Section 1 of this article discusses the concept of bibliographical control and makes a distinction between this term, bibliographical description, and related terms, which are often confused in the literature. It further discusses the function of bibliographical control and criticizes Patrick Wilson's distinction between "exploitative control" and "descriptive control". Section 2 presents projects for establishing bibliographic control from the Library of Alexandria to the Internet and Google, and it is found that these projects have often been dominated by a positivist dream to make all information in the world available to everybody. Section 3 discusses theoretical problems of providing comprehensive coverage and of retrieving documents that are represented in databases and argues that 100% coverage and retrievability is an unobtainable ideal. It is shown that bibliographical control has been taken very seriously in the field of medicine, where knowledge of the most important findings is of utmost importance. In principle it is equally important in all other domains. The conclusion states that the alternative to a positivist dream of complete bibliographic control, is a pragmatic philosophy aiming of optimizing bibliographic control supporting specific activities, perspectives, and interests.