# the threshold

**The threshold where Gödel’s theorems begin to apply**

Put addition and multiplication together and you are over it. Peano arithmetic and set theory both are. Above the threshold a system can describe itself and gets a blind spot. Below it the system is safe but can say little. Self-reference and incompleteness come as a package.

Connects to:
- [why it is safe](https://mapideas.org/i/s_safe)
- [Goldbach](https://mapideas.org/i/s_gold)
- [programs](https://mapideas.org/i/s_prog)
- [checkable or not](https://mapideas.org/i/c_check)
- [the conditions](https://mapideas.org/i/th_cond)

Sources:
- [Wikipedia: Peano axioms](https://en.wikipedia.org/wiki/Peano_axioms)

Source: https://mapideas.org/i/s_thr · open on the map: https://mapideas.org/#s_thr