  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.
