The world is not a theorem

Stuart A. Kauffman, Andrea Roli
The evolution of the biosphere unfolds as a luxuriant generative process of new living forms and functions. Organisms adapt to their environment, and exploit novel opportunities that are created in this continuous blooming dynamics. Affordances play a fundamental role in the evolution of the biosphere, as they represent the opportunities organisms may choose for achieving their goals, thus actualizing what is in potentia. In this paper we maintain that affordances elude a formalization in mathematical terms: we argue that it is not possible to apply set theory to affordances, therefore we cannot devise a mathematical theory of affordances and the evolution of the biosphere.