(*) Paolo Mancosu, Department of Philosophy, UC Berkeley, Berkeley, CA 94720- 2390, USA. Acknowledgements : I would like to thank the Wissenschaftskolleg zu Berlin for having provided the ideal working conditions while writing this paper. Many thanks also to the participants in the workshop « Bernard Bolzano : Philosophy of Logic and Mathematics » (Paris, May 28-30, 1998) for having provided ideal conditions for the delivery and the discussion. The financial help of the France-Berkeley Fund for the organization of the workshop is also gratefully acknowledged. Rev. Hist. Set, 1999, 52/3-4, 429-455