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

March 20, 2020

A sociological reading of George Spencer-Brown’s Laws of Form consists in reading it as a theory of the observer. The paper looks at the “cross” established by the calculus of indications as a universal operator of general, or reflective, negation, presents second-order observation as a means to introduce indeterminacy as a precondition to communication, and reads Spencer-Brown’s primary arithmetic and primary algebra as steps towards an understanding of the (socio-)logical space comprehending any arrangement and re-arrangement of indications and distinctions. A short overview of the history of the notion of “form,” or “idea,” as developed by Plato, disclaimed by Kant and Hegel, and employed by Marx, Simmel, and Cassirer shows that this notion from the beginning hides, and passes on, problems of self-reference and transcendental subjectivity. A way to deal with these problems may be shown by Spencer-Brown’s introduction of imaginary states within equations of the second degree. Imaginary states, or values, allow time, society, nature, and technology to be introduced as references accounting for, exploring, and exploiting the indeterminacy created by them.

Read more… v2, April 2020, reconsidering the crucial role of negation pdf

A somewhat extended version of my contribution to the International Conference “The Unmarked State: Laws of Form 50th Anniversary Conference”, University of Liverpool, August 8–10, 2019 link

2 Comments
  1. Arnd Kulow permalink

    Dear Professor Backer,

    thank you very much for your post. Since I have still my “Schwierigkeiten mit der Negation” in so far as I can not really interpret a negation as implication at least in a logical sense, I would still like to make a short remark from a propositional logic point of view.

    In my world there are four unary operations in propositional logic (classic as well as Heyting style). Two of them anihilate the difference between the input (e.g. 0,1). They produce 0 or 1 as constants. Two of them hold the difference (identity and negation). Identity adds no further information to the input. It is a neutral operation. Negation flips the input and by doing so it adds something new. So from that point of view I strongly agree with you, that negation is a very special operation an can be called a “universal” and imho meaningful operation in a binary context.

    Greetings from the Black Forest

  2. Thomas Hölscher permalink

    for negation and its double way you i.e.everybody interested should be consulting Ulrich Blau “Die dreiwertige Logik der Sprache” – an if you like even more, his op. max.”Die Logikder Unbestimmtheiten und Paradoxien” – (ad negation we don’t have only Luhmann and what he has been reading)

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