This paper attempts to show how Kuhn's and Wittgenstein's works can be of mutual assistance despite their apparent heterogeneity. One face of this project is to analyse the conceptual aspects of paradigm change in physics as described by Kuhn with the help of Wittgensteinian tools, especially what he calls "nonsense" and "grammar", as well as the metaphors of the "hinges' and the "ladder" he employs. On this basis, the paper investigates the process through which a teacher can teach radically new concepts to science students still entrenched in the old incommensurable scientific paradigm. It articulates the thesis according to which the judicious use of nonsense is the indispensable ladder for the elucidation of the novel concepts and for the acquisition of the novel paradigm. The other face of the project is, reciprocally, to use Kuhnian concepts in order to attain a better understanding of Wittgenstein's undertaking. From this side, the paper attempts showing that Wittgenstein's early philosophy in the Tractatus can be understood as a major (perhaps the most) radical "paradigm shift" for the whole "disciplinary matrix" of philosophy. This paradigm change in philosophy is of a very particular kind since it aims to silence philosophy in its entirety by erasing all philosophical problems without exception.