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&P*_{1}… *S&P*_{2} … *S&P*_{n} (the probability of the set meeting *R* is *m*) where *R* was close to 1 then a predictive *explanans* (the *S&P*_{n} ) can be made for future instances of *m* using an inductive-statistical explanation. For if the probability *m*(*S&P*_{n }| *S&P*_{1}… *S&P*_{2} …) 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*.