To respond to comments on consistency.
I see no reason why components of the system need to be internally consistent. And I have indicated that the All is not internally consistent. Generally speaking evolving Somethings are also not consistent. Actually evolving Somethings are a sequence of Somethings in that each new "quantum" of information incorporated into a Something makes it a new system.
Arithmetic and any system that incorporates it can not prove its [their] own consistency.