Generative linguistics is often claimed by Chomsky to have a 'Galilean style', which is intended to position linguistics as a science continuous with standard practise in the natural sciences. These claims, however, are more suggestive than explanatory. The paper will, first, explain just what a Galilean style is. It will then be argued that its application to two key notions in generative linguistics - the competence/performance distinction (with reference to centre-embedding) and the notion of computation - demands a departure from what we might expect of a Galilean style. In this sense, the epithet is misleading. It will also be shown, however, that the 'Galilean' label is appropriate once we factor in the difference between a science concerned with kinematics (the relations between objects in space and time) and one concerned with language.