Context: Second-order cybernetics and its implications have been understood within the cybernetics community for some time. These implications are important for understanding the structure of scientific endeavor, and for researchers in other fields to see the reflexive nature of scientific research. This article is about the role of context in the creation and exploration of our experience. Problem: The purpose of this article is to point out the fundamental nature of the circularity in cybernetics and in scientific work in general. (...) I give a point of view on the nature of objective knowledge by placing it in the context of reflexivity and eigenform. Method: The approach to the topic is based on logical analysis of the nature of circularity. Mathematics and cybernetics are both fundamentally concerned with the structure of distinctions, but there can be no definition of a distinction without circularity, since such a definition would itself be a distinction. The article proceeds by explicating the structure of reflexive domains D where the transformations of the domain are in one-to-one correspondence with the domain itself. Results: I show that every element of a reflexive domain has a fixed point. This means that eigenforms arise naturally in reflexive domains. Furthermore, a reflexive domain is itself an eigenform (at a higher level. This supports the context of a second-order science that would study domains of science as part of a larger cybernetic landscape. Implications: The value of the article is in its concise reformulation of the scientific endeavor as a search for eigenforms in reflexive domains. This new view of science is promising in that it includes the former worlds of apparent objectivity and it embraces those newer worlds of science where the theories and theorists become active participants in the ongoing process of creating knowledge. Constructivist content: I argue that the perspective of reflexive domains constitutes a new way to think about the practice of science, with observers deeply imbedded, and objectivity understood as the mutual search for eigenforms. (shrink)

Upshot: Eigenform is a precondition for distinction and distinction is a precondition for eigenform. While my target article discussed eigenform and reflexivity, it could just as well have discussed distinctions and the emergence of distinctions. This theme was implicit in many of the comments. We make this circularity explicit for the sake of a deeper understanding.

Open peer commentary on the article “The Circular Conditions of Second-order Science Sporadically Illustrated with Agent-based Experiments at the Roots of Observation” by Manfred Füllsack. Upshot: The aim of my commentary is to reflect on fundamental issues related to circularity, distinction and the properties of observers.

Open peer commentary on the article “Circularity and the Micro-Macro-Difference” by Manfred Füllsack. Upshot: Circularity occurs as emergent from either process or context or a combination of process and context.

Context: The question of how to understand the epistemology of set theory has been a longstanding problem in the foundations of mathematics since Cantor formulated the theory in the 19th century, and particularly since Bertrand Russell articulated his paradox in the early twentieth century. The theory of types pioneered by Russell and Whitehead was simplified by mathematicians to a single distinction between sets and classes. The question of the meaning of this distinction and its necessity still remains open. Problem: I (...) am concerned with the meaning of the set/class distinction and I wish to show that it arises naturally due to the nature of the sort of distinctions that sets create. Method: The method of the paper is to discuss first the Russell paradox and the arguments of Cantor that preceded it. Then we point out that the Russell set of all sets that are not members of themselves can be replaced by the Russell operator R, which is applied to a set S to form R(S), the set of all sets in S that are not members of themselves. Results: The key point about R(S) is that it is well-defined in terms of S, and R(S) cannot be a member of S. Thus any set, even the simplest one, is incomplete. This provides the solution to the problem that I have posed. It shows that the distinction between sets and classes is natural and necessary. Implications: While we have shown that the distinction between sets and classes is natural and necessary, this can only be the beginning from the point of view of epistemology. It is we who will create further distinctions. And it is up to us to maintain these distinctions, or to allow them to coalesce. Constructivist content: I argue in favor of a constructivist perspective for set theory, mathematics, and the way these structures fit into our natural language and constructed speech and worlds. That is the point of this paper. It is only in the reach for absolutes, ignoring the fact that we are the authors of these structures, that the paradoxes arise. (shrink)

We propose a framework for analyzing the development, operation and failure to survive of all things, living, non-living or organized groupings. This framework is a sequence of developments that improve survival capability. Framework processes range from origination of any entity/system, to the development of increased survival capability and development of life-forms and organizations that use intelligence. This work deals with a series of developmental changes that arise from the uncovering of emergent properties. The framework is intended to be general, but (...) we see a potential to apply it to scientific topics such as the exploration of the origin of life or the search for life beyond Earth, and to understand some biological issues in evolution and symbiosis, and also to apply to social systems that do not seem to be operating well, to determine their problems and correct them. (shrink)

Justice (Philosophy); history; 20th century.

Currently living people cannot be said to be wronged because of the wrongless emissons of greenhouse gases by past people. According to the usual subjunctive-historical understanding of harm, currently living people cannot be said to be harmed by the impact of greenhouse emissions on their well-being. By relying on a subjunctive-threshold notion of harm we can justify conclusions about both the present generation’s duties not to violate the rights of future generations, and the present generation’s duties to compensate currently living (...) people for the harms inflicted upon them through the lasting impact of wrongless past harms. This interpretation supports a forward-looking understanding of the grounds of our relating to wrongless past harms. The significance of past harms lies in their consequences for the well-being of currently living and future people. The subjunctive-threshold notion of harm lends support to a standard of minimal, general, and universal justice. Those actors who are in a position to fulfill its requirements are under a duty to do so. Especially the rich and powerful countries ought to counteract the harmful impact of past greenhouse emissions. (shrink)

Here, an epidemiological model considering pro and anti-vaccination groups is proposed and analyzed. In this model, susceptible individuals can migrate between these two groups due to the influence of false and true news about safety and efficacy of vaccines. From this model, written as a set of three ordinary differential equations, analytical expressions for the disease-free steady state, the endemic steady state, and the basic reproduction number are derived. It is analytically shown that low vaccination rate and no influx to (...) the pro-vaccination group have similar impacts on the long-term amount of infected individuals. Numerical simulations are performed with parameter values of the COVID-19 pandemic to illustrate the analytical results. The possible relevance of this work is discussed from a public health perspective. (shrink)

The relationship between the United Kingdom and the United States seems to embody most fully the type of the ‘special relationship’ today. It is a relationship founded ultimately on biological kinship, structured by mutual economic and strategic interests and cemented by a sense of political and ‘spiritual’ affinity. At least the broad contours of such contemporary ‘special relationships’ are sufficiently clear. This is far from being the case with those of the Archaic and Classical Greek world, for two main reasons. (...) First, and more decisively, our sources for the history of that world – literary, epigraphical, archaeological – are normally scrappy, discontinuous and variously slanted. Second, and only in part because of the nature of the evidence, the workings of all ancient Greek interstate relationships, whether ‘special’ or not, are in principle controversial. For in the absence of governments and parties in the modern sense it is frequently impossible to explain confidently a particular foreign policy decision taken by a Greek state. A fortiori it is in principle even more difficult to describe and account for ‘special’ relationships between states that apparently transcended purely immediate, local and narrowly self-interested considerations. (shrink)