Phi's Paradox: Consciousness Integration vs. Computability Limits — E8 Intelligence Research
Zenodo (CERN European Organization for Nuclear Research) August 31, 2026 DOI: 10.5281/zenodo.22189547 (opens in new tab)
Study at a glance
AI-extracted from the abstract| Characteristics | Theoretical or philosophical paper Peer reviewed |
|---|---|
| Key points | Argues that Integrated Information Theory's Φ is system-dependent and lacks a closed-form constant, with critiques from Tegmark and algorithmic-information approaches highlighting a fundamental tension between lossless integration and computability. |
Abstract
FINDING: Integrated Information Theory (IIT) formalizes consciousness as a quantity Φ (phi) — the irreducible cause-effect power of a system — but its measurement remains contested; Tegmark and algorithmic-information critiques highlight a fundamental tension between lossless integration and computability. | MATH: IIT defines Φ via the *minimum information partition* (MIP): Φ = min over partitions of the system's cause-effect repertoire distance (Earth Mover's Distance / Wasserstein metric) between the whole and partitioned system. Tegmark's critique uses *effective information* and spectral decomposition of the connectivity matrix; the algorithmic-information approach (arXiv:1405.0126) replaces Shannon entropy with Kolmogorov complexity, yielding Φ_AIT = K(whole) − max_partition K(partitioned), where K is algorithmic complexity. No closed-form constant emerges; Φ is system-dependent, not a universal ratio. | CONNECTION: None direct. IIT's state-space geometry uses probability distribu Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com