Gödel's Incompleteness Theorems (2015)
I always was wondering: Godel proved his theorem regarding formal systems described in Principia Mathematics. In my understanding this is some higher level logic with recursive functions.<p>But how this can be extended to the whole universe of all possible formal systems? Who guarantee that there will be no some new system with quantum-oracle-operator, which will not be affected by incompleteness theorem, and can self-proof self-consistency?<p>Even well known m-recursive functions (which are essentially Turing machines) are wider class than primitive recursive functions used in the proof..