  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.
