Towards a (meta-)mathematical theory of consciousness: universal (mapping) properties of experience
Steven Phillips, Naotsugu Tsuchiya
arXiv Preprint Archive December 13, 2024 via arXiv
Summary
AI-generated from the abstractConscious experience has five essential properties—intrinsicality, information, integration, exclusion, and composition—as proposed by Integrated Information Theory (IIT), but the necessity of these axioms is unclear due to their informal presentation and dependence on a specific mathematical model. A category-theoretic approach, a meta-mathematical framework for making relations between formal structures precise, organizes these five properties around a smaller number of meta-mathematical principles. Category theory characterizes structures by universal mapping properties, a unique-existence condition for all instances. This suggests that the axioms for consciousness correspond to universal mapping properties, leading to the idea that consciousness is a universal property.
Study at a glance
| Characteristics | Theoretical or philosophical paper Peer reviewed |
|---|---|
| Keywords | Consciousness Neuroscience q-bio.nc Mathematical modeling Information theory Cognitive science |
| Key finding | The five essential properties of consciousness from IIT can be organized around universal mapping properties from category theory, suggesting consciousness is a universal property. |
Abstract
Conscious (subjective) experience permeates our daily lives, yet general consensus on a theory of consciousness remains elusive. Integrated Information Theory (IIT) is a prominent approach that asserts the existence of subjective experience (0th axiom), from an intrinsic system of causally related units, and five essential properties (axioms 1-5): intrinsicality, information, integration, exclusion and composition. However, despite empirical support for some aspects of IIT, the supposed necessity of these axioms is unclear given their informal presentation and operationalized dependence on a specific mathematical instantiation as the so-called postulates. The category theory approach presented here attempts to redress this situation. Category theory is a kind of meta-mathematics invented to make relations between formal structures formally precise and so facilitate doing "ordinary" mathematics. In this way, the five essential properties for consciousness are organized around a smaller number of meta-mathematical principles for comparison with IIT. In particular, category theory characterizes mathematical structures by their "universal mapping properties" -- a unique-existence condition for all instances of the structure. Accordingly, axioms 1-5 pertain to universal mapping properties for experience, whence the slogan, "Consciousness is a universal property."