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Hilbert's Programs and Beyond by Wilfried Sieg (2013, Hardcover)
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About this product
Product Identifiers
PublisherOxford University Press, Incorporated
ISBN-100195372220
ISBN-139780195372229
eBay Product ID (ePID)143591286
Product Key Features
Number of Pages448 Pages
Publication NameHilbert's Programs and Beyond
LanguageEnglish
Publication Year2013
SubjectHistory & Philosophy, Logic
TypeTextbook
Subject AreaMathematics, Philosophy
AuthorWilfried Sieg
FormatHardcover
Dimensions
Item Height1.5 in
Item Weight26.5 Oz
Item Length6.6 in
Item Width9.4 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2012-022356
Reviews"Anyone who has at least a passing interest in the philosophy of mathematics, the relatively recent history of mathematics, mathematical logic (especially proof theory), the growth of ideas in mathematics, or the foundations of mathematics, will find this essential reading. Sieg is a major scholar in all of these areas, and he has shown, throughout his career, how work in any of these areas illuminates all of them."--Stewart Shapiro, Notre DamePhilosophical Reviews"Certainly mathematical logicians with a historical bent will eat [Hilbert's Programs and Beyond] all up like candy. But others will, too. It is, or at least should be, the case that all of us have some awareness of the controversies of the early 20th century and the role they played in bringing about the shape of contemporary mathematics. ... To revisit these themes and explore certain of their facets in great detail is a beneficial and pleasantexperience." --MAA Reviews, "Anyone who has at least a passing interest in the philosophy of mathematics, the relatively recent history of mathematics, mathematical logic (especially proof theory), the growth of ideas in mathematics, or the foundations of mathematics, will find this essential reading. Sieg is a major scholar in all of these areas, and he has shown, throughout his career, how work in any of these areas illuminates all of them."--Stewart Shapiro, Notre Dame Philosophical Reviews "Certainly mathematical logicians with a historical bent will eat [Hilbert's Programs and Beyond] all up like candy. But others will, too. It is, or at least should be, the case that all of us have some awareness of the controversies of the early 20th century and the role they played in bringing about the shape of contemporary mathematics. ... To revisit these themes and explore certain of their facets in great detail is a beneficial and pleasant experience." --MAA Reviews, "Anyone who has at least a passing interest in the philosophy of mathematics, the relatively recent history of mathematics, mathematical logic (especially proof theory), the growth of ideas in mathematics, or the foundations of mathematics, will find this essential reading. Sieg is a major scholar in all of these areas, and he has shown, throughout his career, how work in any of these areas illuminates all of them."--Stewart Shapiro, Notre Dame Philosophical Reviews"Certainly mathematical logicians with a historical bent will eat [Hilbert's Programs and Beyond] all up like candy. But others will, too. It is, or at least should be, the case that all of us have some awareness of the controversies of the early 20th century and the role they played in bringing about the shape of contemporary mathematics. ... To revisit these themes and explore certain of their facets in great detail is a beneficial and pleasant experience." --MAA Reviews, "Anyone who has at least a passing interest in the philosophy of mathematics, the relatively recent history of mathematics, mathematical logic (especially proof theory), the growth of ideas in mathematics, or the foundations of mathematics, will find this essential reading. Sieg is a major scholar in all of these areas, and he has shown, throughout his career, how work in any of these areas illuminates all of them."--Stewart Shapiro, Notre Dame Philosophical Reviews, Anyone who has at least a passing interest in the philosophy of mathematics, the relatively recent history of mathematics, mathematical logic (especially proof theory), the growth of ideas in mathematics, or the foundations of mathematics, will find this essential reading. Sieg is a major scholar in all of these areas, and he has shown, throughout his career, how work in any of these areas illuminates all of them.
Dewey Edition23
IllustratedYes
Dewey Decimal510.1
Table Of ContentIntroduction1. 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 KönigsbergII.3 In the shadow of incompletenessII.4 Gödel 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
SynopsisHilbert'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 mathematical logic 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 position of reductive structuralism and explores mathematical capacities via computational models., Hilbert's Programs & 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 mathematical logic and proof theory. They then analyze techniques and results of "classical" proof theory as well as their dramatic expansion in modern proof theory. Thisintellectual experience finally opens horizons for reflection on the nature of mathematics in the 21st century: Sieg articulates his position of reductive structuralism and explores mathematical capacities via computationalmodels., Hilbert's Programs & 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 mathematical logic 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 position of reductive structuralism and explores mathematical capacities via computational models., 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.
LC Classification NumberQA8.4.S545 2013
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