This paper tries to reconstruct the controversy on the possibility of private language. First, we analyse ?epistemological? trends in the argument (Malcolm, Fogelin) showing their failures. Then we analyse ?semantic? versions (Kenny, Tugendhat) finding they also fail. Barry Stroud?s criticism of transcendental arguments as refutations of scepticism allows us to discern the common presupposition that weakens the versions of the argument considered. Moreover, this reconstruction allows us to see how Kripke?s Wittgenstein deals with the problem of the previous discussion in order to avoid committing himself with this presupposition. We consider Kripke?s version to be the only consistent version of the argument. Such a statement obliges us to consider two of the most important criticisms directed against Kripke?s Wittgenstein: The problem of objectivity of the rule: Can a single individual be right in contradicting communal assent?; and the problem of internal relationships between rules and their applications, allegedly violated because of the role played by communal agreement. We claim that our reconstruction of the controversy provides good reasons to show that the above-mentioned objections don?t apply to Kripke?s Wittgenstein version. Indexada en: Clase (Citas Latinoamericanas en Ciencias Sociales y Humanidades); CONUCO (Consorcio Universitario de Indización); HAPI (Hispanic American Periodicals Index); HLAS (Handbook of Latin American Studies); IBR (Internationale Bibliographie der Rezensionen Wissenschaftlicher Literatur); Latindex-Catálogo, Latindex-Directorio; Philosopher´s Index. http://www.latindex.unam.mx/buscador/ficRev.html?folio=3900