Le 12-déc.-05, à 18:07, Tom ([EMAIL PROTECTED]) a écrit :
In response to Stathis' thought experiment, to speak of an experiment
being "set up" in a certain way is to base probabilities on an
"irrelevant" subset of the whole, at least if the multiverse
hypothesis is true. In the Plenitude, there are an additional 10^100
copies still existing, when you say that 10^100 copies are being
shut-down. Talking about these additional 10^100 copies is just as
consistent as talking about the original 10^100 copies (even more
consistent if you consider Bruno's statement about cul-de-sacs.
In the Plenitude, everything washes out to zero. And Bruno, I would
even say that all consistent histories wash out to zero.
I am not sure why you say this.
Bruno, I've been following your posts about Kripke semantics and have
done the exercises, including the one about showing that you need a
symmetrical accessibility relation to have LASE.
Nice !
However, my initial reaction still is that choosing a particular modal
logic is scary to me, sending up red flags about hidden assumptions
that are being made in the process. But I will continue to follow you
as you present your case.
Actually I do agree with you. But in the present case, that is with
comp as I defined it (or much weaker assumption really) we will not to
have to make a choice on the modal logics, they will be given by the
interview of the lobian machine. Precisely G (and G*) will appear to be
the complete and sound logic of the provable (and true)
self-referential statements made by a sound or self-referentially
correct machine. This is a consequence of a theorem in pure
mathematics: Solovay theorem.
Then, the translation of the UDA and in particular of the 1 and 3
notions will lead to the other modal logics we need, without us adding
more (hidden) assumptions than the comp one (or much weaker).
Earlier Stathis wrote:
Bruno: OK but with comp I have argued that OMs are not primitive but
are "generated", in platonia, by the Universal Dovetailer. A 3- OM is
just an UD-accessible state, and the 1-OMs inherit relative
probabilities from the computer science theoretical structuring of the
3-OMs.
Are OMs directly generated by the UD, or does the UD generate the
physical (apparently) universe, which leads to the evolution of
conscious beings, who then give rise to OMs?
Stathis Papaioannou
It's interesting that symmetry (Bruno's requirement for LASE) has come
up lately, because Stathis' question seems to be what we are all
wondering. That's the bottom line of multiverse theories: Where does
the symmetry breaking come from?
Actually comp put a big assymmetry at the start (the natural numbers:
0, 1, 2, 3, 4, ...), and my question for years was how to get the
symmetry which apparently lives at the bottom of physics (already
classical physics, still more with QM-without collapse).
I maintain still that it can't come from the multiverse itself.
But which "multiverse"? remember that the QM, or the existence of any
physical multiverse are not among the hypothesis. Indeed the UDA forces
us to justify completely the appearances of a "physical" multiverse.
Even considering only consistent histories, there is no asymmetry to
be found.
This astonishes me a little bit. The very notion of "history", it seems
to me, is assymetrical. But then I am not sure if you are talking about
the comp consistent extensions of some machine (the comp histories) or
the quantum histories of Everett, Hartle, and Co. ?
I maintain that it needs to come from outside the multiverse, which
is something that we cannot explain.
It certainly (with comp) needs to be explain from outside any notion of
"physical multiverse".
Then the truth-provability gap (capture by the modal logic G* \ G, that
is the set difference between the provable self-referential statements
and the true self-referential statements) will "explain" why we cannot
explain that something.
I should perhaps make some summary.
Bruno
http://iridia.ulb.ac.be/~marchal/
