Hermann Weyl’s Raum - Zeit - Materie and a General Introduction to His Scientific Work
Hermann Weyl’s Raum - Zeit - Materie and a General Introduction to His Scientific Work

Author: Erhard Scholz

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 406

ISBN-13: 3034882785

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Historical interest and studies of Weyl's role in the interplay between 20th-century mathematics, physics and philosophy have been increasing since the middle 1980s, triggered by different activities at the occasion of the centenary of his birth in 1985, and are far from being exhausted. The present book takes Weyl's "Raum - Zeit - Materie" (Space - Time - Matter) as center of concentration and starting field for a broader look at his work. The contributions in the first part of this volume discuss Weyl's deep involvement in relativity, cosmology and matter theories between the classical unified field theories and quantum physics from the perspective of a creative mind struggling against theories of nature restricted by the view of classical determinism. In the second part of this volume, a broad and detailed introduction is given to Weyl's work in the mathematical sciences in general and in philosophy. It covers the whole range of Weyl's mathematical and physical interests: real analysis, complex function theory and Riemann surfaces, elementary ergodic theory, foundations of mathematics, differential geometry, general relativity, Lie groups, quantum mechanics, and number theory.

Feferman on Foundations
Feferman on Foundations

Author: Gerhard Jäger

Publisher: Springer

Published: 2018-04-04

Total Pages: 617

ISBN-13: 3319633341

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This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Gödel’s incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as “What is logic?” and proposed particular positions regarding the foundations of mathematics including, for example, his “conceptual structuralism.” The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman’s work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman’s distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic.

The Number Systems: Foundations of Algebra and Analysis
The Number Systems: Foundations of Algebra and Analysis

Author: Solomon Feferman

Publisher: American Mathematical Soc.

Published: 2003

Total Pages: 434

ISBN-13: 0821829157

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The subject of this book is the successive construction and development of the basic number systems of mathematics: positive integers, integers, rational numbers, real numbers, and complex numbers. This second edition expands upon the list of suggestions for further reading in Appendix III. From the Preface: ``The present book basically takes for granted the non-constructive set-theoretical foundation of mathematics, which is tacitly if not explicitly accepted by most working mathematicians but which I have since come to reject. Still, whatever one's foundational views, students must be trained in this approach in order to understand modern mathematics. Moreover, most of the material of the present book can be modified so as to be acceptable under alternative constructive and semi-constructive viewpoints, as has been demonstrated in more advanced texts and research articles.''

Logic Colloquium 2000 (hardcover)
Logic Colloquium 2000 (hardcover)

Author: Rene Cori

Publisher: CRC Press

Published: 2005-04-25

Total Pages: 425

ISBN-13: 1439865752

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This compilation of papers presented at the 2000 European Summer Meeting of the Association for Symbolic Logic marks the centenial anniversery of Hilbert's famous lecture. Held in the same hall at La Sorbonne where Hilbert first presented his famous problems, this meeting carries special significance to the Mathematics and Logic communities.

CLINICAL HYPNOSIS IN PAIN THERAPY AND PALLIATIVE CARE
CLINICAL HYPNOSIS IN PAIN THERAPY AND PALLIATIVE CARE

Author: Maria Paola Brugnoli

Publisher: Charles C Thomas Publisher

Published: 2015-01-01

Total Pages: 401

ISBN-13: 0398087679

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Anesthetist and pain specialist, Maria Paola Brugnoli, brings together her experience, knowledge and emotional intelligence in this integrative work on clinical hypnosis and pain management. In it, she presents a new system approach to study the neurophysiological states of consciousness to improve the use of clinical hypnosis and mindfulness in pain therapy and palliative care. The book explores the fields of clinical hypnosis and mindfulness as applied to the therapy of suffering and various type of acute and chronic pain, and in dying patients. It is organized in order to show all scientific neuropsychological theories currently in use regarding various types of pain and suffering. The author’s deep sensitivity is most notable in her attention to the dignity of the person in pain. She gathers together the techniques for distracting them from the painful present and transporting them to another dimension. One can imagine her psychological hand-holding and support as she moves her patients from suffering to relief. Ample scripts are provided to the reader for many inductions. The handbook is enriched by medical and hypnotic techniques for pain analgesia as well as hypnotic deepening techniques to activate spiritual awareness. It also indicates when and how to use them with children and adults. With extensive references, this book offers accessible concepts and practical suggestions to the reader. It highlights the relational and the creative process, encouraging each clinician to find his or her own way of facilitating the mechanisms in the patient to alleviate pain and suffering. This book is intended for all the professionals working every day with pain and suffering.

In the Light of Logic
In the Light of Logic

Author: Solomon Feferman

Publisher: Oxford University Press

Published: 1998-11-19

Total Pages: 353

ISBN-13: 0195359836

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In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics. Most troubling among these is the revolutionary way in which Georg Cantor elaborated the nature of the infinite, and in doing so helped transform the face of twentieth-century mathematics. Feferman details the development of Cantorian concepts and the foundational difficulties they engendered. He argues that the freedom provided by Cantorian set theory was purchased at a heavy philosophical price, namely adherence to a form of mathematical platonism that is difficult to support. Beginning with a previously unpublished lecture for a general audience, Deciding the Undecidable, Feferman examines the famous list of twenty-three mathematical problems posed by David Hilbert, concentrating on three problems that have most to do with logic. Other chapters are devoted to the work and thought of Kurt Gödel, whose stunning results in the 1930s on the incompleteness of formal systems and the consistency of Cantors continuum hypothesis have been of utmost importance to all subsequent work in logic. Though Gödel has been identified as the leading defender of set-theoretical platonism, surprisingly even he at one point regarded it as unacceptable. In his concluding chapters, Feferman uses tools from the special part of logic called proof theory to explain how the vast part--if not all--of scientifically applicable mathematics can be justified on the basis of purely arithmetical principles. At least to that extent, the question raised in two of the essays of the volume, Is Cantor Necessary?, is answered with a resounding no. This volume of important and influential work by one of the leading figures in logic and the foundations of mathematics is essential reading for anyone interested in these subjects.