Context: The problems that are most in need of interdisciplinary collaboration are “wicked problems,” such as food crises, climate change mitigation, and sustainable development, with many relevant aspects, disagreement on what the problem is, and contradicting solutions. Such complex problems both require and challenge interdisciplinarity. Problem: The conventional methods of interdisciplinary research fall short in the case of wicked problems because they remain first-order science. Our aim is to present workable methods and research designs for doing second-order science in domains where there are many different scientific knowledges on any complex problem. Method: We synthesize and elaborate a framework for second-order science in interdisciplinary research based on a number of earlier publications, experiences from large interdisciplinary research projects, and a perspectivist theory of science. Results: The second-order polyocular framework for interdisciplinary research is characterized by five principles. Second-order science of interdisciplinary research must: 1. draw on the observations of first-order perspectives, 2. address a shared dynamical object, 3. establish a shared problem, 4. rely on first-order perspectives to see themselves as perspectives, and 5. be based on other rules than first-order research. Implications: The perspectivist insights of second-order science provide a new way of understanding interdisciplinary research that leads to new polyocular methods and research designs. It also points to more reflexive ways of dealing with scientific expertise in democratic processes. The main challenge is that this is a paradigmatic shift, which demands that the involved disciplines, at least to some degree, subscribe to a perspectivist view. Constructivist content: Our perspectivist approach to science is based on the second-order cybernetics and systems theories of von Foerster, Maruyama, Maturana & Varela, and Luhmann, coupled with embodied theories of cognition and semiotics as a general theory of meaning from von Uexküll and Peirce.

Key words: Perspectivism, semiotics, complex phenomena, social systems theory, differentiation of science, perspectival knowledge asymmetries.

Context: This conceptual paper tries to tackle the advantages and the limitations that might arise from including second-order science into global climate change sciences, a research area that traditionally focuses on first-order approaches and that is currently attracting a lot of media and public attention. Problem: The high profile of climate change research seems to provoke a certain dilemma for scientists: despite the slowly increasing realization within the sciences that our knowledge is temporary, tentative, uncertain, and far from stable, the public expectations towards science and scientific knowledge are still the opposite: that scientific results should prove to be objective, reliable, and authoritative. As a way to handle the uncertainty, scientists tend to produce “varieties of scenarios” instead of clear statements, as well as reports that articulate different scientific opinions about the causes and dynamics of change (e.g., the IPCC. This might leave the impression of vague and indecisive results. As a result, esteem for the sciences seems to be decreasing within public perception. Method: This paper applies second-order observation to climate change research in particular and the sciences in general. Results: Within most sciences, it is still quite unusual to disclose and discuss the epistemological foundations of the respective research questions, methods and ways to interpret data, as research proceeds mainly from some version of realistic epistemological positions. A shift towards self-reflexive second-order science might offer possibilities for a return to a “less polarized” scientific and public debate on climate change because it points to knowledge that is in principle tentative, uncertain and fragmented as well as to the theory- and observation-dependence of scientific work. Implications: The paper addresses the differences between first-order and second-order science as well as some challenges of science in general, which second-order science might address and disclose. Constructivist content: Second-order science used as observation praxis (second-order observation) for this specific field of research.

Key words: Second-order science, climate change research, observation theory, theory-dependency, causality, production of knowledge.

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

Within the limits of one chapter, an unconventional way of thinking can certainly not be thoroughly justified, but it can, perhaps, be presented in its most characteristic features anchored here and there in single points. There is, of course, the danger of being misunderstood. In the case of constructivism, there is the additional risk that it will be discarded at first sight because, like skepticism – with which it has a certain amount in common – it might seem too cool and critical, or simply incompatible with ordinary common sense. The proponents of an idea, as a rule, explain its nonacceptance differently than do the critics and opponents. Being myself much involved, it seems to me that the resistance met in the 18th century by Giambattista Vico, the first true constructivist, and by Silvio Ceccato and Jean Piaget in the more recent past, is not so much due to inconsistencies or gaps in their argumentation, as to the justifiable suspicion that constructivism intends to undermine too large a part of the traditional view of the world. Indeed, one need not enter very far into constructivist thought to realize that it inevitably leads to the contention that man – and man alone – is responsible for his thinking, his knowledge and, therefore, also for what he does. Today, when behaviorists are still intent on pushing all responsibility into the environment, and sociobiologists are trying to place much of it into genes, a doctrine may well seem uncomfortable if it suggests that we have no one but ourselves to thank for the world in which we appear to be living. That is precisely what constructivism intends to say – but it says a good deal more. We build that world for the most part unawares, simply because we do not know how we do it. That ignorance is quite unnecessary. Radical constructivism maintains – not unlike Kant in his Critique – that the operations by means of which we assemble our experiential world can be explored, and that an awareness of this operating (which Ceccato in Italian so nicely called consapevolezza operativa) can help us do it differently and, perhaps, better.

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

Currently the global science system undergoes an epochal transformation which can be summarized as a transition from It-Science to Bit-Science. Bit-Science as a new phase in the evolution of science brings about fundamental changes in scientific production processes, significant re-configurations in the architecture of science, new organizations of research designs and complex interaction patterns with the societal and natural environments of science. The emergence of second-order science becomes an essential component for Bit-Science as an institutionalization of reflexivity. In view of these fundamental transformations of the science system a new type of cybernetics can be developed under the name of ‘new cybernetics’ which supersedes the area of traditional cybernetics, introduced by Norbert Wiener and second-order cybernetics, constructed as a new version of cybernetics since the late 1960s with its emphasis on observing systems, goals and observers. The second part of this article explores the new cognitive horizons of new cybernetics as well as its central goals, functions and tasks.

Key words: Second-Order Science, New Cybernetics, Epistemic Modes

Context: Many recent research areas such as human cognition and quantum physics call the observer-independence of traditional science into question. Also, there is a growing need for self-reflexivity in science, i.e., a science that reflects on its own outcomes and products. Problem: We introduce the concept of second-order science that is based on the operation of re-entry. Our goal is to provide an overview of this largely unexplored science domain and of potential approaches in second-order fields. Method: We provide the necessary conceptual groundwork for explorations in second-order science, in which we discuss the differences between first- and second-order science and where we present a roadmap for second-order science. The article operates mainly with conceptual differentiations such as the separation between three seemingly identical concepts such as Science II, Science 2.0 and second-order science. Results: Compared with first-order science, the potential of second-order science lies in 1. higher levels of novelty and innovations, 2. higher levels of robustness and 3. wider integration as well as higher generality. As first-order science advances, second-order science, with re-entry as its basic operation, provides three vital functions for first-order science, namely a rich source of novelty and innovation, the necessary quality control and greater integration and generality. Implications: Second-order science should be viewed as a major expansion of traditional scientific fields and as a scientific breakthrough towards a new wave of innovative research. Constructivist content: Second-order science has strong ties with radical constructivism, which can be qualified as the most important root/origin of second-order science. Moreover, it will be argued that a new form of cybernetics is needed to cope with the new problems and challenges of second-order science.

Key words: Philosophy of science, methodology of science, first-order science, second-order science, Science 2.0, Science II, new cybernetics, second-order cybernetics, scientific novelty, re-entry

George Soros’s reflexivity theory is quite compatible with second order cybernetics. Indeed his work shows how to apply ideas in second order cybernetics to economics, finance, and political science. This paper briefly reviews three theories of reflexivity in cybernetics. It provides an introduction to Soros’s version of reflexivity theory and reviews applications in economics and finance. Soros’s approach to economics is based on different assumptions about information and about human behavior. His approach to finance is more holistic than most current work in finance. He does not emphasize mathematical models but rather sees finance as a human player game with himself as a participant. The paper concludes that Soros’s work is a very important contribution to and expansion of contemporary social science.

Key words: equilibrium theory, reflexivity theory, causal influence diagrams

This paper describes the basic features of the theories of complexity and reflexivity, their early history, their evolution, and reactions to date. Although complexity is a major change from previous modeling methods, it does not violate any informal fallacies or any assumptions underlying the philosophy of science. Reflexivity does. Accepting reflexivity as a legitimate movement in science will require an expansion of the conception of science which still prevails in most fields. A shift from Science One to Science Two is now being discussed. Relevance: The arguments refer to Ashby’s and von Foerster’s work in second-order cybernetics.