Problem: The inclusion of the observer into scientific observation entails a vicious circle of having to observe the observer as dependent on observation. Second-order science has to clarify how its underlying circularity can be scientifically conceived. Method: Essayistic and conceptual analysis, sporadically illustrated with agent-based experiments. Results: Second-order science – implying science in general – is fundamentally and ineluctably circular. Implications: The circularity of second-order science asks for analytical methods able to cope with phenomena of complex causation and “synchronous asynchrony,” such as tools for analyzing non-linearly interacting dynamics, decentralized, clustered networks and in general, systems of complex interacting components.

Key words: Observer dependency, second-order science, complexity, information, intentionality

Purpose: Discusses the notion of eigenform as explicated by Heinz von Foerster wherein an object is seen to be a token for those behaviors that lend the object its apparent stability in a changing world. Design/methodology/approach – Describes von Foerster’s model for eigenforms and recursions and put this model in the context of mathematical recursions, fractals, set theory, logic, quantum mechanics, the lambda calculus of Church and Curry, and the categorical framework of fixed points of Lawvere. Findings: Determines that iterating an object upon itself is seen to be a key to understanding the nature of objects and the relationship of an observer and the apparent world of the observer. Originality/value – Contemplates the concept of recursion in the context of second-order cybernetics.

Key words: Keywords Cybernetics, Philosophical concepts, Mathematical sciences

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.

Key words: reflexive, eigenform, cybernetics, Boolean algebra, knots, magma, Russell paradox, cellular automata

This short dedication to Heinz emphasizes the notions of recursion and learning, second-order cybernetics and ethics as expressed and embodied by von Foerster. These notions act as constant clarifiers in the daily efforts of the author to design software applications or to support others as they steer their own design processes.

In this paper epistemological, ontological and sociological questions concerning the statistical significance of sharp hypotheses in scientific research are investigated within the framework provided by Cognitive Constructivism and the FBST (Full Bayesian Significance Test). The constructivist framework is contrasted with the traditional epistemological settings for orthodox Bayesian and frequentist statistics provided by Decision Theory and Falsificationism.

Key words: autopoiesis, cognitive constructivism, epistemology, ontology, scientific hypotheses, statistical significance tests, social systems, systems theory

Excerpt from the introduction: As everybody here knows, autopoiesis is a neologism, introduced in 1971 by H. Maturana and myself to designate the organization of a minimal living system. The term became emblematic of a view of the relation between an organism and its medium, where its self constituting and autonomous aspects are put at the center of the stage. From 1971, until now much has happened to reinforce this perspective. Some of the developments have to do with the notion of autopoiesis itself in relation to the cellular organization and the origin of life. Much more has to do with the autonomy and self-organizing qualities of the organism in relation with its cognitive activity. Thus in contrast to the dominant cognitivist, symbol-processing views of the 70's today we witness in cognitive science a renaissance of the concern for the embeddedness of the cognitive agent, natural or artificial. My intention rather, profiting from the position of opening this gathering, is to try to indicate some fundamental or foundational issues of the relation between autopoiesis and perception. Whence the title of my talk: a biology of intentionality. Relevance: Since the crisis of classical cognitive science has thrown open the issue of intentionality, in my eyes autopoiesis provides a natural entry into a view of intentionalty that is seminal in answering the major obstacles that have been addressed recently.