Where George Spencer-Brown went wrong – re-entry recalculated

Abstract

Purpose

The paper uncovers a mathematical error in George Spencer-Brown's genesis of re-entry. It distinguishes between the two interpretations of re-entry presented in “Laws of Form”: recursive versus sequential. The Indeterminacy inferred by George Spencer-Brown from his recursive genesis of re-entry is refuted in three different ways. The calculation of the Modulator from “Laws of Form” demonstrates that only the sequential interpretation of re-entry is reasonable. This contributes to the demystification of re-entry and enables a deeper understanding. Finally, six differences between the concept of form from “Laws of Form” and Niklas Luhmann's sociological systems theory are presented.

Design/methodology/approach

Methodologically, the paper uses the ternary logic of discrete mathematics, which extends {0, 1} by “don't care” to {0, 1, -}. George Spencer-Brown's Indeterminicy is refuted by using three different methods: complete induction, Theorems 14 and 15 and the software XBOOLE. For the calculation of the Modulator, the only practical application of re-entry in “Laws of Form”, techniques from automata theory are used.

Findings

The paper reveals a mathematical error in George Spencer-Brown's genesis of the re-entry of “Laws of Form” and refutes the assumption of Indeterminicy. The analysis of the only practical application of re-entry presented by George Spencer-Brown shows that the functioning of this Modulator can only be described correctly with the sequential interpretation of re-entry.

Originality/value

The paper emphasizes the interdisciplinary potential of sociology and information technology and provides methods and tools of discrete mathematics for use in the analysis of the works of George Spencer-Brown and Niklas Luhmann.

Citation

Oksas, A. (2024), "Where George Spencer-Brown went wrong – re-entry recalculated", Kybernetes, Vol. ahead-of-print No. ahead-of-print. https://doi.org/10.1108/K-09-2023-1722