Re: Smullyan Shmullyan, give me a real example

From: Bruno Marchal <marchal.domain.name.hidden>
Date: Wed, 10 May 2006 16:52:21 +0200

Le 10-mai-06, à 04:19, Russell Standish a écrit :

> James Higgo published a web page describing the history of quantum
> suicide aka comp suicide. The notion obvious predates both Tegmark and
> Marchal - and there is some anecdotal evidence that Edward Teller knew
> about the argument in the early eighties. It appears to have been a
> "dirty little secret", which has only really been considered
> acceptable talk in polite scientific circles in the last 10 years or
> so.



I explain quantum suicide, and I use it to explain the "comp
immortality" in:
Marchal B., Informatique théorique et philosophie de l’esprit. Actes du
3ème colloque international de l’ARC, Toulouse 1988.

I have presented orally the paper at Toulouse in 1987. The paper
contains the movie graph argument, and a much earlier version of that
paper contains the RE paradox, one of many version of the UDA. That
earlier paper has been published in two parts later under the forms:

        Marchal B., Mechanism and Personal Identity, proceedings of WOCFAI 91,
M. De Glas & D. Gabbay (Eds), Angkor, Paris, 1991.
Marchal B., 1992, Amoeba, Planaria, and Dreaming Machines, in Bourgine
& Varela (Eds), Artificial Life, towards a practice of autonomous
systems, ECAL 91, MIT press.


Look, you can see my work as the given of a purely arithmetical (more
generally lobian) "reconstruction" of Lucas-Penrose type of argument
against mechanism. Only, such argument does not show that we are not
machine but only that *in case* we are machine *then* we cannot know
which machine we are, nor can we know which computational paths support
us, and there is already an indeterminacy there. Then I illustrate that
we (I mean the (hopefully) lobian machines) can reflect that
indeterminacy. You can see it as a generalization of Everett's
embedding of the physicists in the physical world; where instead I
embed the mathematician (actually some arithmetican) in the
mathematical (arithmetical) world. In both case this makes sense only
when we distinguished first person and third person discourse.


But now, my preceding point was just that the existence of the
discourse about "quantum suicide" or "quantum immortality", which
appears from empirical reasons, confirms the general statement that
comp implies that any machine looking at herself below its substitution
level should discover empirically the indetermination about which
computations which support her, from which the comp immortality
follows.

Obviously (?) I am suspecting a big part of the physical emerges
"already" from the impossible statistics on number relations once you
mix addition and multiplication. The advantage of the
"self-referential" approach (just made easier by comp, but it works on
many type of non-machine or generalized infinite machines) is that it
provides at its roots a difference between the truth and the true
discourses on those questions (got through G* \ G and its intensional
variants), the arithmetical "Hypostases" as I am tempted to call them
since I read Plotinus.

You can see what I am mainly trying to say as: "oh look we can
*already* interview a universal machine about fundamental questions". I
illustrate this by interviewing a lobian machine on the logics of the
communicable, knowable and "bettable" (by Universal Machines)
pertaining on verifiable propositions (here verifiable = accessible by
the Universal Dovetailer.
The goal: extract the whole measure on the relative continuations. Not
just the logic of certainty.
The problem at this stage is mathematical and concerns the existence of
not of some Hopf algebra of trees capable of explaining how to
renormalize in front of the "arithmetical" white rabbits.

Bruno


http://iridia.ulb.ac.be/~marchal/


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Received on Wed May 10 2006 - 10:53:29 PDT

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