Save

The Philosophy of the Cosmonomic Idea and the Philosophical Foundations of Mathematics

In: Philosophia Reformata
Author: Danie Strauss1
View More View Less
  • 1 School of Philosophy, Faculty of Arts and Humanities, North-West University, Potchefstroom, Republic of South Africa, dfms@cknet.co.za
Download Citation Get Permissions

Access options

Get access to the full article by using one of the access options below.

Institutional Login

Log in with Open Athens, Shibboleth, or your institutional credentials

Login via Institution

Purchase

Buy instant access (PDF download and unlimited online access):

€29.95$34.95

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.

Content Metrics

All Time Past Year Past 30 Days
Abstract Views 80 80 3
Full Text Views 8 8 0
PDF Views & Downloads 19 19 0