Paul Halmos – författare

This book is an informal, although systematic presentation of lectures given by the author on Boolean algebras at the graduate level. In characteristic bold and fresh style, he treats Boolean algebras, develops some intriguing ideas, and provides rare insights. Exercises are generously sprinkled through the text for course study.

First Published in 1998. This is Volume IV of eighteen in the Sociology of Behaviour and Psychology series This is a study of social isolation, plus its causes. Written in 1952 rather than just ask what is wrong with the state of the world today, Dr Halmos turns to scientific analysis, constructive criticism and positive suggestion has he passes from study of basic social forces, through historical and empirical investigations, to the practical problems of reform and therapy. He has penetrated below the facile generalisations of common experience by distinguishing between neurotic types -the anxious, the depressed and the hysterical-and studying the different ways in which each is related to social isolation or participation.

First Published in 1998. This is Volume XVIII, the final of eighteen in the Sociology of Behaviour and Psychology series. Initially written in 1957, this book deals centrally with the concepts of 'normal' and 'abnormal' in human personality and behaviour. It seeks to establish whether one or the other of these can be defiled and thereby an absolute measure of man educed.

First Published in 1998. This is Volume XVIII, the final of eighteen in the Sociology of Behaviour and Psychology series. Initially written in 1957, this book deals centrally with the concepts of 'normal' and 'abnormal' in human personality and behaviour. It seeks to establish whether one or the other of these can be defiled and thereby an absolute measure of man educed.

First Published in 1998. This is Volume IV of eighteen in the Sociology of Behaviour and Psychology series This is a study of social isolation, plus its causes. Written in 1952 rather than just ask what is wrong with the state of the world today, Dr Halmos turns to scientific analysis, constructive criticism and positive suggestion has he passes from study of basic social forces, through historical and empirical investigations, to the practical problems of reform and therapy. He has penetrated below the facile generalisations of common experience by distinguishing between neurotic types -the anxious, the depressed and the hysterical-and studying the different ways in which each is related to social isolation or participation.

Are human misery, poverty and despair a result of personal inadequacy or social injustice? Therefore is the solution to these problems psychotherapy or political action? In one of the most important books on social work for a decade, Paul Halmos tries to resolve a dilemma which many social workers experience acutely – the conflict between a desire to help those in need and a fear that, by doing so, they merely support a political system which should, itself, be changed. Such a dilemma was highlighted during the sixties when 'casework' and personal counselling became discredited by the 'rediscovery' of widespread poverty and inequality in western society. To many the only solution seemed to be urgent and radical political action. For Professor Halmos the realities are more complex – an exclusive preoccupation with either personal or political solutions is unlikely to prove fruitful – what is needed is a dual sensitivity and balance. Yet for the author it is the political solution which carries within it the greater risk and he warns of the dangers inherent in the total politicization of social concerns. He argues that social action can become political action and ultimately political control.

Are human misery, poverty and despair a result of personal inadequacy or social injustice? Therefore is the solution to these problems psychotherapy or political action? In one of the most important books on social work for a decade, Paul Halmos tries to resolve a dilemma which many social workers experience acutely – the conflict between a desire to help those in need and a fear that, by doing so, they merely support a political system which should, itself, be changed. Such a dilemma was highlighted during the sixties when 'casework' and personal counselling became discredited by the 'rediscovery' of widespread poverty and inequality in western society. To many the only solution seemed to be urgent and radical political action. For Professor Halmos the realities are more complex – an exclusive preoccupation with either personal or political solutions is unlikely to prove fruitful – what is needed is a dual sensitivity and balance. Yet for the author it is the political solution which carries within it the greater risk and he warns of the dangers inherent in the total politicization of social concerns. He argues that social action can become political action and ultimately political control.

The theory of Boolean algebras was created in 1847 by the English mat- matician George Boole. He conceived it as a calculus (or arithmetic) suitable for a mathematical analysis of logic. The form of his calculus was rather di?erent from the modern version, which came into being during the - riod 1864-1895 through the contributions of William Stanley Jevons, Aug- tus De Morgan, Charles Sanders Peirce, and Ernst Schr. oder. A foundation of the calculus as an abstract algebraic discipline, axiomatized by a set of equations, and admitting many di?erent interpretations, was carried out by Edward Huntington in 1904. Only with the work of Marshall Stone and Alfred Tarski in the 1930s, however, did Boolean algebra free itself completely from the bonds of logic and become a modern mathematical discipline, with deep theorems and - portantconnections toseveral otherbranchesofmathematics, includingal- bra,analysis, logic, measuretheory, probability andstatistics, settheory, and topology. For instance, in logic, beyond its close connection to propositional logic, Boolean algebra has found applications in such diverse areas as the proof of the completeness theorem for ?rst-order logic, the proof of the Lo ' s conjecture for countable ?rst-order theories categorical in power, and proofs of the independence of the axiom of choice and the continuum hypothesis ? in set theory. In analysis, Stone's discoveries of the Stone-Cech compac- ?cation and the Stone-Weierstrass approximation theorem were intimately connected to his study of Boolean algebras.

Here is an introduction to modern logic that differs from others by treating logic from an algebraic perspective. What this means is that notions and results from logic become much easier to understand when seen from a familiar standpoint of algebra. The presentation, written in the engaging and provocative style that is the hallmark of Paul Halmos, from whose course the book is taken, is aimed at a broad audience, students, teachers and amateurs in mathematics, philosophy, computer science, linguistics and engineering; they all have to get to grips with logic at some stage. All that is needed to understand the book is some basic acquaintance with algebra.