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

Abstract

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, even if disguised as 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. v5