Towards a (meta-)mathematical theory of consciousness: universal (mapping) properties of experience
arXiv Preprint Archive – December 13, 2024
Source: arXiv
Summary
Consciousness, one of nature's most fascinating phenomena, may be understood through universal mathematical patterns. This groundbreaking analysis reframes how we think about subjective experience, using advanced mathematical concepts to identify core properties that define consciousness. The work bridges neurobiology (q-bio.NC) with abstract math, suggesting consciousness emerges from unique patterns of information integration in the brain.
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."