Recently Carolyn Brighouse and Jeremy Butterfield have argued that Dav
id Lewis's counterpart theory makes it possible both to believe in the
reality of spacetime points and to consider general relativity to be
a deterministic theory, thus avoiding the 'hole argument' of John Earm
an and John Norton. Butterfield's argument relies on Lewis's own count
erpart-theoretic analysis of determinism. In this paper, I argue that
this analysis is inadequate. This leaves a gap in the Butterfield-Brig
house defence against the hole argument.