Danie Strauss: "The Significance of a Non-Reductionist Ontology for the Disciplines of Mathematics and Physics--An Historical and Systematic Analysis"
The history of mathematics is centered on the struggle to come to terms with the relationship between discreteness and continuity, i.e. to understand the uniqueness and mutual coherence of number and space. Unfortunately throughout its history mathematics opted for one-sided extremes. The history of the concept of matter in physics is employed to show how different modes of explanation dominated the science, starting with the Pythagorean thesis that everything is number and the subsequent switch to space as an orientation point. The 20th century explored the meaning of (physical) energy-operation and thus paved the way for a different understanding of matter. Problems regarding natural laws, individualization, the structure of physical entities and their interlacement in molecular structures are dealt with in terms of the systematic distinctions entailed in a non-reductionist ontology.
2008 July 15