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Hilbert's programs and beyond /
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 investigation...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Oxford University Press,
©2013.
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| Colección: | Logic and computation in philosophy.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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 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; Z.