Metaphysics and mathematics: Perspectives on reality

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.

The Set Theory and the Description of Infinity: the Nature of Infinity Perceived from Metaphysics and Ontology

“…Consider a circumstance, people think about Kant yesterday, and People think about Kant now. Thinking about Kant is the thing that they think of and it does not change due to time passage, however, the time passage provides me with a reason to distinguish think about Kant [1,8], the first time People think about Kant and the second time they think about Kant. This is the same metaphysical reason why they could denote natural numbers, i.e., the intuitive way of counting.…”