The aim of this paper is twofold: firstly, the author attempts to present Wittgenstein's later philosophy as coherent with neuroscientific investigations of human linguistic abilities; secondly he sketches a picture of the current neuroscience in order to find the coherent solution to the problem of 'hard' basis of the grammar. The central role in his presentation of Wittgenstein's philosophy of language is played by the concept of the 'form of life'. He describes two most common interpretations of this concept. At the first glance it seems to refer to the common but culture-related and conventional set of practices which serve as a ground for linguistic behaviour inside a community. However, the totally contingent base of the language cannot explain many obviuos human abilities with the capability to learn the mother tongue in the first place. Neither this is Wittgenstein's point, for certain occurances of the concept of 'form of life' refer to something much more stable and cross-cultural than just a convention regarding practices. The author bounds this meaning of the concept to another key notion of a 'primitive reaction'. The question concerning biological basis of human cognitive abilities in language formation and understanding is then addressed in order to explain some of the characteristics of the remarks presented by Wittgenstein. He addresses the problem of the nativity of general and particular language rules, trying to find common and undisputable ground for further discussion regarding syntactic and semantic features of language communication. The inconclusive results of modern research lead to the cautious notion of compatibility of Wittgenstein's philosophy of language and the cognitive theories of cross-culturally interchangeable grammar basis. In the summary he presents the view of language as imperfect tool of communication hoping to develop more precise and adequate model of cognitive grammar consistent with the philosophy of the second Wittgenstein.