This study addresses the feasibility of the classical notion of parameter in linguistic theory from the perspective of parametric hierarchies. A novel program-based analysis is implemented in order to show certain empirical problems related to these hierarchies. The program was developed on the basis of an enriched data base spanning 23 contemporary and 5 ancient languages. The empirical issues uncovered cast doubt on classical parametric models of language acquisition as well as on the conceptualization of an overspecified Universal Grammar that has parameters among its primitives. Pinpointing these issues leads to the proposal that (i) the (bio)logical problem of language acquisition does not amount to a process of triggering innately pre-wired values of parameters and (ii) it paves the way for viewing language, epigenetic ('parametric') variation as an externalization-related epiphenomenon, whose learning component may be more important than what sometimes is assumed.