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Author: Danie Strauss

Dooyeweerd was struck by the fact that different systems of philosophy expressly oriented their philosophic thought to the idea of a divine world order. The dialectic of form and matter permeated both Greek and medieval philosophy. The distinction between natural laws and laws of nature is highlighted with reference to Descartes and Beeckman. A key distinction for an understanding of the order of the world is given in the difference between modal laws and type laws. In order to substantiate this claim, an explication of the nature of the order for the world has to explore elements derived from the four most basic modes of explanation: number (the one and the many), space (universality), the kinematic (constancy), and the physical aspect (change). These points of entry serve theoretical thought with terms that may either be employed in a conceptual way or in a concept-transcending way. The influence of nominalism on the thought of Dooyeweerd is analyzed in some more detail.

In: Philosophia Reformata
Author: Danie Strauss

Abstract

Since the discovery of the paradoxes of Zeno, the problem of infinity was dominated by the meaning of endlessness—a view also adhered to by Herman Dooyeweerd. Since Aristotle, philosophers and mathematicians distinguished between the potential infinite and the actual infinite. The main aim of this article is to highlight the strengths and limitations of Dooyeweerd’s philosophy for an understanding of the foundations of mathematics, including Dooyeweerd’s quasi-substantial view of the natural numbers and his view of the other types of numbers as functions of natural numbers. Dooyeweerd’s rejection of the actual infinite is turned upside down by the exploring of an alternative perspective on the interrelations between number and space in support of the idea of infinite totalities, or infinite wholes. No other trend has succeeded in justifying the mathematical use of the actual infinite on the basis of an analysis of the intermodal coherence between number and space.

In: Philosophia Reformata
Author: Danie Strauss

Since the discovery of the paradoxes of Zeno, the problem of infinity was dominated by the meaning of endlessness—a view also adhered to by Herman Dooyeweerd. Since Aristotle, philosophers and mathematicians distinguished between the potential infinite and the actual infinite. The main aim of this article is to highlight the strengths and limitations of Dooyeweerd’s philosophy for an understanding of the foundations of mathematics, including Dooyeweerd’s quasi-substantial view of the natural numbers and his view of the other types of numbers as functions of natural numbers. Dooyeweerd’s rejection of the actual infinite is turned upside down by the exploring of an alternative perspective on the interrelations between number and space in support of the idea of infinite totalities, or infinite wholes. No other trend has succeeded in justifying the mathematical use of the actual infinite on the basis of an analysis of the intermodal coherence between number and space.

In: Philosophia Reformata