Hilberts Programs and Beyond

Hardcover | March 7, 2013

byWilfried Sieg

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Hilbert's Programs and 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 mathematicallogic 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 positionof reductive structuralism and explores mathematical capacities via computational models.

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Hilbert's Programs and 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 mathematicallogic and proof theory. They then analyze tech...

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 Departm...
Format:HardcoverDimensions:448 pages, 9.25 × 6.12 × 0.98 inPublished:March 7, 2013Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0195372220

ISBN - 13:9780195372229

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Table of Contents

Introduction1. A perspective on Hilbert's Programs2. MilestonesI. Mathematical rootsI.3 Dedekind's analysis of numberI.4 Methods for real arithmeticI.5 Hilbert's programs: 1917-1922II. AnalysesHistoricalII.1 Finitist proof theory: 1922-1934II.2 After KonigsbergII.3 In the shadow of incompletenessII.4 Godel at Zilsel'sII.5 Hilbert and Bernays: 1939SystematicalII.6 Foundations for analysis and proof theoryII.7 Reductions of theories for analysisII.8 Hilbert's program sixty years laterII.9 On reverse mathematicsII.10 Relative consistency and accessible domainsIII. Philosophical horizonsIII.1 Aspects of mathematical experienceIII.2 Beyond Hilbert's reach?III.3 Searching for proofs