The author nicely reviews the early results in inductive inference and gives a good picture of these results. He considers general learners, that is, learners that are not limited by their computational abilities but only by general topological limitations of the classes to be learnt from text. Therefore some theorems which hold in inductive inference only for uniformly recursive classes are here stated and applied to all families of sets, as restrictions on the learner from the ability to compute the hypotheses are not considered. The value of this work is that the author connects the community of researchers in inductive inference with pointers to the work of \textit{R. M. Wharton} [Inf. Control 26, 236--255 (1974; Zbl 0309.68063)], \textit{K. Johnson} [Philos. Sci. 71, No. 4, 571--592 (2004; Zbl 1562.68072)] and \textit{P. Niyogi} [The computational nature of language learning and evolution. Cambridge, MA: MIT Press (2006; Zbl 1559.91002)], which has more or less been overlooked by the community. On the other hand, the author himself is not aware of most of the ongoing research in inductive inference. For example, he does not cite the main textbooks in the area, which are the two editions (they are quite different in material presented) of the textbook [\textit{D. N. Osherson} et al., Systems that learn. An introduction to learning theory for cognitive and computer scientists. Cambridge, MA: MIT Press (1985; Zbl 1559.68004); second edition by \textit{S. Jain} et al. Cambridge, MA: MIT Press (1999; Zbl 1559.68003)]. Some of the items he aims at have been investigated by other researchers in quite some depth. Also the observation that for every text \(T\) and every language \(L\) any probability distribution on all words with the overall probability of each word being positive satisfies that the probability of the symmetric differences between \(L\) and the set \(\{T(0),T(1),\ldots,T(n)\}\) goes to \(0\) is known to researchers; learning criteria based on this observation are investigated. Other notions like partial learning are not mentioned in this paper, though that learning notion fixes the shortcoming that in the usual model of Gold the class of all r.e. languages is not learnable. In summary, this is a nice article about the start of inductive inference and some more recent works overlooked in the research area; however, for getting a complete overview of the field, the interested reader should also read the two books cited above and also study more recent works by authors still active in the area of inductive inference. In particular the connections between learnability and recursion theory is not visible from the work presented here.