Le 16-oct.-07, à 12:37, I said, in a post to John Mikes,
> Agreed. It was just a parabola for driving attention against any use
> of authoritative argument in the field of fundamentals.
> Ah! But the lobian machine too can be shown allergic to such argument.
> It's a universal dissident. Unforunately, humans, like dog are still
> attracted to the practical philosophy according to which the "boss is
> right" (especially when wrong!)
Please remind I talk as a platonist, having the long run in mind.
Obviously, (sadly I think), the "boss is right" theory has some
selective, darwinian, advantage in the short run. The poor self-moving
carnivore, before asking itself "to be or not to be" goes through some
long "to eat or to be eated", forcing it to take quick decisions in
presence of partial information, and here the "boss" can help, a lot,
indeed. A little like in an army where "orders" are usual and natural,
or in conventional or typed programming with its well-behaved
subroutines. It is not yet completely clear (arithmetical) why and if
it has to be so locally everywhere, for the (sound) lobian machine or
lobian entity (cf S4Grz). But the fundamentals have to be coherent with
the long run, and so, in the limit at least, the lobian entity has to
demolish, indeed, all authoritative arguments. An hard (transfinite)
task.
Marc, I am just telling you what the self-referentially platonist
machine suggest: invoking some entity (being it machine, human, god, or
whatever) as smarter is akin to give a name to something unameable. You
can reason about it, but you cannot identify them with anything.
All,
Recall just PA is a less rich lobian machine that ZF, also a lobian
machine. Less rich means less rich the in size of their set of
arithmetical sentences they can prove, I mean ZF proves more
arithmetical sentences than PA).
Then, it is like if PA , after having proved correctly that ZF can
prove the consistency of PA; concludes in its own consistency.
True: ZF proves the consistency of PA.
True: PA can proves that! i.e: PA can prove that ZF proves the
consistency of PA.(even RA can prove that for those who reminds the
weak RA)
True: PA cannot deduce from that that PA is consistent.
True: PA cannot prove its own consistency (consistency of PA)
true: ZF cannot prove its own consistency ..... Hmmm unless ZF is
inconsistent.
I am 100% confident in the consistency (and even soundness) of PA.
I am 99,99999998 % confident in the consistency of ZF (and even less in
absence of coffee I'm afraid)
Bruno
> PS Perhaps this week I will got the time to send the next post in the
> "observer-moment = Sigma_1 sentence".
http://iridia.ulb.ac.be/~marchal/
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Received on Tue Oct 16 2007 - 09:11:33 PDT