects). 
>
>
> I think that this is deeply flawed. We cannot identify the physical and 
> the mathematical. We might try theory on the physical, or on the mental, or 
> on the mathematical, which might suggest relation between those thing, but 
> I doubt any non trivial theory would identify them, unless enlarging the 
> sense of the words like mental, physical.
>
>
Isn't it simpler to assume there is only one type of existence?  What are 
the actual flaws of a mathematical universe?  A physical system can be 
mathematically encoded by its corresponding set of world lines.  This 
encoding is an isomorphism.  A very simple example of what I mean is the 
nearly parabolic path taken by a projectile.  The set of world lines would 
be some subset of R^4 or R^n if it turns out that n != 4.  I am aware that 
indeterminacy due to Heisenberg's uncertainty principle kicks in here so we 
may never "know" which subset of R^n a physical system is isomorphic to but 
by a pigeonhole principle, the physical system must be isomorphic to some 
subset of R^n, several in fact.


 

> With computationalism, the coupling consciousness/physical is a 
> phenomenon, person perceptible through numbers relations when they (the 
> persons) bet on their relative self-consistency. This explains the 
> appearance of the physical, without going out of the arithmetical. It works 
> thanks to Church thesis and the closure of the comp everything (UD*, 
> sigma_1 completeness).
>
>
> How are you defining consciousness here? 

>
> It's not super clear to me that the cocompletion of the category of all 
> structures C exists though since C is not a small category and thus 
> Yoneda's lemma doesn't apply.  I would have to fine-tune the argument to 
> work in the case of the category C I have in mind.
>
>
> The n-categories might be interesting, but we don't need so rich ontology. 
> If we are machine, the cardinality of the basic TOE is absolutely 
> undecidable from inside. Omega is enough.
>
> Do you have an argument that proves that our minds can't transcend 
"inside"? 

>
>
> If the cocompletion of C is the One, that which all mathematical 
> structures can be embedded, then the parallel universe question would be a 
> matter of logic and category theory; it would depend on how you defined 
> "the visible universe" and "parallel" universe.
>
>
> You will have to define an observer, its points of view, and to take into 
> account its many distributions in that super-mathematical structure, but 
> you can't do that, as you will need an even bigger structure to define and 
> study the indeterminacy. So you will have to limit your notion of observer 
> and use some "comp" hypothesis (an infinite variant if you want).
>
> With comp, it is easier: you cannot really take more than arithmetic. God 
> created the Natural Numbers, all the rest belong to the (singular and 
> collective) number's imagination. If nature refutes this, it will still 
> remain time to add the infinities needed. I think.
>
>
> How is the arithmetical structure going to give rise to a description of 
reality that takes into account observer, its points of view, and its many 
distributions without the need to study the indeterminacy? 

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