Gear Günther,
Le 31-mars-08, à 19:01, Günther Greindl a écrit :
>
> 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?
Yes. The comp "intelligible matter" hypostases give the modal logic
corresponding to quantum logic, except that I loose the necessitation
rule.
The significance of this remains to be seen of course.
>
>>> 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)
OK. This is part of what I intended to explain to David, Barry, Mirek
and some others.
In a nutshell, the restriction to the sigma_1 sentences *is* the
translation of the comp hyp in the language of a Lobian machine.
Why?
Because you can characterize a Turing Universal Prover Machine by the
fact that she can prove all true Sigma_1 sentences. So Turing
Universality can be defined by the modal formula p -> []p, for p
sigma_1. A lobian machine is not only universal, but "knows" that she
is universal, i.e. she can prove all the formula p -> []p for p
Sigma_1. Adding the axiom p -> []p to the logic G, gives the
self-reference logic of the computationalist lobian machine. The
Universal Dovetailer is equivalent to the set of true sigma_1 sentences
together with their many proofs.
This is explained at the end of most of my papers, but needs some
amount of knowledge of recursion theory.
>
> 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.
Not at all. Everything comes from the mathematical description of what
is a Universal dovetailer (and motivated by UDA which is itself based
on the first person indeterminacy, and its invariance for some
transformation).
>
> But why should the Plenitude restrict itself to such theories?
Necessity follows from the informal UDA, and then the precise math is
given by the formal (arithmetical) UDA. Remember that we postulate comp
at the start. (After, the results go trough with very strong weakening
of the comp hyp).
> Or is
> your view just that the others do not give rise to observers?
The others give rise to observer, but use principle which I think
should be justified.
>
>> 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;
Hmmm... I would say that 3rd person white rabbit appear when there are
too much universes with aberrant histories. Too much universes with too
much talking white rabbits having clocks in their hands and saying "too
late, too late ..."?
> 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".
I don't understand. (In general the first person is forgotten or
assimilated to third person constructs like brain through some identity
thesis, this cannot work by the Movie Graph argument or by Maudlin's
Olympia: we have discuss this).
>
> 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.
Yes.
>
> 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 ;-))
Yes :)
Best,
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Wed Apr 02 2008 - 06:38:37 PDT