The Mathematics of Language and Thought, Volume 1
This substantial, two volume work, has taken 23 years to complete. It presents a new axiom based meta-language which unifies all branches of formal logic, probability theory, set theory, causality, and basic mathematics. It also describes the deep structure of natural language and natural human reasoning. Volume 1 provides the theory and Volume 2 the formal proofs.
The purpose of the book is to make formal logic and reasoning more accessible to non-specialists, and does so by providing a single, intuitive form of symbolism which can be manipulated in a similar manner to algebra. Unlike algebra, however, only the rules of the meta-language itself, and none from other systems, are used in this manipulation. The language lies, therefore, at the foundation of human reasoning.
The meta-language contains several innovations. It treats everything as a bounded entity in space-time, i.e., as a system, including relationships and information. It also improves on conventional set theory, tense logic, epistemic logic, and complex causality. Importantly, it offers a means of manipulating qualitative concepts such as those found in the social sciences, as well as the quantitative concepts to which conventional mathematics is applied.
The Mathematics of Language and Thought, Volume 2
This book contains the mathematical proofs in support of Volume 1
Symbolic Reasoning in a Nutshell
This short document explains the basic symbolism used in my book, The Mathematics of Language and Thought.
Social Systems Theory in Practice – An Example
Intuitively, many of us sense that there are intangible “forces” that are beyond our individual control and that shape our society. In this article, I draw together the information provided in my previous articles on evolution, psychology, organisations, and systems theory, to show that these intangible “forces” are, in fact, tangible processes. These processes provide an understanding of why society is as it is. To a limited extent, the processes also provide an understanding of where society is heading unless we intervene.
Systems Theory from a Cognitive and Physicalist Perspective
The cognitive perspective holds that we are our minds and cannot escape the constraints imposed by their biology and evolutionary history. Nevertheless, human cognition is a reasonably accurate representation of reality. Physicalism holds that space-time comprises the whole of reality and that everything, including abstract concepts and information, exists within it.
From this perspective, I describe some of the main concepts in systems theory. They include: the importance of structure in forming meaningful systems; the nature of relationships, causality, and physical laws; and the significance of recursion, hierarchy, holism, and emergence. I also discuss cognitive factors including: our mental limitations; the nature of information and language; and our search for knowledge in a world of complexity and apparent disorder.
The paper concludes with the implications of this perspective for General System Theory and Social Systems Theory and suggests further work to advance these disciplines.
A Systems Model of Human Organisation
This short monograph describes a model of human society based on the principles of general systems theory. The model can help us to understand human interaction at all levels. It can also be used to identify behavioural changes which might lead to social improvements such as the prevention of conflict and the alleviation of poverty.
A Systems Model of Leadership and Followership
This monograph follows on from A Systems Model of Human Organisation. It describes the processes involved in the command or leadership components and in subordinate or follower components of human society. It recommended that it be read in conjunction with the two sets of diagrams below which support it.
Logic Causality and Systems
This set of Powerpoint slides describes a means of translating systems and causal processes into symbolic logic.
Leader & Follower Process Diagrams
This is a set of A3 causality diagrams which illustrate the processes described in “A Systems Model o the processes involved set of A3 diagrams.
Rational Understanding – Articles 1 to 42
On 4th June, 2022, I had been posting at Rational-Understanding.com for a year. This first year’s articles are combined here into a small booklet.
How Organisations and Hierarchies Arise
Articles 53 to 70 combined to form a single pdf document.
How to Reunite a Nation
This articles offers a solution to divisive politics in the USA.