Journal of Physical Mathematics

What Mathematics is the Most Fundamental?

Lev FM

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Standard mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. In the first part of this note we argue that the situation is the opposite: standard mathematics is only a degenerate case of finite one in the formal limit when the characteristic of the ring or field used in finite mathematics goes to infinity, and finite mathematics is more pertinent for describing nature than standard one. In the second part we argue that foundation of finite mathematics is natural while foundational problems of standard mathematics are not fundamental.

Article information

Source
J. Phys. Math., Volume 6, Number 1 (2015), 4 pages.

Dates
First available in Project Euclid: 23 July 2015

Permanent link to this document
https://projecteuclid.org/euclid.jpm/1437658583

Digital Object Identifier
doi:10.4172/2090-0902.1000129

Subjects
Primary: 03Axx: Philosophical aspects of logic and foundations 01Axx: History of mathematics and mathematicians

Keywords
Standard mathematics Finite mathematics Infinity Galois fields

Citation

FM, Lev. What Mathematics is the Most Fundamental?. J. Phys. Math. 6 (2015), no. 1, 4 pages. doi:10.4172/2090-0902.1000129. https://projecteuclid.org/euclid.jpm/1437658583


Export citation