%0 Journal Article
%J Constructivist Foundations
%V 4
%N 3
%P 121-137
%A Kauffman, L. H.
%T Reflexivity and Eigenform: The Shape of Process
%D 2009
%U https://cepa.info/133
%X Purpose: The paper discusses the concept of a reflexive domain, an arena where the apparent objects as entities of the domain are actually processes and transformations of the domain as a whole. Human actions in the world partake of the patterns of reflexivity, and the productions of human beings, including science and mathematics, can be seen in this light. Methodology: Simple mathematical models are used to make conceptual points. Context: The paper begins with a review of the author’s previous work on eigenforms - objects as tokens for eigenbehaviors, the study of recursions and fixed points of recursions. The paper also studies eigenforms in the Boolean reflexive models of Vladimir Lefebvre. Findings: The paper gives a mathematical definition of a reflexive domain and proves that every transformation of such a domain has a fixed point. (This point of view has been taken by William Lawvere in the context of logic and category theory.) Thus eigenforms exist in reflexive domains. We discuss a related concept called a “magma.” A magma is composed entirely of its own structure-preserving transformations. Thus a magma can be regarded as a model of reflexivity and we call a magma “reflexive” if it encompasses all of its structure-preserving transformations (plus a side condition explained in the paper). We prove a fixed point theorem for reflexive magmas. We then show how magmas are related to knot theory and to an extension of set theory using knot diagrammatic topology. This work brings formalisms for self-reference into a wider arena of process algebra, combinatorics, non-standard set theory and topology. The paper then discusses how these findings are related to lambda calculus, set theory and models for self-reference. The last section of the paper is an account of a computer experiment with a variant of the Life cellular automaton of John H. Conway. In this variant, 7-Life, the recursions lead to self-sustaining processes with very long evolutionary patterns. We show how examples of novel phenomena arise in these patterns over the course of large time scales. Value: The paper provides a wider context and mathematical conceptual tools for the cybernetic study of reflexivity and circularity in systems.
%G en
%2 Second-Order Cybernetics
%5 ok
%0 Journal Article
%J Journal of Theoretical Biology
%V 372
%N
%P 179-191
%A Montévil, M.
%A Mossio, M.
%T Biological organisation as closure of constraints
%D 2015
%U https://cepa.info/3629
%X We propose a conceptual and formal characterisation of biological organisation as a closure of constraints. We first establish a distinction between two causal regimes at work in biological systems: processes, which refer to the whole set of changes occurring in non-equilibrium open thermodynamic conditions, and constraints, those entities which, while acting upon the processes, exhibit some form of conservation (symmetry) at the relevant time scales. We then argue that, in biological systems, constraints realise closure, i.e. mutual dependence such that they both depend on and contribute to maintaining each other. With this characterisation in hand, we discuss how organisational closure can provide an operational tool for marking the boundaries between interacting biological systems. We conclude by focusing on the original conception of the relationship between stability and variation which emerges from this framework. – Highlights:Biological systems realise both organisational closure and thermodynamic openness, Organisational closure is a closure of constraints, Constraints exhibit conservation (symmetry) at the relevant time scales, Closure draws the boundaries between interacting biological systems, Closure is a principle of biological stabilisation.
%G en
%5 ok
%0 Journal Article
%J Biosemiotics
%V 2
%N
%P 101-115
%A Sharov, A. A.
%T Role of utility and inference in the evolution of functional information
%D 2009
%U https://cepa.info/1005
%X Functional information means an encoded network of functions in living organisms, which is represented by two components: code and an interpretation system, which together form a self-sustaining semantic closure. The interpretation system consists of inference rules that control the correspondence between the code and the function. The utility factor operates at multiple time scales: short-term selection drives evolution towards higher survival and reproduction rates within a given fitness landscape, and long-term selection favors those inference rules that support adaptability and lead to evolutionary expansion of certain lineages. Inference rules make short-term selection possible by shaping the fitness landscape and defining possible directions of evolution, but they are under the control of the long-term selection of lineages. Communication normally occurs within a set of agents with compatible interpretation systems, which I call a “communication system” (e.g., a biological species is a genetic communication system). This view of the relation between utility and inference can resolve the conflict between realism/positivism and pragmatism. Realism overemphasizes the role of inference in evolution of human knowledge because it assumes that logic is embedded in reality. Pragmatism substitutes usefulness for truth and therefore ignores the advantage of inference. The proposed concept of evolutionary pragmatism rejects the idea that logic is embedded in reality; instead, inference rules are constructed within each communication system to represent reality, and they evolve towards higher adaptability on a long time-scale. Relevance: This paper applies pragmatism and ineractivism (Bickhard) to biological evolution. It suggests that biosemiotics rests on evolutionary pragmatism.
%G en
%5 ok
%0 Journal Article
%J Cybernetics & Human Knowing
%V 21
%N 1–2
%P 80-97
%A Steffensen, S. V.
%A Pedersen, S. B.
%T Temporal dynamics in human interaction
%D 2014
%U https://cepa.info/2396
%X Elaborating a model first presented in Uryu, Steffensen, and Kramsch (2014), the article discusses two conceptualizations of time and time scales in human interaction. One takes a starting point in a scalar hierarchy of tiered time scales and the other starts from a specification hierarchy of temporal ranges. While the time scales of the former by definition are observer-dependent, those of the latter relate the temporal dynamics of complex dialogical systems (Steffensen, 2012) to a series of causal frames, including physical, biological, social, cognitive and interactional constraints. Being the outcome of an evolutionary trajectory towards growing complexity, these constraints are the enabling conditions of human interaction, and as such they give rise to multistable dialogical systems. While this article focuses on the presentation of an ecological model of temporal ranges and time scales, its methodological implications and interpretive potentials are explored in Pedersen and Steffensen (2014).
%G en
%5 ok