Architecture of Modern Mathematics: Essays in History and Philosophy

J. Ferreirós, J. J. Gray0-19-856793-6, 978-0-19-856793-6

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.

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Table of contents :
Contents……Page 6
Acknowledgements……Page 8
List of Contributors……Page 10
Introduction……Page 14
Reinterpretations in the History and Philosophy of Foundations……Page 58
Frege and the Role of Historical Elucidation: Methodology and the Foundations of Mathematics……Page 60
Riemann’s Habilitationsvortrag at the Crossroads of Mathematics,Physics, and Philosophy……Page 80
The Riemannian Background to Frege’s Philosophy……Page 110
‘Axiomatics, Empiricism, and Anschauung in Hilbert’s Conceptionof Geometry: Between Arithmetic and General Relativity’……Page 146
Explorations into the emergence of Modern Mathematics……Page 170
Methodology and metaphysics in the development of Dedekind’stheory of ideals……Page 172
Emmy Noether’s ‘Set Theoretic’Topology: From Dedekind to theRise of Functors……Page 200
Tarski on models and logical consequence……Page 222
A Path to the Epistemology of Mathematics: Homotopy Theory……Page 252
Alternative Views and Programs in the Philosophy of Mathematics……Page 274
Felix Hausdorff ’s ConsideredEmpiricism……Page 276
Practice-related symbolic realism in H.Weyl’s mature view of mathematical knowledge……Page 304
From Kant to Hilbert: French philosophy of concepts in the beginning of the twentieth century……Page 324
Relative Consistency and Accessible Domains……Page 352
Coda……Page 382
Modern mathematics as a cultural phenomenon……Page 384
References……Page 410
Name Index……Page 446
Subject Index……Page 452