Re: The vanishing of the Necessitation rule -> The vanishing of "all universes"?

From: Bruno Marchal <>
Date: Fri, 13 Sep 2002 17:25:44 +0200

At 10:44 -0400 11/09/2002, Stephen Paul King wrote:

>Dear Bruno,
> I have been reading your paper "Computation, Consciousness and the
>Quantum" and am puzzled by the statement:
>"...I mention we loose, with the Z logics, the necessitation rule. Because
>of that we loose the facilities of Kripke world-semantics, and in fact, at
>this stage it can be argued that we loose $all$ the universes."
> Why this puzzles me is that it seems obvious that if we "loose $all$ the
>universes" we also loose the one that we experience. How is it possible to
>have even 1-indeterminancy without the existence of at least one universe,
>even if it is a "solipsist's one"?

Hi Stephen,

(You could have choose a passage with less orthographical errors :(
by "loose" I was meaning "lose", of course ....)

Coming back to your question.
It all depends what we really mean by "universe".
Technically the loss of necessitation rule just forbid the use of the
possible world semantics. We loose the Kripke worlds, but we still
have notions of neighborhoods, deformed Kripke frames, etc.
It just means that the traditional Kripke tools are no more available.
But I am not sure those remarks will help because you are probably
using the word "universe" in the more ontological sense I was alluding

When I say it could be that there is no universe, I mean that it could
be that there is no stuffy, or substancial or primitive universe.
I will not try to be rigorous here, just convey the idea.

Comp is the principle that you, me, people, persons, is (are)
sort of "relative numbers". For example in a high techno-comp society
people understands this equivalence in a concrete way because they can
change their bodies like they can change their car, etc.
They remain "invariant" for
any change of stuff which conserve some amount of (classical,
duplicable)information. Your number is *relative* to the choice
of your local implementation relatively to the story you are betting
the consistency.
Now a series of thought experiments
shows that once you accept such a possibility, then your relative
immateriality will automatically extend to all your possible environment.

With comp you cannot know if you are implemented in a "real stuffy"
computer, or if you are implemented in a purely immaterial one
"living" in Arithmetic. Actually comp force you to bet that your
experience now
is an average off all the coherent stories compatible with what you take
as your memories. What is needed is a weak-logical sort of connectness.

>How is it possible for me to even justify
>my belief that I am actually sitting in front of my keyboard and computer
>monitor and writting these words if "we loose $all$ the universes"?

We lose only the stuffy universes. We don't (necessary) lose the
coherent stories. We don't even lose the result of the observation
made by others (where observation = interaction) because there are evidences
that those stories are entangled in one way or in another ways.
(The hard thing is to derive the precise "entangling rules" from comp ...).

All computations exist in Platonia if you want, so all dreams exists in
Platonia, (dreams, with comp, are just sheaf of computations seen
from inside), so that you can only bet on some degree of consistency
of the dream
you feel from inside (1-person experience).

Computer science makes notion of consistency and
coherence mathematically manageable, although counterintuitive) and
first results confirm that comp is still plausible (at least).

Now you can (re)define "universe" as the average product of your
consistent computations making up your memories. Just remember it is
not made of smaller parts, it is just a (hopefully but most probably at
least partially sharable) dream which results ultimately from the many
many coherent relations between numbers. A stuffy universe does neither
explain what is the stuff it is made from, nor where does that stuff
comes from, nor how that stuff could be related to the experience we live
and, most probably, share.

> It could be that I do not understand how you reconstruct an appearence
>of a 1-person expereince with only arithmetical realism and the church

I do to things:
1) I listen to what you can say once you accept comp, if only for the
sake of the argument. (Through the universal dovetailler argument (UDA) for
2) I listen to what the consistent machine can prove about herself
and about its probable (consistent and coherent) histories (Arithmetical
form of the UDA, make possible thanks to Godel, Lob, Solovay, and many

>Your thesis (and that of Schmidhuber and others) explicitly excludes
>any reality to the "hardware" required to "implement" the "objects"
>represented by UTM's or equivalents and merely assumes the existence of a
>"Platonia" that exists a priori.
> This is mere hypostatiation and since we can prove, via your our
>reasoning, the non-existence of the Necessitation rule for Z logics, what
>difference does it make if we can merely point at pixels on our Monitors or
>spots of ink on our hardcopies and claim: "See "S4Grz = S4Grz*", that thus
>... "truth is provability, provability is truth"". We can make any claim we
>like but if our theories themselves forbid the very exixtence of a universe,
>such as the one containing 1-person experiences and some 3-indeterminant
>version of space-time-momentumenergy, this is all academic sophistry!

It is just intended as an (hopefully flawless) proof that AS FAR AS we
are willing to accept a digital brain substitution (betting on some
unknowable level) then, epistemologically, physics must be derivable from
machine psychology. (and "ontologically" what remains is proposition like
2+4=6, Fermat theorem, twin conjecture, computer science, etc...
essentially number theory + all the sciences you can get from number
theory seen from inside from some angle, and averaging on those angle, etc.).

It makes comp eventually testable. Just compare the "machine psycho" physics
with the apparently empirical facts (well described by QM today). Of course
I tend to argue that QM really looks comp is true, cf the many
world/histories, subtle averaging, + the technical results, ...

I do not explicitly exclude the "reality of the hardware". I show only that
such a reality cannot be used to explain why we believe in that reality.
So, indeed, as far as comp can be true, why to postulate it?

> Please help me understand what I am missing!

Then help me to understand what you are missing: let me know at which step
of the Universal Dovetailer Argument (links to UDA in my URL) you say no?
It would help to know where you find the argument unclear, or weak,
or vague, etc.
Don't tell me you don't swallow the conclusion, no consistent
machines really can! (And remember comp can be false but we keep
using it
as far as no clear contradiction (not just a sense of weirdness appears).


Received on Fri Sep 13 2002 - 08:33:16 PDT

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