In the Light of Logic

Solomon (Professor of Philosophy and Mathematics Feferman

ISBN 10: 0195080300 / ISBN 13: 9780195080308

Verlag: Oxford University Press Inc Jan 1999, 1999

Beschreibung

Neuware - 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 Cantorelaborated 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 aheavy 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 Beginning with a previously unpublished lecture for a general audience, Deciding the Undecidable, Feferman examines the famous list of twenty-three mathematical problems posed by David Hilbert,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 workand thought of Kurt Godel, 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 Godel has been identified as the leading defender of set-theoreticalplatonism, 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 twoof the essays of thevolume, 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.

Bestandsnummer des Verkäufers 9780195080308

Bibliografische Details

• Titel: In the Light of Logic
• Verlag: Oxford University Press Inc Jan 1999
• Erscheinungsjahr: 1999
• Sprache: Englisch
• ISBN-10: 0195080300
• ISBN-13: 9780195080308
• Einband: Buch
• Zustand: Neu
• Abmessungen: 234B x 163 H x 32 T Millimeter Breite: 234 mm, Höhe: 163 mm, Tiefe: 32 mm
• Gewicht: 710 Gramm

Über diesen Titel

Inhaltsangabe

Solomon Feferman is one of the leading figures in the philosophy of mathematics. This volume brings together a selection of his most important recent writings, covering the relation between logic and mathematics, proof theory, objectivity and intentionality in mathematics, and key issues in the work of Gödel, Hilbert, and Turing. A number of the papers appeared originally in obscure places and are not well-known, and others are published here for the first time. All of the material has been revised and annotated to bring it up to date.

Über die Autorin bzw. den Autor

Charlotte y Peter Fiell son dos autoridades en historia, teoría y crítica del diseño y han escrito más de sesenta libros sobre la materia, muchos de los cuales se han convertido en éxitos de ventas. También han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Diseño del siglo XX, El diseño industrial de la A a la Z, Scandinavian Design y Diseño del siglo XXI.