Meta-Induction and the Prediction Game: A New View On Hume's Problem

I start this paper with three conceptual clarifications: (1.) What do I mean with the problem of induction? I mean Hume's problem: how can we rationally justify the inductive transfer of regularities from past observations to the unobserved future, or from finite samples to a potentially infinite population. Hume's question is the most fundamental problem about induction and I am inter-ested in a positive solution of this problem. (2.) Which is the method of induction I am trying to justify? Admittedly, there are several different methods of induction. But there is just one most basic method- the so-called straight rule: Straight rule: Transfer the relative frequency of a given event type E(x) from the ob-served events to the conjectured frequency-limit p(E) in the indefinite future. Reichenbach (1949, 446), Salmon (1961, 1974b, 89-95), Rescher (1980, ch. VI.3) and others authors have given strong arguments showing that the straight rule is the most effective method of approximating the frequency limit of a random sequence of discrete events. Inductions in non-random sequences are more-or-less reducible t