The world is not a theorem
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.
Keywords
Cite
@article{arxiv.2101.00284,
title = {The world is not a theorem},
author = {Stuart A. Kauffman and Andrea Roli},
journal= {arXiv preprint arXiv:2101.00284},
year = {2021}
}
Comments
Minor changes in abstract and sec.2 Added a paragraph in sec.3 on the role of non-ergodicity; added also a paragraph on Turing machines and syntactic information. Sec.5 added a paragraph for clarifying the difference between our statement and the case of chaotic dynamical systems