George Spencer-Brown

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George Spencer-Brown, also George Spencer Brown (pseudonyms James Keys, Richard Leroy; born April 2, 1923 in Grimsby , Lincolnshire , † August 25, 2016 in Market Lavington near Devizes , Wiltshire ), was a British mathematician , psychologist, poet and Songwriter.


Spencer-Brown studied at the University of London and London Hospital Medical College from 1940 to 1943. From 1943 to 1947 he was in the Royal Navy (radio operator, communications engineer, hypno-pain therapist; lieutenant 1946).

In 1947 he began studying at Trinity College at the University of Cambridge . He left Cambridge in 1952 to continue his studies at Oxford , where he was also a research fellow until 1958 . In 1957 he published his doctoral thesis on probability theory entitled Probability and Scientific Inference. The work was supervised by the British logician William Kneale .

Spencer-Brown had been in contact with Bertrand Russell since 1960 . In the 1960s he worked as an engineer for the British railways. This was followed by several years of collaboration with the psychiatrist Ronald D. Laing in the areas of psychotherapy and child rearing.

In 1976 he was visiting professor of mathematics at the University of Western Australia , 1977 for computer science at Stanford University , 1980-81 for pure mathematics at the University of Maryland . His lectures dealt with the four-color problem in maps and with Formal Arithmetics of Second Order. Spencer Brown was also a military advisor in Washington, DC on codes , code decryption, and optics .

Spencer-Brown submitted a treatise in 1977 in which he attempted to prove the four-color theorem. This “proof” has not yet been accepted by the professional community and has not even been recognized as a debatable contribution. In 2006 he also published a sketch of the evidence with which he claimed to have proven the main features of the Riemann Hypothesis . However, the author himself recognized that this evidence was unsuitable and in 2008 published a second sketch of the evidence, which followed a completely different line of argument and also appeared in Laws of Form . In addition, Spencer-Brown also assured that the Goldbach hypothesis and the Fermat hypothesis could only be proven with the assumption of imaginary truth values, as provided in his calculus . All these claims have led to Spencer-Brown no longer being taken seriously as a mathematician, especially since the four-color problem and Fermat's conjecture were proven even without Spencer-Brown's calculus.

Spencer-Brown was a half-blue in chess (that is, an excellent chess player in university competition) during his student days at Cambridge, also held two world records in gliding and was a sports correspondent for the Daily Express .

Laws of Form

Masterpiece Spencer-Brown are the Laws of Form (German: Laws of Form ) from 1969. It deals with classical problems of logic in an unusual today approach. What is special is that Spencer-Brown only uses two different characters for his “laws”: on the one hand the well-known equal sign, on the other hand a kind of negation or delimitation operator. The book is controversial among experts: some regard it as ingenious, others as original, but trivial in terms of knowledge value, because it is merely an operational reformulation of propositional logic . In fact, the calculus follows earlier attempts by Charles Sanders Peirce and Maurice Sheffer to write Boolean algebra with only one character. Later work by Peirce, initially to write entitative, then existential graphs with which this goal could be pursued, remained unknown to Spencer-Brown.

The originality of the Calculus of Indications developed by Spencer-Brown in the Laws of Form lies in the introduction of the unmarked state and the discovery of its meaning. Only with the unmarked state does the calculation become suitable for self-reference and paradox. Via the detour via the void , the form of the distinction leads back to the observer who makes the distinction. At the same time, however, the distinction - and with it the observer - becomes, what it is not, a reference to indistinguishability as a prerequisite for every distinction. The Laws of Form influenced and shaped the thinking of the scientists Heinz von Foerster , Louis Kauffman , Niklas Luhmann , Humberto Maturana and Francisco Varela , among others .


Spencer-Brown defines the English term “form” as a unit of an encompassing distinction with its inside and outside in the space of distinction it creates. Using such a distinction, one can then only name the inside, the outside and the distinction itself remain unnamed.

Unmarked space

In the Laws of Form , the author also describes the observer's dilemma: Every observation made by an observer, and thus a distinction , implies a second distinction: the first is the distinction between the object being observed (indication) - the second is the distinction made with the first distinction implicit distinction of the marked state from an unmarked state.

Such an observation of observation is also called “ re-entry ” and can be used universally as a theoretical figure, beyond mathematics. In the case of the sociologist Niklas Luhmann , for example, as a re-entry into the distinction, it becomes a central figure in Luhmann's systems theory .

Five years before the Laws of Form was published , Italo Calvino, in his short story Un segno nello spazio, tells the story of an observer, named Qfwfq, who became entangled in his own markings and who, like a literary experiment, explores the epistemological foundations (and dangers) of an observation second Okay reads.

Love letters

Two years later Spencer-Brown wrote under the pseudonym James Keys Only two can play this game (German: This game is only for two ). In contrast to the laws of form , this is a book about love. He wrote it after a broken love affair with a young student. Almost a third of it is an open love letter made up of twelve poems and stories to the former girlfriend. Brown himself says of the book: “In the Laws of Form I have tried, as far as I could, to describe the masculine side of things, just as in this book I try, as far as my limited abilities allow, something about the feminine side accept."


"A statement can not only be true, false or meaningless, but also imaginary."

- Laws of Form

“There is a game that children play when the tide comes in. They build a supposedly impenetrable sand wall around themselves to keep the water out as long as possible. Of course the water seeps through from below and at some point it breaks through the wall and floods everyone. Adults play a similar game. You surround yourself with a supposedly impenetrable wall of arguments to keep reality out. But reality seeps through from below, at some point breaks through the wall and floods us all. "

- Only two can play this game

"It is a sign of our culture's colossal predilection for the male principle that we believe we can invalidate any serious piece of literature by refuting it with arguments."



  • Dirk Baecker : Form and forms of communication. Suhrkamp, ​​Frankfurt am Main, 2005.
  • Dirk Baecker (ed.): Calculus of form. Suhrkamp, ​​Frankfurt am Main 1993.
  • Dirk Baecker (ed.): Problems of form. Suhrkamp, ​​Frankfurt am Main 1993.
  • Dirk Baecker: George Spencer-Brown and the subtle difference. In: Frankfurter Allgemeine Zeitung . October 14, 1997 (Review of the Laws of Form, available online from FAZ ).
  • Felix Lau: The Form of Paradox. An introduction to the mathematics and philosophy of the Laws of Form by George Spencer-Brown. Carl Auer, Heidelberg 2005.
  • Niklas Luhmann: Identity - what or how? In: Sociological Enlightenment. Volume 5, Opladen 1990, pp. 14-30.
  • Tatjana Schönwälder-Kuntze, Katrin Wille, Thomas Hölscher: George Spencer Brown: An introduction to the "Laws of Form". Wiesbaden 2009 (2nd revised edition).
  • Louis H. Kauffman: Time, Imaginary Value, Paradox, Sign and Space. Essay on the ideas of the Laws of Form in connection with Peirce (PDF file; 176 kB).
  • Louis H. Kauffman: Laws of Form - An Exploration in Mathematics and Foundations. (PDF file; 2.92 MB).
  • Eric W. Weisstein : Spencer-Brown Form . In: MathWorld (English). Internet article on the implementation of the forms in Mathematica.

Web links

Individual evidence

  1. Dirk Baecker : Message of death on: August 26, 2016. Retrieved August 27, 2016.
  2. ^ George Spencer Brown: Probability and Scientific Interference. London 1957.
  3. Published as Appendix V in the 2nd edition of the German-English edition of the Laws of Form (1999). See also G. Spencer-Brown: Claim of Proof to Four-Color Theorem. To the Editors of Nature. ( Memento from December 15, 2005 in the Internet Archive ). 17th December 1976.
  4. The “Proof” first appeared online ( PDF file ) and has been available since 2008 as Appendix IX of the new English edition of the Laws .
  5. ^ Laws of Form. EP Dutton, New York, 1979, pp. 19, 111, 125.
  6. Philip Meguire: Boundary algebra. A Simple Notation for Boolean Algebra and the Truth Function. University of Canterbury. College of Business and Economics. Department of Economics. Working Paper 02/2007, p. 72.
  7. See George Spencer-Brown: Laws of Form. Dutton, New York 1969/1979, p. 143 (About the Author).
  8. ^ Charles Sanders Peirce: A Boolean Algebra with One Constant (1880). In: Charles Hartshorne, Paul Weiss (Eds.): Collected Papers of Charles Sanders Peirce . Vol. 4: The Simplest Mathematics. MA: Harvard UP, Cambridge 1933, pp. 13-18; and Maurice Sheffer: A Set of Five Independent Postulates for Boolean Algebras, with Applications to Logical Constants. 1913, in: Transactions of the American Mathematical Society. 14: 481-488 (1913).
  9. ^ Robert Burch:  Charles Sanders Peirce. In: Edward N. Zalta (Ed.): Stanford Encyclopedia of Philosophy . .
  10. See also Louis H. Kauffman: Self-Reference and Recursive Forms. In: Journal of Social and Biological Structures: Studies in Human Sociobiology. 10, 1 (1987), pp. 53-72.
  11. Cf. Niklas Luhmann: Die Paradoxie der Form. In: Dirk Baecker (ed.): Calculus of form. Suhrkamp, ​​Frankfurt am Main 1993, pp. 197-212.
  12. Cf. Dirk Baecker, Alexander Kluge : From the benefit of unsolved problems. Merve, Berlin 2003, pp. 87-93.
  13. German: A Sign in Space (1964). In: Ders .: Cosmicomics. German by Burkhart Kröber, Hanser, Munich 1989, pp. 227-239.