Restructuring General Algebra: An Approach Based on the Idea of Operational Descriptions
by
Rudolf Wille
TU Darmstadt

An answer to the question "Why develop general algebra as we do today?" can be seen in the desire to support humans in their thought, judgments and actions. A general claim is that algebra serves humans as a language for "good" descriptions of facts, systems, and relationships of our scientifically and technologically formed world. The specific nature of algebraic descriptions lies in the use of operations and their structural properties. Thus, the general understanding of algebra as the structure theory of sets with operations combines well with the understanding of algebra as language for operational descriptions and also with Peirce's understanding of mathematics as a cosmos of forms for potential realities. That algebra serves indeed as a good description language can be easily confirmed by many prominent examples. The lecture gives a systematic approach to those algebraic descriptions.

Date received: March 26, 2002