The hole argument meets Noether's theorem

The hole argument of general relativity threatens a radical and pernicious form of indeterminism. One natural response to the argument is that points belonging to different but isometric models should always be identified, or ‘dragged-along’, by the diffeomorphism that relates them. In this paper, I first criticise this response and its construal of isometry: it stumbles on certain cases, like Noether’s second theorem. Then I go on to describe how the essential features of Einstein\rq{}s point-coincidence' response to the hole argument avoid the criticisms of the drag-along response’ and are compatible with Noether’s second theorem.