Daniel F. M. Strauss
The Significance of a Non-Reductionist Ontology for the Disciplines of Mathematics and Physics–an Historical and Systematic Analysis

Abstract

Mathematics

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. It started out in Greek culture with the Pythagorean claim that “everything is number.” The discovery of incommensurability by Hippasus of Metapont (450 B.C.) caused a crisis because within the assumed form-giving function of number the formless (infinite) was revealed. This resulted in a switch to space – the geometrization of mathematics. Moreover, it inspired a space metaphysics lasting until Descartes and Kant. During the nineteenth century, however, Cauchy, Weierstrass, Dedekind and Cantor once again pursued the path of an arithmeticistic approach. Of particular significance in this regard is set theory as it was developed by Cantor (including his theory of transfinite arithmetic. When Russell and Zermelo independently in 1900 and 1901 discovered the fundamental inconsistency of Cantor's set theory, mathematics gave birth to three schools of thought, the logicist school (Russell, GĂ¶del), the intuitionist school (PoincarĂ©, Brouwer, Heyting, Weyl and Dummett), and the axiomatic formalist school (guided by the foremost mathematician of the twentieth century, David Hilbert and still largely dominating the scene of contemporary mathematics). By exploring questions, such as whether 2+2=4? and whether a line can be defined as the shortest distance between two points, systematic distinctions are introduction on the basis of a third option never explored in the history of mathematics: accept the uniqueness and irreducibility of number and space, and on that basis, analyze the mutual coherence between these two aspects of reality.

Physics

The history of the concept of matter is employed in order to show how different modes of explanation dominated the scene, starting with the Pythagorean thesis that everything is number and the subsequent switch to space as an orientation point. The long legacy of a space metaphysics lasted well into the modern era, for both Descartes and Kant still characterized material things in term of space. It was Galileo who introduced motion as a new mode of explanation in the formulation of the law of inertia. This opened the way for the world view of classical physics – the world as an inter-play of particles in motion. The law of inertia implies that motion is something given, and that therefore instead of trying to deduce or explain it, it should be accepted as a mode of explanation in its own right. Motion is original and unique and indeed embodies a distinct mode of explanation different from those used by the Pythagoreans (number) and the Eleatic school of Parmenides (space). If motion does not need a causing force, then at most it is possible to speak of a change of motion (acceleration or deceleration) – and this does need a physical force. The dominance of the mechanistic main tendency of classical physics lasted up to Heinrich Hertz (end of the 19th century). 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.

Biography
 D.F.M. Strauss was born in Bloemfontein, South Africa (1946).  He enrolled as a student at the University of the Orange Free State in 1965 where he obtained a BA Degree in 1967 (majors: History, Mathematics, Philosophy).  In 1968, he completed BA Honnours (Philosophy) and Political Science III.  His MA Thesis was published in 1969: Philosophy and the Special Sciences (358 pp.).  At the Free University of Amsterdam, he studied systematic philosophy; modern philosophy, and General Theory of Law and Dutch Penal Law (doctoral examination cum laude in November 1970).  His PhD dissertation was on Concept and Idea (1973).  At the then UOFS, he was Senior Lecturer in Philosophy until 1976; then promoted to Associate Professor and in October 1978 to be the Head of the Department of Philosophy.  Between 1994 and 1996, he was the First Director of the Dooyeweerd Centre, assuming at once the position of General Editor of the Collected Works of the Dutch philosopher Herman Dooyeweerd.  Between 1998 and 2002, he was Dean of the Faculty of Humanities.  Since his resignation as Dean in 2001, he published 2 Books and 76 articles in 17 different Journals spread over 12 different scholarly disciplines (22 presentations were given: National: 11; International: 11).

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