03158nam 2200565 450 991081539090332120230803041340.00-19-970715-4(CKB)3710000000623033(EBL)4704597(SSID)ssj0001630480(PQKBManifestationID)16377430(PQKBTitleCode)TC0001630480(PQKBWorkID)12111982(PQKB)11776296(MiAaPQ)EBC4704597(Au-PeEL)EBL4704597(CaPaEBR)ebr11274033(OCoLC)953436326(MiAaPQ)EBC5746261(EXLCZ)99371000000062303320161012h20132013 uy 0engur|n|---|||||txtccrHilbert's programs and beyond /Wilfried SiegOxford, [England] ;New York, New York :Oxford University Press,2013.©20131 online resource (452 p.)Logic and computation in philosophyDescription based upon print version of record.0-19-537222-0 Includes bibliographical references and index.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 laterII.9 On reverse mathematicsII.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; ZDavid 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.Logic and computation in philosophy.MathematicsPhilosophyMathematicsPhilosophy.510.1Sieg Wilfried1945-56703MiAaPQMiAaPQMiAaPQBOOK9910815390903321Hilbert's programs and beyond3989503UNINA