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AG 4: Semiotic Epistemology and Mathematics Education

Research Group on Semiotic Epistemology and Mathematics Education

The Research Group is a part of the Institut für Didaktik der Mathematik at the University of Bielefeld. It studies the development of knowledge in historical and epistemological perspectives. The main interest is the relation between social and object-centered aspects of learning processes. One important thesis is that the process of learning mathematics can be used as a paradigm for discussing major problems of epistemology. The theoretical framework is provided by the philosophy of Charles S. Peirce and, in particular, by his considerations on the concept of sign, the process of generalization, and the role of continuity within the latter. The following projects are in progress:

  1. Learning as a process of generalization (Michael Otte, Michael Hoffmann).
  2. Peirce's Philosophy of Mathematics in the Context of his "Evolutionary Realism". The Peircean Principle of Continuity (Otte, Hoffmann). With respect to the philosophy of mathematics, the thesis is that Peirce's emphasis on the reality of generals, together with his semiotic model of the processuality of generalization, offers the possibility for a mathematical realism which is not reducible to the distinction of Logicism, Formalism and Intuitionism. And with respect to philosophy, the thesis is that the Peircean approach to the mathematical process of generalization can be understood as a paradigm which may be of special interest for problems of epistemology, ontology and the development of social communities. Insofar as the concepts of processuality and evolution are based on the possibility of continuity, a main problem is the role of the concept of continuity in Peirce's philosophy.
  3. The symmetry of subjectivity and objectivity in scientific generalization. Studies concerning the foundation of scientific rationality in the mathematical philosophy of Charles S. Peirce and his followers (Otte, Thomas Mies, Hoffmann).
  4. Didactical aspects in Wittgenstein's philosophy of mathematics (Norbert Meder).
  5. The Axiomatization of Arithmetic (Mircea Radu).
  6. The interdependence of logic, ethics and aesthetics (Otte, Hoffmann).

For more information contact Prof. Dr. Michael Otte or Dr. Michael Hoffmann, Institut für Didaktik der Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld. E-mail:, or:

Last change: March 14, 1997