Is there some principled way to assign probabilities to conjectures written in PA or ZFC before they are proven or disproven? We introduce a new algorithm for doing this, which satisfies a criterion we call Garrabrant induction that has many nice asymptotic consequences. In particular, the algorithm learns to “trust itself” in that it assigns high probability to its own predictions being accurate (it can refer to itself because ZFC and PA can talk about algorithms). It also assigns high probabilities to provable statements much faster than proofs can be found for them, as long as the statements are easy to write down. More generally, the algorithm was developed as a candidate model for defining “good reasoning” when computational resources are limited. This talk will given an overview of the algorithm, the Garrabrant induction criterion, and its currently known implications.