Hilbert's Programs and Beyond.
Sieg, Wilfried.
Hilbert's Programs and Beyond. - 1st ed. - 1 online resource (452 pages)
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.
9780199707157
Hilbert, David, 1862-1943.
Mathematics--Philosophy.
Electronic books.
QA8.4.S545 2013
510.1
Hilbert's Programs and Beyond. - 1st ed. - 1 online resource (452 pages)
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.
9780199707157
Hilbert, David, 1862-1943.
Mathematics--Philosophy.
Electronic books.
QA8.4.S545 2013
510.1