Le 18-nov.-05, à 05:26, Stephen Paul King a écrit :
> It seems logical. The Notion of "Everything" is 1st person in the
> sense that one, any one, can find itself within it. Nothing, on the
> other hand, only makes sense as seen from some external vantage point,
> hence it is 3rd person.
I can understand why there is no notion of first person nothingness
(and this is the base of the non cul-de-sac appearing with the first
person notion(*).
But for "everything" I think we can have some third person notions.
Typical examples are the complete trace of the running of the UD,
written UD*, or a model of PA, ZF, etc.
The first person notion of everything (the 1-plenitude) is, assuming
comp, so big that it is unnamable by any machine (provably so if the
"person" is some fixed not too complex Lobian machine, like a theorem
prover for PA).
Bruno
(*) For those who remembers the modal introduction: a no-cul-de-sac
multiverse (a multiverse where all observer-moment/world/state are
transitory) verifies the formula []p -> <>p (the so-called deontic
formula d). Note that d is not a theorem of G, but is a theorem of G*.
d is the well known main axiom for the deontic logic of obligation
/permission: indeed a world where d is false is a world where something
is obligatory and not permitted. You can put anyone in jail-cul-de-sac
there!
General question: what do you prefer, as notation (illustrated on the
formula d) :
Box p -> Diamond p
Bp -> Dp
[]p -> <>p ?
Are there people who does not see that
1) whatever the truth value of p, Bp -> Dp is true in all the worlds of
a non-cul-de-sac multiverse.
2) if Bp -> Dp is true in all world of multiverse, whatever the truth
value of p is given in each world, then the multiverse is a
non-cul-de-sac multiverse.
This is easy. If you don't see this, it means you don't remember the
definition of Kripke semantics, or that you don't know classical logic.
Modal logic is really the general theory of Multiverses, and other
multimultiverses, you know. I hardly doubt we will be able to proceed
without getting more familiar with it.
I am actually teaching modal logic and students ask me summary notes. I
am thinking making them in English and posting them to the list. The
post by uv makes me think I should soon or later explain more about
Solovay theorem, which makes the link betwwen the metamathematical
results of Godel, Lob and the G and G* logics discovered by Solovay,
and which are pillar of the interview of the universal machine.
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Fri Nov 18 2005 - 08:53:19 PST