Source
McKenzie (2025), LIT-141, Emergence: from physics to biology, sociology, and computer science, arXiv v4, 187 pp., read in full in NOTE-124. NOTE-124 files the book as a hub reference and says “No THEORY follows”. Its reason is that the definition is stipulated and the characteristics’ relations are left open, not that the book shows nothing. This document states only what its counterexamples show, and is Proposed for that reason.
What was actually shown
The definition (§2.1). A property of a system of many parts, scales or iterations is emergent iff “the individual parts of the system do not have this property”. An alternative test: the property is absent when the parts’ states are assigned at random, as at high temperature (p. 11). McKenzie does not claim this definition is better than its rivals (p. 12).
The marks. Twelve further characteristics, six called objective (discontinuities, universality, diversity with limitations, modification of the parts, order, modularity) and six subjective (self-organisation, unpredictability, irreducibility, contextuality and downward causation, intra-stratum closure, complexity). The count is given as twelve in §2 and thirteen in §22.
The counterexamples.
- Novelty without discontinuity: the Kondo effect, “novelty does not necessarily imply discontinuity” (p. 58); Fermi liquids; quantum-statistics crossovers (p. 61).
- Discontinuity without novelty: the liquid–gas transition, which is adiabatically connected (p. 13).
- Novelty without unpredictability: BKT and the hexatic phase were predicted first, “unpredictability is not equivalent to novelty” (p. 65), as were spin ice and some quantum-statistics properties.
- Novelty with reduction: Butterfield’s four rigorous cases, “novelty is not sufficient for irreducibility” (§2.9, p. 20).
What could have come out otherwise. Any of the marks could have turned out to travel with novelty in every case examined. Four of them do not.
What this does not say
- That novelty is the right definition. It is stipulated. On a definition that builds in, say, unpredictability, the third counterexample is no counterexample.
- That the marks are unrelated. The book shows some non-entailments by example. It does no systematic logical analysis, and §24 leaves the relations open.
- That most physicists hold weak emergence because of this. That is the author’s impression (§22), not an argument.
- That molecular structure is evidence of strong emergence, or that it is not. §15 argues it is not, against Primas, Cartwright and Hendry, from the Born–Oppenheimer treatment and non-BO calculations. That is a separate argument, not carried here.
- That LLM emergent abilities show a phase transition. The book’s opening sentence on Wei et al. (“concrete and rigorous”) is undercut by its own later paragraph: no agreed metric, order parameter or finite-size analysis (p. 138).
Connections
- Rizi (LIT-150) takes emergence to be a many-to-one coarse-graining that stays predictive, cites this book for the mesoscale, and gives no measure that would decide the criterion. NOTE-153 files no THEORY from it, and neither does this audit.
- Information-theoretic criteria. Effective information (THEORY-222), the ΦID account (THEORY-497) and synergy bias across scales (THEORY-581) each make one mark quantitative. §14 notes that Hoel’s needs a coarse-graining fixed beforehand and that Rosas’s gives a sufficient condition only.
- Dualities (THEORY-459). The book quotes Crowther that neither side of AdS/CFT should be called emergent, the position De Haro and Butterfield develop.
- The editorial (LIT-021) sorts emergence by whether the pattern was “expected”, the unpredictability mark this document separates from novelty. NOTE-007 records that “expected” is never defined there.