Comment by rdevilla

> It all sort of ties into Heisenberg's uncertainty theorem. A system cannot be fully described from within that system.

Surely you are talking about Godel incompleteness, not Heisenberg's uncertainty principle; in which case they're actually not the same system - the verification/proof language is more like a metalanguage taking the implementation language as its object.

(Godel's observation for mathematics was just that for formal number systems of sufficient power, you can embed that metalanguage into the formal number system itself.)