Metaphysics and mathematics: Perspectives on reality
Open Access
- 8 February 2017
- journal article
- Published by AOSIS in HTS Teologiese Studies / Theological Studies
- Vol. 73 (3), 8 pages
- https://doi.org/10.4102/hts.v73i3.4663
Abstract
The essence of number was regarded by the ancient Greeks as the root cause of the existence of the universe, but it was only towards the end of the 19th century that mathematicians initiated an in-depth study of the nature of numbers. The resulting unavoidable actuality of infinities in the number system led mathematicians to rigorously investigate the foundations of mathematics. The formalist approach to establish mathematical proof was found to be inconclusive: Gödel showed that there existed true propositions that could not be proved to be true within the natural number universe. This result weighed heavily on proposals in the mid-20th century for digital models of the universe, inspired by the emergence of the programmable digital computer, giving rise to the branch of philosophy recognised as digital philosophy. In this article, the models of the universe presented by physicists, mathematicians and theoretical computer scientists are reviewed and their relation to the natural numbers is investigated. A quantum theory view that at the deepest level time and space may be discrete suggests a profound relation between natural numbers and reality of the cosmos. The conclusion is that our perception of reality may ultimately be traced to the ontology and epistemology of the natural numbers.Keywords
This publication has 7 references indexed in Scilit:
- The Emperor's New MindPublished by Oxford University Press (OUP) ,1989
- Georg Cantor and Pope Leo XIII: Mathematics, Theology, and the InfiniteJournal of the History of Ideas, 1977
- The unreasonable effectiveness of mathematics in the natural sciences. Richard courant lecture in mathematical sciences delivered at New York University, May 11, 1959Communications on Pure and Applied Mathematics, 1960
- On Computable Numbers, with an Application to the Entscheidungsproblem. A CorrectionProceedings of the London Mathematical Society, 1938
- On Computable Numbers, with an Application to the EntscheidungsproblemProceedings of the London Mathematical Society, 1937
- Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme IMonatshefte für Mathematik, 1931
- Über das UnendlicheMathematische Annalen, 1926