The Laws of Form Controversy

PHI 108.01 Logical and Critical Reasoning, Frances Bottenberg

Randolph Thompson Dible II

July 26, 2009

There are unfortunate problems in the academic reception of George Spencer-Brown's Laws of Form1. The Laws of Form is a meta-thematic account of the consequences of just crossing (or making or drawing) a distinction (or difference), and of how the world in all its forms of distinction arises from the proemial act (or how we represent such a severance). The work is highly significant, yet there is only a handful of scholars who appreciate it. The main problem may be the unconventional and mystical2 nature of the work, but of those who are aware of it, some reject it on the grounds of triviality, equating it with common knowledge (Boolean algebra in particular). This is unfortunate because these problems of reception reduce the exposure of the work to inquiring minds and undervalue the methods of the author.

These problems were anticipated by the author when he wrote it, and knew that if it were to see the light of day, he would require some recommendation. Ludwig Wittgenstein faced similar problems in the publication of his logical calculus, the Tractatus Logico Philosophicus, and found relief in a forward by Bertrand Russell. Thus, George Spencer-Brown, then a post-graduate student of both Wittgenstein and Russell sought the same.

"In 1965, a young mathematician, G Spencer Brown, pressed me to go over his work since, he said, he could find no one else who he thought could understand it. As I thought well of what little of his work I had previously seen, and since I felt great sympathy for those who are trying to gain attention for their fresh and unknown work against the odds of established indifference, I agreed to discuss it with him. But as the time drew near for his arrival, I became convinced that I should be quite unable to cope with it and with his new system of notation. I was filled with dread. But when he came and I heard his explanations, I found that I could get into step again and follow his work. I greatly enjoyed those few days, especially as his work was both original and, it seemed to me, excellent."3

Russell came to endorse the work with his highest regards, remarking, "Not since Euclid's Elements have we seen anything like it", as stated on the book jacket of some editions of Laws of Form, "In this book G. Spencer Brown has succeeded in doing what,

1 George Spencer-Brown, Laws of Form, George Allen and Unwin Ltd., 19692 See Jack Engstrom, “Laws of Form and the Mystical Void”, Cybernetics and Human Knowing, Volume 8, Numbers 1-2, 2001. Throughout Laws of Form, Spencer-Brown makes mystical comments about the nature of genesis found in the book, as well as implying in the 1994 Preface that the calculus of indications is the “links of conditioned coproduction” of Sakyamuni Buddha.3 Bertrand Russell, Autobiography, George Allen and Unwin Ltd., 1967

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in mathematics, is very rare indeed. He has revealed a new calculus, of great power and simplicity. I congratulate him." Spencer-Brown gives this account of his relationship with Russell:

"Laws of Form was the only work in the entire history of the planet to which Russell gave his unqualified approval. It is the one book he had always wanted to write, and actually tied to, but unfortunately it came out as Principia. This was, for him, a major tragedy, and was largely responsible for his spending his latter days in fruitless political protests. He once asked me, "Do you think I wasted ten years of my life writing Principia?" What could I say? I couldn't say it was good, because he knew it was bad. In the end I said, rather lamely, 'No, Bertie. If you hadn't written the Principia, I couldn't have written the Laws.' The moment I said it, I realized it would be of no comfort to him at all. For some obscure reason we would all choose to be the spring, rather than the ground from which it sprang."4

The Laws of Form is the laws by which form (that which is comprised of distinctions) or archetype arise from an ultimate reality of a formless, unmarked state, through a mathematical hierarchy, up to the point where there is explicit self-reference or consciousness. Boundary mathematics and knot theory5 stem from this work, as do second-order cybernetics6 and autopoietic theory7. The author himself explains that it is the rediscovery of conditioned coproduction8, the only way of constructing an apparent universe.

The Laws of Form

The work begins with an explication of the form: "We take as given the idea of distinction and the idea of indication, and that we cannot make an indication without drawing a distinction. We take, therefore, the form of distinction for the form."9 Then, the definition of distinction is given: "Distinction is perfect continence."10 The word "continence" here means containment, as elucidated in the 2008 edition11. He continues the short chapter (all chapters are short because they are concise or condensed, as often occurs in pure mathematics) with an explication of the notion of distinction, its motive, and its denotation, and proceeds to give the two axioms or laws that become apparent with such a notion of distinction. The first is the law of calling: "The value of a call made again is the value of the call." The second is the law of crossing: "The value of a crossing made again is not the value of the crossing." The notation is significant in its use of only one token, the mark of distinction, the mark that indicates the crossing of a

4 Laws of Form, George Spencer-Brown, Bohmeier Verlag, 2008, pp. vii, footnote5 See the works of mathematicians Louis Kauffman, Richard Shoup, and William Bricken6 Especially Heinz von Foerster7 See the works of Humberto Maturana and Francisco Varela, creators of autopoietic theory8 A Lion's Teeth, George Spencer-Brown, Bohmeier Verlag, 1994, pp. 12, 149 Laws of Form, George Spencer-Brown, George Allen and Unwin Ltd., 1969, Ch. 110 ibid.11 Laws of Form, George Spencer-Brown, Bohmeier Verlag, 2008, footnote.

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distinction. There is another value, but it has no mark, no symbol, just a blank, unmarked space. This is significant because of the pervasive nature of the unmarked state.

Chapter 2, "Forms Taken Out of the Form", begins with the injunction "Draw a distinction." He calls this the first distinction, and he names the state distinguished by the first distinction the marked state. He then introduces his elegant form of notation used in the book—which is a simple mark that could just as well be a circle drawn on a plane space, similar to the notation used by Charles Sanders Peirce in his logical work (especially, his existential graphs12)—utilizing no token to indicate the unmarked state. In the subsequent chapters he continues to introduce canons (principles or rules) and theorems as he expounds the primary, non-numerical arithmetic, as he builds upon the calculus of indications (the two axioms or laws as equations) from the initial theorems, the “theorems of representation”. Theorems 8 and 9 are variance and invariance, called "theorems of connection", and are the gate to a new calculus made of pure algebraic theorems or "theorems of the second order" which develop “The Primary Algebra” (Ch. 6). He then brings it all together to give Equations of the Second Degree (Ch. 11) in which is introduced the imaginary unit, the square root of minus one, as "oscillation without duration" or the "first time" which allows the form to re-enter its own indicative space from the outside, from a higher dimension, as is characteristic of observation and awareness.

The "Flaws of Form"13

Although much of the problem of the Laws of Form's reception is unarticulated because the Laws of Form is relatively abstruse and technical, many critics refer to Paul Cull and William Frank's seemingly thoughtful paper, "Flaws of Form". The authors contend that Spencer-Brown has "merely reinvented Boolean algebra but in an obscure notation," and "At best, Brown has produced a new axiomatization for Boolean algebra."14 Indeed, Laws of Form can be interpreted for Boolean algebra, but as the introduction to Laws of Form begins, " A principal intention of this essay is to separate what are known as algebras of logic from the subject of logic, and to re-align them with mathematics." In other words, it is not logic, but meta-mathematics or protologic15. He continues:

"Such algebras, commonly called Boolean, appear mysterious because accounts of their properties at present reveal nothing of any mathematical interest about their arithmetics. Every algebra has an arithmetic, but Boole designed his algebra to fit logic, which is a possible interpretation of it, and certainly not its arithmetic. Later authors have, in this respect, copied Boole, with the result that nobody hitherto appears to have made any sustained

12 Charles Sanders Peirce, Collected Papers of Charles Sanders Peirce, Harvard University Press, 193313 Paul Cull and William Frank, "Flaws of Form", International Journal of General Systems, 1979, Vol. 5, pp. 201-211 14 ibid.15 Laws of Form is described as protologic in Michael Schiltz’ “Space is the Place: Laws of Form and Social Systems”, Thesis Eleven, Volume 88, Number 1, pp. 8-30

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attempt to elucidate and to study the primary, non-numerical arithmetic of the algebra in everyday use which now bears Boole's name."16

Besides Spencer-Brown's mathematical explanation of his "principal intention", a recent comment by William Bricken (of the Boundary Institute) at the lawsofform.org yahoo group, offered a concise rebuttal of the "Flaws of Form" triviality charge. Dr. Bricken identifies the crux of Frank and Cull's misunderstanding with their substitution of the Boolean operator "0" for Spencer-Brown's lack of any marking to indicate the unmarked state. They seem to do this in order to "fix" it up so it appears to be the same as Boolean algebra (which they do because they contend that is what it actuality is). Without this modification, Frank and Cull insist that Spencer-Brown violates the most basic truth of information theory, "at least two symbols are required to convey information."17 Laws of Form is taken by some to be the kernel or nucleus of information science and systems theory18, so clearly, someone must be wrong about this. And as Bricken points out, "[Frank and Cull] forget that the Shannon [and] Weaver brand of information theory (that I presume they had in mind) addresses sequential streams of binary variations, not spatial arrays."19 Bricken explains:

"This is sufficient to demonstrate that LoF is not Boolean Algebra (although it can be interpreted as Boolean Algebra). There is a many-to-one map from Boolean Algebra to LoF, so LoF is not isomorphic to Boolean Algebra [the charge of Frank and Cull as well as other critics]. By replacing "blank" by "0", the many-to-one map is degraded into an isomorphism, permitting these blind men to claim that because they are holding onto the elephant's leg, all elephants are trees."

"...C&F are viewing the representational space as positional and structured, permitting, for instance, only one correct place to put the "0"."

"The mark does not exclude crossing from the outside inwards, this asymmetry frees LoF of the dualism that permeates Boolean structures. So freed, it is then simple to build "logic" without any concept of False. Or, to be a bit more accurate, Truth is confounded with Existence."20

In short, Dr. Bricken shows that in this case, an effort was made to dismiss the work for not conforming to the Boolean structure they mistook it for. The difference is enormous. One begins to wonder whether Frank and Cull have read the Laws of Form. The comment about the many-to-one mapping of Laws of Form to Boolean algebra best articulates how these authors have missed the point and also how so many others follow suit.

16 George Spencer-Brown, Laws of Form, George Allen and Unwin, 1969, "Introduction"17 "Flaws of Form", Paul Cull and William Frank, International Journal of General Systems, 1979, pp. 20218 Marcia J. Bates, "The Invisible Substrate of Information Science", Journal of the American Society for Information Science, Volume 50, Number 12, 1999, for starters. 19 From the Yahoo group "Laws of Form" , comments by William Bricken in response to Alex Harvey: http://tech.groups.yahoo.com/group/lawsofform/message/183720 ibid.

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The Frank and Cull paper is the best example I know of criticism of Laws of Form. Other branches of criticism attack the sociologist and philosopher Niklas Luhmann, as an exponent of social systems theory who draws heavily on Laws of Form, and these criticisms have their own problems, to which one could add rebuttals, but that goes beyond the scope of this topic. Suffice it to say that some people face the powerful unknown or unfamiliar with fear, so rather than embracing the novelty, perhaps in wanting of a more rebellious nature, respond with articulating their feelings of insecurity, as the world they thought they comprehended is taken away. Laws of Form is the mathematical work that brought the observer or the living subject back into science21.

The crux of the matter is the role of self-reference in both the Laws of Form, and in the history of Western science and philosophy. Spencer-Brown begins the book with a seeming paradox, but one that is our existential state:

"There can be no distinction without motive, and there can be no motive unless contents are seen to differ in value"

Although the first distinction comes into being by bootstrapping itself into existence from the void or unmarked state (in the primary action of difference: here, difference as self-reference), the same operation is present in all forms of distinction at every even depth of crosses. In Chapter 11, this is called the “Re-entry” of the form into itself, and it is about the construction of time out of (marked and unmarked) space.

In the preface to the 1994 edition of the Laws of Form, Spencer-Brown explains the ground of the work, which is "the point" so to speak:

"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. 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".

"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."

These mystical statements are the ground of Laws of Form, and so the work is met with the same fear of the unknown, and yet radically personal nature of reality. This explains the unarticulated objections and reservations many academics have when reviewing the Laws of Form (as well as much of the articulated ones). At the conclusion of the book, we find that "We see that the first distinction, the mark, and the observer are

21 Notice the relationship of Bertrand Russell's Theory of Types’ linearization of self-referential logical dilemmas in Principia Mathematica to the Laws of Form, stated earlier in this paper.

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not only interchangeable, but, in the form, identical." Clearly, statements such as these, although necessary, will be met with some misunderstanding, and moreover, a good deal of emotion.

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