•  54
    A framework linking non-living and living systems: Classification of persistence, survival and evolution transitions (review)
    with L. Dennis, R. W. Gray, J. Brender McNair, and N. J. Woolf
    Foundations of Science 14 (3): 217-238. 2009.
    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…Read more
  •  30
    The Physics of Reality: Space, Time, Matter, Cosmos (edited book)
    with Richard L. Amoroso and Peter Rowlands
    World Scientific Publishers. 2013.
    A truly Galilean-class volume, this book introduces a new method in theory formation, completing the tools of epistemology. It covers a broad spectrum of theoretical and mathematical physics by researchers from over 20 nations from four continents. Like Vigier himself, the Vigier symposia are noted for addressing avant-garde, cutting-edge topics in contemporary physics. Among the six proceedings honoring J.-P. Vigier, this is perhaps the most exciting one as several important breakthroughs are i…Read more
  •  27
    Reflexivity and Eigenform: The Shape of Process
    Constructivist Foundations 4 (3): 121-137. 2009.
    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 previou…Read more
  •  26
    The Russell Operator
    Constructivist Foundations 7 (2): 112-115. 2012.
    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 stil…Read more
  •  22
    Mathematical Work of Francisco Varela
    Constructivist Foundations 13 (1): 11-17. 2017.
    This target article explicates mathematical themes in the work of Varela that remain of current interest in present-day second-order cybernetics. Problem: Varela’s approach extended biological autonomy to mathematical models of autonomy using reflexivity, category theory and eigenform. I will show specific ways that this mathematical modeling can contribute further to both biology and cybernetics. Method: The method of this article is to use elementary mathematics based in distinctions to consis…Read more
  •  19
    Cybernetics, Reflexivity and Second-Order Science
    Constructivist Foundations 11 (3): 489-497. 2016.
    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 cybernet…Read more
  •  18
    Eigenform and Reflexivity
    Constructivist Foundations 12 (3): 246-252. 2017.
    Purpose: I introduce the concept of eigenform in the context of second-order cybernetics and discuss eigenform and eigenbehavior in the context of reflexivity. The point of eigenform is that it is a concept arising along with the observer at the point where the observer and the observed are apparently the same and yet apparently different. It is this nexus of the observer and the observed that is central to second-order cybernetics. Method: The article is designed as a formal introduction with e…Read more
  •  14
    Author's Response: Self-Reference and the Self
    Constructivist Foundations 13 (1): 28-30. 2017.
    In this response, I revisit the themes of my article on the mathematical work of Varela and I attempt to clarify the linguistic and human meanings of the terms “self-reference” and “self.”
  •  13
    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.
  •  12
    Eigenform Encoding and Spacetime (review)
    Constructivist Foundations 12 (3): 279-280. 2017.
    An eigenform is both a symbol for a process and the instantiation of a process itself. As such, eigenform provides a new entry to spacetime, as a unification of entity, place and process.
  •  12
    Many Forms of Circularity
    Constructivist Foundations 12 (1): 24-25. 2016.
    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.
  •  7
    Author's Response: Eigenform, Action, the Continuous and the Discrete
    Constructivist Foundations 12 (3): 260-264. 2017.
    I discuss the epistemology of action and its relation to the continuous and the discrete, relative to eigenform, eigenbehavior and the deeper structure of eigenforms in relation to the construction of our personal and apparently objective worlds.
  •  3
    Circularity and Distinction
    Constructivist Foundations 10 (1): 55-56. 2014.
    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
  •  3
    What Lies Beyond Language?
    Constructivist Foundations 15 (3): 282-283. 2020.
    Gasparyan shows the relationship of eigenform with semiosis. In agreement with her, I discuss these ideas from my own viewpoint.
  • This special double issue of _Cybernetics and Human Knowing_ is comprised of a collection of papers devoted to the cybernetics and mathematics of Charles Sanders Peirce with a special focus on its synergies with George Spencer-Brown's thinking. Peirce was a truly original American philosopher and logician working in the late 1800s and early 1900s; Spencer-Brown is an English polymath, best known as the author of _Laws of Form_. The contributions reflect the extraordinary richness of Peirce's wor…Read more