All induction problems may be phrased in a way that depicts a sequence of predictions. Inductive problems will contain a previous indicator or explanans for the explanandum. For instance, Carl Hempel’s example of Jones’ infection:
Where j is Jones, p is the probability, Sj is Jones’ infection, Pj is he being treated with penicillin, and Rj is his recovery. If the probability of observing R at any time given the past observations of S&P1… S&P2 … S&Pn (the probability of the set meeting R is m) where R was close to 1 then a predictive explanans (the S&Pn ) can be made for future instances of m using an inductive-statistical explanation. For if the probability m(S&Pn | S&P1… S&P2 …) is a computable function, the range of data is finite then a posterior predication M can be made from m. M can be legitimately referred to as a universal predictor in cases of m. This is where Hempel rejects the requirement of maximal specificity (RMS), contra Rudolph Carnap, in which the RMS is a maxim for inductive logic that states that this is a necessary condition for rationality of any given knowledge situation K. Let K represent the set of data known in m. According to Hempel we cannot have all the material for K.