economics Paradigm Challenge

Infinity doesn't actually exist in the real world; it’s just a glitch in how we use language to talk about math.

April 10, 2026

Original Paper

The Recursive Illusion: Why Infinity Is a Property of Language, Not of the World

Paul F. Accornero

SSRN · 6261778

The Takeaway

We often think of space or numbers going on forever, but this paper argues that infinity is just a side effect of our symbols being able to repeat themselves. It suggests that the real world is entirely finite, and we have mistaken our own descriptive tools for a physical property of reality.

From the abstract

This paper argues that mathematical infinity is not an intrinsic property of space, matter, or numbers, but a feature of language. Specifically, of any symbolic system powerful enough to support recursive self-reference. What we call "infinite divisibility" is generated by the grammar of mathematical notation (which permits recursive operations such as x/2 without termination), not by the physical or mathematical space itself. The infinity resides in the rule, not in the world the rule describes