At 03:31 18/12/04 -0500, Jesse Mazer wrote:
>I don't think Bruno's last post was really implying that "everything"
>would be inconsistent, I thought his point was more that you can't
>consider things like the collection of all possible sets to itself be a "set".
Exactly. It is the machine which gives a name to something too big which
will take the risk of being inconsistent. The big "all" is not made
inconsistent by allowing the possibility of inconsistent machines.
Remark.
Actually it is already consistent for a consistent loebian machine to be
inconsistent, and this is not only true *about* any consistent Lobian
machine, but it is communicable by any of them (provable by G* but already
by G). Cf FU.
It is again the second incompleteness theorem: (t = true or "p_>p")
CONSISTENT t -> NOT(PROVABLE(CONSISTENT t)), or by the duality between
CONSISTENT and PROVABLE:
CONSISTENT t -> CONSISTENT (NOT (CONSISTENT t))
Bruno
http://iridia.ulb.ac.be/~marchal/
Received on Sat Dec 18 2004 - 12:10:06 PST