This time I'll repeat only a fraction of the 500 lines in your reply:

>From [EMAIL PROTECTED]:
> Suppose you "survive" only through a simulation of
> the big bang at the level of the quantum superstring, membrane, etc. 
> then the "correct level of substitution" is the level of the quantum
> superstring, membrane, etc. 
> 
> Remember the definition of COMP, it says that *there exists* such a
> level. It does not say that "this" or "that" *is* the correct level.

Ok.

> It is a sort of admission of ignorance. This ignorance is 
> fundamental. Indeed it  has been shown (independently by a 
> lot of people---ref in my papers) that comp entails we cannot
> know the correct levels. 
> We can bet on it, though, and we can make reasoning
> relatively to correct bets.
> 
> Normally a constructive philosopher should abandon comp right here,
> because it follows from that theorem that we cannot be machine in
> any constructive sense.

Which theorem? Send pointer to its proof. Not to its informal
description, but to its proof. 

(One reason why I doubt this: isn't the lowest possible level - embodied
by what's computable in the limit - sufficient? Why not run all universes
GTM-computable in the limit?  If one of them is ours, then the set-up
is constructive.)

> You miss the point. Even the one who as PI on his T-shirt is
> wrong if he believes PI helps him to predict the issue of the
> next self-duplication.
> Note that if the program remains as lenghty as the sequence, as it
> happens for most Schmidhubers---in the iterated self-duplication,
> these sequence are called uncomputable by Solovay, Chaitin, etc.

Not uncomputable. Any past is finite. So it is at worst random or
"Martin-Loef-random" or incompressible.  None of those you cite is
careless when it comes to the difference between countable and uncountable
sets. None claims one can compute a continuum by dovetailing. Dovetailing
will be forever limited to the countable realm.

> >Is there a probability distribution on this set
> >(if not, you cannot predict anything)? Which one?
> 
> You talk really as if probability was the only manner you
> know for quantifying uncertainty.
> 
> Beside probability there exist other ways to handle the 
> uncertain. The one I know
> the best is Dempster-Shafer theory. 
> (I have work some years with expert in that field).
>
> Not only I do not restrict myself to the uniform distribution, but 
> I don't share your assumption that the only way for quantifying 
> uncertainty is probability. Why not Dempster-Shafer theory of evidence ?

The various Dempster-Shafer (DS) approaches are no alternatives
to probability theory. They are extensions designed to facilitate
handling of uncertainty in contexts where lack of belief does not imply
disbelief. But DS is essentially about hulls confining sets of
traditional distributions, and thus compatible with the traditional
framework of Bayesian statistics. (Variants of DS that are not yield
paradoxical results.)
 
> In the first part of my thesis:
> I am not pretending that I have solved the mind-body problem, nor
> the problem of the origin of the physical laws, nor the QCU.
> But I have rigorously proved that with comp these problems are 
> equivalent.

It is this recurring type of claim I find so irritating: "rigorous 
proof" without formal framework. 

> A weakness is that I am lead toward hard mathematics.

What a strange remark. The weakness of your texts is that they are
so informal.

> >Which unique formalisation? Please write it down!
> >How can you possibly isolate it by informal reasoning? 
> 
> I was talking *there* about the modal logic G, G*, 
> S4Grz, Z1, Z1*, etc.
> These formal logics are intensional (modal) variation of the
> provability logics  of the sound  self-referentially correct 
> machine. I have provide semantics, and theorem provers.
> See explanation and technical details in my thesis and in my 
> papers.

Your thesis is in French. Your papers are informal. They always include
sentences such as: "Actually such proof and clarification is one of the
main result in my thesis ... without going into details I will briefly
try to convey the main line of the argument" (p 4 of paper dated sept
24, 2000).  Then follow informal examples, references to philosophers,
and unsubstantiated claims such as "the UD generates all real numbers",
when it only generates all their finite prefixes, which is a fundamental
difference.

Then there is your "invariance lemma: the way you quantify 1-indeterminacy
is independent of (3-)time, (3-)place, and (3-)real/virtual nature of the
reconstitution." This does not make sense, because if the (3-) probability
distribution on the possible futures and reconstitutions does depend on
time or place or other things (why not?) then 1-indeterminacy does so,
too. Under most distributions, some futures are less likely than others.
Hence there are nontrivial, distribution-dependent, probabilistic
1-predictions as well as "quantifications of 1-indeterminacy" that depend on
time/space/other things.

> You are also telling us that informal classical mathematics is vague 
> because they admit sets like the set of all functions from one 
> infinite set to another. I am not the one isolated here in making
> sense of these sets. You cannot pretend I am the one 
> pretending 1+1=3! It is a dishonest rhetorical trick.

no comment

> Those who have patiently follow the steps are in general quite 
> shocked by the conclusion (the reversal),
> but then, at least, they act honestly: either searching or
> hoping for a precise flaw,  or just abandoning comp. 

have not met anyone whom you shocked - cannot comment on this

> It looks like it does not occur to your mind that *perhaps* 
> I have a point and that you just don't have seen it yet.

I have been hoping you have a nontrivial point - the only reason 
why I kept encouraging you to explain yourself.

> Why not trying being a little more modest, mister "I-am-right". 
> Have you a prejudice against 
> the whole approach or what ?

I am prejudiced against claims of rigorous proof when even the 
assumptions are unclear; and against statements that are plain 
wrong, such as "the UD generates all real numbers".

> >Algorithmic TOEs are about computable probability distributions on
> >universe histories computable in the limit.  Such histories subsume
> >all computable evolutions of all computable observers, including the
> >conscious ones, if there are any.
> 
> You ask me to give a formal definition of delay when I use it
> in the every-day life folk sense, and you are willing to talk
> on consciousness without clarification ????

Please read again. If "consciousness" is indeed a well-defined concept,
and if there are any "conscious" computable observers, then they will be
computed. Otherwise they won't. In either case there is no need to define
consciousness - I have not seen a convincing definition anyway. Similarly,
there is no need to define "love", although it might be an important
concept to certain computable observers in certain computable universes.

>From [EMAIL PROTECTED]  Sun Feb 18 01:16:16 2001
>The exchange between Bruno and Juergens is, I believe, instructive and 
>constructive as it forces them to refine their positions.

Where did I have to refine mine?

JS

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