As for the counting argument, that’s less well known. When I first heard it in undergrad (in the context of learning about Solomonoff Induction) it struck me as another important milestone of intellectual progress, that doesn’t solve the problem but probably brings us closer. I felt the same way about one of the things that makes solomonoff induction work (how hypotheses that are simpler have “more look-alikes” and thus when grouped together with look-alikes more measure) and subjective Bayesianism. Finally, I’m excited about something proven in Logical Induction—that logical inductors have the Occam Property. I still haven’t got around to understanding it deeply and thinking about what it means though. All in all I remain optimistic that the problem of induction has a solution.
As for the counting argument, that’s less well known. When I first heard it in undergrad (in the context of learning about Solomonoff Induction) it struck me as another important milestone of intellectual progress, that doesn’t solve the problem but probably brings us closer. I felt the same way about one of the things that makes solomonoff induction work (how hypotheses that are simpler have “more look-alikes” and thus when grouped together with look-alikes more measure) and subjective Bayesianism. Finally, I’m excited about something proven in Logical Induction—that logical inductors have the Occam Property. I still haven’t got around to understanding it deeply and thinking about what it means though. All in all I remain optimistic that the problem of induction has a solution.