Modern system of mathematics and a pair of hidden contradictions in its foundation
Abstract
Purpose
The paper's aim is to show a pair of deeply hidden contradictions in the system of mathematics.
Design/methodology/approach
The paper takes a conceptual approach to the problem.
Findings
It is indicated that it is an intrinsic attribute of modern mathematics and its theoretical foundation to mix up the intensions and methods of two different thoughts of infinities, which provides the basis of legality for using the methods of analysis, produced by combining the two kinds of infinities, in the study of the modern mathematical system. In this paper, by exactly employing the method of analysis of mixing up potential and actual infinities, we card the logical and non‐logical axiomatic systems for modern mathematics. The outcome of our carding implies that in modern mathematics and its theoretical foundation, some axioms implicitly assume the convention that each potential infinity equals an actual infinity, while some other axioms implicitly apply the belief that “each potential infinity is different of any actual infinity.”
Originality/value
By using the concepts of potential and actual infinities, the authors uncover two contradictory thinking logics widely employed in the study of mathematics.
Keywords
Citation
Zhu, W., Lin, Y., Gong, N. and Du, G. (2008), "Modern system of mathematics and a pair of hidden contradictions in its foundation", Kybernetes, Vol. 37 No. 3/4, pp. 438-445. https://doi.org/10.1108/03684920810863390
Publisher
:Emerald Group Publishing Limited
Copyright © 2008, Emerald Group Publishing Limited