Dear Bruno,

>> The things I am unclear about are:
>> 1) maximally complete computational histories going through a state ->
>> what are these?
> We assume comp ok? So for example, my current relative mind state can  
> be associated with a computational state. By Church thesis, this state  
> is accessed an infinity of times by the Universal Dovetailer through an  
> infinity of infinite computations. OK? A complete computational history  
> is just such an infinite computation. Sometimes I use the word  
> "history" to refer to the internal view of some machine whose current  
> state has been accessed by the UD. In that case some similarity  
> equivalence class is in play. To get the math of those similarity  
> classes I proceed in interviewing such machines.

Ah OK, I understand. The equivalence class found in the interview - do 
you have results already?

>> 2) Why do they correspond to _consistent_ extensions, and how do you
>> define these consistent extensions (in a normal logical way -> no
>> contradiction; or differently?)-
> Just "no contradiction". Now a computation is not per se a theory, so  
> the notion of contradiction is not directly applicable. That is why I  
> identify a computation with a proof of a Sigma_1 sentence of  
> (elementary, Robinsonian) arithmetic. Of course this leads to the white  
> rabbit issue, a lot of statement are relatively consistent and false at  
> the same time, like the "self-inconsistency statement" (by Godel's  
> second theorem the proposition "I am inconsistent" is consistent (when  
> asserted by a Robinsonian machine or a Lobian machine).
> I recall that a Robinsonian machine is a machine having Turing  
> Universal abilities, but without the introspective power to acknowledge  
> that. On the contrary Lobian machine are universal and know that they  
> are universal.

Ok, this is also clearer now. What my problem is that these restrictions 
  seem somewhat arbitrary to me (only sigma_1 sentences etc)

It seems very much like picking out some well-behaved classes of 
mathematical "objects" so that one get's nice resultes, compatible with 
observable universe.

But why should the Plenitude restrict itself to such theories? Or is 
your view just that the others do not give rise to observers?

> Thanks for the references out of line. I will read those papers once I  
> have the time. At first sight it looks like the cosmologists begin to  
> be aware of a (third person) white rabbit problem. It will still take  
> time before they realize the first person white rabbit problem. The  
> reason is that they have no formation on the "mind-body" problem I  
> think.

The 3rd person white rabbit would be the many universes; but I think 
they are also aware of first person white rabbit, as they discuss the 
Boltzmann brain quite literally as a "brain" in some papers - which just
oozes away after some time or immediately after "cogito ergo sum".

The central problem in all approaches seems (as the many discussions on 
this topic on the everything list also show) the _measure_ on the 
universes/OMs whatever.

Maybe on should adopt some a priori "rational" principles to constrict 
possible universes (in line of symmetry, invariance, closure etc)

(Of course, closure is one of these principles in your adopting Church 
Thesis as a vantage point for selecting from all math. objects; which 
contradicts my objection above ;-))


Günther Greindl
Department of Philosophy of Science
University of Vienna


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