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.
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 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.
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.
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.
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.