How some infinities cause problems in classical physical theories

In this paper we review a 1992 excursion of Jean Paul Van Bendegem into physics, ‘How Infinities Cause Problems in Classical Physical Theories’, in the light of two later models concerning colliding balls, of Pérez Laraudogoitia and of Alper and Bridger, respectively. We show that Van Bendegem anticipated the model of Alper and Bridger by six years, but we also argue that his conditions for the avoidance of problems in these models are not entirely adequate. For although a veto on actual infinity seems to be required, allowing a potential infinity remains a viable option.