M. Otte – Författare

Time and again, philosophy, in trying to untangle the issues surrounding the an­ alytic-synthetic distinction, has doubted that such a distinction can significantly be drawn at all. We think, in face of the varied and age-old discussions on it, that such reflections amount only to one more documentation of the tenacity of the problems behind this distinction. We could even be justified in promoting the thesis that this distinction refers to the complex relationship between the universe of meanings and the universe of objects and thus concerns each domain of human thinking where a form of objectivity is pursued. If one accepts such a thesis, one will find it very natural that this distinction has so frequently occurred in the history of mathematics and in philosophical discussions about mathematics. Since Plato, we may encounter quite a number of interpretations of the ideas of analysis and synthesis, which are related in one sense or other with mathematical thought. Mathematicians of all ages have ap­ pealed to them in order to distinguish different forms and styles in their argumen­ tation and expositions. Philosophers have referred to them for clarification of the specific character of mathematics in its relations to knowledge in general. In the present volume various instances of the analytic-synthetic distinction are discussed in relation to the history and philosophy of mathematics, and some new perspectives about possible interpretations and consequences are suggested.

I. Some Characteristic Features of the Passage From the 18th to the 19th Century 1. The following notes grew out of reflections which first led us to send out invitations to, and call for papers for, an interdisciplinary workshop, which took place in Bielefeld from 27th to 30th November, 1979. The status and character of this preface is therefore somewhat ambiguous: on the one hand it does not comment extensively on the articles to follow, on the other hand it could not have been conceived and written in the way it was without knowledge of all the contributions to this volum- which contains revised editions of papers for the workshop - nor without the cooperation of the participants in the above mentioned symposium. Furthermore, although the following may sound slightly programmatic and summary, we hope that it will be sufficiently explicit to provide some key words and concepts useful for further scholarly work. Perhaps the most important result of our efforts is the very structure of these notes: it is aimed at providing methodological orientations for the investigation of what turned out to be a very peculiar period in the history of science. xi H. N. Jahnke and M. Otte (eds.), Epistemological and Social Problems of the Sciences in the Early Nineteenth Century, xi-xlii. Copyright © 1981 by D. Reidel Publishing Company. xii H. N. JAHNKE ET AL.

BACOMET cannot be evaluated solely on the basis of its publications. It is important then that the reader, with only this volume on which to judge both the BACOMET activities and its major outcome to date, should know some­ thing of what preceded this book's publication. For it is the story of how a group of educators, mainly tutors of student-teachers of mathematics, com­ mitted themselves to a continuing period of work and self-education. The concept of BACOMET developed during a series of meetings held in 1978-79 between the three editors, Bent Christiansen, Geoffrey Howson and Michael Otte, at which we expressed our concern about the contributions from mathematics education as a discipline to teacher education, both as we observed it and as we participated in it. The short time which was at the teacher-educator's disposal, allied to the limited knowledge and experience of the students on which one had to build, raised puzzling problems concerning priorities and emphases. The recognition that these problems were shared by educators from many different countries was matched by the fact that it would be fruitless to attempt to search for an internationally (or even nationally) acceptable solution to our problems. Different contexts and traditions rule this out.

BACOMET cannot be evaluated solely on the basis of its publications. It is important then that the reader, with only this volume on which to judge both the BACOMET activities and its major outcome to date, should know some­ thing of what preceded this book's publication. For it is the story of how a group of educators, mainly tutors of student-teachers of mathematics, com­ mitted themselves to a continuing period of work and self-education. The concept of BACOMET developed during a series of meetings held in 1978-79 between the three editors, Bent Christiansen, Geoffrey Howson and Michael Otte, at which we expressed our concern about the contributions from mathematics education as a discipline to teacher education, both as we observed it and as we participated in it. The short time which was at the teacher-educator's disposal, allied to the limited knowledge and experience of the students on which one had to build, raised puzzling problems concerning priorities and emphases. The recognition that these problems were shared by educators from many different countries was matched by the fact that it would be fruitless to attempt to search for an internationally (or even nationally) acceptable solution to our problems. Different contexts and traditions rule this out.