> 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 

> 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? 

You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To view this discussion on the web visit 
To post to this group, send email to everything-list@googlegroups.com.
To unsubscribe from this group, send email to 
For more options, visit this group at 

Reply via email to