The idea behind this special theme journal issue was to continue the work we have started with the INBIOSA initiative (www.inbiosa.eu) and our small inter-disciplinary scientific community. The result of this EU funded project was a white paper (Simeonov et al., 2012a) defining a new direction for future research in theoretical biology we called Integral Biomathics and a volume (Simeonov et al., 2012b) with contributions from two workshops and our first international conference in this field in 2011. The initial impulse (...) for this effort was given a year earlier by a publication of one of the guest editors of this issue (Simeonov, 2010) in this journal. This time we wish to provide a broader forum and more space to elaborate in detail some of the most interesting concepts we have encountered in our discussions, as well as to invite some new contributions of particular interest in the field. Another goal we had in mind was to collect and review as many provocative perspectives as possible on the same key topic we are interested before making a decision to follow a more focused notion that would lead to a funded research program. Therefore we welcomed the generous suggestion of Professor Denis Noble, FRS, who is also editor of this journal to prepare a special theme issue entitled: “Can biology create a profoundly new mathematics and computation?” It has taken a while to invite and collect the contributions. Most of them had a couple of revision cycles and adjustments after having been thoroughly discussed with colleagues, incl. the editors of this issue. We think that the result we have obtained at the end is a satisfactory one, since we succeeded to integrate a diversity of original, but sometimes controversial and mutually excluding concepts organized within chapters of a self-contained volume. The task of compiling all this was not easy at all. Despite our efforts to position the articles of different authors and themes in a way allowing their easy comprehension and relation to each other within the individual chapters, some of them still require a sort of introduction to dissolve possible ambiguities. This is what we are going to do in the following few paragraphs with the hope that the reader (and some of the authors) would excuse our failures. (shrink)

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. (shrink)

In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to (...) the commutator of the True and False operators of matrix logic, still with a quantum superposed state related to a Moebius surface, and as the physical field at the basis of Spencer-Brown’s primitive distinction in the protologic of the calculus of distinction. In this setting, paradox, self-reference, depth, time and space, higher-order non-dual logic, perception, spin and a time operator, the Klein bottle, hypernumbers due to Musès which include non-trivial square roots of ±1 and in particular non-trivial nilpotents, quantum field operators, the transformation of cognition to spin for two-state quantum systems, are found to be keenly interwoven in a world conception compatible with the philosophical approach taken for basis of this article. The Klein bottle is found not only to be the topological in-formation for self-reference and paradox whose logical counterpart in the calculus of indications are the paradoxical imaginary time waves, but also a classical-quantum transformer (Hadamard’s gate in quantum computation) which is indispensable to be able to obtain a complete multivalued logical system, and still to generate the matrix extension of classical connective Boolean logic. We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation, generates the matrix logic which supersedes the classical logic of connectives and which has for particular subtheories fuzzy and quantum logics. Thus, from a primitive distinction in the vacuum plane and the axioms of the calculus of distinction, we can derive by incorporating paradox, the world conception succinctly described above. (shrink)

In previous works we have established that the spacetime probabilistic organization of the quantum theory is determined by the spacetime characteristics of the operations by which the observer produces the objects to be studied (“states” of microsystems) and obtains qualifications of these. Guided by this first conclusion, we have then built a “general syntax of relativized conceptualization” where any description is explicitly and systematically referred to the two basic epistemic operations by which the conceptor introduces the object to be qualified (...) and then obtains qualifications of it. Inside this syntax there emerges a general typology of the relativized descriptions. Here we show that with respect to this typology the type of the predictive quantum mechanical descriptions acquires a precise definition. It appears that the quantum mechanical formalism has captured and has expressed directly in a mathematical language the most complex form in which can occur a first descriptional phase that lies universally at the bottom of any chain of conceptualization. The main features of the Hilbert-Dirac algorithms are decoded in terms of the general syntax of relativized conceptualization. This renders explicit the semantical contents of the quantum mechanical representations relating each one of these to its mathematical quantum mechanical expression. Basic insufficiencies are thus identified and, correlatively, false problems as well as answers to these, or guides toward answers. Globally the results obtained provide a basis for future attempts at a general mathematical representation of the processes of conceptualization. “Il pourrait, en effet, être dangereux pour l'avenir de la Physique qu'elle se contente trop facilement de purs formalismes, d'images floues et d'explications toutes verbales s'exprimant par des mots à signification imprécise”—Louis de Broglie,Certitudes et Incertitudes de la Science (Albin Michel, Paris, 1965). (shrink)

Here I examine Bernard Suits’s definition of games and explain why that definition is in need of reference to representation or, put more generally, to semiosis. And, once admitting the necessity of the representational in games, Suits’s definition must also then admit the essential paradoxy of games.

Intentionality is a mark of the mental, as Brentano (1874) noted. Any representation or conception of anything has the feature of intentionality, which informally put, is the feature of being about something that may or may not exist. Visual artworks are about something, whether something literal or abstract. The artwork is a mentalized physical object. Aesthetic experience of the artwork illustrates the nature of intentionality as we focus attention on the phenomenology of the sensory exemplar. This focus of attention on (...) the exemplar in aesthetic experience simultaneously exhibits what the intentional object is like and what our conception of it is like. The exemplar is Janus-faced, looking in one direction outward toward the objects conceived and in the other direction inward toward our conceiving of them. It shows us what intentionality is like and how we know it. (shrink)

A theory of syllogistic reasoning is proposed, derived from the medieval doctrine of 'distribution of terms'. This doctrine may or may not furnish an adequate ground for the logic of the syllogism but does appear to illuminate the psychological processes involved. Syllogistic thinking is shown to have its origins in the approach and avoidance behaviour of pre-verbal organisms and, in verbal (human) organisms, to bridge the gap between the intuitive grasp shown by most of us of the validity of simple (...) logical arguments and the failure of intuition in more complex arguments that require resort to calculation. Some difficulties are considered affecting the use of syllogisms as experimental material. These include failure on the part of the investigator to take account of the fact that a syllogism is always part of a continuing argument in which the topic of the argument is known to all parties and the possibility that subjects may find ways of appearing to solve syllogisms without actually doing so. (shrink)

We are concerned with two modes of describing the dynamics of natural systems. Global descriptions require simultaneous global coordination of all dynamical operations. Global dynamics, including mechanics, remain invariant in the absence of external perturbation. But, failing impossible global coordination, dynamical operations could actually become coordinated only locally. In local records, as in global ones, the law of the excluded middle would be strictly observed, but without global coordination it could only be fullfilled sequentially by passing causative factors forward onto (...) subsequent contiguous operations.The local dynamics of sequential operations would be indefinite with regard to how commitments will be made which will avoid violating the law of the excluded middle, but any resulting record will be as definite as if there had been global coordination. While maintaining an agential capacity for making contingent choices internally, local dynamics could be cumulated into a global record of seemingly simultaneous operations. Natural selection within a framework of local dynamics would have a capacity for making opportunistic commitments, but its effects in a posterior record can be reduced to the mechanistic neodarwinian version as if there had been a global dynamics. However, the resulting global description falsifies the actual material nature of the dynamics. (shrink)

With reference to Mead, Peirce, speech act theory, conversation analysis, and Luhmann's phenomenological grounded version of systems theory, the paper tries to reconstruct actions as products of communication. A triadic sequence is identified as the elementary unit for the intersubjective constitution of an act. This unit combines three achievements: (a) the constitution of meaning by sequential attribution, (b) the intersubjective coordination of attributed meanings, and (c) the reproduction of rules, guiding the process of constitution and coordination of attributed meanings. Then, (...) using the tools of systems theory and applying them to empirical results of ethnomethodology and conversation analysis, it is shown how the rule scheme is integrated in a triadic sequence, functioning on three different levels of communication. Finally, a specific form of repair after next turn is discussed, relating it to the function of preserving the structure of conversational types. The analysis of such conversational types opens a possible realm of cooperation between conversation analysis and Luhmann's version of systems theory. (shrink)

This article proposes complementing actor-network theory (ANT) with Niklas Luhmann’s communication theory, in order to overcome one of ANT’s major shortcomings, namely, the lack of a conceptual repertoire to describe virtual processes such as sense-making. A highly problematic consequence of ANT’s actualism is that it cannot explain the differentiation of economic, legal, scientific, touristic, religious, medical, artistic, political and other qualities of actual entities, assemblages and relationships. By recasting Luhmann’s theory of functionally differentiated communication forms and sense-making as dealing with (...) different types of virtual attractors calling for actualizations in concrete assemblages, I propose a symmetrical understanding of societal differentiation processes as based on the co-production of virtual attractors and actual assemblages. (shrink)

The background of the article is Marxism's lack of a notion of management. The article suggests that anyone rethinking capitalism should pause for a moment to check on the evidence for such a notion. It seems necessary because today's theory of capitalism can no longer be content with a structural theory of the conflict between capital and labour, but must integrate a poststructural, or operational, theory of how capitalism is sustained on a day-to-day basis by organized projects in networks. The (...) article develops a notion of `management by strata', which is matched to the traditional role of hierarchies, and a notion of `management by ties', which is tuned to the newly discovered role of hierarchies in networks. The method used in the article is a theoretical study based on the sociological theories of social systems and networks. (shrink)

The article inquires into the uneasiness of sociological systems theory about culture. Culture alternatively is called the solution to the problem of double contingency (Parsons) and removed from this solution (Luhmann). It is shown that meaning is the more basic term whose description reveals a form rule of social systems which is only patterned, yet not understood by culture. Culture is a memory and control device of society. It may be conceived of as providing the distinction of correct versus incorrect (...) behaviour. But who decides on the correctness or incorrectness of this distinction? Sociological thinking takes off where the cultural and the social are distinguished. (shrink)

In accordance with the contemporary state of the natural sciences, Wolfgang Sohst here presents an extended ontological model where the process is the first cosmological category, not objects. Her starts with very few primordial categories of becoming that even precede the fundamental concepts of physics and mathematics. Since Democritus, ie. for about 2,400 years, all cultures of European descent rest mainly on the presupposition that substances and their properties provide the inventory of our world. This, however, contradicts the formerly and (...) still today lively intuition (intellectually up to Heraclitus, again in Aristotle and only then resurgent with Hegel) that objects are not the dominating aspect of what we are living in. Rather, the basis of our cosmos is a world process as the result of the complementary relationship of particular objects and their mutual efficiencies. (shrink)

The context of an operational description is given by the distinction between what we consider as relevant and what as irrelevant for a particular experiment or observation. A rigorous description of a context in terms of a mathematically formulated context-independent fundamental theory is possible by the restriction of the domain of the basic theory and the introduction of a new coarser topology. Such a new topology is never given by first principles, but depends in a crucial way on the abstractions (...) made by the cognitive apparatus or the pattern recognition devices used by the experimentalist. A consistent mathematical formulation of a higher-level theory requires the closure of the restriction of the basic theory in the new contextual topology. The validity domain of the so constructed higher-level theory intersects nontrivially with the validity domain of the basic theory: neither domain is contained in the other. Therefore, higher-level theories cannot be totally ordered and theory reduction is not transitive. The emergence of qualitatively new properties is a necessary consequence of such a formulation of theory reduction (which does not correspond to the traditional one). Emergent properties are not manifest on the level of the basic theory, but they can be derived rigorously by imposing new, contextually selected topologies upon context-independent first principles. Most intertheoretical relations are mathematically describable as singular asymptotic expansions which do not converge in the topology of the primary theory, or by choosing one of the infinitely many possible, physically inequivalent representations of the primary theory (Gelfand–Naimark–Segal-construction of algebraic quantum mechanics). As examples we discuss the emergence of shadows, inductors, capacitors and resistors from Maxwell’s electrodynamics, the emergence of order parameters in statistical mechanics, the emergence of mass as a classical observable in Galilei-relativistic theories, the emergence of the shape of molecules in quantum mechanics, the emergence of temperature and other classical observables in algebraic quantum mechanics. (shrink)

The reflexive character of enactive theory is spelled out, in an effort to make explicit that which is usually implicit in debate: that we are responsible for the distinctions we draw, and that ultimately, the world that we collectively characterize is a joint production. Enaction, as treated here, is not a positivist scientific field, but an epistemologically self-conscious way to ground our understanding of the value-saturated lives of embodied beings. This stance is seen as entirely congruent with the scientific field (...) of ecological psychology, which is itself then cast as a specific example of the kind of science that can be done in an enactive mode. (shrink)

Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...) be crucial, and show how one may provide responses to Maddy's concerns based on a careful analysis of 'multiverse practice'. (shrink)

G. F. Stout is famous as an early twentieth century proselyte for abstract particulars, or tropes as they are now often called. He advanced his version of trope theory to avoid the excesses of nominalism on the one hand and realism on the other. But his arguments for tropes have been widely misconceived as metaphysical, e.g. by Armstrong. In this paper, I argue that Stout’s fundamental arguments for tropes were ideological and epistemological rather than metaphysical. He moulded his scheme to (...) fit what is actually given to us in perception, arguing that our epistemic practices would break down in an environment where only universals were given to us. (shrink)

El concepto de memoria social es una de las categorías que más relevancia adquirió en la producción teórica de Niklas Luhmann en los últimos años de su vida. Tal concepto se encuentra, en una buena parte, inspirado en la memory fuction descripta por el matemático inglés George Spencer Brown. La memoria social pretende dar cuenta de un rendimiento de memoria propio de la sociedad, independiente de las memorias de los sistemas psíquicos y neurofisiológicos. En este trabajo se abordará el tema (...) críticamente, poniendo atención en la operatividad de la memoria social, para poder observar a qué preguntas responde. Además, se analizará detenidamente el tipo de apropiación que hace Luhmann de la función de oscilador y memoria tomada de Spencer Brown, evaluando la consistencia de tal decisión. También será de suma importancia estimar si el sociólogo alemán arriba a una teoría de la memoria social capaz de desprenderse de la metáfora del almacén o depósito, tal como él dice haberlo hecho al proponer esta formulación.The concept of social memory is between those categories, which acquired more relevance in Niklas Luhmann’s theoretic production in the last years of his life. This concept is largely inspired in the memory function depicted by the English mathematician George Spencer Brown. Social memory tries to account for the own memory performance of society, which is independent from the memories of the psychic and neurophysiologic systems. This paper deals critically with this topic, focusing the attention on the operativity of the social memory, in order to observe to which questions it can answer. In addition, it will be carefully analyzed how Luhmann utilizes the Spencer Brown’s oscillator and memory functions, so to evaluate the consistency of Luhmann’s decision to include these concepts in his theory. It will also be of great importance to estimate if the German sociologist develops a theory of social memory with the capacity to get rid of the storage metaphor, as he expected to have done with this formulation. (shrink)

Abstract This essay explores what it means to be human in an age of infomedia. Appropriating Niklas Luhmann's systems theory/media theory in dialogue with other resources, I propose a post-Luhmannian paradigm of (1) extended media/meaning that conceives the world as world multimedia systems processing variegated meanings, and (2) an embodied, contextualized soft posthumanist anthropology that conceives the human as emergent collective phenomena of distinct meaning making by body-mind-society-technology media couplings. I argue: (1) Homo sapiens is Homo medialis distinct with mediatic (...) communication that emerged to cope with contingencies. (2) Evolution is the mediatization/codification of the world that culminated with the outcome of Homo medialis uniquely equipped to process transcendent meanings and to mediatize the world via diverse media—Mediatized Co-Mediatizer or Codified Co-Codifier. (3) This anthropic universe is possibly the most “meaningful” (full of meaning possibilities) of all possible worlds. (4) Social fragmentation could be an optimization; science-and-religion is an infomedium optimizing religion's manifest and science’ latent observation of divine manifestations. (shrink)

Problem: Is constructivism contradicted by the reductionist determinism inherent in digital computation? Method: Review of examples from dynamical systems sciences, agent-based modeling and artificial intelligence. Results: Recent scientific insights seem to give reason to consider constructivism in line with what computation is adding to our knowledge of interacting dynamics and the functioning of our brains. Implications: Constructivism is not necessarily contradictory to digital computation, in particular to computer-based modeling and simulation. Constructivist content: When viewed through the lens of computation, in (...) many of its aspects constructivism seems in line with what currently is held to be valid in science. (shrink)

We present a category-theoretical analysis, based on the concept of generic figures, of a diagrammatic system for propositional logic ). The straightforward construction of a presheaf category \ of cuts-only Existential Graphs provides a basis for the further construction of the category \ which introduces variables in a reconstructedly generic, or label-free, mode. Morphisms in these categories represent syntactical embeddings or, equivalently but dually, extensions. Through the example of Peirce’s system, it is shown how the generic figures approach facilitates the (...) formal investigation of relations between syntax and semantics in such diagrammatic systems. (shrink)

The standard theory of languages has two levels, one centering on the study, teaching, and application of natural languages, and the other on formal languages and formal systems as applied throughout the mathematical and empirical sciences, in analytic philosophy, and for computer programming, software engineering, artificial intelligence, and related technologies. On both of these levels, standard language theory is dualistic, defining languages in isolation from their domains of discourse and treating attributes in isolation from their objective instances while omitting important (...) properties and functions ordinarily provided or executed by language users, automata, or physical systems on which they appear to supervene. This decoupling of languages from their universes, and from necessary linguistic functions such as display, processing, interpretation, and communication, has profound epistemological bearing, limiting scientific knowledge by precluding the linguistic formulation of any verifiable comprehensive description of reality. This paper proposes that in addition to the two existing levels of standard language theory involving natural and formal languages and systems, the theory of language be recognized to possess a third "metaformal" level on which languages and their universes are "wrapped" in a uniquely structured, totally self-contained metalanguage, the Metaformal System, which restores missing linguistic functionality while using a supertautological intelligibility criterion to generically couple languages with their universes on a fundamental level of shared structure and dynamics, thereby restoring the potential for a verifiable comprehensive and fully connected understanding of the reality we share. (shrink)

In March 2016, an interdisciplinary group met for two days and two evenings to explore the implications for policy making of second-order science. The event was sponsored by SITRA, the Finnish Parliament's Innovation Fund. Their interest arose from their concern that the well-established ways, including evidence-based approaches, of policy and decision making used in government were increasingly falling short of the complexity, uncertainty, and urgency of needed decision making. There was no assumption that second-order science or second-order cybernetics would reveal (...) any practical possibilities at this early stage of enquiry. On the other hand, some members of the group are practioners in both policy and in facilitating change in sectors of society. Thus, the intellectual concepts were strongly grounded in experience. This is an account of the deliberations of that group and some reflections on what came out of the various shared contributions and ensuing dialogues. The overall conclusion of the event is that there definitely are possibilities that are worthy of further research and exploration. (shrink)

Nothing seems more possible to me than that people some day will come to the definite opinion that there is no copy in the… nervous system which corresponds to a particular thought, or a particular idea, or, memory.WittgensteinIn a recent essay it was emphasized that brain and mind appear to the mind as complementary and reciprocally recursive domains of a hermeneutic circle (Fischer, 1987). An outstanding and not yet recognized feature of this hermeneutic circle is that interpretation within this circle (...) is not rule-governed and hence appears self-organized: individual features of the world (or the brain) become intelligible in terms of the whole context (of the mind)… while the entire context becomes intelligible through individual features (or brain functions). How, or from where then is significance arising? (shrink)

Current conceptions of the integration of computers into society often depend on the view that the human mind, as well as the computer, is a computational system. This view is widely taken to have broad implications for educational policy. We present a critique of the premise and some of the conclusions of the above argument. It is here shown that the thesis that the human mind is a computational system is, in principle, not scientifically supportable. It is also shown that, (...) even if the computational theory of mind were held for non-scientific reasons, the educational implications often derived from it do not follow. (shrink)

Discussions about the appropriate way of assessing and managing new or emerging technologies—like nanomaterials—expose the problematic relationship between scientific knowledge production and regulatory decision-making. On one hand, there is a strong demand for scientific expertise to support decisions, especially by analyzing risks and hazards when uncertainties are prevalent and society’s stakes are high. On the other hand, science is criticized for its authoritative claim to objectivity and for keeping the inherent uncertainty, ambiguity, and selectivity of scientific observation latent. Requests for (...) more transparency in science can lead to revealing, to risk managers and the public, the indeterminacy in knowledge production processes. This has consequences for the prevalence of scientific knowledge in decision-making, because it increases uncertainty on both sides of the breach between science and decisions: scientists lose confidence regarding the scientifically tested knowledge which they pass on, and risk managers lose confidence regarding their decisions based on this knowledge. Nonetheless, the concept of “probabilistic risk assessment” remains an important heuristic for dealing with potential future events. This paper addresses questions of the function of scientific risk assessment in organized risk management. The main argument in this paper is that knowledge alone no longer functions as a mechanism for absorbing uncertainty. Accordingly, the interaction between science and decisions must enable a temporarily stable commitment to manage new threats like products and applications coming from the field of nanoscience and nanomaterials. (shrink)

A high level of complexity and a continuous and always changing relationship among its elements characterizes modern world society. As a result, a constant differentiation and specialization of diverging social fields aiming to reduce the uncertainty emerging from that complexity takes place. Paradoxically, as differentiation and specialization increase, they become a new source of uncertainty. In order to confront this self-producing ambiguity, some social operations develop structural interdependencies with a sufficient level of operational stability that distinguish them from their environment. (...) In this paper this is called contextual differentiation, i.e. the emergence of differentiated contexts of interaction, decision and symbolization that make possible a mutilayered concretization of social functions in supranational contexts. With regard to the differentiation of law, economy and sports this process is analyzed and illustrated in four case studies: the Bill & Melinda Gates Foundation, the Bank for International Settlements, FIFA, the game and its publics, and the international commercial arbitration. La sociedad mundial moderna se caracteriza por su alta complejidad, es decir, por la continuamente cambiante interrelación de sus elementos. El resultado de ello es una constante diferenciación y especialización de espacios sociales orientada a manejar la incertidumbre que esa complejidad genera. Paradójicamente, la diferenciación y especialización es nuevamente una fuente de complejidad. Para enfrentar esta ambigüedad auto-producida, determinadas operaciones sociales se distinguen por generar interdependencias estructurales que logran una estabilidad operacional suficiente para distinguirlas de su entorno. A ello se le denomina en este artículo diferenciación contextual, esto es, la emergencia de contextos diferenciados de interacción, decisión y simbolización que posibilitan una concretización múltiple de funciones sociales en espacios supranacionales. Esto se observa especialmente a propósito de la diferenciación del derecho, la economía y el deporte, y se ilustra con cuatro estudios de caso: la Bill & Melinda Gates Foundation, el Bank for International Settlements, la FIFA, el juego y sus públicos, y el arbitraje comercial internacional. (shrink)

With an aim to develop a public theology for an age of information media (or media theology), this article proposes a new God-concept: God is a communicative system sui generis that autopoietically processes meaning/information in the supratemporal realm via perfect divine media ad intra (Word/Spirit). For this task, Niklas Luhmann's systems theory is critically appropriated in dialogue with theology. First, my working postmetaphysical/epistemological stance is articulated as realistic operational constructivism and functionalism. Second, a series of arguments are advanced to substantiate (...) the thesis: (1) God is an observing system sui generis ; (2) self-referential communication is divine operation; (3) unsurpassable complexity is divine mystery; (4) supratemporal autopoiesis of meaning is divine processing; (5) agape is the symbolic medium of divine communication. Third, this communicative model of God is developed into a trinitarian theology, with a claim that this model offers a viable alternative beyond the standard (psychic, social, process) models. Finally, some implications of this model are explored for constructive theology (conceiving creation as divine mediatization) and for science-and-religion in terms of derivative models: (1) God as a living system sui generis and (2) God as a meaning system sui generis. (shrink)

In this article an epistemological framework is proposed in order to integrate the emergentist thought with systemic studies on biological autonomy, which are focused on the role of organization. Particular attention will be paid to the role of the observer’s activity, especially: (a) the different operations he performs in order to identify the pertinent elements at each descriptive level, and (b) the relationships between the different models he builds from them. According to the approach sustained here, organization will be considered (...) as the result of a specific operation of identification of the relational properties of the functional components of a system, which do not necessarily coincide with the intrinsic properties of its structural constituents. Also, an epistemological notion of emergence—that of “complex emergence”—will be introduced, which can be defined as the insufficiency, even in principle, of a single descriptive modality to provide a complete description of certain classes of systems. This integrative framework will allow us to deal with two issues in biological and emergentist studies: (1) distinguishing the autonomy proper of living systems from some physical processes like those of structural stability and pattern generation, and (2) reconsidering the notion of downward causation not as a direct or indirect influence of the whole on its parts, but instead as an epistemological problem of interaction between descriptive domains in which the concept of organization proposed and the observational operations related to it play a crucial role. (shrink)

We think of a boundary whenever we think of an entity demarcated from its surroundings. There is a boundary (a line) separating Maryland and Pennsylvania. There is a boundary (a circle) isolating the interior of a disc from its exterior. There is a boundary (a surface) enclosing the bulk of this apple. Sometimes the exact location of a boundary is unclear or otherwise controversial (as when you try to trace out the margins of Mount Everest, or even the boundary of (...) your own body). Sometimes the boundary lies skew to any physical discontinuity or qualitative differentiation (as with the border of Wyoming, or the boundary between the upper and lower halves of a homogeneous sphere). But whether sharp or blurry, natural or artificial, for every object there appears to be a boundary that marks it off from the rest of the world. Events, too, have boundaries — at least temporal boundaries. Our lives are bounded by our births and by our deaths; the soccer game began at 3pm sharp and ended with the referee's final whistle at 4:45pm. It is sometimes suggested that even abstract entities, such as concepts or sets, have boundaries of their own, and Wittgenstein could emphatically proclaim that the boundaries of our language are the boundaries of our world. Whether all this boundary talk is coherent, however, and whether it reflects the structure of the world or simply the organizing activity of our mind, are matters of deep philosophical controversy. (shrink)

We present a category-theoretical analysis, based on the concept of generic figures, of a diagrammatic system for propositional logic (Peirce’s Existential Graphs α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}). The straightforward construction of a presheaf category EGα∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {E}}}{{\mathcal {G}}}_{\alpha ^{*}}$$\end{document} of cuts-only Existential Graphs (equivalent to the well-studied category of finite forests) provides a basis for the further construction of the category EGα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} (...) \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathcal {E}}}{{\mathcal {G}}}_\alpha $$\end{document} which introduces variables in a reconstructedly generic, or label-free, mode. Morphisms in these categories represent syntactical embeddings or, equivalently but dually, extensions. Through the example of Peirce’s system, it is shown how the generic figures approach facilitates the formal investigation of relations between syntax and semantics in such diagrammatic systems. (shrink)

Globalization processes imply the self-deconstruction of the hierarchy of legal norms. Thus, legal pluralism is no longer only an issue for legal sociology, but becomes a challenge for legal practice itself. Traditionally, rule making by `private regimes' has been subjugated under the hierarchical frame of the national constitution. When this frame breaks, then the new frame of legal institutions can only be heterarchical. The origin of global non-state law as a sequence of recursive legal operations is an `as if', not (...) only a founding myth as a self-observation of law, rather the legal fiction of concrete past operations. This fiction, however, depends on social conditions outside legal institutions, on a historical configuration in which it is sufficiently plausible to assume that in earlier times, too, legal rules were applied. (shrink)

The hypothesis of this paper is that language is one more Eigenform, the “external” description of which is impossible. It follows that the application of second-order cybernetics to Eigenform might be adequate. In this article, I would like to concentrate on one relatively small aspect of the idea of Eigenform suggested by Foerster, Kauffman and Spenser-Brawn. I will use Foerster`s recursive approach namely that neither observer nor the thing observed can precede each other, but instead mutually assume each other. In (...) my research, language would stand in the place of the observer, and in the place of the thing – the world itself. To specify further, I focus on the problem of noting, and in particular, on how signs correspond to things. Therefore, I will try to show that the sign and the object do not precede one another and do not exist isolated from each other, but on the contrary, condition each other. Thus, language creates the world of objects, but in turn, it is created by the world. Thus it is a model of self-referentiality, which arranges the form of language as Eigenform as the idea of “mutual referentiality,” as we see it in the relation between language and the world. (shrink)

It is well known that Niklas Luhmann’s theory of social systems is grounded in Spencer-Brown’s seminal Laws of Form (LoF) or ‘calculus of indications’. It is also known that the reception of the latter has been rather problematic. This article attempts to describe the construction of LoF, and confront it with Niklas Luhmann’s ontological and epistemological premises. I show how LoF must be considered a protologic, or research into the fundamentals of logical systems. The clue to its understanding is to (...) be found in its profoundly topological conception of common mathematics and (Boolean) algebra. Both are explained as direct offspring of their planar orientation. Self-reference is a justified instance of an extended, more intricate topological arrangement. Its consequences for ontology (non-identity) and epistemology (autology), I argue, have been adopted correctly by Niklas Luhmann. Separate sections are devoted to how Spencer-Brown’s notion of re-entry relates to Luhmann’s definition of system/environment, and to a comparison between Luhmann’s and Parsons’ functionalism. (shrink)

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. 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. 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. (shrink)

Autopoietic theory is increasingly seen as a candidate for a radical theory of law, both in relation to its theoretical credentials and its relevance in terms of new and emerging forms of law. An aspect of the theory that has remained less developed, however, is its material side, and more concretely the theory’s accommodation of bodies, space, objects and their claim to legal agency. The present article reads Luhmann’s theory of autopoietic systems in a radical and material manner, linking it (...) on the one hand to current post-structural theorisations of law and society, and on the other hand extending its ambit to accommodate the influx of material considerations that have been working their way through various other disciplines. The latter comprises both a materialisation of the theory itself and ways of conceptualising the legal system as material through and through. This I do by further developing what I have called Critical Autopoiesis, namely an acentric, topological, post-ecological and posthuman understanding of Luhmann’s theory, that draws on Deleuzian thought, feminist theory, geography, non-representational theory, and new material and object-oriented ontologies. These are combined with some well-rehearsed autopoietic concepts, such as distinction, environment and boundaries; Luhmann’s earlier work on materiality continuum; more recent work on bodies and space; as well as his work on form and medium in relation to art. The article concludes with five suggestions for an understanding of what critical autopoietic materiality might mean for law. (shrink)

This paper is concerned with the role of self-observation in managing complexity in meaning systems. Revising Niklas Luhmann's theory of mass media, we approach the mass media system as a social sub-system functionally specialized in the coupling of psychic systems' self-observation and social systems' self-observation.According to Autopoietic Systems Theory and von Foerster's second order cybernetics, self-observation presupposes a capability for meta-observation that demands a specific distinction between observer and actor. This distinction seems especially relevant in those social contexts where a (...) separation between the action of observation and other social actions is required. However, in those social contexts where the defining action is precisely observation, the border between observer and actor is blurred.We shall consider the significant divergence between the implicit and the explicit epistemologies of the mass media system, which appears to be characterized by the explicit assumption of a classic objectivist epistemology, on one side, and a relativist epistemology on the other, posing a hybrid epistemic status somewhere in between science and arts. (shrink)

Following an earlier paper (Wetherick, 1989), the analysis of syllogistic reasoning via the medieval doctrine of “distribution of terms” is pursued and completed. The doctrine was not originally presented as an explanation of syllogistic reasoning but turns out to furnish one. It is shown that: It is impossible to assert two propositions having a distributed middle term in common without, at the same time, tacitly asserting the valid conclusion, if any. When the middle term is distributed but no valid conclusion (...) follows, this is a consequence of the distributional status of the subject and predicate terms. When the middle term is not distributed the propositions have nothing but a name in common. The logic of Spencer Brown (1969) is employed to show that logic is implicit in the behaviour of any organism that survives by making distinctions (e.g. between prey/non-prey; predator/non-predator). It is suggested that animal organisms answer this description by definition. Cognitive structures have evolved in the human organism so as to permit the conversion of habitual associations into universal propositions thus allowing formal logic and mathematics. This view appears to require a reversion to psychologism in logic, the consequences are considered and judged acceptable. (shrink)

This essay interprets the meaning of one of the cards in aTarot deck, "The Magician," in the context of process philosophy in the tradition of Alfred North Whitehead. It brings into the conversation the philosophical legacy of American semiotician Charles Sanders Peirce as well as French poststructuralist Gilles Deleuze. Some of their conceptualizations are explored herein for the purpose of explaining the symbolic function of the Magician in the world. From the perspective of the logic of explanation, the sign of (...) the Magician is an index of nonmechanistic, mutualist or circular, causality that enables self-organization embedded in coordination dynamics. Its action is such as to establish an unorthodox connection crossing over the dualistic gap between mind and matter, science and magic, process and structure, the world without and the world within, subject and object, and human experience and the natural world, thereby overcoming what Whitehead called the paradox of the connectedness of things. The Magician represents a certain quality that acts as a catalytic agent capable of eliciting transmutations, that is, the emergence of novelty. I present a model for process∼structure that uses mathematics on the complex plane and the rules of projective geometry. The corollary is such that the presence of the Magician in the world enables a particular organization of thought that makes pre-cognition possible. (shrink)

This article consists of three parts. The first explores the relation between paradox, de-paradoxication, and time, which I hold to be a relatively unattended yet very important tandem of concepts in Luhmann's work (Luhmann, 1993, 1995; Rasch, 2000). The second part will try to theoretically think through (de-paradoxicalize) a conundrum of present time: globalization and its opponents. In the third and last part, I briefly explore the paradox of conscious evolution, taking into account the specifics of the relations between social (...) systems of communication and individual psychic systems in Luhmann's theory. (shrink)

Mathematics is a struggle for many. To make it more accessible, behavioral and educational scientists are redesigning how it is taught. To a similar end, a few rogue mathematicians and computer scientists are doing something more radical: they are redesigning mathematics itself, improving its ergonomic features. Charles Peirce, an important contributor to ordinary symbolic logic, also introduced a rigorous but non-symbolic, graphical alternative to it that is easier to picture. In the spirit of this iconic logic, George Spencer-Brown founded iconic (...) mathematics. Performing iconic arithmetic, algebra, and even trigonometry, resembles doing calculations on an abacus, which is still popular in education today, has aided humanity for millennia, helps even when it is merely imagined, and ameliorates severe disability in basic computation. Interestingly, whereas some intellectually disabled individuals excel in very complex numerical tasks, others of normal intelligence fail even in very simple ones. A comparison of their wider psychological profiles suggests that iconic mathematics ought to suit the very people traditional mathematics leaves behind. (shrink)

Context: Society is faced with “wicked” problems of environmental sustainability, which are inherently multiperspectival, and there is a need for explicitly constructivist and perspectivist theories to address them. Problem: However, different constructivist theories construe the environment in different ways. The aim of this paper is to clarify the conceptions of environment in constructivist approaches, and thereby to assist the sciences of complex systems and complex environmental problems. Method: We describe the terms used for “the environment” in von Uexküll, Maturana & (...) Varela, and Luhmann, and analyse how their conceptions of environment are connected to differences of perspective and observation. Results: We show the need to distinguish between inside and outside perspectives on the environment, and identify two very different and complementary logics of observation, the logic of distinction and the logic of representation, in the three constructivist theories. Implications: Luhmann’s theory of social systems can be a helpful perspective on the wicked environmental problems of society if we consider carefully the theory’s own blind spots: that it confines itself to systems of communication, and that it is based fully on the conception of observation as indication by means of distinction. (shrink)