Contents:
Volume 8 No. 1-2, 2001 All files are in pdf format, for which you may need to download the
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Louis H. Kauffman
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Columns
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by Louis H. Kauffman and Søren Brier Special Issue: Peirce and Spencer-Brown: History and Synergies in Cybersemiotics In this issue of Cybernetics and Human Knowing we have a collection of papers devoted to the cybernetics and mathematics of Charles Sanders Peirce with a special focus on its synergies with Spencer Brown’s thinking. We hope that the theme in this issue reflects the extraordinary richness of C. S. Peirce’s work and his relevance to our present concerns and creativity in cybernetics. The theme is part of the journal’s development of the area of cybersemiotics where Peirce and Spencer-Brown each have delivered the logical foundations. The similarities in the focus on some of the deep foundational subjects are astonishing, amongst those especially the concept of the void or Firstness and the continuum plus the continuity of mind and matter! Peirce was a truly original American philosopher and logician working in the late 1800’s and early 1900’s on the east coast of the United States. His father, Benjamin Peirce was a mathematician at Harvard University, a pioneer in abstract algebra and well known for the dictum “Mathematics is the Science that draws necessary conclusions.” Peirce was brought up in the intellectual environs of his father, and carried the philosophy of mathematics and logic to heights unimagined. Peirce, for personal and political reasons, spent the last 20 years of his life in virtual isolation from teaching, and in this time wrote volumes of material on mathematics, logic and philosophy that, thanks to his wife and friends, have been preserved and published after his death. These works are a continuing source of ideas and inspiration to scholars of mathematics, logic and cybernetics. The papers in the thematic part of this issue are each reflections on Charles Sanders Peirce’s work, its historical and present influence. The article “One, Two, Three ... Continuity: C. S. Peirce and the Nature of the Continuum” by Robin Robertson is a very accessible introduction to Peirce’s revolutionary views on infinity and the continuum that goes beyond the present basis for mainstream mathematics conception of infinitesimals. Peirce’s view is compared with Zeno’s, Weirstrass, Dedekind and Cantor’s and the problems their solutions generate. Robertson points out how Peirce’s Synechism connects his metaphysics and his view on mathematics and meaning into a unique viewpoint that may be the foundations from which present, seemingly insurmountable, problems in mathematics and science can be reformulated in a fruitful way connecting to Spencer-Brown and Bohr’s work, dealing with the limits of mechanicism. The article “Precursors to Laws of Form in C.S. Peirce’s Collected Papers” by Jack Engstrom shows how Peirce’s mathematics is related to the distinction based mathematics and philosophy of G. Spencer-Brown. He further discusses the metaphysical conceptions of the void or the unmarked state relating it to the mystical worldview. “In the world’s most complicated card trick” Robertson tells the story about Peirce’s combination of mathematics and a magical card trick that could have made him a fortune. The article “Peirce’s Influence on Today’s Mathematical Logic” by William Howard discusses Peirce’s influence on modern mathematical logic and second order cybernetics from a historical perspective. He points out Peirce’s influence on especially the semantic aspect of mathematical logic. The article “The Mathematics of Charles Sanders Peirce” by Louis H. Kauffman discusses the structure of the diagrammatic systems that Peirce used for logic and for mathematics. He starts with an analysis of Peirce’s “Sign of illiation”, which is a “portmanteau” sign (a sign containing two or more functions). The article shows the direct connection of these systems with the corresponding system of Spencer-Brown. It further shows the way in which the evolution of the diagrammatic systems is related to the evolution of logic, philosophy, cybernetics and mathematics such as the evolution of a Sign of itself (Peirce’s view of the human condition). It ends on reflective note “We ourselves are portmanteau signs of a complex order. We are packing cases of multiple meanings large enough to make a human being a sign of itself.” Finally this article explicates the relation of the amazing structure of the logical garnet of Shea Zellweger (a construction well known to Peirce scholars) to the work of both C.S. Peirce and Spencer-Brown. The article “Signs in action: Tarot as a self-organized system” by Inna Semetsky analyzes the structure of the Tarot and the relation of symbols to the Jungian psychology of the unconscious in Peircian terms. The ASC column “Cybernetics of Fixed Points” by Louis H. Kauffman is a fictional dialogue in a bar among imaginary representatives for cybernetics (von Foerster , Maturana) and logic (Russell, Church) representing views of both dead and present researchers. The universe is the bartender and Peirce is one of the visitors. The column, A (cybernetic) musing: Constructing my cybernetic world, by Ranulph Glanville draws a process oriented self-reflecting line through more than 30 years of his own work in cybernetics where ”he is not trying to do science or anything like that: “I am trying to set up a system within which we can have such a science.” He then very clearly describes the his project as “..how can we account for a world which each of us sees differently, and which, as a result, we cannot be sure is the same world?”, and summarizes the basic results of this endeavor so far. The book reviews are by Nina Ort of the new German edition of Handbuch der Semiotic by Winfied Nöth, which is one of the few semiotics handbooks that take small detours into information theory, cybernetics and cybersemiotics, comparing viewpoints making comparisons of viewpoints. Winfried Nöth reviews Semiotica’s special issue Biosemiotica edited by Jesper Hoffmeyer and Claus Emmeche. This book is one of the newest and most comprehensive discussions of the enlargement of semiotics from human language to encompass the sign games of all living systems, thereby covering a great part of the same area as cybernetics and information theory, which also inspire several articles. The artist of this issue is Jørn Særker Sørensen. Poems by Lawren Bale. We welcome Robin Robertson as a new consultant editor.  |
