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9780198567936

Architecture of Modern Mathematics Essays in History and Philosophy

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  • ISBN13:

    9780198567936

  • ISBN10:

    0198567936

  • Format: Hardcover
  • Copyright: 2006-06-29
  • Publisher: Oxford University Press

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Summary

This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research and how a number of historical accounts can be deepened by embracing philosophical questions.

Table of Contents

Acknowledgements vii
List of Contributors
ix
Introduction 1(44)
J. Ferreiros
J.J. Gray
REINTER PRETATIONS IN THE HISTORY AND PHILOSOPHY OF FOUNDATIONS
45(112)
Frege and the Role of Historical Elucidation: Methodology and the Foundations of Mathematics
47(20)
Michael Beaney
Riemann's Habilitationsvortrag at the Crossroads of Mathematics, Physics, and Philosophy
67(30)
Jose Ferreiros
The Riemannian Background to Frege's Philosophy
97(36)
Jamie Tappenden
Axiomatics, Empiricism, and Anschauung in Hilbert's Conception of Geometry: Between Arithmetic and General Relativity
133(24)
Leo Corry
EXPLORATIONS INTO THE EMERGENCE OF MODERN MATHEMATICS
157(104)
Methodology and metaphysics in the development of Dedekind's theory of ideals
159(28)
Jeremy Avigad
Emmy Noether's `Set Theoretic' Topology: From Dedekind to the Rise of Functors
187(22)
Colin McLarty
Tarski on models and logical consequence
209(30)
Paolo Mancosu
A Path to the Epistemology of Mathematics: Homotopy Theory
239(22)
Jean-Pierre Marquis
ALTERNATIVE VIEWS AND PROGRAMS IN THE PHILOSOPHY OF MATHEMATICS
261(108)
Felix Hausdorff's Considered Empiricism
263(28)
Moritz Epple
Practice-related symbolic realism in H. Weyl's mature view of mathematical knowledge
291(20)
Erhard Scholz
From Kant to Hilbert: French philosophy of concepts in the beginning of the twentieth century
311(28)
Hourya Benis Sinaceur
Relative Consistency and Accessible Domains
339(30)
Wilfried Sieg
CODA
369(28)
Modern mathematics as a cultural phenomenon
371(26)
Jeremy Gray
References 397(36)
Name Index 433(6)
Subject Index 439

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