An enactivist-inspired mathematical model of cognition.

The authors develop a mathematical framework for cognitive systems—both artificial and natural—that aligns with enactivism, a philosophical position in cognitive science. They identify five core enactivist tenets and build a model that avoids attributing contentful symbolic representations to agents, instead treating the nervous system, body, and environment as an inseparable whole. The central concept is a sensorimotor system, a special case of a transition system. They introduce the notion of sufficiency as a foundational concept, proving a uniqueness theorem about minimal sufficient refinements, which correspond to an optimal attunement of an organism to its environment. This framework aims to make enactivist ideas accessible to computer scientists, AI researchers, and roboticists, while providing philosophers a mathematical tool for clarifying debates.

Study at a glance

Abstract

In this paper we start from the philosophical position in cognitive science known as enactivism. We formulate five basic enactivist tenets that we have carefully identified in the relevant literature as the main underlying principles of that philosophy. We then develop a mathematical framework to talk about cognitive systems (both artificial and natural) which complies with these enactivist tenets. In particular we pay attention that our mathematical modeling does not attribute contentful symbolic representations to the agents, and that the agent's nervous system or brain, body and environment are modeled in a way that makes them an inseparable part of a greater totality. The long-term purpose for which this article sets the stage is to create a mathematical foundation for cognition which is in line with enactivism. We see two main benefits of doing so: (1) It enables enactivist ideas to be more accessible for computer scientists, AI researchers, roboticists, cognitive scientists, and psychologists, and (2) it gives the philosophers a mathematical tool which can be used to clarify their notions and help with their debates. Our main notion is that of a sensorimotor system which is a special case of a well studied notion of a transition system. We also consider related notions such as labeled transition systems and deterministic automata. We analyze a notion called sufficiency and show that it is a very good candidate for a foundational notion in the "mathematics of cognition from an enactivist perspective." We demonstrate its importance by proving a uniqueness theorem about the minimal sufficient refinements (which correspond in some sense to an optimal attunement of an organism to its environment) and by showing that sufficiency corresponds to known notions such as sufficient history information spaces. In the end, we tie it all back to the enactivist tenets.