A Calculus for Self Reference, Autopoiesis, and Indications

Source: FIVE TYPES OF SYSTEMS PHILOSOPHY

Bunge’s three types of systems philosophies are expanded to five:

• atomism (the world is an aggregate of elements, without wholes; to be understood by analysis),
• holism (ultimate reality is a whole without parts, except as illusory manifestations; apprehended intuitively),
• emergentism (parts exist together and their relations, connections, and organized interaction constitute wholes that continue to depend upon them for their existence and nature; understood first analytically and then synthetically),
• structuralism (the universe is a whole within which all systems and their processes exist as depending parts; understanding can be aided by creative deduction),
• and organicism (every existing system has both parts and whole, and is part of a larger whole, etc.; understanding the nature of whole-part polarities is a clue to understanding the nature of systems.

How these five types correlated with theories of conceptual systems and methodologies is also sketched.

Source: https://www.uboeschenstein.ch/texte/spencer-brown.html

Any indication implies duality, we cannot produce a thing without coproducing what it is not, and every duality implies triplicity: what the thing is, what it isn’t, and the boundary between them. Thus you cannot indicate anything without defining two states, and you cannot define two states without creating three elements. None of these exists in reality, or separately from the others. 

Key Terms

• G. Spencer Brown
• Self-indication
• Self-reference
• Self-referential systems
• Calculus of Indications
• Paradoxes
• Autonomy
• F. Varela
• Dirk Baecker
• Calculus for Self Reference
• Calculus for Autopoiesis
• Laws of Form
• Distinctions
• Indications
• L H Kauffman
• H Maturana
• Athanasios Karafillidis
• Lambda Calculus
• Alanzo Church
• Diamond Calculus
• William Bricken

A Calculus for Indication

George Spencer-Brown

Source: https://www.uboeschenstein.ch/texte/spencer-brown.html

George Spencer Brown Laws of Form Cognizer Co. 1994 Limited Edition

Preface to the 1994 Limited Edition page VII A generation has grown up since Laws of Form was first published in English. Human awareness has changed in the meantime, and what could not be said then it can be said now. In particular, I can now refer to the falseness of current scientific doctrine, what I call scientific duplicity: that appearance and reality are somehow different. Since there is no means, other than appearance, for studying reality, they are definitely the same.  But the scientist not only supposes they are different, and that he is „gradually finding out“ the one by means of the other; he supposes also that awareness (which he mistakenly confuses with consciousness) of the reality-apperance is something that is different again; and that the universe might have „existed“ for „billions of years“ amid total unawareness of what was going on.   This I shall have two call scientific triplicity. Again by definition, there can be no appearance that is not an awareness of appearance, and, of course, no awareness that is not an appearance of awareness. And since the scale of real-unreal cannot apply to appearance in general (as it can distinguish, for example, between real and toy soldiers), whatever appears, as appearance, must be equally real and unreal. Reversing the false distinctions, we arrive at what I call the triple identity, notably the definitional identity of reality, appearance, and awareness. It is remarkable how all the „building blocks“ of existence appear as triunions. (Compare the so-called „divine trinity“ of Christianity, which is merely a summary of our perception of how to construct the formation of any thing whatever.) It ist he triunion that apparently provides the magic inflatory principle that makes it all seem like it’s really there. The word „there“ supplies the trick. There exists and reality in no „where“ fort he „there“ to be. Nor is there any „when“. All these are constructions of imagination, inventions of apparently stable formations for the apparent appearances. Hence another expression of the triple identity: the identity of imaginability, possibility, and actuality. The universe is simply what would appear if it could.   Its laws are the laws of the possible, called by Sakyamuni the links of conditioned coproduction, called by me the calculus of indications. Each teaches exactly the same teaching, how what cannot possibly be anything comes to appear as if it were something. Since there is only one way this can happen, the teaching is always the same. Unfortunately, human beings have a childish propensity to turn what ever they learn into religions, and when this happens the original teaching is corrupted. A thing is not possible unless it is imaginable, and we could never confirm that it was possible unless it appeared in actuality. Thus what is possible will always be found to exist, and its actual existence (for exemple helium, carbon 60) will be discovered soon after its possibility has been imagined. What exists is formally constructed by postulating the imagination of a hypothetical being that is supposed to perceive it, and different beings will bring about the construction of different existences. (Not only physical existence, but all creation is subject to the same law.) A totally different being will construct a completely different existence: „The world of the happy is altogether different from the world of the unhappy“. Wittgenstein, Tractatus, 1922 „We“ make an existence by taking apart the elements of a triple identity. The existence ceases when we put them together again.  Sakyamuni, the only other author who evidently discovered these laws, remarked in this context, „Existence is duality: nonexistence is non-duality. (The more a being cultivates consciousness at the expense of awareness, the stupider it becomes. Western civilisation has promoted consciousness and neglected awareness almost to the point of complete idiocy. I have had to spend the greater part of a lifetime undoing and reversing the destructive ravages of my one-sided education.) Any indication implies duality, we cannot produce a thing without coproducing what it is not, and every duality implies triplicity: what the thing is, what it isn’t, and the boundary between them. Thus you cannot indicate anything without defining two states, and you cannot define two states without creating three elements. None of these exists in reality, or separately from the others.   In reality there never was, never could be, and never will be anything at all. There! You always knew with its. No other answer makes sense. All I teach is the consequences of there being nothing. The perennial mistake of Western philosophers has been to suppose, with no justification whatever, that nothing cannot have any consequences. (The idea that the creation must be a consequence of „something“ is moronic. No thing can have any consequence whatever. If there were originally something, it would poison the whole creative process. Only nothing is unstable enough to give origin to endless concatenations of different appearances.) On the contrary: not only it can: it must. And one of the consequences of there being nothing is the inevitable appearance of „all this“. No problem! Page XXIX: A Note on the Mathematical Approach The theme of this book is that the universe comes into being when a space is severed to or taken apart. The skin of a living organism cuts off an outside from an inside. So does the circumference of a circle in a plane. By tracing the way we represent such a severance, we can begin to reconstruct, with an accuracy and coverage that appear almost uncanny, the basic forms underlying linguistic, mathematical, physical, and biological science, and can begin to see how familiar laws of our own experience follow inexorably from the original act of severance. The act is itself already remembered, even unconsciously, as our first attempt to distinguish different things in a world where, in the first place, the boundaries can be drawn any where we please. At this stage the universe cannot be distinguished from how we act upon it and the world may seem like shifting sand beneath our feet. Although all forms, and thus all universities, are possible, and any particular form is mutable, it becomes evident that the laws relating such forms of the same in any universe. It is this sameness, the idea that we can find a reality which is independent of how the universe actually appears, that lends such fascination to the study of mathematics. That mathematics, in common with other art forms, can lead us beyond ordinary existence, and can show us something of the structure in which all creation hangs together, is no new idea but mathematical texts generally begin the story somewhere in the middle, leaving the reader to pick up the thread as best he can. Here the story is traced from the beginning.

Source: Laws of Form / 1994 Limited Edition

Source: Laws of Form / 1994 Limited Edition

Source: Laws of Form / 1994 Limited Edition

Source: Laws of Form / 1994 Limited Edition

Source: Laws of Form / 1994 Limited Edition

Source: Laws of Form / 1994 Limited Edition

Source: Laws of Form / 1994 Limited Edition

A Calculus for Self Reference

Francisco Varela

https://www.tandfonline.com/doi/abs/10.1080/03081077508960828

An extension of the calculus of indications (of G. Spencer Brown) is presented to encompass all occurrences of self-referential situations. This is done through the introduction of a third state in the form of indication, a state seen to arise autonomously by self-indication. The new extended calculus is fully developed, and some of its consequences for systems, logic and epistemology are discussed.

A Calculus for Autopoiesis

Dirk Baecker

This paper looks once more at the understanding and definition of autopoiesis as developed by Humberto R. Maturana, Francisco J. Varela, and Ricardo Uribe (Varela/Maturana/Uribe 1974; Maturana 1981; Maturana/Varela 1980; Varela 1979a). We will not go into the philology of comparing the different versions of the understanding and definition of autopoiesis, into the different attempts to get its record straight, or into the question whether not only living but also social systems may be considered autopoietic by well-defined criteria (Zeleny 1981; Zeleny/Hufford 1992; Fleischaker 1992; Geyer 1992; Bourgine/Stewart 2004; Luisi 2003). We will instead focus on just one question: whether George Spencer-Brown’s Laws of Form (2008) presents us with a possibility of translating Maturana’s definition into a kind of a calculus. Francisco J. Varela tried to do this, only to discover that he had to add a further autonomous state to the calculus of indications to make it fit for modeling self reference (Varela 1975, 1979b). We share criticism of this attempt that addresses the idea that the distinction itself, in the form identical to the observer (Spencer-Brown 2008: 63) is already the autonomous state Varela thought he needed to introduce (Kauffman 1978; Varga von Kibéd 1989).

Instead of going into this extended discussion at this point, we turn to another discussion on social systems as autopoietic systems that establish and unfold their own paradox into a play with their distinctions, frames, and values that equals their iterative reproduction (Luhmann 1990a, 1992; Hutter 1979: 194-200, 1989: 28-33, 1990). That is, we look again at Maturana’s emphasis on components, networks, and boundaries and try to figure out how thisemphasis can translate into an understanding of form that knows about self-reference, paradox, and play.

My Related Posts

Autocatalysis, Autopoiesis and Relational Biology

Cybernetics, Autopoiesis, and Social Systems Theory

Reflexivity, Recursion, and Self Reference

Society as Communication: Social Systems Theory of Niklas Luhmann

Boundaries and Relational Sociology

Networks, Narratives, and Interaction

Semiotic Boundaries

Social and Symbolic Boundaries

Boundaries and Distinctions

Boundaries and Networks

Charles Sanders Peirce’s Visual Logic: Diagrams and Existential Graphs

Steps to an Ecology of Mind: Recursive Vision of Gregory Bateson

Knot Theory and Recursion: Louis H. Kauffman

Frames, Communication, and Public Policymaking

Key Sources of Research

Self-Reference: Reflections on Reflexivity

edited by S.J. Bartlett, P. Suber

A Calculus for Autopoiesis

Baecker, Dirk,

(June 1, 2012).

in: Dirk Baecker und Birger P. Priddat (eds.), Ökonomie der Werte: Festschrift zum 65. Geburtstag von Michael Hutter, Marburg: Metropolis, 2013, 249-267,

Available at SSRN: https://ssrn.com/abstract=2073362 or http://dx.doi.org/10.2139/ssrn.2073362

A CALCULUS FOR SELF-REFERENCE

J. FRANCISCO & G. VARELA (1975) 

International Journal of General Systems, 2:1, 5-24, 

DOI: 10.1080/03081077508960828

https://www.tandfonline.com/doi/citedby/10.1080/03081077508960828?scroll=top&needAccess=true

Click to access VarelaCSR.pdf

Click to access varela_calculus.pdf

THE ARITHMETIC OF CLOSURE

FRANCISCO J. VARELA & JOSEPH A. GOGUEN (1978) 

Journal of Cybernetics, 8:3-4, 291-324, 

DOI: 10.1080/01969727808927587

https://www.tandfonline.com/doi/abs/10.1080/01969727808927587?src=recsys

SYSTEMS AND DISTINCTIONS; DUALITY AND COMPLEMENTARITY

JOSEPH A. GOGUEN & FRANCISCO J. VARELA (1979) 

International Journal of General Systems, 5:1, 31-43, 

DOI: 10.1080/03081077908960886

https://www.tandfonline.com/doi/abs/10.1080/03081077908960886?src=recsys

NETWORK SYNTHESIS AND VARELA’S CALCULU 

LOUIS H. KAUFFMAN (1978) 

International Journal of General Systems, 4:3, 179-187, 

DOI: 10.1080/03081077808960682

https://www.tandfonline.com/doi/abs/10.1080/03081077808960682

ISOMORPHISMS OF SPENCER-BROWN’S LAWS OF FORM AND VARELA’S CALCULUS FOR SELF-REFERENCE

DANIEL G. SCHWARTZ (1981) 

International Journal of General Systems,6:4, 239-255, 

DOI: 10.1080/03081078108934802

https://www.tandfonline.com/doi/abs/10.1080/03081078108934802

FIVE TYPES OF SYSTEMS PHILOSOPHY

ARCHIE J. BAHM (1981) 

International Journal of General Systems, 6:4, 233-237, 

DOI: 10.1080/03081078108934801

https://www.tandfonline.com/doi/abs/10.1080/03081078108934801?src=recsys

LAWS OF FORM AND FINITE AUTOMATA 

PETER TURNEY (1986) 

International Journal of General Systems, 12:4, 307-318, 

DOI: 10.1080/03081078608934939

https://www.tandfonline.com/doi/abs/10.1080/03081078608934939?src=recsys

FLAWS OF FORM

PAUL CULL & WILLIAM FRANK (1979) 

International Journal of General Systems, 5:4, 201-211, 

DOI: 10.1080/03081077908547450

https://www.tandfonline.com/doi/abs/10.1080/03081077908547450?src=recsys

INTRODUCTORY COMMENTS TO FRANCISCO VARELA’ S CALCULUS FOR SELF-REFERENCE, 

RICHARD HERBERT HOWE & HEINZ VON FOERSTER (1975) 

International Journal of General Systems, 2:1, 1-3, 

DOI: 10.1080/03081077508960827

ON THE LAWS OF FORM

ROBERT A. ORCHARD (1975) 

International Journal of General Systems, 2:2, 99-106, 

DOI: 10.1080/03081077508547493

EPISTEMOLOGY, SEMANTICS, AND SELF-REFERENCE, 

ANNETTA PEDRETTI (1980) 

Journal of Cybernetics, 10:4, 313-339, 

DOI: 10.1080/01969728008927652

Snakes all the Way Down: Varela’s Calculus for Self-Reference and the Praxis of Paradise

André Reichel

First published: 14 October 2011

https://doi.org/10.1002/sres.1105

Systems Research and Behavioral Science

Volume 28, Issue 6
Special Issue: Autopoiesis, Systems Thinking and Systemic Practice: The Contribution of Francisco Varela
November/December 2011
Pages 646-662

https://onlinelibrary.wiley.com/doi/full/10.1002/sres.1105

https://www.researchgate.net/publication/227670222_Snakes_all_the_Way_Down_Varela%27s_Calculus_for_Self-Reference_and_the_Praxis_of_Paradise

Click to access REI_2011_Snakes.pdf

Self-Reference and Time According to G. Spencer-Brown

Andreas Kull

Max-Planck-Institut fu ̈r Extraterrestrische Physik

D-85740 Garching, Germany

http://sfile-pull.f-static.com/image/users/112431/ftp/my_files/sbrown.pdf?id=11014655

A Note on the Possibility of Self-Reference in Mathematics

Arieh Lev

Click to access 1908.02539.pdf

Mathematical Work of Francisco Varela

Louis H. Kauffman • University of Illinois at Chicago, USA • kauffman/at/uic.edu

Constructivist Foundations

Volume 13 · Number 1 · Pages 11–17

2017

 http://constructivist.info/13/1/011

Click to access 011.kauffman.pdf

Virtual logic — the calculus of indications

Author: Kauffman, L.H.
Source: Cybernetics & Human Knowing, Volume 5, Number 1, 1 January 1998, pp. 63-68(6)
Publisher: Imprint Academic

Virtual logic – self-reference and the calculus of indications

Author: Kauffman, L.H.
Source: Cybernetics & Human Knowing, Volume 5, Number 2, 1 February 1998, pp. 75-82(8)
Publisher: Imprint Academic

https://www.ingentaconnect.com/content/imp/chk/1998/00000005/00000002/11

Virtual Logic — symbolic logic and the calculus of indications

Author: Kauffman, L.H.
Source: Cybernetics & Human Knowing, Volume 5, Number 3, 1 March 1998, pp. 63-70(8)
Publisher: Imprint Academic

https://www.researchgate.net/publication/263247376_Virtual_Logic_–_symbolic_logic_and_the_calculus_of_indications

Peirce and Spencer-Brown: history and synergies in cybersemiotics

Authors: Kauffman, L.H.; Brier, S.
Source: Cybernetics & Human Knowing, Volume 8, Numbers 1-2, 1 January 2001, pp. 3-5(3)
Publisher: Imprint Academic

Peirce’s Existential Graphs

Author: Kauffman, Louis
Source: Cybernetics & Human Knowing, Volume 18, Numbers 1-2, 2011, pp. 49-81(33)
Publisher: Imprint Academic

Virtual Logic–Number and Imagination

Author: Kauffman, Louis
Source: Cybernetics & Human Knowing, Volume 18, Numbers 3-4, 2011, pp. 187-196(10)
Publisher: Imprint Academic

An Esoteric Guide to Spencer-Brown’s Laws Of Form

Author: Miller, S.
Source: Cybernetics & Human Knowing, Volume 21, Number 4, 2014, pp. 31-67(37)
Publisher: Imprint Academic

Gregory Bateson, Heterarchies, and the Topology of Recursion

Author: Harries-Jones, Peter
Source: Cybernetics & Human Knowing, Volume 12, Numbers 1-2, 2005, pp. 168-174(7)
Publisher: Imprint Academic

Virtual Logic–Set Theory and the Continuum Hypothesis

Author: Kauffman, L.H.
Source: Cybernetics & Human Knowing, Volume 21, Number 3, 2014, pp. 63-74(12)
Publisher: Imprint Academic

Ontopoiesis, Autopoiesis, and a Calculus Intended for Self-Reference

Randolph T Dible

https://www.academia.edu/36670762/Ontopoiesis_Autopoiesis_and_a_Calculus_Intended_for_Self_Reference

SELF–REFERENCE, PHENOMENOLOGY, AND PHILOSOPHY OF SCIENCE

by

Steven James Bartlett

website: http://www.willamette.edu/~sbartlet

Click to access BARSPA-20.pdf

Structural Reflexivity and the Paradoxes of Self-Reference

Rohan French

university of groningen

rohan.french@gmail.com

ERGO Volume 3, No. 05, 2016

DOI: https://doi.org/10.3998/ergo.12405314.0003.005

https://quod.lib.umich.edu/e/ergo/12405314.0003.005/–structural-reflexivity-and-the-paradoxes-of-self-reference?rgn=main;view=fulltext

Self-Reference

Stanford Encyclopedia of Philosophy

https://plato.stanford.edu/entries/self-reference/

A Calculus for Autopoiesis

Baecker, Dirk,

(June 1, 2012).

in: Dirk Baecker und Birger P. Priddat (eds.), Ökonomie der Werte: Festschrift zum 65. Geburtstag von Michael Hutter, Marburg: Metropolis, 2013, 249-267,

Available at SSRN: https://ssrn.com/abstract=2073362 or http://dx.doi.org/10.2139/ssrn.2073362

Life and mind: From autopoiesis to neurophenomenology. A tribute to Francisco Varela

EVAN THOMPSON

Canada Research Chair in Cognitive Science and the Embodied Mind, Department of Philosophy, York University (E-mail: evant@yorku.ca)

Phenomenology and the Cognitive Sciences 3: 381–398, 2004.

Click to access pcs-life-and-mind.pdf

George Spencer-Brown’s laws of form fifty years on: why we should be giving it more attention in mathematics education

Steven Watson University of Cambridge

MATHEMATICS TEACHING RESEARCH JOURNAL

Special Issue on Philosophy of Mathematics Education Summer 2020 Vol 12 no 2

Click to access v12n2-George-Spencer-Brown-s-laws-of-form-fifty-years-on.pdf

SECOND ORDER CYBERNETICS

Ranulph Glanville,

CybernEthics Research, UK and Royal Melbourne Institute of Technology University, Australia

Click to access Glanville-SECOND_ORDER_CYBERNETICS.pdf

A Formal Theory of Calculus of Indication

Tadao Ishii

Click to access 229975592.pdf

George Spencer Brown
Laws of Form (Calculus of Indications)

Dr. Randall Whitaker

Website

http://www.enolagaia.com/GSB.html#LoF

Working the Form: George Spencer-Brown and the Mark of Distinction

• June 2015

Dirk Baecker

• Zeppelin University

https://www.researchgate.net/publication/278210110_Working_the_Form_George_Spencer-Brown_and_the_Mark_of_Distinction

“Spencer-Brown, Peirce, Girard, and the Origin of Logic.” 

Rosa, António Machuco.

Contagion: Journal of Violence, Mimesis, and Culture 22 (2015): 65–88. https://doi.org/10.14321/contagion.22.1.0065.

https://www.jstor.org/stable/10.14321/contagion.22.1.0065

The Brown-4 Indicational Calculus

Arthur M. Collings

Cybernetics and Human Knowing. Vol. 24 (2017), nos. 3-4, pp. 75-101

Click to access 75-101.pdf

Triplicity in Spencer-Brown, Lacan, and Poe

Don Kunze
Department of Architecture, Penn State University

Click to access triplicity.pdf

SPACE IS THE PLACE: THE LAWS OF FORM AND SOCIAL SYSTEMS 

Michael Schiltz

Thesis Eleven, Number 88, February 2007: 8–30

SAGE Publications (London, Thousand Oaks, CA and New Delhi)

DOI: 10.1177/0725513607072452

Click to access Schiltz-LoFandSocialSystems.pdf

Distinction is Sufficient

William Bricken

March 2017

Click to access DistinctionIsSufficient.180327.pdf

Bayesian inference and the world mind

John O. Campbell

Click to access 1210.8031.pdf

Comment: Socializing a Calculus

The Emergence of a Theory of Social Forms and a Sociological Notation

Athanasios Karafillidis

Cybernetics and Human Knowing. Vol. 20, nos. 3-4, PP· 108-141

Click to access Karafillidis_Socializing.pdf

Shape of things to come: From the ‘laws of form’ to management in the post-growth economy

André Reichel

Ephemera 2017

http://www.ephemerajournal.org

volume 17(1): 89-118

Click to access 17-1reichel.pdf

AN ESOTERIC GUIDE TO SPENCER-BROWN’S LAWS OF FORM 

Seth T. Miller, PhD Cand.

Click to access An-Esoteric-Guide-to-Laws-of-Form.pdf

Laws of Form

George Spencer Brown

1969

Click to access Spencer-Brown,%20George%20-%20Laws%20of%20Form.pdf

Click to access Ciber-3a-29-out.-Spencer-Brown-Laws-of-Form.pdf

Introduction

Neocybernetic Emergence

bruce clarke and mark b. n. hansen

Click to access clarke-e-hansen-neocybernetic-emergence.pdf

SEMIOTIC ABSTRACTIONS
IN THE THEORIES OF GOTTHARD GÜNTHER AND GEORGE SPENCER BROWN

By Rudolf Matzka, Munich, May 1993

Click to access semabs.pdf

Diamond Calculus of Formation of Forms

A calculus of dynamic complexions of distinctions as an interplay of worlds and distinctions

Rudolf Kaehr Dr.phil

ISSN 2041-4358

https://www.yumpu.com/en/document/view/35498897/diamond-calculus-of-formation-of-forms-thinkart-lab

Click to access rk_Diamond-Calculus-of-Formation-of-Forms_2011.pdf

Iconic Arithmetic: Simple Sensual Postsymbolic

THE DESIGN OF MATHEMATICS FOR HUMAN UNDERSTANDING

William Bricken,Ph.D.

Click to access iconicarithmetic01will.pdf

Catjects

Dirk Baecker

Universität Witten/Herdecke

dirk.baecker@uni-wh.de

https://osf.io/preprints/socarxiv/73mht/

Some-thing from No-thing: G. Spencer-brown’s Laws of Form

Click to access Robertson-Laws_of_Form.pdf

Roth, S., Heidingsfelder, M., Clausen, L. and Laursen, K.B. (2021), “Editorial Note”, 

Roth, S., Heidingsfelder, M., Clausen, L. and Laursen, K.B. (Ed.) George Spencer Brown’s “Design with the NOR”: With Related Essays, Emerald Publishing Limited, Bingley, pp. 1-5. 

https://doi.org/10.1108/978-1-83982-610-820211001

A Sociological Reading of George Spencer-Brown’s Laws of Form

Baecker, Dirk,

(January 4, 2021).

Louis H Kauffman, Andrew Compton, Leon Conrad, Fred Cummins, Randolph Dible, Graham Ellsbury, and Florian Grote (eds.), Laws of Form – A Fiftieth Anniversary,

Available at SSRN: https://ssrn.com/abstract=3678663 or http://dx.doi.org/10.2139/ssrn.3678663

Descriptions as Distinctions George Spencer Brown’s Calculus of Indications as a Basis for Mitterer’s Non-dualistic Descriptions

March 2013

Constructivist Foundations 8(2):202-209
Authors: Patricia Ene

https://www.researchgate.net/publication/292484884_Descriptions_as_Distinctions_George_Spencer_Brown%27s_Calculus_of_Indications_as_a_Basis_for_Mitterer%27s_Non-dualistic_Descriptions

Mathematics and Models for Autopoiesis

John Mingers 1995

In: Self-Producing Systems. Contemporary Systems Thinking. Springer, Boston, MA.

https://doi.org/10.1007/978-1-4899-1022-6_4

https://link.springer.com/chapter/10.1007/978-1-4899-1022-6_4

Lecture by Louis Kauffman on work of F Varela

Mind and Life Europe

2021

Life and Work of Francisco Varela: Amy Cohen Varela | Ouroboros Seminars 2021 | Varela 20/30

Mind and Life Europe

Playlist 1 of 14

On the application of the Calculus of Indications (George Spencer-Brown)

Leon Conrad

Laws of Form Course – An Introduction to George Spencer-Brown’s ‘Laws of Form’

Leon Conrad

Playlist of 18 Videos

Live webinar with the Dalai Lama: “Dialogue for a Better World – Remembering Francisco Varela”

Mind and Life Europe

2022

Keynote: Explorations in Laws of Form — Louis H Kauffman

Kunstforum Den Haag

An Ontological Interpretation of Laws of Form — Randolph Dible

Spencer-Brown Form

https://mathworld.wolfram.com/Spencer-BrownForm.html

Laws of Form – An Exploration in Mathematics and Foundations

by Louis H. Kauffman UIC

Click to access Laws.pdf

George Spencer Brown

https://www.uboeschenstein.ch/texte/spencer-brown.html

George Spencer Brown’s “Design with the NOR”: With Related Essays

Edited by
PROF STEFFEN ROTH
La Rochelle Business School, France

University of Turku, Finland

PROF MARKUS HEIDINGSFELDER
Xiamen University Malaysia, Malaysia

MR LARS CLAUSEN
UCL University College, Denmark

University of Flensburg, Germany

DR KLAUS BRØND LAURSEN
University of Aarhus, Denmark

2021

Click to access 9781839826115-TYPE23-NR2.pdf

https://www.emerald.com/insight/content/doi/10.1108/978-1-83982-610-820211013/full/pdf?title=prelims

A Calculus of Negation in Communication

Dirk Baecker

Cybernetics and Human Knowing. Vol. 24 (2017), nos. 3-4, pp. 17-27

Click to access 17-27.pdf

Distinction and the Foundations of Arithmetic

Thomas J. McFarlane 
thomasmc@stanfordalumni.org
December 2001
First revision October 2007
Second revision March 2011

http://www.integralscience.org/lot.html

THE ARITHMETIC AND ALGEBRA OF GEORGE SPENCER-BROWN

R.W. SHARPE

Click to access Arithmetic_and_Algebra_of_George_Spencer_Brown.pdf

The Mathematics of Charles Sanders Peirce

Louis H. Kauffman

Cybernetics & Human Knowing, Vol.8, no.1–2, 2001, pp. 79–110

Click to access CHK.pdf

Foreword: Laws of Form

Louis H. Kauffman

Cybernetics and Human Knowing. Vol. 24 (2017), nos. 3-4, pp. 5-15

Click to access 5-15F_0.pdf

Peirce and Spencer-Brown: History and Synergies in Cybersemiotics

Louis H. Kauffman, Soren Brier
Imprint Academic, 2007

The Mathematics of Boundaries: A Beginning

William Bricken

william@wbricken.com

In: Barker-Plummer, D., Cox, R., Swoboda, N. (eds) Diagrammatic Representation and Inference. Diagrams 2006. Lecture Notes in Computer Science(), vol 4045. Springer, Berlin, Heidelberg.

https://doi.org/10.1007/11783183_8

Click to access 05-pubs.pdf

https://link.springer.com/chapter/10.1007/11783183_8

Syntactic Variety in Boundary Logic

William Bricken

Click to access 01syntactic-variety.pdf

Laws of Form: A Fiftieth Anniversary (Hardcover)

By Louis H. Kauffman (Editor), Fred Cummins (Editor), Randolph Dible (Editor)

https://www.booksonb.com/book/9789811247422

https://www.worldscientific.com/worldscibooks/10.1142/12563?cmpid=6350db6df59e5b0001f79b4b&utm_campaign=Dynamic+Search+Ads&utm_source=Google&utm_medium=cpc&sub2=&sub3=&sub4=55561943429&sub5=322830954718&sub6=336010695&sub7=c&sub8=&sub9=g&sub10=&ref_id=CjwKCAiAhqCdBhB0EiwAH8M_GhoK4tjkBCyoJF_sWaBwMa77nkoIwAcfD0rxF_n5V8hlg-6WD3Y2jxoCpDIQAvD_BwE&gclid=CjwKCAiAhqCdBhB0EiwAH8M_GhoK4tjkBCyoJF_sWaBwMa77nkoIwAcfD0rxF_n5V8hlg-6WD3Y2jxoCpDIQAvD_BwE#t=aboutBook

Form and Medium: A Mathematical Reconstruction

Author: Michael Schiltz

Date published: August 2003

http://www.imageandnarrative.be/inarchive/mediumtheory/michaelschiltz.htm

System as Difference

Niklas Luhmann

Click to access Ciber-8c-3-dez-Luhmann-2006-System-as-Difference.pdf

Logical Graphs

https://oeis.org/wiki/Logical_Graphs

On the Curious Calculi of Wittgenstein and Spencer Brown

Authors
Gregory Landini
University of Iowa
DOI: https://doi.org/10.15173/jhap.v6i10.3400

JHAP Vol. 6 No. 10 (2018)

https://jhaponline.org/jhap/article/view/3400

Additional Resources

Source: A CALCULUS FOR SELF-REFERENCE

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