Hilbert's Programs and Beyond

Hilbert's Programs and Beyond

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Description

Hilbert's Programs & Beyond presents the foundational work of David Hilbert in a sequence of thematically organized essays. They first trace the roots of Hilbert's work to the radical transformation of mathematics in the 19th century and bring out his pivotal role in creating mathematical logic and proof theory. They then analyze techniques and results of "classical" proof theory as well as their dramatic expansion in modern proof theory. This intellectual experience finally opens horizons for reflection on the nature of mathematics in the 21st century: Sieg articulates his position of reductive structuralism and explores mathematical capacities via computational models.show more

Product details

  • Hardback | 464 pages
  • 160.02 x 238.76 x 43.18mm | 725.74g
  • Oxford University Press Inc
  • New York, United States
  • English
  • New.
  • 9 illus.
  • 0195372220
  • 9780195372229
  • 1,093,098

Review quote

Anyone who has at least a passing interest in the philosophy of mathematics, the relatively recent history of mathematics, mathematical logic (especially proof theory), the growth of ideas in mathematics, or the foundations of mathematics, will find this essential reading. Sieg is a major scholar in all of these areas, and he has shown, throughout his career, how work in any of these areas illuminates all of them. * Stewart Shapiro, Notre Dame Philosophical Reviews * [T]his collection is rich in both historical detail and philosophical ideas, living up to Sieg's exhortations for philosophy of mathematics to integrate conceptual, technical, and historical aspects into its perspective. * Oran Magal, Philosophia Mathematica *show more

About Wilfried Sieg

Wilfried Sieg is the Patrick Suppes Professor of Philosophy at Carnegie Mellon University. He received his Ph.D. from Stanford University in 1977. From 1977 to 1985, he was Assistant and Associate Professor at Columbia University. In 1985, he joined the Carnegie Mellon faculty as a founding member of the University's Philosophy Department and served as its Head from 1994 to 2005. He is internationally known for mathematical work in proof theory, historical work on modern logic and mathematics, and philosophical essays on the nature of mathematics. Sieg is a Fellow of the American Academy of Arts and Sciences.show more

Table of contents

INTRODUCTION; I. MATHEMATICAL ROOTS; II. ANALYSES; HISTORICAL; SYSTEMATICAL; III. PHILOSOPHICAL HORIZONSshow more