Bich L. (2006) Autopoiesis and emergence. In: Minati G., Pessa E. & Abram M. (eds.) Systemics of emergence: Research and development. Springer, Berlin: 281–292. https://cepa.info/2320

Autopoietic theory is more than a mere characterization of the living, as it can be applied to a wider class of systems and involves both organizational and epistemological aspects. In this paper we assert the necessity of considering the relation between autopoiesis and emergence, focusing on the crucial importance of the observer’s activity and demonstrating that autopoietic systems can be considered intrinsically emergent processes. From the attempts to conceptualize emergence, especially Rosen’s, autopoiesis stands out for its attention to the unitary character of systems and to emergent levels, both inseparable from the observer’s operations. These aspects are the basis of Varela’s approach to multiple level relationships, considered as descriptive complementarities.

Bich L. & Damiano L. (2008) Order in the nothing: Autopoiesis and the Organizational Characterization of the Living. Electronic Journal of Theoretical Physics 4(1): 343–373. https://cepa.info/2318

An approach which has the purpose to catch what characterizes the specificity of a living system, pointing out what makes it different with respect to physical and artificial systems, needs to find a new point of view – new descriptive modalities. In particular it needs to be able to describe not only the single processes which can be observed in an organism, but what integrates them in a unitary system. In order to do so, it is necessary to consider a higher level of description which takes into consideration the relations between these processes, that is the organization rather than the structure of the system. Once on this level of analysis we can focus on an abstract relational order that does not belong to the individual components and does not show itself as a pattern, but is realized and maintained in the continuous flux of processes of transformation of the constituents. Using Tibor Ganti’s words we call it “Order in the Nothing”. In order to explain this approach we analyse the historical path that generated the distinction between organization and structure and produced its most mature theoretical expression in the autopoietic biology of Humberto Maturana and Francisco Varela. We then briefly analyse Robert Rosen’s (M, R)-Systems, a formal model conceptually built with the aim to catch the organization of living beings, and which can be considered coherent with the autopoietic theory. In conclusion we will propose some remarks on these relational descriptions, pointing out their limits and their possible developments with respect to the structural thermodynamical description.

Cárdenas M. L. C., Letelier J.-C., Gutierrez C., Cornish-Bowden A. & Soto-Andrade J. (2010) Closure to efficient causation, computability and artificial life. Journal of Theoretical Biology 263(1): 79–92. https://cepa.info/3631

The major insight in Robert Rosen’s view of a living organism as an (M, R)-system was the realization that an organism must be “closed to efficient causation”, which means that the catalysts needed for its operation must be generated internally. This aspect is not controversial, but there has been confusion and misunderstanding about the logic Rosen used to achieve this closure. In addition, his corollary that an organism is not a mechanism and cannot have simulable models has led to much argument, most of it mathematical in nature and difficult to appreciate. Here we examine some of the mathematical arguments and clarify the conditions for closure.

This paper has two primary aims. The first is to provide an introductory discussion of hyperset theory and its usefulness for modeling complex systems. The second aim is to provide a hyperset analysis of several perspectives on autonomy: Robert Rosen’s metabolism-repair systems and his claim that living things are closed to efficient cause, Maturana and Varela’s autopoietic systems, and Kauffman’s cataytically closed systems. Consequences of the hyperset models for Rosen’s claim that autonomous systems have non-computable models are discussed.

First paragraph: The interest in Jakob von Uexküll in semiotics is obvious – he was a starter and pioneer of the semiotic approach in biology in thetwentieth century. The extension of semiotics from humanities, wheresemiotics has been centered during the period of its most intensive develo-pment, to the field of biology, has taken place gradually, with the mostdecisive steps taken onlyvery recently. The conclusion of this development is most fundamental – sign systems embrace all living systems, and the roots of semiotics lie in biology. On the other hand, Uexküll’s main ideawas to build up a biology which can handle the vital processes, and whichcan include the subject, the living self; or life itself, in the sense of Robert Rosen…

Letelier J.-C., Soto-Andrade J., Guíñez Abarzúa F., Cornish-Bowden A. & Luz Cárdenas M. (2006) Organizational invariance and metabolic closure: analysis in terms of (M, R) systems. Journal of Theoretical Biology 238(4): 949–961. https://cepa.info/3628

This article analyses the work of Robert Rosen on an interpretation of metabolic networks that he called (M, R) systems. His main contribution was an attempt to prove that metabolic closure (or metabolic circularity) could be explained in purely formal terms, but his work remains very obscure and we try to clarify his line of thought. In particular, we clarify the algebraic formulation of (M, R) systems in terms of mappings and sets of mappings, which is grounded in the metaphor of metabolism as a mathematical mapping. We define Rosen’s central result as the mathematical expression in which metabolism appears as a mapping f that is the solution to a fixed-point functional equation. Crucially, our analysis reveals the nature of the mapping, and shows that to have a solution the set of admissible functions representing a metabolism must be drastically smaller than Rosen’s own analysis suggested that it needed to be. For the first time, we provide a mathematical example of an (M, R) system with organizational invariance, and we analyse a minimal (three-step) autocatalytic set in the context of (M, R) systems. In addition, by extending Rosen’s construction, we show how one might generate self-referential objects f with the remarkable property f(f)=f, where f acts in turn as function, argument and result. We conclude that Rosen’s insight, although not yet in an easily workable form, represents a valuable tool for understanding metabolic networks.

Starting from the modeling relation, as introduced by the late Robert Rosen, we propose a relational method for studying impredicative systems, which are natural systems that have models containing hierarchical cycles. The general theory of impredicative systems vastly generalizes autopoietic systems, and has implications in the biological, psychological, and social realms, from which we offer many exemplifications. The method is formulated in category theory in terms of alternate descriptions and their functorial connections.

Mossio M. & Bich L. (2014) La circularité biologique: Concepts et modèles. In: Varenne F., Silberstein M., Dutreuil S. & Huneman P. (eds.) Modéliser et simuler: Epistémologies et pratiques de la modélisation et de la simulation. Volume 2. Editions Matériologiques, Paris: 137–170. https://cepa.info/4490

This chapter offers an overview of the theoretical and philosophical tradition that, during the last two centuries, has emphasised the central role of circularities in biological phenomena. In this tradition, organisms realise a circular causal regime insofar as their existence depends on the effects of their own activity: they determine themselves. In turn, self-determination is the grounding of several biological properties and dimensions, as individuation, teleology, normativity and functionality. We show how this general idea has been theorised sometimes through concepts, sometimes through models, and sometimes through both. We analyse the main differences between the various contributions, by emphasising their strengths and weaknesses. Lastly, we conclude by mentioning some contemporary developments, as well ass some future research directions.

Mossio M., Longo G. & Stewart J. (2009) A computable expression of closure to efficient causation. Journal of Theoretical Biology 257(3): 489–498. https://cepa.info/3630

In this paper, we propose a mathematical expression of closure to efficient causation in terms of λ-calculus, we argue that this opens up the perspective of developing principled computer simulations of systems closed to efficient causation in an appropriate programming language. An important implication of our formulation is that, by exhibiting an expression in λ-calculus, which is a paradigmatic formalism for computability and programming, we show that there are no conceptual or principled problems in realizing a computer simulation or model of closure to efficient causation. We conclude with a brief discussion of the question whether closure to efficient causation captures all relevant properties of living systems. We suggest that it might not be the case, and that more complex definitions could indeed create crucial some obstacles to computability.

Poli R. (2010) The complexity of self-reference - A critical evaluation of Luhmann’s theory of social systems. Journal of Sociocybernetics 8(1–2): 1–23. https://cepa.info/450

The paper presents the basic elements of Niklas Luhmann’s theory of social systems and shows that his theories follow quite naturally from the problem of the reproduction of social systems. The subsequent feature of the self-referentiality of social systems is discussed against the theory of hierarchical loops, as developed in particular by Robert Rosen. It will be shown that Rosen’s theory is more general than Luhmann’s. The nature of anticipatory systems and the problem of conflict are used as testing grounds to verify some interesting articulations of the general theory of hierarchical loops.