The Philosophy of the Cosmonomic Idea and the Philosophical Foundations of Mathematics
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...
| Published in: | Philosophia reformata |
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| Main Author: | |
| Format: | Electronic Article |
| Language: | English |
| Check availability: | HBZ Gateway |
| Journals Online & Print: | Drawer...
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| Fernleihe: | Fernleihe für die Fachinformationsdienste |
| Published: |
Brill
2021
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| In: |
Philosophia reformata
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| Further subjects: | B
Infinity
B discreteness B whole-parts relation B Zeno’s paradoxes B defining mathematics B modal aspects B anticipatory and retrocipatory analogies B at once infinite |
| Online Access: |
Volltext (lizenzpflichtig) Volltext (lizenzpflichtig) |
| Summary: | 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. |
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| ISSN: | 2352-8230 |
| Contains: | Enthalten in: Philosophia reformata
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| Persistent identifiers: | DOI: 10.1163/23528230-bja10014 |