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.
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))