Le 25-mars-08, à 13:35, Günther Greindl a écrit :
> Dear Bruno,
> I have used the Easter holidays to read again through your SANE 2004
> paper, and I have a question regarding step 7.
> (I am fine with step 1-6, step 8 seems OK but I will withhold judgment
> until I understand step 7 ;-)
Nice. Step eight is the more difficult, but for some people---those who
have never start to believe in a *primary* physical universal--- it can
be considered as redundant.
> 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.
> 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
> 3) And how do you treat the Boltmann brain issue which crops up in
> modern cosmology but also in a UD generating _all_ computational
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
I hope this can help you a bit.
I take the liberty to put online the references you gave me because I
think it is of general interest:
http://arxiv.org/abs/hep-th/0611043 (Andrei Linde)
http://arxiv.org/abs/hep-th/0610079 (Don Page)
The New York Times had a piece about this stuff in January:
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