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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