idea

Escape routes from Löb’s theorem that match the intuition of humility

Partial trust: you trust yourself for restricted classes of statements. Trust the level below: Feferman’s progressions, where each system vouches for the previous one but not for itself. Probabilistic self-trust: work attributed to Christiano and colleagues says a probabilistic version can talk about its own reliability if it allows a small margin of error. Certainty breaks it, and calibrated doubt does not. verify

Connects to

• Löb’s theorem
• the AI version
• trust
• the ladder

Sources

1. Feferman, S. (1962). Transfinite recursive progressions of axiomatic theories. Journal of Symbolic Logic 27(3), 259–316.