> > > > > 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? -- You received this message because you are subscribed to the Google Groups "Everything List" group. To view this discussion on the web visit https://groups.google.com/d/msg/everything-list/-/XqN5TmRQ1n0J. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
