On Dec 31, 1:42 am, Bruno Marchal <[email protected]> wrote: > On 29 Dec 2010, at 13:50, Brian Tenneson wrote: > > >>> If a complete description of arithmetical truth is not possible, > >>> what > >>> exactly are we talking about? > > >> We, humans, have a rather good intuition of what is a true > >> arithmetical sentence, independently of the fact that we have to > >> recognize that it can be quite tricky to decide if this or that > >> arithmetical proposition is true or not. > > > But if arithmetical truth can not be described then what are we > > talking about? > > About God, or Everything, or the ONE, or the one-who-has-no- > description, etc. The big thing, that is, or the big nothing ...
Spot on. That's what I've been secretly themeing my paper to be about underneath the surface. > > > What our intuition tells us? I'm still unclear as to > > why a complete description of reality is not possible because we > > apparently can know what we're talking about when we talk about > > arithmetical truth, despite arithmetical truth not being recursively > > enumerable. > > The proof that we cannot *know* what is arithmetical truth is related > to the fact that we cannot know if mechanism is true. So we can > already not know if some arithmetical relations make people or zombie. > We can only know that IF mechanism is true THEN we cannot know which > number(s)/machine(s) we are, etc. > We can have a description of reality, but not a complete theory > answering all the questions that we can formulate in the theory. So if a TOE is not recursively enumerable, it still might be captured in some finite set of statements like how arithmetic can be captured in the Peano axioms. That arithmetical truth is not recursively enumerable can somehow be derived from these first principles, right? Perhaps the same is true of a TOE. That's what I'm wondering. > > Accepting some hypothesis, we can make statement on 'reality'. > With the hypothesis "digital mechanism", we can state that reality is > not recursively enumerable, neither pi_i or sigma_i for any positive > integer i, etc. In particular we can know, relatively to that > hypothesis, that reality does not admit any finite complete description. How can we know that? "Reality is the totality of all that exists" is a finite complete description. 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. > > It means that the "theory of everything" cannot answer all question > written in its language. It means that many surprises will ever attend > us, and that some mystery will remain forever. But we can account > epistemologically for those surprises and mysteries. 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. 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. > OK. But that is not an effective theory, nor a theory at all with the > definition given. You talk about the model, which is what we talk > about: the intended model of a theory of everything (including matter, > consciousness, taxes and death, ...). > 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. > > I thought we agree that a theory has to be finite? Axiom schemata in ZF are infinitely many statements, aren't they? > > 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 =) It is the overall, basic structure of what exists. The reduced product of all structures is a key to this. > > I am really not seeing how one can have an outside view of the > > ultimate reality based on what you've said. Can you explain it in > > more simple terms? If there were an outside to ultimate, then it > > wasn't ultimate to start with. > > You are the one invoking NF so that the universe U of sets is a set! > You should be less annoyed than anyone else with the idea of an > ultimate reality being an object by itself. > Such U belongs to U. > So that U can serve itself as an outside view of itself! > But I don't need NF, because with mechanism just a diophantine degree > 4 polynomial can do the trick, or any other universal ... > But U is not outside U. > read more » Sorry, it seems to have eaten your post here...hmm. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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.
