Mathematical Knowledge and the Role of an Observer: Ontological and epistemological aspects

TL;DR

This paper explores the ontological and epistemological aspects of mathematics, emphasizing its nature as a knowledge system dependent on observers, which explains its structural effectiveness.

Contribution

It offers a novel analysis of mathematics as an observer-dependent knowledge system, highlighting its structural nature and philosophical implications.

Findings

Mathematics is fundamentally an observer-dependent structure.

The structural nature of mathematics accounts for its effectiveness.

Mathematical existence depends on nonstandard observer-related factors.

Abstract

As David Berlinski writes (1997), the existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself. Here we analyze the essence of mathematics making the main emphasis on mathematics as an advanced system of knowledge. This knowledge consists of structures and represents structures, existence of which depends on observers in a nonstandard way. Structural nature of mathematics explains its reasonable effectiveness.