Naturalized induction is an open problem in Friendly AI: Build an algorithm for producing accurate generalizations and predictions from data sets, that treats itself, its data inputs, and its hypothesis outputs as reducible to its physical posits. More broadly, design a workable reasoning method that allows the reasoner to treat itself as fully embedded in the world it's reasoning about.
Naturalized inductors are associated with naturalism in contrast to 'Cartesian' inductors, reasoners that assume a strict boundary between themselves and their environments. The standard example of an idealization of Cartesian induction is Solomonoff induction, an uncomputable but theoretically fruitful specification of a hypothesis space, prior probability distribution, and consistent reassignment of probabilities given data inputs. As Solomonoff induction is currently the leading contender for a formalization of universally correct — albeit physically unrealizable — inductive reasoning, an essential step in formally defining the problem of naturalized induction will be evaluating the limitations of Solomonoff inductors such as AIXI.
Sequece by Rob Bensinger, imported from the wiki. Additional material after the sequence: Formalizing Two Problems of Realistic World-Models by Nate Soares.