In recent years an increasing quantity of UK legislation has introduced blended or ‘hybridised’ procedures that blur the previously clear demarcation between civil and criminal legal processes, typically on the grounds of normatively-motivated political expediency. This paper provides a critical perspective on instances of procedural hybridisation in order to illustrate that, first, the reliance upon civil law measures to remedy criminal law infractions can raise human rights issues and, second, that such instrumental criminal justice strategies deliberately circumvent the enhanced procedural (...) protections of the criminal law. By conceptualising the rule of law as a structural coupling between the political and legal systems, and due process rights as necessary and self-imposed limitations upon systemic operations, this paper employs a systems-theoretical approach to critique this balancing act between expediency and principle, and queries the circumstances under which legislation contravening the rule of law can be said to lack legitimacy. (shrink)

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)

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)

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)

This article praises the development of second order cybernetics by von Foerster, Maturana, and Varela as an important step in deepening our understanding of the bio-psychological foundation of the dynamics of information, cognition, and communication. Luhmann's development of the theory into the realm of social communication is seen as a necessary and important move. The triple autopoietic differentiation between biological, psychological, and social-communicative autopoiesis and the introduction of a technical concept of meaning is central. Finally, the paper shows that second (...) order cybernetics lacks explicit and ontological concepts of emotion, meaning, and a concept of signs. C. S. Peirce's theory is introduced for this purpose. It is then shown, through Varela's development of Spencer Brown's ‘Laws of Form’ from a dual to a dynamic triadic categorical structure, that both theories are triadic and second order, and therefore can be fruitfully fused to a Cybersemiotics. (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)

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)

A cluster of similar trends emerging in separate fields of science and philosophy points to new opportunities to apply biosemiotic ideas as tools for conceptual integration in theoretical biology. I characterize these developments as the outcome of a “relational turn” in these disciplines. They signal a shift of attention away from objects and things and towards relational structures and processes. Increasingly sophisticated research technologies of molecular biology have generated an enormous quantity of experimental data, sparking a need for relational approaches (...) that could help to find recurrent patterns in the mass of data. Earlier conceptions of relational biology and cybernetics, once deemed too abstract and speculative, are now resurrected and applied by means of new computational and simulation tools. I think this receptivity should be extended to incorporate nets of semiotic relations as heuristic guides for discerning global patterns of interactions in living systems. In this article I review aspects of systems biology and new directions in evolutionary theory, focusing on the role of circular and downward causation in relational structures and dynamical networks. I also indicate promising avenues of integration of some ideas of biosemiotics with those emerging from these new currents in biology. Relational developments in biology bear a telling similarity to a parallel relational turn presently manifest in the philosophy of science, rooted in the philosophy of physics and mathematics and in different varieties of structural and informational realism. The recognition of the relational nature of reality within these disciplines entails a tacit repudiation of nominalistic biases in science that have hindered the reception of semitiotic conceptions in biology. In previous investigations I explored connections between two kinds of relational structures: the networks of self-referential circular loops that appear pervasively in living systems, and the triadic relational structures that Peircean semiotics places at the basis of all semiotic transactions. Current relational views in the sciences seem oblivious to the difference between dyadic and triadic relations. Incorporating this essential distinction from biosemiotics into other fields could be a first step in seizing the opportunities opened by the relational turn for a renewal of biology and of natural philosophy in general, across disciplinary boundaries. (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)

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)

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)

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)

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)

Atoms, molecules, organisms distinguish layers of reality because of the causal links that govern their behavior, both horizontally (atom-atom, molecule-molecule, organism-organism) and vertically (atom-molecule-organism). This is the first intuition of the theory of levels. Even if the further development of the theory will require imposing a number of qualifications to this initial intuition, the idea of a series of entities organized on different levels of complexity will prove correct. Living systems as well as social systems and the human mind present (...) features remarkably different from those characterizing non-living, simple physical and chemical systems. We propose that super-complexity requires at least four different categorical frameworks, provided by the theories of levels of reality, chronotopoids, (generalized) interactions, and anticipation. (shrink)

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)

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)

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 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)

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)

Although it is conceded that distinct knowledge domains do presentparticular problems of coming to know, in thispaper it is argued that it is possible to construct a domain independent modelof the processes of coming to know, one inwhich observers share understandings and do soin agreed ways. The model in question is partof the conversation theory of Gordon Pask. CT, as a theory of theory construction andcommunication, has particular relevance forfoundational issues in science and scienceeducation. CT explicitly propounds a ``radicalconstructivist'' epistemology. (...) A briefaccount is given of the main tenets of RC andCT's place in that tradition and the traditionsof cybernetics. The paper presents a briefnon-technical account of the main concepts ofCT including elaborations by Laurillard andHarri-Augstein and Thomas. As part of CT, Pask also elaborated a methodology – knowledgeand task analysis – for analysing the structureof different knowledge domains; thismethodology is sketched in outline. (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)

Living systems are characterized by unique properties that make them resistant to the ``information-processingperspective'' of traditional cognitive science.This paper details those unique properties andoffers a new theoretical framework forunderstanding the behavior of living systems.This framework leans heavily on ideas fromgeneral systems theory (specifically Bateson'sinteractionist perspective), semiotics, andMerleau-Ponty's phenomenology. The benefits ofusing this framework are illustrated withexamples from two different domains: immunologyand verbal interaction.

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)

Peirce’s diagrammatic system of Existential Graphs (EGα)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EG_{\alpha })$$\end{document} is a logical proof system corresponding to the Propositional Calculus (PL). Most known proofs of soundness and completeness for EGα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EG_{\alpha }$$\end{document} depend upon a translation of Peirce’s diagrammatic syntax into that of a suitable Frege-style system. In this paper, drawing upon standard results but using the native diagrammatic notational framework of the graphs, we present (...) a purely syntactic proof of soundness, and hence consistency, for EGα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EG_{\alpha }$$\end{document}, along with two separate completeness proofs that are constructive in the sense that we provide an algorithm in each case to construct an EGα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$EG_{\alpha }$$\end{document} formal proof starting from the empty Sheet of Assertion, given any expression that is in fact a tautology according to the standard semantics of the system. (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)

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)

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)

This contribution offers the author’s personal experience with a project that took place 25 years ago in Latin America. This was about Second Order Auditing in Colombia during the second part of the 1990s. This project was carried out at the Country’s National Auditing Office, and was an application of the Viable System Model and the Viplan Methodology to a National Context. It was an innovative project at the CGR, focused on Second Order Auditing, to improve communications within the fabric (...) of the Colombian government. Its emphasis was building responsible trust between public enterprises, ministries and political agencies. Its emphasis was building communications between ministries and public entities, with the aim of increasing their effectiveness. At its core were methodological and epistemological developments. Key questions it attempted to answer were how to model the complexity of the enterprises and how to transform the auditors’ views of their relations with people in public entities, from one focused on requesting information, to one focused on communications. Structural changes were proposed for the National Audit Office and state enterprises, and hundreds of auditors were trained, through epistemological methodological workshops, in second order auditing and the reports of their auditing were debated extensively in government and beyond. This paper finishes with a short discussion of these transformations in the light of organisational cybernetics and in particular of the Viable System Model. (shrink)

This article expands on what Bernard Stiegler describes as “The Ordeal of Truth”. Through an evolutionary account of cognition and its exteriorization in human technology, I highlight a recurring tension in philosophy between the “as-if” nature of our models and representations, and the doubt that infects even our most stable understanding of the world. Truth is here associated to the process of metastabilization that characterizes the biological organism. The famous case of Clive Wearing’s severe amnesia, as well as the fictional (...) treatment of amnesia in Christopher Nolan’s Memento, are recalled to highlight the connection between truth and memory, and more importantly the contingent character of the formation of thoughts, and the desperate nature of the construction of truths, through the evolutionarily conditioned “subjective necessity” to link the before and the after, the cause and the effect. I show that this same ordeal is reflected in the philosophy of science in what is known as “pessimistic meta induction”, which I put into dialogue with the growing pessimism about knowledge in contemporary technological culture known as “post truth”. Finally, a possible way out of this pessimism is briefly sketched: a compromise such that, without recourse to objective truth, and in full acceptance of an always already biased relation to the world, future technologies might be designed to incrementally reduce our biases, through an intrinsic mapping of the relative falsity of our models, rather than through some idealized extrinsic relation to an unattainable noumenal real. (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)

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)

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)

Actor-Network-Theory (ANT) offers an ‘infra-language’ of the social that allows one to trace social relations very dynamically, while at the same time dissolving human agency, thus providing a flat and de-centred way into sociology. However, ANT struggles with its theoretical design that may lead us to reduce agency to causation and to conceptualize actor-networks as homogeneous ontologies of force. This article proposes to regard ANT’s inability to conceptualize reflexivity and the interrelatedness of different ontologies as the fundamental problem of the (...) theory. Drawing on Günther, it offers an ‘infra-language’ of reflexive relations while maintaining ANT’s de-centred approach. This would enable us to conceptualize actor-networks as non-homogeneous, dynamic and connecting different societal rationales while maintaining the main strengths of ANT. (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)

This paper proposes a social account for the origin of the truth value and the emergence of the first declarative sentence. Such a proposal is based on two assumptions. The first is known as the social intelligence hypothesis: that the cognitive evolution of humans is first and foremost an adaptation to social demands. The second is the function-first approach to explaining the evolution of traits: before a prototype of a new trait develops and the adaptation process begins, something already existing (...) is used for a new purpose. Applied to the emergence of declarative sentences (statements), this suggests something already existing––natural signs (such as indexical objects)––was used for the declarative function and thereby integrated into communication. I show that index display (such as the display of hunting trophies) can imply a conceptual structure similar to that informing the syntax of sentences. The view developed in this paper is broadly consistent with the argumentative theory of Mercier and Sperber, which suggests that reasoning is less adapted to decision making than to social purposes such as winning disputes. In this paper I extend this view to the evaluation of propositions expressed in declarative sentences. According to my proposal, the first declarative sentence emerged as the negation of the (implicit) negation of an implicit statement. Thereby, I suggest that the binary structure of the truth value underlying any declarative sentence is founded on disagreements based on conflicts of interests. (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)

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)

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)

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)

The new practices of human resource management can be seen as an expression of management communication, which has become increasingly pedagogical. This article is based on Luhmann systems theory regarding second-order observation. The article tries to observe how management communications observe the self-observations of employees, and claims that these observations take place within the code of the pedagogic. A number of effects are discussed: how the employee becomes a formator of him/herself as the medium child, how the employee is expected (...) to observe him/herself with a corrective pedagogical gaze, and finally how this installs a kind of a self-screening of the employee. (shrink)

Complex phenomena such as play, creativity or innovation are familiar, yet difficult to describe in a systematic manner. In this short article I propose six necessary conditions for any comprehensive description of play. Against this background I discuss my systems-theoretic, constructivist and practice-informed approach to play.

Name der Zeitschrift: Zeitschrift für Religionswissenschaft Jahrgang: 26 Heft: 1 Seiten: 1-51.

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)