One interesting suggestion in selecting natural against nonnatural languages is that children master a language by selecting a grammar for it from an innately determinated class of candidates. It is the learning strategy to which the child conforms that determines the subset of innate grammars that can be successfully paired with incoming languages. The concept of 'exact identifiability' is defined as the first characteristics of the learning functions implemented by children, a variety of learning strategies are presented, the more realistic being totality, nontriviality and memory-limitedness. It is revealed that a theory of natural language is adequate only if the class of languages it specifies as natural is exactly identifiable by a total, nontrivial, n- memory-limited learning machine (for some reasonable choice of n). Both, the restrictedness and psychological reality of the strategies are discussed.