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Blake is relatively well-known, but who was J M Robertson? What's his connection with George Spencer-Brown? And how exactly did J M Robertson influence George Spencer-Brown?

George Spencer-Brown (1923–2016) is the author (among other works) of the undeservedly little-known book, Laws of Form (1969/2011), which was a key inspiration for Niklas Luhmann (1927–1998). But what inspired George Spencer-Brown? This paper explores two key influences on George Spencer-Brown and his work: the English poet and artist, William Blake (1757–1827) and the Scottish rationalist, politician and author, J M Robertson (1856–1933).

The paper points to a broken link between George Spencer-Brown's work and Niklas Luhmann's.

These questions are explored from two perspectives: first, George Spencer-Brown's works and their debt to (1) Blake's work, from which he quotes in a number of instances and to (2) J M Robertson's (in particular, the latter's Letters on Reasoning (1905) and Rationalism (1912)); second, my personal connection to Spencer-Brown, who mentored me through Laws of Form and with whom I developed a close friendship involving regular weekly telephone conversations for the greater part of the last four years of Spencer-Brown's life. I share anecdotes and stories that connect George Spencer-Brown and J M Robertson that span George Spencer-Brown's lifetime – from his school days to his dying days. Both Blake's and Robertson's influences are relevant to Spencer-Brown's view of morality. The paper looks at specific connections between Blake's work and J M Robertson's on the one hand and George Spencer-Brown's on the other.

The traditional liberal-arts curriculum of the word-based Trivium (grammar, dialectic/logic, rhetoric) and the number-based Quadrivium (arithmetic, geometry, astronomy, music) has an intrinsic unity. Used in an integrated way, it provides a tool for self-development, self-realisation and self-integration. The purpose of this paper is to outline the core nature of the integrative quality of the liberal-arts curriculum, trace the gradual disintegration of the curriculum from its adoption in classical Greece, and provide practical suggestions for the re-integration of the curriculum in the context of modern educational practice.

The paper presents a philosophical survey of the history of the theory and practice relating to the intrinsic integrated quality of liberal-arts education from pre-classical Greece to the present day.

The integrated quality of the liberal-arts curriculum has experienced a gradual disintegration from its adoption in classical Greece to the twenty-first century. The paper provides practical suggestions for the re-integration of an integrated approach to the curriculum in the context of modern educational practice.

Re-engaging with the integrated quality of the liberal-arts curriculum is vital for fulfilling the purpose of education as a practice: that of enabling a human being to flourish in a holistic way, in order to take an active role within a civil society.

The paper provides a valuable antidote to overly rational thinking by arguing for the need to restore the intrinsic integrative quality of the liberal-arts curriculum in educational practice in order to support the flourishing of individuals, society in order for the emergence of a mutually supportive interaction between them to appear.

The purpose of this paper is to review the management of air pollution in Mexico and strategies that have been considered to correct the issues, including potential future directions to further improve air quality for Mexico’s environment and people.

Different serious academic databases were searched for material regarding the issue of air pollution in Mexico, such as Scopus and Social Science Citation Index. Regional concern was an important factor that was considered in this review. Material was considered based on its recency, academic importance and veracity. The studies selected mainly ranged from the mid-1990s to 2018.

Air pollution in Mexico has been a primary issue for the country’s administration and that of Mexico’s North American neighbour, the USA. It has contributed significantly to climate change and has had detrimental effects on both the environment and on the health of Mexican citizens in various ways. While efforts to ameliorate the situation have been relatively strong, it is hoped that ongoing cooperation between Mexico, the USA and Canada will influence the development of stricter emissions standards.

This paper considers current circumstances and whether enough has been done to mitigate Mexico’s significant air pollution problem. It also considers several recommendations made by commentators as to potential future directions to rectify the issues, as no similar review has been made for a developing Country.

The paper combines the systems theoretical perspective on the evolution of societal differentiation and the emergence of codes in communication. By combining the approach by Niklas Luhmann with a historical theology on the development of Christian morality split between God and Devil, it recreates a sociological point of observation on contemporary moral forms by a temporary occupation of the retired Christian Devil.

The article combines a Luhmannian systems theoretical perspective on the evolution of societal differentiation with a concept of emerging codes in communication. The latter is based on on the development of a Christian view of morality being split between God and Devil. It establishes a sociological point of observation on contemporary moral forms through the temporary invocation of the retired figure of the Christian Devil.

The proposed perspective develops a healthy perspective on the exuberant distribution of a health(y) morality across the globe during the pandemic crisis of 2020–21. The temporary invocation of the retired Christian Devil as point of departure in this sociological analysis allows for a disturbing view on the unlimited growth of the morality of health and its inherent dangers of dedifferentiating the highly specialised forms of societal differentiation and organisation.

By applying the diabolical perspective, the analytical framework creates a unique opportunity to observe the moral encodings of semantic forms in detail, while keeping the freedom of scientific enquiry to choose amongst available distinctions in the creation of sound empirical knowledge. This article adopts a neutral stance, for the good of sociological analysis. The applications of the term “evil” to observations of communication are indifferent to anything but itself and its qualities as scientific enquiry.

This paper aims to show how a sociological description – a swarm analysis of the Nazi dictatorship – initially made with the means borrowed from George Spencer-Brown’s Calculus of Indications, can be transformed into a digital circuit and with which methods and tools of digital mathematics this digital circuit can be analyzed and described in its behavior. Thus, the paper also aims to contribute to a better understanding of Chapter 11 of “Laws of Form.”

The analysis uses methods of automata theory for finite, deterministic automata. Basic set operations of digital mathematics and special set operations of the Boolean Differential Calculus are used to calculate digital circuits. The software used is based on ternary logic, in which the binary Boolean logic of the elements {0, 1} is extended by the third element “Don’t care” to {0, 1, −}.

The paper confirms the method of transforming a form into a digital circuit derived from the comparative functional and structural analysis of the Modulator from Chapter 11 of “Laws of Form” and defines general rules for this transformation. It is shown how the indeterminacy of re-entrant forms can be resolved in the medium of time using the methods of automata theory. On this basis, a refined definition of the degree of a form is presented.

The paper shows the potential of interdisciplinary approaches between sociology and information technology and provides methods and tools of digital mathematics such as ternary logic, Boolean Differential Calculus and automata theory for application in sociology.