In the Light of Logic (Logic and Computation in Philosophy)

Feferman, Solomon

ISBN 10: 0195080300 / ISBN 13: 9780195080308

Published by Oxford University Press, 1998

First printing. Signed and inscribed on the half title page by the author - a gift inscription to Charles D. Parsons, the late professor of Philosophy of Mathematics and Kant scholar from Harvard University, who was a friend of Feferman. The book is signed and dated by Parsons on the ffep. Parsons made scant markings throughout the text in pen - mostly just lines in the margins next to specific points in the text, but some short written notes as well. The DJ and book are in VG condition. DJ has some surface scratching, bumping at top/bottom of spine and corners; DJ has a 0.5 in rip on back-top corner, which is creasing back a bit; DJ has small chips and rips at corners; DJ flap corners creased back. Hardcover boards have some minor bumping on bottom edges, and light cornerwear. Hinges and binding tight. Other than Parsons' markings, text is bright and clean and clear. Seller Inventory # ABE-1729627358239

Synopsis:

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Beginning with a previously unpublished lecture for a general audience, Deciding the Undecidable, Feferman examines the famous list of twenty-three mathematical problems posed by David Hilbert,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.

About the Author: Solomon Feferman is at Stanford University.

Bibliographic Details

Title: In the Light of Logic (Logic and Computation...
Publisher: Oxford University Press
Publication Date: 1998
Binding: Hardcover
Condition: Very Good
Dust Jacket Condition: Very Good
Signed: Inscribed by Author(s)
Edition: 1st Edition