Felix Lev.  Finite Mathematics as the Foundation of Classical Mathematics and Quantum Theory.

This article by Felix Lev explores the idea that finite mathematics can serve as the foundation for classical mathematics and quantum theory. Lev argues that a specific choice of finite mathematics can provide a more general framework for physical theories, including quantum theory. The article focuses on chapter 6 of Lev's book, which discusses why finite mathematics is more general than infinitary mathematics and why the latter is a degenerate case of the former. The text explores the concept of finite rings or fields versus classical integer arithmetic, and argues that if the number of elements in the finite rings or fields tends to infinity, classical integer arithmetic can be considered a degenerate case. The article also discusses the notion of generality in classical mathematics and its relationship to finite mathematics, drawing parallels with physical notions such as Planck's constant and the velocity of light. It references the work of the Hungarian logic and relativity school and discusses the equivalence of theories and the concept of translation between theories. The text concludes by highlighting the diversity of views on the relationship between mathematics and the real world. [Extracted from the article]