Hilbert's Programs and Beyond.

Cover -- Contents -- Introduction -- In.1 A Perspective on Hilbert's Programs -- In.2 Milestones -- I: Mathematical roots -- I.1 Dedekind's analysis of number: systems and axioms -- I.2 Methods for real arithmetic -- I.3 Hilbert's programs: 1917-1922 -- II: Analyses: Historical -- II.1 Finitist proof theory: 1922-1934 -- II.2 After Königsberg -- II.3 In the shadow of incompleteness: Hilbert and Gentzen -- II.4 Gödel at Zilsel's -- II.5 Hilbert and Bernays: 1939 -- Systematical -- II.6 Foundations for analysis and proof theory -- II.7 Reductions of theories for analysis -- II.8 Hilbert's program sixty years later -- II.9 On reverse mathematics -- II.10 Relative consistency and accessible domains -- III: Philosophical horizons -- III.1 Aspects of mathematical experience -- III.2 Beyond Hilbert's reach? -- III.3 Searching for proofs (and uncovering capacities of the mathematical mind) -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- M -- N -- O -- P -- R -- S -- T -- V -- W -- Z.

David Hilbert was one of the great mathematicians who expounded the centrality of their subject in human thought. In this collection of essays, Wilfried Sieg frames Hilbert's foundational work, from 1890 to 1939, in a comprehensive way and integrates it with modern proof theoretic investigations. Ten essays are devoted to the analysis of classical as well as modern proof theory; three papers on the mathematical roots of Hilbert's work precede the analytical core, and three final essays exploit an open philosophical horizon for reflection on the nature of mathematics in the 21st century.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.