Le 25-mars-06, à 00:51, George Levy a écrit :
>
> Dear members of the list, Bruno and those who understand G.
>
> I have read or rather tried to read Smullyan's book. His examples are
> totally fabricated. I will never meet the white knight in the island of
> liars and truthtellers.
Nor will any Lobian machines. The knight/knave Island is just a trick
for having simple self-referential statements. I think you miss the
"heart of the matter" section and the "godelized universe". Not your
fault and despite my love of Smullyan I am quasi willing to say
Smullyan miss it too. The missing piece is Church thesis. And then with
comp we can understand that lobian machines "live" in a Godelized
Universe. I will come back on this.
> I need examples which are relevant to life, at
> least the way I understand it in the context of the many-worlds.
OK, OK, I work on this since many years. Modal logics and Solovay's
theorems provides a tools for progressing, but this need some
understanding of computer science and mathematical logic.
>
> Einstein (or maybe someone writing about relativity) came up with the
> paradox of the travelling aging twin. Schroedinger came up with his
> cat's paradox. Tegmark came up with the quantum suicide experiment.
Actually I came up before but this is anecdotical. But I have
elaborated it in the comp frame. It is the UDA. You have acknowledge
understanding it years ago. The interview of the lobian machine just
illustrate how we can already interview of universal machine on the UDA
question, and extract the logic of the "physical propositions".
> Granted, I will never travel near the speed of light; I will never put
> a
> cat in a box equipped with a random and automatized killing device; and
> I will not attempt suicide; my wife would just kill me. However, these
> examples fired up my imagination: travelling near the speed of light,
> existing in a superposition of state, surviving a nuclear bomb under
> your chair.
>
> Smullyan's white knigth had the mission to teach me about the logic of
> G
> and G*. Sorry, he failed.
All right, but this is just because he miss Church Thesis and Comp. His
purpose actually is just to introduce you to Godel and Lob theorems,
not to computer science. The heart of the matter is that mathematical
systems (machines, angels, whatever) cannot escape the diagonalisation
lemma, and so life for them is like the life of those reasoners
travelling on fairy knight Knave island with curious self-referential
question.
With comp *we* cannot escape those diagonal propositions.
> The white knight does not fire up my
> imagination. I don't care about his island and about his questions.
> However I do care about life, death and immortality. The many-world
> does
> seem to guarantee a form of immortality, at least according to some
> interpretations. I consider this issue to be very relevant since sooner
> or later each one of us will be facing the issue of death or of
> non-death.
I thought you did understand that comp entails different forms of
immortality. The interveiw of the lobian machine makes it possible to
get more precise consequences, including testable one (some already
tested).
>
> I would like someone to come up with an extreme adventure story like
> the
> travelling twin, Schroedinger's cat, or Tegmark's suicide experiment to
> illustrate G and G*. For example this story would describe a close
> brush
> with death.. It would create a paradox by juxtaposing 1) classical or
> common sense logic assuming a single world,
UDA shows rather directly the impossibility of single world.
> 2) classical or common sense
> logic assuming the many-world,
?
> and 3) G/G* logic assuming the many-world.
Assuming comp, the third person worlds are the computational histories.
An history is a computations as seen by from some internal point of
view. the fact that correct self-referential propositions obeys G and
G* makes it possible to describe those "histories"
>
> What would the white knight do if he were living in the many-world?
> What
> kind of situations would highlight his talent to think in G. Would his
> behavior appear to be paradoxical from our logical point of view?
The white knight, (well actually any Knight on the Knight Knave
Island!) are not even reasoners. None types of reasoner applies
including G.
The intuitive explanation why physics emerges from numbers and numbers'
dream is already given in the UDA. Smullyan just introduce the logics
of self-reference (the provable one, G, and the true one, G*). The
relation with our field is the content of one half of my posts (the
other half being UDA itself). I think you miss the diagonalization
notion. I will work on that. I will give you "real examples", but don't
throw out FU to quickly. He makes something hard easy, but indeed
don't give to much motivations, except some allusions to AI here and
there.
Bruno
PS. I will answer other posts asap.
http://iridia.ulb.ac.be/~marchal/
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Received on Sat Mar 25 2006 - 09:56:51 PST