In order to handle presuppositions in the scope of attitude verbs, the
binding theory allows presuppositions triggered in a subject's beliefs
to be bound at the matrix level; and it allows presuppositions trig-
gered in non-doxastic attitudes to be bound in the subject's beliefs
(Geurts, 1999; Maier, 2015). However, we argue that this leads to seri-
ous overgeneration, for example it predicts that the unacceptable `Sue
will come to the party, but Bill is sure that she won't and that only
Sue will come to the party' should be equivalent to the acceptable `Sue
will come to the party, but Bill is sure that nobody will come to the
party'. This is because the presupposition triggered by `only Sue will
come to the party' should be able to be bound at the matrix level. We
discuss some responses to this problem, but argue that they all have
shortcomings.