On 06 Mar 2009, at 18:06, Günther Greindl wrote:

> The idea was that the numbers encode moments which don't have  
> successors
> (the guy who transports), that's why there exist alien-OMs encoded in
> numbers which destroy all the machines (if we assume that arithmetic  
> is
> consistent).

Hmmm.... (Not to clear for me, I guess I miss something. I can build  
to much scenario from you say here).

Of course we are in complex matter. It is good to recall that UDA is  
essentially a question. It is an rgument of the kind; "did you see  
that taking comp seriously the mind-body problem is two times more  
complex that in the usual Aristotelian version of it. We have not only  
to find a theory of mind/consciousness/psyche:soul/first-person; but  
we have to extract the physical laws (laws of the observable), if  
there exists any, from that theory of mind.

But now it happens that the theory of mind already exists, if we  
continue to take the comp hyp seriously. Indeed, it is computer  
science, alias intensional and extensional number theory (or  
combinators ...). here there are the "bombs" (creative bomb) of Post  
Turing ... discover of the mathemaical concept of "universal machine",  
and of Gödel' Bernay Hilbert Löb's discovery of the formal probability  
predicate, expressible in arithmetic, and some of its key and stable  
properties, leter capture completely (at some level) by Solovay.  
Roughly speaking Universal Machine + induction axioms gives Löbian  
Machine, and this is the treshold she remains Lobian in all its  
correct extension. It is the ultimate modest machine.

The discovery if the universal machine is a discovery is one of the  
very rare "absolute" notion. It makes "computable" an absolute notion.
Now, is the universal machine really universal? That is the content,  
in the digital realm, of Church Thesis.
Gödel discovery is that there is no corresponding notion of  
provability. If you are interested in just arithmetical truth, truth  
concerning relations between natural numbers, you cannot have a theory  
or a machine enumerating all the true propositions. You will have with  
chance a succession of theories: like Robinson Arithmetic, Peano  
Arithmetic, Zermelo-Fraenkel set theory, ZF+there is an inaccessible  
cardinal, whatever ... Each of them will prove vaster and vaster  
portion of arithmetical truth, but none will get the complete picture;  
like us, obviously today at least.

>> If a successor state requires something impossible, *that* successor
>> state will be impossible, but it does not mean there will not be  
>> other
>> successor states, indeed, for mind corresponding on machine's  
>> state, a
>> continuum of successor states exists.
> This is the issue at stake: from what do you gather that all machine
> states have a continuum of successor states (the aleph_0/aleph_1 is  
> not
> at issue now; it suffices to say: at least one successor state)?
> After all, there are halting computations.

By step seven.
A machine halt only relatively to a universal machine which executes  
it. The whole problem for *us* is that we cannot not know which  
univerrsal machine we are, nor really which universal machine supports  
us. The UD generates your state S again, and again, and again an  
infinity of time (UD-step time) in many similar and less similar  
computational histories. The first person expectations have to be  
defined (by UDA(1-6) on *all* computational histories. If only due to  
those stupid histories dovetailing on the reals while generating your  
state S, makes the cardinal of the set of all (infinite) computational  
histories going through that state S a continuum.

That the "UDA" informal view.

In AUDA, the first person view is given by the conjunction of  
provability with truth. We lose kripke accessibility, but we get a  
richer topology, close to histories with continuous angles in between;  
but it is heavily technical. Each hypostases has its own mathematics.

Surely more later,



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