A new approach to quantum theory is proposed in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an observer or to some communicating observers. Group actions are defined on these variables, and group representation theory is the basis for developing the (...) Hilbert space formalism here. Operators corresponding to accessible theoretical variables are derived, and in the discrete case, it is proved that the possible physical values are the eigenvalues of these operators. The focus of the paper is some mathematical theorems paving the ground for the proposed foundation of quantum theory. It is shown here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. This simplifies the theory considerably: To reproduce the Hilbert space formulation, it is enough to assume the existence of two complementary variables. The interpretation inferred from the proposed foundation here may be called a general epistemic interpretation of quantum theory. A special case of this interpretation is QBism; it also has a relationship to several other interpretations. (shrink)

"This book is interesting and well-written. The research methods were explained clearly and conclusions were summarized nicely. It is a relatively quick read at only 130 pages. Anyone who has been told, or who has told others, that mathematicians make better thinkers should read this book." MAA Reviews "The authors particularly attend to protecting positive correlations against the self-selection interpretation, merely that logical minds elect studying more mathematics. Here, one finds a stimulating survey of the systemic difficulties people have with (...) basic syllogisms and deductions." CHOICE connect "The authors particularly attend to protecting positive correlations against the self-selection interpretation, merely that logical minds elect studying more mathematics. Here, one finds a stimulating survey of the systemic difficulties people have with basic syllogisms and deductions." CHOICE Connect For centuries, educational policymakers have believed that studying mathematics is important, in part because it develops general thinking skills that are useful throughout life. This 'Theory of Formal Discipline' (TFD) has been used as a justification for mathematics education globally. Despite this, few empirical studies have directly investigated the issue, and those which have showed mixed results. Does Mathematical Study Develop Logical Thinking? describes a rigorous investigation of the TFD. It reviews the theory's history and prior research on the topic, followed by reports on a series of recent empirical studies. It argues that, contrary to the position held by sceptics, advanced mathematical study does develop certain general thinking skills, however these are much more restricted than those typically claimed by TFD proponents. Perfect for students, researchers and policymakers in education, further education and mathematics, this book provides much needed insight into the theory and practice of the foundations of modern educational policy. (shrink)

The book attempts to build a bridge across three cultures: mathematical statistics, quantum theory and chemometrical methods.

Man's interpretations of natural phenomena change and develop gradually in accordance with his knowledge of them and the accumulation of scientific data about them. In studying a subject, it is very important to understand the history of the development of the subject and the general state of theoretical thinking on the subject. By so doing, we can embrace the experience and knowledge secured by scholars in the past and broaden our vision in order to avoid tortuous paths. The author of (...) this article will review biological theories and the history of their development as the beginning of our study of the histories of natural science and philosophy. (shrink)

This title tells the story of democracy through the perspective of tragic drama. It shows how the ancient tales of greatness and its loss point to the potential dangers of democracy then and now.

Social theory is a crucial resource for the social sciences. It provides rich insights into how human beings think and act and how contemporary social life is constructed. But often the key ideas of social theorists are expressed in highly technical and difficult language that can hide more than it reveals. The new edition of this popular book continues to cut to the core of what social theory is about. Covering key themes from the classical thinkers onwards, including Marxism, post-structuralism, (...) phenomenology, feminism and more, the second edition features a new chapter on Actor-Network Theory and enhanced discussion of postcolonial theory. Wide ranging in scope and coverage, the book is concise in presentation and free from jargon. Showing why social theory matters, and why it is of far-reaching social and political importance, the book is ideal for readers seeking a clear, crisp mapping of a complex but very rewarding area. (shrink)

CONTENTS.--Preface.--I. Our knowledge of God.--II. Sources and growth of the Logos-Christology.--III. Development and permanent value of the Logos-Christology.--IV. The problem of personality.--V. Thought and will.--VI. The problem of sin.

On several levels, there is now a debate whether the concept of God can be made compatible with modern science. In an attempt to elucidate this debate, I give an account of my own experiences from writing a book on the foundation of quantum mechanics. In my opinion, one can give two independent arguments for the existence of God by taking as departure an epistemic (knowledge-based) interpretation of quantum theory. However, I also argue that any religious belief should be the (...) result of an existential choice governed by each person’s own context (history and culture). In particular, I give my account of Christianity as a religion connected to our western culture, how one as a scientist can relate to the relevant dogmas. (shrink)

The well known Bell experiment with two actors Alice and Bob is considered. First the simple deduction leading to the CHSH inequality under local realism is reviewed, and some arguments from the literature are recapitulated. Then I take up certain background themes before I enter a discussion of Alice’s analysis of the situation. An important point is that her mind is limited by the fact that her Hilbert space in this context is two-dimensional. General statements about a mind’s limitation during (...) a decision process are derived from recent results on the reconstruction of quantum theory from conceptual variables. These results apply to any decision situation. Let all the data from the Bell experiment be handed over to a new actor Charlie, who performs a data analysis. But his mind is also limited: He has a four-dimensional Hilbert space in the context determined by the experiment. I show that this implies that neither Alice nor Charlie can have the argument leading to the CHSH inequality as a background for making decisions related to the experiment. Charlie may be any data analyst, and he may communicate with any person. It is argued that no rational person can be convinced by the CHSH argument when making empirical decisions on the Bell situation. (shrink)

This book is about disobedience. Positive disobedience. Disobedience as a kind of professional behaviour. It shows how teachers can survive and even influence an education system that does staggering damage to potential. More importantly it is an arm around the shoulder of disobedient teachers who transform people's lives, not by climbing promotion ladders but by operating at the grassroots.Disobedient Teaching tells stories from the chalk face. Some are funny and some are heartbreaking, but they all happen in New Zealand schools.This (...) book says you can reform things in a system that has become obsessed with assessment and tick-box reporting. It shows how the essence of what makes a great teacher is the ability to change educational practices that have been shaped by anxiety, ritual and convention. Disobedient Teaching argues the transformative power of teachers who think and act. (shrink)

The struggle to create and sustain meaning in our everyday lives is fought using cultural ingredients to spin the webs of meaning that keep us going. To help reveal the complexity and intricacy of the webs of meaning in which they are suspended, Tom Inglis interviewed one-hundred people in their native home of Ireland to discover what was most important and meaningful for them in their lives. Inglis believes language is a medium: there is never an exact correspondence between what (...) is said and what is felt and understood. Using a variety of theoretical lenses developed within sociology and anthropology, Inglis places their lives within the context of Ireland's social and cultural transformations, and of longer-term processes of change such as increased globalisation, individualisation, and informalisation. (shrink)