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
Social and Symbolic Boundaries
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
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
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
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
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
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
Structural Reflexivity and the Paradoxes of Self-Reference
Rohan French
university of groningen
ERGO Volume 3, No. 05, 2016
DOI: https://doi.org/10.3998/ergo.12405314.0003.005
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.
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
SECOND ORDER CYBERNETICS
Ranulph Glanville,
CybernEthics Research, UK and Royal Melbourne Institute of Technology University, Australia
A Formal Theory of Calculus of Indication
Tadao Ishii
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
“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
Triplicity in Spencer-Brown, Lacan, and Poe
Don Kunze
Department of Architecture, Penn State University
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
Distinction is Sufficient
William Bricken
March 2017
Click to access DistinctionIsSufficient.180327.pdf
Bayesian inference and the world mind
John O. Campbell
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
AN ESOTERIC GUIDE TO SPENCER-BROWN’S LAWS OF FORM
Seth T. Miller, PhD Cand.
Laws of Form
George Spencer Brown
1969
Click to access Spencer-Brown,%20George%20-%20Laws%20of%20Form.pdf
Introduction
Neocybernetic Emergence
bruce clarke and mark b. n. hansen
SEMIOTIC ABSTRACTIONS
IN THE THEORIES OF GOTTHARD GÜNTHER AND GEORGE SPENCER BROWN
By Rudolf Matzka, Munich, May 1993
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.
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
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
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
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
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
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
The Mathematics of Charles Sanders Peirce
Louis H. Kauffman
Cybernetics & Human Knowing, Vol.8, no.1–2, 2001, pp. 79–110
Foreword: Laws of Form
Louis H. Kauffman
Cybernetics and Human Knowing. Vol. 24 (2017), nos. 3-4, pp. 5-15
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
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
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
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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TAKUHEI SHIMOGAWA, YASUHIKO TAKAHARA. (1994) RECONSTRUCTION OF G. SPENCER BROWN’S THEME. International Journal of General Systems 23:1, pages 1-21.
Gary C. Berkowitz, David R. Greenberg, Charles A. White. (1991) MULTIPLICITY AND INDETERMINACY IN THE DYNAMICS OF FORMAL INDICATIONAL AUTOMATA. Cybernetics and Systems 22:3, pages 237-263.
Gary C. Berkowitz, David R. Greenberg, Charles A. White. (1988) AN APPROACH TO A MATHEMATICS OF PHENOMENA: CANONICAL ASPECTS OF REENTRANT FORM EIGENBEHAVIOR IN THE EXTENDED CALCULUS OF INDICATIONS. Cybernetics and Systems 19:2, pages 123-167.
PETER TURNEY. (1986) LAWS OF FORM AND FINITE AUTOMATA. International Journal of General Systems 12:4, pages 307-318.
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