> > > How can we know that? "Reality is the totality of all that exists" is > > a finite complete description. > > Well, that is my favorite definition of reality. But it is not a > theory: you don't say what exist. > RA says what exist. It says that 1 exists (Ex(x = s(0)), it says that > you current computational states exists.

It's not meant to be a theory, it's a description and a definition. > > > Now I'm assuming, for the sake of argument, that "totality," "all", > > and "exists" have finite complete descriptions. And if these words > > don't, then no words do and we might as well be talking about > > asdjedwjef. > > Well, as you know, if we limit ourself to first order language, we can > talk in a metaphysics-free language. > With mechanism this works well for the ontology, but for the > epistemology we have to give meaning to the standard model, and > eventually to the full analytical truth, and beyond. To explain > mechanism, we need people having a notion of consciousness, enough for > doubting they can survive a digital substitution. > Beyond? Interesting. So to explain mechanism there is a contingency. > > > > What I'm after is what else we can say about a TOE. Given what a TOE > > is, it does answer all questions written in its language. > > Are you not confusing the theory, and the subject of the theory. I'm not confused on this, actually. I know the difference between remarks about a TOE and the TOE itself. All my research is dedicated to remarks about a TOE, which is I think caused a big misunderstanding between us in the past. > > We might need to introduce an intermediate notion. Let us call that > the realm. With mechanism the numbers, structured by addition and > multiplication is the Realm of Everything: ROE. But that is what I > called above the ontology. For a (naïve) physicalist the Realm is > given by particles structured by their force (fermions and bosons, the > quantum law). > > The epistemology will be given by higher order substructures of the > ontological structure. Physical brains for the physicalist, Löbian > numbers for the digital mechanist. For a mechanist, a physical brain > appearance for numbers has to be justified by the numbers' structure. Ok. I'm interested in both, but moreso the digital mechanist side. Unfortunately, I know nothing of digital mechanism. Your ROE is curious. > > > One way to describe something, a real basic way to describe something, > > is to form an aggregate of all things that meet that description. > > There may be no effective procedure for deciding whether or not A is > > in that aggregate, whatever. The point is that that is one way to > > describe something. > > Thus reality basically describes itself. > > Reality is an aggregate and as such is a TOE, a complete description > > of reality. > > But that is the trivial "TOE". You are saying "take the territory for > map". That is all I need to show that a TOE exists. It's a trivial, brutal proof. Not elegant, I know. > > What is the nature of a TOE, though? I know actually finding a TOE > > might be difficult to say the least but we can at least say some > > things about the nature of a TOE. > > It is what unifies what we know, believe, feel, observe, guess .. > into a coherent picture. I see. It makes sense, given all the data. > > Axiom schemata in ZF are infinitely many statements, aren't they? > > Oh! Take Von Neumann Bernays Gödel instead. It is more powerful than > ZF, and it admits finite presentation. ZF is OK. I really meant finite > or recursively enumerable theories, or theories having a finite > presentation. They are (abstract ) machine or programs. I'm just saying that a very popular set theory uses infinitely many statements, as I'm sure you know. Which is why I question your belief that we 'ought' to stick to only finitely checkable proofs. Who really wants to check a proof anyway? I know, it's a required task in order to decide if someone is talking out of their butt. The thing about ZF is that it does have a finite presentation which uses infinitely many axioms (technically). SO why can't a TOE have a similar finite/infinite presentation? > > > > >> With mechanism: what exist basically (the true relation between > >> numbers) is conceptually very simple, and is enough to understand > >> that > >> the "every appearances" is infinitely complex, but highly structured. > > > Well, that's what I've been trying to prove. I guess I can stop now > > =) > > Sorry :-/ No, it's good. I can rest a bit. > The facts is that if mechanism is true, I really don't see how we can > escape the conclusion that elementary arithmetic is enough, and the > internal epistemology of arithmetic "explains" all the dreams, why > their are stable, why some are sharable, etc. > Eventually, interpreting the ONE of Plotinus by Arithmetical truth > gives back a transparent interpretation of a neopythagorean > neoplatonist Theology. And my point is only that the physics of > machine is already enough precise to be confronted with the > observation, and the gift is big given that we have a way to explain > qualia and quanta at once. > BTW, a lot of works remains ... > I doubt you will find something as universal as a something like Post- > Church-Turing universal. > IMO, the real bomb of the 20th century is Church thesis and the > discovery of the universal 'numbers'. > The embedding relation you are searching is, I think, partial or total > turing emulation. The UD builds them all. The UD* is just a splashed > universal machine. The UD is an avatar of the universal machine. The > keyword is 'universal' and it make sense by Church's thesis (Post's > law, Turing's thesis). > Perhaps the object you search is some initial object in a category > with Turing-morphism, or something ... Well the definition of embedding on wiki that doesn't involve elementary seems adequate, though forcing someone to believe that's what embedding really means will be some work, if it's even possible. Unfortunately, I don't know what a Turing-morphism is except by what I can guess. I believe strongly that I can do what I claim without such machinery. > > > It is the overall, basic structure of what exists. The reduced > > product of all structures is a key to this. > > Well, with mechanism, what exists is not what is important. I chose > the numbers, but I could prefer the combinators, or the hereditarily > finite n-categories, etc. > What is important is the epistemology, that is mind and matter, person > and personal experiences, the stability of dreams, laws and > contingencies ..., the relation between universal numbers, etc. > Matter is part of epistemology (that is what the UDA, including the > Movie-Graph-Argument is all about). > What exists is not what is important? Perhaps. I want to give the nature of existence, yes, without having to specify what exists. > > > But U is not outside U. > > U is belonged by U. Still, U is not outside U. I am taking 'outside' to be "proper." > > Even a physicalist can suggest a 3-view from outside like the quantum > vaccum (which is really just a quantum universal dovetailer) or > Everett's Universal (Schroedinger) Waves, or a universal (Heisenberg) > matrix. > But this does not gives the inside view per se. You need a theory of > mind (1-person, qualia) and a way to unify it with the observation and > the 3-big-reality. Digital mechanism gives all this on a plate at > once. It justifies, by the self-reference logics and their intensional > variants how the consciousness/realities or qualia/quanta couplings > emerge from the number relations, from the points of view of those > universal (Löbian) numbers-relations. > >> Sounds really interesting. Too bad you can't be my phd advisor. 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