# free certainty

**Why a broken system proves “I am consistent”**

An inconsistent system proves everything, true and false alike, including “I am consistent”. So a proof of consistency from inside is worth nothing. A healthy system cannot give one, and a broken one gives it for free.

Connects to:
- [complete, incomplete](https://mapideas.org/i/w_comp)
- [trust](https://mapideas.org/i/w_trust)
- [the asymmetry](https://mapideas.org/i/h_asym)
- [second theorem](https://mapideas.org/i/th_second)
- [Löb’s theorem](https://mapideas.org/i/h_lob)
- [broken signature](https://mapideas.org/i/p_sig)

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