Introduction. Relational biology, founded by Nicolas Rashevsky and developed by Robert Rosen, asks what organisation a system must have to be alive, abstracting from the material it is made of. Rosen’s answer is the (M,R)-system: a metabolism component that converts inputs to outputs, and a repair component that regenerates the metabolism, arranged so that every efficient cause of a component is itself produced within the system — “closure to efficient causation.” Life Itself (1991) formalises this in category theory and argues that such systems have no largest model and are therefore not simulable by a Turing machine; that non-computability claim has published category-theoretic objections and should be treated as a live argument. Anticipatory Systems (1985) adds a second idea: an anticipatory system contains a predictive model of itself and its environment and changes its present state in accordance with the model’s predictions, which distinguishes it from a reactive feedback controller. Underlying both is the modelling relation: a formal system models a natural one only when an encoding map from natural to formal, a decoding map back, and the inferential rules of the formal system together commute — the same result is obtained whichever way round the diagram one goes.
Important authors. Robert Rosen (1934–1998) studied under Rashevsky at Chicago, worked at the Center for Theoretical Biology at SUNY Buffalo, and was professor of biophysics at Dalhousie University from 1975. A. H. Louie, his student, continued the mathematical programme. Matteo Mossio and Alvaro Moreno (IHPST Paris; University of the Basque Country) lead the philosophical line on organisational closure that descends from Rosen and from autopoiesis. Roberto Poli (Trento) built the field of anticipation studies on the 1985 book.
Importance for cybernetics and the VSM. Rosen worked in critical dialogue with cybernetics rather than within it, and does not engage Beer. Two imports. Anticipation is System Four stated more precisely than Beer stated it — an internal model of self and environment driving present action — with a formal apparatus attached. And (M,R)-systems give a minimal viability set derived rather than surveyed: metabolism plus repair with closure, which the §3.3 table places beside Beer’s five. The modelling relation is the deeper contribution: it converts “is the VSM a description or a claim about the world” from a philosophical grumble into a technical requirement, and the VSM has never specified either map.
Importance for the article. §2.2 uses the modelling relation as the technical form of the instrumental/constitutive distinction: a claim that a formal system models a natural one requires specified encoding and decoding maps and a check that the diagram commutes, and “the VSM has never specified either map.” §3.3 places (M,R)-systems in the rival-set table and notes anticipatory systems as the sharper System Four. Both come from Applying new lenses (C5 §III), and both are Tier C, marked † in v02. A reviewer will press on three things: whether the paper has read Rosen or is citing the critique’s summary (read him before deposit); whether the non-computability claim is being leaned on (it is not, and §3.3 should say so); and whether the modelling relation is a standard the VSM could meet at all, since Rosen’s encoding maps presuppose measurable observables. The answer is that Demonstration IV’s formal specification (§9, IVa) is the encoding map being written for the first time, and that the demand is the one §2.3 already makes: outcome-independent indicators of function.
Sources in the reading list.
- the chapter on the modelling relation and the definition of an anticipatory system; the 2012 reissue has useful commentary.
- the (M,R)-system and closure to efficient causation; the non-computability argument to be cited only as contested.
Other important sources and authors.
- Rosen, R. (1958). A relational theory of biological systems. Bulletin of Mathematical Biophysics, 20, 245–260 — the first (M,R)-system paper.
- Rosen, R. (2000). Essays on Life Itself. Columbia University Press — the accessible restatements and replies to critics.
- Louie, A. H. (2009). More Than Life Itself: A Synthetic Continuation in Relational Biology. Ontos Verlag — the mathematical continuation by Rosen’s student.
- Chu, D., & Ho, W. K. (2006). A category theoretical argument against the possibility of artificial life: Robert Rosen’s central proof revisited. Artificial Life, 12(1), 117–134 — the principal published objection to the non-computability proof.
- Mossio, M., & Moreno, A. (2010). Organisational closure in biological organisms. History and Philosophy of the Life Sciences, 32(2–3), 269–288 — the current philosophical treatment of closure, linking Rosen to autopoiesis (T1.7).
- Poli, R. (2010). The many aspects of anticipation. Foresight, 12(3), 7–17 — anticipation as a field, and where Rosen’s definition sits in it.