Le 07-janv.-08, à 18:12, John Mikes wrote (to Hal Ruhl)
> I read your post with appreciation (did not follow EVERY word in it
> though) - it reminded me of my "Naive Ode (no rhymes) of Ontology"
> dating back into my "pre-Everythinglist" times, that started something
> "...In the Beginning there was Nothingness ( - today I would add:
> observer of itself). When it realized that it IS nothingness, that was
> providing this information - making it into a Somethingness. The rest
> is history. (Chris Lofting would say: it went alongside
> Differentiation and Integration).
> A minor remark: I would not denigrate Mama Nature by using the word
> 'bifurcation' - indicating that "only 2" chances in the impredicative
> unlimited totality.
> As a second (even more minor) remark: "All possible states" sounds to
> me as being restricted to the level "WE" find possible.
Who "WE"? (I guess you are used to this question by me, with me =
> cave-times (I don't go further) we have encountered many things that
> looked like impossible. I wonder if Bruno's unlimited Loebian Machine
> considers anything 'iompossible'?
Be careful. The Loebian Machine is a *machine*, that is a finite
limited creature (infinitely patient though!).
Now, if you agree to modelize (at least) necessity by
provability and possibility by consistency, then the facts are that
a sound Lobian Machine can refute, and thus can show the inconsistency
of all elementary arithmetical truth.
So 1=2 is impossible (inconsistent) for a lobian machine.
More weird is the fact that there is NO propositions that a Lobian
Machine can show possible !!!
Even the arithmetical obvious fact that 1 = 1 cannot be shown possible,
that is consistent, by the sound Lobian Machine.
This is a direct consequence of Godel's second incompleteness (with
the completeness theorem in the background). No proposition beginning by
consistent, like Dt, which I have also written <>t, or ~B~f or ~~t,
can be proved by the sound machine (G does not prove any such
but most are true, and peoved by G*).
> Have a good 2008
I wish you the best,
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