Laws of Form

The main goal of this contribution is to introduce a cross-platform application to learn-teach syllogistic. We call this application dasasap for develop all syllogisms as soon as possible. To introduce this application we show the logical foundations for the game with a system we call L , and its interface developed with LiveCode.

Lynnclaire Dennis had perhaps the most profound near-death experiences (NDEs) ever documented. So much so, the world's leading provider of science and health information (Elsevier) published an academic/scientific textbook about a new mathematical discovery found in Lynnclaire Dennis' near-death experience. It is a new geometric structure which matches the dynamics of living and life-like (social) systems and has applications in general systems theory, a universal systems model, human clinical molecular genetics modelling, medical informatics, astrophysics, education and other areas of study.

The fall of reductionist approaches to explanation leaves biology with an unescapable challenge: how to decipher complex systems. This entails a number of very critical questions, the most basic ones being: "What do we mean by 'complex'?" and "What is the system we should look for?" In complex systems, constraints belong to a higher level that the molecular one and their effect reduces and constrains the manifold of the accessible internal states of the system itself. Function is related but not deterministically imposed by the underlying structure. It is quite unlikely that such kind of complexity could be grasped by current approaches focusing on a single organization scale. The natural co-emergence of systems, parts and properties can be adopted as a hypothesis-free conceptual framework to understand functional integration of organisms, including their hierarchical or multilevel patterns, and including the way scientific practice proceeds in approaching such complexity. External, "driving" factors-order parameters and control parameters provided by the surrounding microenvironment-are always required to "push" the components' fate into well-defined developmental directions. In the negative, we see that in pathological processes such as cancer, organizational fluidity, collapse of levels and dynamic heterogeneity make it hard to even find a level of observation for a stable explanandum to persist in scientific practice. Parts and the system both lose their properties once the system is destabilized. The mesoscopic approach is our proposal to conceptualizing, investigating and explaining in biology. "Mesoscopic way of thinking" is increasingly popular in the epistemology of biology and corresponds to looking for an explanation (and possibly a prediction) where "nontrivial determinism is maximal": the "most microscopic" level of organization is not necessarily the place where "the most relevant facts do happen." A fundamental rethinking of the concept of causality is also due for order parameters to be carefully and

The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing, and if nature were not worth knowing, life would not be worth living."-Henri Poincaré.

A formal model of the processes of digestion in a hypothetical cell is developed and discussed as a case study of how the threefold logic of Peircean semiotics works within Rosen's paradigm of relational ontology. The formal model is used to demonstrate several fundamental differences between a relational description of biological processes and a mechanistic description. The formal model produces a logic of embodied generalization that is mediated and determined by the cell through its interactions with the environment. Specifically, the synchronization of the functions of pattern recognition and semantic attribution results in an open and adaptive learning system that is stabilized by a hermeneutical circle. The relational principles of biosemiotics demonstrated through this case study are applicable to other biological systems, as well as to the relational ontology of systems theory and relativistic quantum theory.

Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.d-nb.de abrufbar. © Springer Fachmedien Wiesbaden GmbH, ein Teil von Springer Nature 2020 Das Werk einschließlich aller seiner Teile ist urheberrechtlich geschützt. Jede Verwertung, die nicht ausdrücklich vom Urheberrechtsgesetz zugelassen ist, bedarf der vorherigen Zustimmung des Verlags. Das gilt insbesondere für Vervielfältigungen, Bearbeitungen, Übersetzungen, Mikroverfilmungen und die Einspeicherung und Verarbeitung in elektronischen Systemen. Die Wiedergabe von allgemein beschreibenden Bezeichnungen, Marken, Unternehmensnamen etc. in diesem Werk bedeutet nicht, dass diese frei durch jedermann benutzt werden dürfen. Die Berechtigung zur Benutzung unterliegt, auch ohne gesonderten Hinweis hierzu, den Regeln des Markenrechts. Die Rechte des jeweiligen Zeicheninhabers sind zu beachten. Der Verlag, die Autoren und die Herausgeber gehen davon aus, dass die Angaben und Informationen in diesem Werk zum Zeitpunkt der Veröffentlichung vollständig und korrekt sind. Weder der Verlag, noch die Autoren oder die Herausgeber übernehmen, ausdrücklich oder implizit, Gewähr für den Inhalt des Werkes, etwaige Fehler oder Äußerungen. Der Verlag bleibt im Hinblick auf geografische Zuordnungen und Gebietsbezeichnungen in veröffentlichten Karten und Institutionsadressen neutral.

His research interest is in the field of RF & Wireless Communication and low power IoT devices. George Spencer Brown (1923-2016) engaged in multiple disciplines throughout his life. His first publication was a proposed doctoral thesis: Probability and Scientific Inference (1957). In 1969, his book "Laws of Form" was published for the first time and it has never been out of print since. It has been amended with numerous prefaces and appendices throughout the course of his lifetime. Later publications were sometimes published under the pseudonym James Keys. He had multiple connections to universities and business endeavors in the UK and overseas during his lifetime. His work on the foundations of philosophy and mathematics has inspired generations of thinkers across disciplines from the social sciences, physics, engineering, biology, and philosophy.

His research interest is in the field of RF & Wireless Communication and low power IoT devices. George Spencer Brown (1923-2016) engaged in multiple disciplines throughout his life. His first publication was a proposed doctoral thesis: Probability and Scientific Inference (1957). In 1969, his book "Laws of Form" was published for the first time and it has never been out of print since. It has been amended with numerous prefaces and appendices throughout the course of his lifetime. Later publications were sometimes published under the pseudonym James Keys. He had multiple connections to universities and business endeavors in the UK and overseas during his lifetime. His work on the foundations of philosophy and mathematics has inspired generations of thinkers across disciplines from the social sciences, physics, engineering, biology, and philosophy.

If the autopoiesis concept has been of enormous benefit for the description of the society and in particular for the radical revolution of the theory of social systems in the work of Luhmann, with the phenomenon of the indexicality developed by Garfinkel it seems to have happened exactly the opposite. It has been not taken advantages of the unsuspected potentialities of the indexicality in the theory of the interaction systems, it seemed even to have been forgotten that the setting in use of the language in the systems of conversational interaction is only possible by means of the context realization of indexicals expressions. In this work, I argue that the indexical autopoiesis of the interaction systems forces to a deeply change in the theorem of the double contingency.

Cancer is a highly complex disease due to the disruption of tissue architecture. Thus, tissues, and not individual cells, are the proper level of observation for the study of carcinogenesis. This paradigm shift from a reductionist approach to a systems biology approach is long overdue. Indeed, cell phenotypes are emergent modes arising through collective non-linear interactions among different cellular and microenvironmental components, generally described by "phase space diagrams", where stable states (attractors) are embedded into a landscape model. Within this framework, cell states and cell transitions are generally conceived as mainly specified by generegulatory networks. However, the system s dynamics is not reducible to the integrated functioning of the genome-proteome network alone; the epithelia-stroma interacting system must be taken into consideration in order to give a more comprehensive picture. Given that cell shape represents the spatial geometric configuration acquired as a result of the integrated set of cellular and environmental cues, we posit that fractal-shape parameters represent "omics descriptors of the epithelium-stroma system. Within this framework, function appears to follow form, and not the other way around.

This is perhaps one of the first texts that lead the attention of its Farsi readers to the importance of the non-arithmatic calculus of G. Spencer Brown to come into a better understanding of Jacques Lacan's psychoanalysis as well as his approach onto the Freudian "Unary Trait".

Norman Lindsey’s ‘magic pudding’ is a pudding with personality – it can change its ingredients at will – whether providing its owners with a hearty steak and kidney main course or a plum pudding dessert, the quality of its mood remains the same. It is a grumpy, unpleasant character that loves to complain, resents being eaten, yet loves being the centre of attention at any meal. However much of it is eaten, its substance remains unchanged; it despises any abuse of power, and is a stickler for correctness and justice.
It has much in common with logic, which Mortimer Adler described (along with its Trivium partners, grammar and rhetoric) as ‘an intellectual or liberal art … and a formal science … concerned with the forms of any subject-matter’.  George Spencer-Brown compared a pudding or cake to music and to mathematics. The difference, where logic is concerned, is that logic is an  instrument of the intellect acting in and on itself through the means of reason. It is a triplicity: at once taste, pudding, and recipe / music, musical performance and score / mathematical demonstration, mathematical practice, and mathematical proof.
Think, for a moment, of how logic has been used, treated, and interpreted over the centuries, from its beginnings in oral traditions and the arguments characters get into in early epics, to more recent forays into algebraic and mathematical logics … if logic were to come to life and comment on how it’s been treated – as the magic pudding is able to do – what might it say? If it were defending itself in a court of law against abuse, who might it draw on for its defence; who might it accuse?

Thinking the Float Tank is an interdisciplinary conference that will conclude the group exhibition Gödel, Escher, Bach (May 19 - August 27, 2023) at the contemporary art museum West Den Haag in The Hague, the Netherlands. The artistic exhibition Gödel, Escher, Bach is based on the theme of self-reference, which Douglas Hofstadter’s famous book of the same title highlights. Thinking the Float Tank is a float-tank think-tank existing in a space devoted to the history and continuing development of the science and philosophy of flotation.

Historical Context
Fifty years ago John Lilly and Alan Watts brought the mathematician Georg Spencer-Brown to the Esalen Institute in California for a conference called the American University of Masters, or AUM conference. The AUM conference, and the Form and Void conference series in the following years (1974 and 1975), marked a turning point in the history of cybernetics and systems science because it was the place where many luminaries gathered and received the wisdom of Spencer-Brown’s 1969 book Laws of Form. Alan Watts was already into Laws of Form, having written a chapter about it in his mountain journal Cloud-Hidden, Whereabouts Unknown (1971), but it was John Lilly’s use of Laws of Form in the float tank as a guidebook to traveling between universes that established the AUM conference as the founding event of a new kind of scientific culture. This revolution knocked science of consciousness into the first person, and Lilly captured that spirit in the frame of the float tank.

Workshop: Reconstructing the “Void Method”
Thinking the Float Tank includes a workshop component dedicated to the reconstruct of Lilly’s use of Laws of Form in the float tank, which is what Lilly referred to as the “void method.” The workshop, led by the conference curator Randolph Dible and by one of Lilly’s original workshop participants Jerry Swatez, will aim to regenerate the essence of Lilly’s void method as well as a more robust cybernetic and phenomenological version of Lilly’s flotation science by harnessing advanced philosophical techniques that were not available to Lilly in the early days of flotation.

Topics
Topics addressed by the conference include: phenomenology, ontology, and metaphysics, Kyoto School metaphysics, history of flotation science in John Lilly’s milieu, sensory deprivation and spiritual reality, second-order cybernetics and second-order phenomenology, recent psychedelic advances, the absolute infinite, completeness, and the speculative reconstructing Lilly’s “Void Method.”

Sources
Sources for these topics include: John Lilly’s metaprogramming paradigm, Edmund Husserl’s phenomenological metaphysics, Eugen Fink’s second-order phenomenology, Heinz von Foerster’s second-order cybernetics, Theodor Conrad’s phenomenological psychology, Hedwig Conrad-Martius’ ontological phenomenology, George Spencer-Brown’s calculus of indications, techniques of meditative absorption, altered states of consciousness, mysticism, theosophy, philosophia perennis, and novel creative mentations.

www.randolphdible.com

The research is dedicated to the analysis of law enforcement civil aspects in legal regulation of public relations, determination of its character and value as security instrument of their effectiveness.It is set that law realization is considered in such forms as law fulfillment, law application, law enforcement, law fulfillment and law termination accompanying the motion of civil-law relations.Law enforcement legal nature is stipulated by the objective necessity to influence on the behavior of participants of such civil-law relations to ensure their compliance with the legal model. It is proved that the reason for law enforcement in the course of civil-law relations realization is such character of their development, reality and affiliation of which in view of their social value is provided individually-legal instructions given by public authority. Realization of subjective civil rights and legal obligations in private relation is provided by the acceptance of individual legal act...

Diese Masterarbeit diskutiert die philosophischen Grundlagen der Laws of Form von George Spencer-Brown, ihre Relevanz für die Systemtheorie sowie ihre Rezeption durch Niklas Luhmann. Dabei werden verschiedene Schlüsselfragen zu den Laws of Form beantwortet, einschließlich ihres Zwecks, ihrer Relevanz und ihrer Anwendbarkeit. Der Grundgedanke ist, dass die Laws of Form eine Sprachphilosophie sind, die in Struktur und Inhalt an Wittgensteins Werk angelehnt sind. Sie entwickeln ein Regelwerk für die Verwendung der Befehlssprache und behandeln die Entstehung der Objektivität als eine Konsequenz der Befolgung von Befehlen. Sie enthalten auch eine semiotische Komponente, indem sie die Trennung von Signifikat und Signifikant von einem Befehl abhängig machen. Aus dieser Semiotik leitet sich der mathematische Formalismus ab, welcher als das Indikationskalkül bezeichnet wird. Die Masterarbeit erklärt auch das Konzept des Re-entry sowie der Interpretation des Indikationskalkül. Darüber hinaus wird die Rezeption der Laws of Form in der Systemtheorie von Heinz von Foerster, Varela und Maturana kritisch diskutiert. Die These ist, dass Spencer-Brown mit dem Feld sowohl inhaltlich als auch historisch wenig zu tun hatte. Genauso wird kritisch auf die Missverständnisse in der Rezeption von Niklas Luhmann und Dirk Baecker eingegangen. Viel wichtiger klärt diese Masterarbeit darüber auf, welche Rolle Spencer-Brown in der soziologischen Systemtheorie spielte und spielen sollte. Darüber hinaus wird eine Grundlage für eine neue soziologische Leseart der Laws of Form gelegt und ein neuer Entwurf für eine soziologische Interpretation des Indikationskalküls vorgestellt.

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The concept of imaginary logical values was introduced by Spencer-Brown in Laws of Form, in analogy to the square root of-1 in the complex numbers. In this paper, we develop a new approach to representing imaginary values. The resulting system, which we call BF, is a four-valued generalization of Laws of Form. Imaginary values in BF act as cyclic fourvalued operators. The central characteristic of BF is its capacity to portray imaginary values as both values and as operators. We show that the BF algebra is an stronger, axiomatically complete extension to Laws of Form capable of representing other four-valued systems, including the Kauffman/Varela Waveform Algebra and Belnap's Four-Valued Bilattice. We conclude by showing a representation of imaginary values based on the Artin braid group.

Man’s notion of ‘information’ is essential as it guides human thinking, planning, and consequent actions. Situations such as the Haiti earthquake in 2010, the financial crisis in Greece in 2010, and the oil slick in the Gulf of Mexico in 2010 are just a few instances of constant growing empirical dilemmas in our global society where information plays a central role. The meaning of what information is has clear implications for how we deal with it in our practical lives, which in turn may give rise to situations that we would prefer to be without. In this sense, the notion of information has evidently presented the need to question what it really means and how it dominates the functioning of our global society. To address this fundamental issue of information, two questions are explored and presented in this paper: What notions of information are dominating the scholarly literature? And what are the differences between these notions? To answer these questions, we have conducted a com...

Giving structure to your fiction is essential - and it can be challenging. Leon Conrad, author of 'Story and Structure: A complete guide' outlines a simple structure he uses at every stage of the writing process, and explains how you can use it to find your way through your story and make your writing flow.

Although there is ongoing debate about the mathematical influence of George Spencer-Brown’s novel formalisms, one thing can hardly be denied: there is an intuitive and aesthetic simplicity to his notation which, if nothing else, deserves scholarly admiration and consideration. Of course, it is one thing to simply sit back and imbibe the simplicity of Spencer-Brown’s “distinction” or “mark” and another thing entirely to meditate on what exactly makes these notions so intuitively pleasing and “amenable to common sense.” I invite the reader to both indulge in the former and dabble in the latter, as we journey into an investigation of self-evidence as it relates to Spencer-Brown’s notations and, moreover, logical notation in general. In this paper I draw on C.S. Peirce’s semiotics and philosophy of mathematics and Spencer-Brown’s passion for maximally self-evident formalism to craft a new breed of logical representation. I also highlight Hans Freudenthal’s masterful “Lincos,” an underappreciated language devised to be understood by any conceivable form of extraterrestrial life. In the end I offer a style of self-evident logical notation that effectively collapses the boundary between (1) metalanguage and object language, (2) definiendum and definiens and (3) sign and universe of discourse.

Copyright 2008 Fordham University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopy, recording, or any other—except for brief ...

In a chapter of Laws of Form—A Fiftieth Anniversary (August, 2022), “First Philosophy and the First Distinction: Ontology and Phenomenology of Laws of Form,” I contributed some ways of generally tying the paradigm of Spencer-Brown from its first principle, the first distinction, to first philosophy, as broadly understood from Ancient Greek philosophy to contemporary phenomenology and cybernetic philosophy. In this next development, I aim to connect this work on first philosophy to a work of ultimate philosophy. This will take the form of articulating a new universal ontology of reality and ultimate reality, based on the formal-ontological paradigm of Laws of Form.
Universal ontology is the ultimate intention of first philosophy. It brings in its wake the speculative metaphysical project of grounding all things in a common foundation, in common terms, somewhat paradoxically including the kinds of things that are not things at all. Such universality stands on a hypothesis of true reality that entails a true metaphysical system and its connection to a hypostatic series of realities: antepenultimate reality, penultimate reality, and finally, the ultimate reality from which it originates. Such a project should be understood in conventional as well as novel terms, as it seeks to approximate the cognition of a vision, method, and doctrine appropriate to the ultimate truth of being: it should present a theory of being including along with all beings beings that are beyond being. The theory itself should be a theory of forms that is also a theory of possible theory-forms. The universal ontologies of the phenomenologists Edmund Husserl and Hedwig Conrad-Martius are here synthesized with George Spencer-Brown’s paradigm to contribute such a system.

Cancer is a highly complex disease due to the disruption of tissue architecture. Thus, tissues, and not individual cells, are the proper level of observation for the study of carcinogenesis. This paradigm shift from a reductionist approach to a systems biology approach is long overdue. Indeed, cell phenotypes are emergent modes arising through collective non-linear interactions among different cellular and microenvironmental components, generally described by "phase space diagrams", where stable states (attractors) are embedded into a landscape model. Within this framework, cell states and cell transitions are generally conceived as mainly specified by generegulatory networks. However, the system s dynamics is not reducible to the integrated functioning of the genome-proteome network alone; the epithelia-stroma interacting system must be taken into consideration in order to give a more comprehensive picture. Given that cell shape represents the spatial geometric configuration acquired as a result of the integrated set of cellular and environmental cues, we posit that fractal-shape parameters represent "omics descriptors of the epithelium-stroma system. Within this framework, function appears to follow form, and not the other way around.

A navegação consulta e descarregamento dos títulos inseridos nas Bibliotecas Digitais UC Digitalis, UC Pombalina e UC Impactum, pressupõem a aceitação plena e sem reservas dos Termos e Condições de Uso destas Bibliotecas Digitais, disponíveis em https://digitalis.uc.pt/pt-pt/termos. Conforme exposto nos referidos Termos e Condições de Uso, o descarregamento de títulos de acesso restrito requer uma licença válida de autorização devendo o utilizador aceder ao(s) documento(s) a partir de um endereço de IP da instituição detentora da supramencionada licença. Ao utilizador é apenas permitido o descarregamento para uso pessoal, pelo que o emprego do(s) título(s) descarregado(s) para outro fim, designadamente comercial, carece de autorização do respetivo autor ou editor da obra. Na medida em que todas as obras da UC Digitalis se encontram protegidas pelo Código do Direito de Autor e Direitos Conexos e demais legislação aplicável, toda a cópia, parcial ou total, deste documento, nos casos em que é legalmente admitida, deverá conter ou fazer-se acompanhar por este aviso.

George Spencer-Brown's Laws of Form is a mathematical treatise that calls for philosophical interpretation. Its core component, the calculus of indications, progresses from the simple act of drawing a distinction, through a number of levels of the indication of that distinction, until it finally reaches the level of real existence and the universe as we know it. While applicable to any special case of indication and semantic expression, this calculus is simultaneously a direct analysis of the underlying and ubiquitous substratum of creation from nothing. This means that Laws of Form should be understood as offering a theory of being (an ontology) and a theory of form (a phenomenology) on the common ground of an intuitive simplicity. The calculus of indications gives us a way of understanding everything-every possible object, every overall gestalt, every possible world, every thing; in both the precise literal sense and the diffuse metaphorical sense-as a form of indication, and all indication-the very form; codified by this calculus-as based on an original and primary distinction at the boundary between everything and nothing. This ultimate boundary, called the first distinction; stands in a very peculiar relation to every familiar thing in our conscious experience. This singular peculiarity of the first distinction should be regarded on the basis of mathematical ontology, in terms of what is called prima philosophia, first philosophy (Greek: πρώτη φιλοσοφία), and in such terms we can determine its ontological and phenomenological status. ...

A presentation is provided of a method — the Membership Table Method (MTM) — to determine the validity of categorical syllogisms. This method makes it possible for each syllogism to be assigned a specific set. If this set is equal to the universal set U, then the categorical syllogism considered is valid, and if that set is not equal to U, then that categorical syllogism is not valid. In other words, any categorical syllogism is valid if and only if its respective set, according to the MTM, is equal to the universal set U. The conclusion of a valid categorical syllogism whose premises are true is true.

A navegação consulta e descarregamento dos títulos inseridos nas Bibliotecas Digitais UC Digitalis, UC Pombalina e UC Impactum, pressupõem a aceitação plena e sem reservas dos Termos e Condições de Uso destas Bibliotecas Digitais, disponíveis em . Conforme exposto nos referidos Termos e Condições de Uso, o descarregamento de títulos de acesso restrito requer uma licença válida de autorização devendo o utilizador aceder ao(s) documento(s) a partir de um endereço de IP da instituição detentora da supramencionada licença. Ao utilizador é apenas permitido o descarregamento para uso pessoal, pelo que o emprego do(s) título(s) descarregado(s) para outro fim, designadamente comercial, carece de autorização do respetivo autor ou editor da obra. Na medida em que todas as obras da UC Digitalis se encontram protegidas pelo Código do Direito de Autor e Direitos Conexos e demais legislação aplicável, toda a cópia, parcial ou total, deste documento, nos casos em que é legalmente admitida, deverá conter ou fazer-se acompanhar por este aviso.

PURPOSE

Blake is relatively well-known, but who was J M Robertson? What's his connection with George Spencer-Brown? And how exactly did J M Robertson influence George Spencer-Brown?

DESIGN/METHODOLOGY/APPROACH

George Spencer-Brown (1923-2016) is the author (among other works) of the undeservedly little-known book, Laws of Form (1969/2011), which was a key inspiration for Niklas Luhmann (1927-1998). But what inspired George Spencer-Brown?

This paper explores two key influences on George Spencer-Brown and his work: the English poet and artist, William Blake (1757-1827) and the Scottish rationalist, politician and author, J M Robertson (1856-1933).

FINDINGS

The paper points to a broken link between George Spencer-Brown's work and Niklas Luhmann's.

ORIGINALITY/VALUE

These questions are explored from two perspectives: first, George Spencer-Brown's works and their debt to (1) Blake's work, from which he quotes in a number of instances and to (2) J M Robertson's (in particular, the latter's Letters on Reasoning (1905) and Rationalism (1912)); second, my personal connection to Spencer-Brown, who mentored me through Laws of Form and with whom I developed a close friendship involving regular weekly telephone conversations for the greater part of the last four years of Spencer-Brown's life. I share anecdotes and stories that connect George Spencer-Brown and J M Robertson that span George Spencer-Brown's lifetime from his school days to his dying days. Both Blake's and Robertson's influences are relevant to Spencer-Brown's view of morality. The paper looks at specific connections between Blake's work and J M Robertson's on the one hand and George Spencer-Brown's on the other.

A navegação consulta e descarregamento dos títulos inseridos nas Bibliotecas Digitais UC Digitalis, UC Pombalina e UC Impactum, pressupõem a aceitação plena e sem reservas dos Termos e Condições de Uso destas Bibliotecas Digitais, disponíveis em https://digitalis.uc.pt/pt-pt/termos. Conforme exposto nos referidos Termos e Condições de Uso, o descarregamento de títulos de acesso restrito requer uma licença válida de autorização devendo o utilizador aceder ao(s) documento(s) a partir de um endereço de IP da instituição detentora da supramencionada licença. Ao utilizador é apenas permitido o descarregamento para uso pessoal, pelo que o emprego do(s) título(s) descarregado(s) para outro fim, designadamente comercial, carece de autorização do respetivo autor ou editor da obra. Na medida em que todas as obras da UC Digitalis se encontram protegidas pelo Código do Direito de Autor e Direitos Conexos e demais legislação aplicável, toda a cópia, parcial ou total, deste documento, nos casos em que é legalmente admitida, deverá conter ou fazer-se acompanhar por este aviso.

Abstract: An interpretive and constructive understanding of information can be developed by drawing on a number of premises of autopoiesis in combination with Spencer-Brown’s laws of form. Such understanding views information as self-referential meaning construction by observing an object. Therefore, information can be perceived as form resulted from individuals ’ making distinction of their environment. By analyzing forms — token of indications — one can empirically understand what information is constructed. Such investigation is a qualitative exploration of human actions and interpretations.

"The Inner Story of The Further Shores of Knowing" is an essay about the play, The Further Shores of Knowing: A Metaphysical Musical Fantasy, in the volume of the same title, edited by Michael Urheber and Jack Engstrom (pages 119-135). The published book of the script also contains essays by Foster Gamble, Louis Kauffman, and Randolph Dible. This play is an instance of what I am calling "astral theurgy," which draws the participant into a symbolic narrative matrix that coalesces with the perennial story of transcendental philosophy, and with the spiritual and world-historical theme of integrality. This 'lnner Story' is also our common, universal story as cosmic, human, and spiritual beings within the largest compass of the far sphere; the infinite sphere as the fabled further shore. The agents of this symbolic matrix of story employ George Spencer-Brown's Laws of Form as a way of making the crossing to the further shore, through the umbilical point of the far sphere, at the pole star.

This essay explores the Mathematics of Charles Sanders Peirce. We concentrate on his notational approaches to basic logic and his general ideas about Sign, Symbol and diagrammatic thought. In the course of this paper we discuss two notations of Peirce, one of Nicod and one of Spencer-Brown. Needless to say, a notation connotes an entire language and these contexts are elaborated herein. The first Peirce notation is the portmanteau (see below) Sign of illation. The second Peirce notation is the form of implication in the existential graphs (see below). The Nicod notation is a portmanteau of the Sheffer stroke and an (overbar) negation sign. The Spencer-Brown notation is in line with the Peirce Sign of illation. It remained for Spencer-Brown (some fifty years after Peirce and Nicod) to see the relevance of an arithmetic of forms underlying his notation and thus putting the final touch on a development that, from a broad perspective, looks like the world mind doing its best to remember the significant patterns that join logic, speech and mathematics. The movement downward to the Form ("we take the form of distinction for the form."[9, Chapter 1, page 1]) through the joining together of words into archetypal portmanteau Signs can be no accident in this process of return to the beginning. We study a system of logic devised by Peirce based on a single Sign for inference that he calls his 'Sign of illation". We then turn to Peirce's Existential Graphs. The Existential Graphs lead to a remarkable connection between the very first steps in Logic and mirror plane symmetries of a "Logical Garnet" [30] in three dimensional space. Peirce's ideas about these graphs are related to his ideas about infinity and infinitesimals, and with his more general philosophy that regards a human being as a Sign. It is the intent of this paper to bring forth these themes in both their generality and their particularity. It is amazing that three dimensional geometry is closely allied to the first few distinctions of Logic. It is my intent in this paper to make that aspect crystal clear.

This paper is an exposition and review of the research related to the Riemann Hypothesis starting from the work of Riemann and ending with a description of the work of G. Spencer-Brown, culminating in his Denjoy proof of the RH.

> arXiv:2010.13781
[v1] Mon, 26 Oct 2020 01:41:00 UTC (30 KB)
[v2] Thu, 21 Jan 2021 05:53:55 UTC (31 KB)
[v3] Mon, 14 Mar 2022 07:09:27 UTC (34 KB)

> "Laws of Form: A Fiftieth Anniversary", Series on Knots and Everything, Vol 72, World Scientific, 2023.

Popular theatre belongs to the duplex form of communication the purpose of which is information dissemination packed in people’s discourse aiming consciousness building required for social and institutional change. It is a participatory endeavor using communication devices to

... This is shown as the following mark: ... Death is the only truth in our life. The body of your abbu [father] has disappeared but he will continue to be with us as a golden part of our memory and source of inspiration to be right when everything else seems wrong. Be his soul in peace. ...

Inclusion diagrams are introduced as an alternative to using Venn diagrams to determine the validity of categorical syllogisms, and are used here for the analysis of diverse categorical syllogisms. As a preliminary example of a possible generalization of the use of inclusion diagrams, consideration is given also to an argument that includes more than two premises and more than three terms, the classic major, middle and minor terms in categorical syllogisms.

A presentation is provided of a method-the Membership Table Method (MTM)-to determine the validity of categorical syllogisms. This method makes it possible for each syllogism to be assigned a specific set. If this set is equal to the universal set U, then the categorical syllogism considered is valid, and if that set is not equal to U, then that categorical syllogism is not valid. In other words, any categorical syllogism is valid if and only if its respective set, according to the MTM, is equal to the universal set U. The conclusion of a valid categorical syllogism whose premises are true is true.

To date, the Calculus of Indications (hereafter ‘CoI’) in George Spencer-Brown’s book 'Laws of Form' has been applied mainly in the fields of mathematics, logic, and social theory through the work of Kauffman, Varela, Luhmann, and others. Its application to literary analysis and narrative studies has been minimal, although Bouissac mentions the CoI and suggests its application in relation to the ‘Saussurean unfinished agenda’ (2006, pp. 256, 260). Berensmeyer (2004), Clarke (2008), and Kunze (2018) are, to my knowledge, the only narrative scholars to have drawn on Spencer-Brown’s work in print to date.  In his presentation at The Unmarked State Laws of Form 50th Anniversary Conference (LoF50), Freystetter (2019) draws out a metaphorical relationship between the narrative account of the unfolding of the universe in Genesis I and the presentation of the CoI as unfolding from the first distinction, seeing the Hebrew account as a precursor and generator of the CoI.  As such, his work—fascinating as it is—lies outside the scope of this paper, which looks solely at the application of the CoI to literary analysis and narrative studies.

The focus of this paper is to critically evaluate the directly relevant approaches cited above in terms of how they relate to Spencer-Brown’s work, and ask to what extent they reveal the underlying workings of the CoI, starting with Clarke’s work, proceeding to Kunze’s and then Berensmeyer’s. In the process I intend to situate my own work in the context of Spencer-Brown’s and to add some thoughts on how the CoI might be applied to the process of narrative analysis and in the analysis of social systems.

Inclusion diagrams are introduced as an alternative to using Venn diagrams to determine the validity of categorical syllogisms, and are used here for the analysis of diverse categorical syllogisms. As a preliminary example of a possible generalization of the use of inclusion diagrams, consideration is given also to an argument that includes more than two premises and more than three terms, the classic major, middle and minor terms in categorical syllogisms.

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 ist profoundly topological conception of common mathematics and (Boolean) algebra. Both are explained as direct offspring of their planar orientation. Selfreference 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.

George Spencer-Brown's Laws of Form is a mathematical treatise that calls for philosophical interpretation. Its core component, the calculus of indications, progresses from the simple act of drawing a distinction, through a number of levels of the indication of that distinction, until it finally reaches the level of real existence and the universe as we know it. While applicable to any special case of indication and semantic expression, this calculus is simultaneously a direct analysis of the underlying and ubiquitous substratum of creation from nothing. This means that Laws of Form should be understood as offering a theory of being (an ontology) and a theory of form (a phenomenology) on the common ground of an intuitive simplicity. The calculus of indications gives us a way of understanding everything-every possible object, every overall gestalt, every possible world, every 'thing' in both the precise literal sense and the diffuse metaphorical sense-as a form of indication, and all indication-the very 'form' codified by this calculus-as based on an original and primary distinction at the boundary between everything and nothing. This ultimate boundary, called "the first distinction," stands in a very peculiar relation to every familiar thing in our conscious experience. This singular peculiarity of the first distinction should be regarded on the basis of mathematical ontology, in terms of what is called prima philosophia, first philosophy (Greek: πρώτη φιλοσοφία), and in such terms we can determine its ontological and phenomenological status. ...