This paper take sup the theory put forward by Gunther Grewendorf (1995) that Wittgenstein's conception of language as a publicly constituted 'life form' is compatible with Chomsky's conception of language as a human 'organ', although this conception could undoubtedly be characterized to a certain extent as a private-language conception in Wittgenstein's sense. In a first step, it is shown how Chomsky's model of an autonomous syntax module or a universal grammar can indeed by characterized as a 'private-language' conception. This is essentially related to the construction of this module as a material, neural state (Chomsky 1995), as a linguistic 'knowledge', whose manner of functioning cannot become apparent to the speaker. In a second step, the major points of Grewendorf's argumentation are summarized. In spite of a very precise and accurate reconstruction of Wittgenstein's argument, the reconstruction ultimately follows Kripke's interpretation, which, as is well known, trivializes this argument. The decisive aspect for Grewendorf's argumentation is his theory - which here undoubtedly contradicts Wittgenstein's text and logic - that the differentiation between know and believe to know is irrelevant for Wittgenstein's refutation of the possibility of a private language. It is, thirdly, demonstrated that Chomsky's theory would be tenable, or not affected by Wittgenstein's argument, if the existence of the syntax module could be demonstrated irrespective of the reference to performance phenomena. Fourthly, and finally, it is then shown by using grammatical categories as theoretical predicates that this is not possible for purely logical reasons. Chomsky can only give these predicates a second extension, i.e. use them as descriptors of neural states, if he simultaneously defines them extensionally on the first level by deriving them in a generative grammar which culminates in assigning lexicon elements to terminal categories. Otherwise it would be simply impossible to correlate statements on the forms of the syntax module with statements on surface forms. The autonomous syntax module is thus, on the one hand, identified as a private-language construction par excellence and with Wittgenstein it is shown why such a construction is logically untenable. In parallel to this , attention is drawn to recent developments in the theory of neural networks, in which Chomsky's basic argument from his Skinner review that without 'innate ideas' a child would not be in a position to develop a perfect grammar from imperfect linguistic data is factually and definitively refuted. The human brain is certainly capable of learning inductively or analogically on the basis of similarity relations. Fodor's theory of the autonomy of brain modules in essence contradicts recent findings on the interlinkage of modules enabling the brain to become self-organizing.
