Towards a (meta-)mathematical theory of consciousness: universal (mapping) properties of experience
Steven Phillips, Naotsugu Tsuchiya
arXiv Preprint Archive December 13, 2024 preprint
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper |
|---|---|
| Keywords | Consciousness Neuroscience q-bio.nc Mathematical modeling Information theory Cognitive science |
| Key points | Proposes that the five essential properties of consciousness in IIT can be understood as universal mapping properties in category theory, providing a more formal and precise foundation for the theory. |
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."