It will be argued that the overcoming and avoiding of dogmatism is a decisive feature of the change in Wittgenstein"s thinking that takes place in the beginning of the 1930s when he starts to emphasise the autonomy of the grammar of language and to talk about grammatical pictures and language games as objects of comparison. By examining certain crucial features in this change in Wittgenstein"s thinking, it will be shown that he received decisive impulses and ideas from new developments in mathematics and natural science in the early twentieth century. These ideas include the axiomatisation of geometry and, in general, Hilbert"s axiomatic method, but also relativity theory and the so-called method of ideal elements. By drawing upon certain analogies rather than theory-constructions, these ideas affected not only his thinking about mathematics, but also his thinking about language and the nature of philosophy in general.