The world is not a theorem

TL;DR

This paper argues that affordances, key to biological evolution and adaptation, cannot be formalized using set theory, challenging the possibility of a set-based mathematical theory of biosphere evolution.

Contribution

It introduces a philosophical argument against formalizing affordances with set theory, impacting the modeling of biological evolution.

Findings

Affordances are fundamental to biosphere evolution.

Set theory cannot adequately formalize affordances.

A set-based mathematical theory of biosphere evolution is not feasible.

Abstract

The evolution of the biosphere unfolds as a luxuriant generative process of new living forms and functions. Organisms adapt to their environment, exploit novel opportunities that are created in this continuous blooming dynamics. Affordances play a fundamental role in the evolution of the biosphere, for organisms can exploit them for new morphological and behavioral adaptations achieved by heritable variations and selection. This way, the opportunities offered by affordances are then actualized as ever novel adaptations. In this paper we maintain that affordances elude a formalization that relies on set theory: we argue that it is not possible to apply set theory to affordances, therefore we cannot devise a set-based mathematical theory of the diachronic evolution of the biosphere.