The Architecture of Modern Mathematics : Essays in History and Philosophy

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. 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 Aimed at both students and researchers in philosophy, mathematics and the history of science, this edited volume, authored by leading scholars, highlights foremost developments in both the philosophy and history of modern mathematics. - ;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 lat